Why the speed of light cannot be exceeded according to Special Relativity

[Cartesiantheater]

EDIT- as far as my part in this thread, I don't believe anything I have posted really answers the question until you get to post #20. Before then, I am basically handwaving math, but not explaining where it comes from. Post 20 explains where the math I cite comes from.


They tell you things and then you have to accept them by faith. Well, not anymore. In this thread you will learn WHY the speed of light cannot be exceeded according to Special Relativity , theoretically speaking (well, more like ONE of the reasons the speed of light cannot be exceeded). We will take a small trip through algebra and special relativity, but I promise it will be easy to understand, as long as you read the two semi-hard parts a few times over.

Number 1.)

First, I will introduce you to a Greek letter, gamma: y. This letter represents a algebraic function that shows up in several places in special relativity.

All of the next few things, until you reach "Number 2.)" will simply be me showing that y is used throughout Special Relativity. You don't necessarily have to understand any of them to get the point.

Time dilation (the equation describing the slowing of time between two observers):

Δt = yΔtp

which reads in English as "the change in time measured by the observer moving with respect to the clock measuring time is equal to the change in time measured by the observer at rest with respect to the clock TIMES the value of y." (this means that the observer moving with respect to the clock will experience SLOWER time than the observer at rest with respect to the clock ). The little subscript "p" is just a way to distinguish the two times. Don't worry about it. tp is called "proper time," and is just a way to distinguish between a moving and non-moving perspective.

[B]Length Contraction (similar to time dilation; objects will contract based upon motion):

L = Lp/ y

This means that when you're in relative motion with an object, the measured length of that object will be less than the measured length of that object when you are at rest with respect to it (by a factor of 1/ y). Lp is called "proper length," and will be defined like this: The proper length of an object is the length measured by someone at rest relative to the object.



The Energy equation according to Special Relativity:

E = ymc^2 (the famous "E = mc^2" is REST energy, but TOTAL energy requires the y, because we must include Kinetic energy when we're talking about total energy)

Relativistic Linear Momentum:

p ≡ ymu

where p is momentum, m is mass, and u is velocity. One interesting thing to note is that when u approaches zero, the classical definition of momentum, momentum equals mass times velocity, or p = mu, becomes accurate. (u and p are emboldened because they are vectors, which is irrelevant to this discussion, but just in case you were curious that is why)

Working with Lorentz Velocity Transformations:

If an object has velocity components along the y and z axes, the components as measured by an observer are:

u'y = uy/y(1 - uxv/c^2)

and


u'z = uz/y(1 - uxv/c^2)




The purpose of all this so far? To show that the value y is hugely important in Special Relativity.

And now for the reason that the speed of light can never be exceeded according to the theory:

Number 2.)

What IS y? y is the following:

1/ √(1 - v^2/c^2)

One divided by the square root of one minus velocity squared over the speed of light squared.


It's so simple...

What happens when your velocity is greater than the speed of light? Let's let our velocity be 400 000 meters per second (the speed of light is ≈ 300 000 meters/second), and work out a time dilation problem:

Δt = yΔtp

We'll let Δtp equal 5 hours.

So, what happens when we solve for Δt when our velocity is 400 000 m/s?


Δt = y 5 hours

Now, we plug in y and get the following:

Δt = [1/ √(1 - (400 000 )^2 / (300 000 )^2 ) ] 5 h

Δt = [1/ √(1 - 1.77777778)] 5h

Δt = [1 / √ ( -0.77777778)] 5 h

WHOA! Look! You have a NEGATIVE square root! In real life we cannot work with negative square roots (imaginary numbers).

It turns out that EVERY time your velocity is greater than the speed of light, you will get an imaginary number in your y. This is EXACTLY one of the reasons in Special Relativity that the speed of light can NEVER be exceeded- if velocity is greater than c, you WILL get an imaginary number in your answer.

Now you know- it really is that simple (at least this of the many reasons is).

Enjoy.

[DontBeAfraid]

hmm.... CT, you explained how the math of the equation works but you did not put into words WHY a thing cant possibly go faster than light.... Einstien didnt start with the equation, he started with the observation and wrote the equation to fit it. So, and I really am curious as this is still kinda shady to me, why is it that as matter approaches the speed of light that it takes more and more energy to increase its speed? Why does that energy needed increase exponentially while the speed increases linearly? Or hell, maybe even logarithmically(sp).

I understand it has something to do with "mass increasing"?

[Cartesiantheater]

Actually, and this will be a shocker, "although the Michelson-Norley experiment was preformed before Einstein published his work on relativity, it is not clear whether or not Einstein was aware of the details of the experiment." (Physics for Scientists and Engineers,6th Edition, pg 1251).

To the best of my knowledge, special relativity was a "theory driven theory" and he actually did start with equations- the equations Maxwell used to describe electromagnetism- and he used them in a novel way. "It is important to recognize that Einstein was working on electromagnetism when he developed the special theory of relativity. He was convinced that Maxwell's equations were correct, and in order to reconcile them with one of his own postulates, he was forced into the revolutionary notion that space and time are not absolute." (same text book, pg 1254)

So, special relativity was one of those magical moments where theory was thought up and was shown to make sense before observation (that is, it wasn't designed to describe some observation, other than Maxwell's). The idea came first and only later was confirmed by observation. As far as the Michelson-Morley experiment that inadvertently showed the invariance of the speed of light, Einstein made no mention of trying to explain that- his speed of light postulate only coincidently matched this (this is one of the reasons his theories are considered with such pseudo-holiness).



Anyway, to your question.

Unfortunately, THAT question lies mostly in the realm of general relativity, but I'll give it a shot. This is the best I can do at this point.

My text book has an answer, but they put it like this: "It is left as an end-of-chapter problem (Problem 69) to show that under relative conditions, the acceleration a of a particle decreases under the action of a constant force, in which case
a ∝ (1 - u^2/c^2)^(3/2). From this proportionality, we see that as the particle's speed approaches c, the acceleration caused by any finite force approaches zero. Hence, it is impossible to accelerate a particle from rest to a speed u ≥ c. This argument shows that the speed of light is the ultimate speed, as noted in the preceding section." (same text book, pg 1268)

I'll take a look at that later today and see if I can prove that acceleration is proportional to that value, but I have no reason not to trust my text book.. Sorry that once again it is theoretical and mathematical, but look at that equation.

As u (velocity) gets bigger and bigger, closer and closer to the speed of light, you're going to get closer and closer to this: (1 - 1)^(3/2) which equals 0 (because you've got in that equation 1 minus a fraction of the square of your speed over the square of the speed of light. If velocity is EQUAL to the speed of light, you have a value of ONE for that fraction, which would make the value of the proportionality equal zero, which would mean no more acceleration). With a finite force your acceleration will be proportional to a value that approaches zero as your velocity approaches the speed of light. So, using the reasoning of limits, your acceleration will eventually stop, and this will happen BEFORE your velocity ever EQUALS the speed of light, therefore you can never reach that speed.

- unless of course you have an infinite force, I guess (for obvious reasons my text and my professor did not really discuss the possibility and results of having an infinite force, so I've got a blank there, but presumably you'd be able to reach c with an infinite force)

Basically then, you'd need an infinite force to over come the limiting value that you can approach with acceleration, because acceleration is fundamentally limited by the proportionality a ∝ (1 - u^2/c^2)^(3/2).



Again, sorry it is nothing but theory and math, but I've got nothing else at this point.


Now, again, I've not mentioned the mass energy connection, Here's all I got on that:

E^2 = (p^2)(c^2) + (mc^2)^2

where p is the magnitude of momentum and is defined as:

mu/ √(1 - u^2/c^2)

with u as velocity, m as mass, E as energy and c as the speed of light.

One thing to note is that the (p^2)(c^2) represents the kinetic energy involved with the particle- which is important since we're talking about the velocity of the object. Once again I'd have to use the same reasoning as before, you'll get a nonsense answer if you allow velocity to surpass that of light (an imaginary number).


Hopefully the discussion on the proportionality of acceleration will be of some use, even though it's more theory and math.

If a ∝ (1 - u^2/c^2)^(3/2),

the larger the speed you accelerate to the less and less you will be able to accelerate, and therefore you cannot ever actually achieve the speed of light.

The bottom line is this:

As u → c, a → 0.


At this point that's all I got. Does that help any at all?


EDIT- as for WHERE all this math comes from, I presume it comes from Einstein's theory rather than some observation, but to date has been shown to match up with observation. Within the context of the math I can understand why, but as to how and why these particular equations were derived, that is beyond me. I imagine it all starts with Maxwell and electromagnetism.

[DontBeAfraid]

At this point that's all I got. Does that help any at all?Maybe somebody.... but not me. I already understand how the math works.... What I want to know is ... I guess, by what mechanism or means does equal "spent" force equal different amounts of internal energy on objects equal in everything except relative velocities. I suppose that maybe its starting to look like this might be like asking what makes gravity work. We have lots of examples of the way it works but not really the why or how of it. Like the illustration where planets are rolling around each other on a curved universe.... That has always bothered me in that it uses gravity to explain gravity....

edit: changed a word that didnt fit.

[iulian28ti]

Aren't there some theoretical particles named tachyons that are supposed to travel faster than light?

[Cartesiantheater]

At this point that's all I got. Does that help any at all?Maybe somebody.... but not me. I already understand how the math works....

Well, if you want a better understanding of why those particular equations work you'd have to start with Maxwell's work on electromagnetism, which is beyond me at this point so you're on your own there.


What I want to know is ... I guess, by what mechanism or means does equal "spent" force equal different amounts of internal energy on objects equal in everything except relative velocities.

What do you mean by "spent" force? I'm not sure what you mean here.

As far as how force and matter are interchangeable, I would say that E = mc^2 and what not are just useful models that happen to explain the observed fact that the decomposition of matter releases energy.


I suppose that maybe its starting to look like this might be like asking what makes gravity work.

That line of discussion takes you right out of special relativity and into general relativity, which of course is quite over my head amigo.



We have lots of examples of the way it works but not really the why or how of it.

Yeah, you're right. I think maybe I worded the title of this thread wrong. It should have been "Why according to the theory of special relativity c cannot be exceeded," implying that we were dealing only with the given mathematical model rather than the reason it works and how it was derived.

I don't know though, if we can ever answer the questions of why and how (although string theory makes the claim regarding why certain particles exist).

Regardless, both in practice (up to now) and according to the mathematical model c cannot be passed if you're starting from a slower velocity. If c can be passed, we'd have causal violations, which could be bad news for all of applied logic anyway.


Like the illustration where planets are rolling around each other on a curved universe.... That has always bothered me in that it uses gravity to explain gravity....

I can see how that would. Depending on how I look at it, I feel that way at times as well.

But I think it helps to first make sure that you've got it that there is absolutely no absolute position of rest or absolute frame of reference.

From there, don't think of gravity as anything but a useful word, and instead just envision both acceleration and mass having the same affect on space-time, warping it. The more massive objects or the fastest accelerating objects warp it more, so a much less massive object will tend to move in accordance with the warping of the much more massive object (even though the small object warps space-time as well).

As for why massive or accelerating objects warp space-time, I don't know if there is a satisfactory answer to that question, other than to say that the model that predicts it matches observation really well.




Aren't there some theoretical particles named tachyons that are supposed to travel faster than light?

To the best of my knowledge those theoretical particles don't accelerate to the speed of light, but are already moving that fast.

Also, from what I know of these ideas, tachyons, they're not really faster than light particles. And even if they do move faster than light, they cannot transfer information faster than light (or even at all) and as such even in a model in which they exist they can hardly be spoken of to exist anyway. To my understanding (which is exceedingly weak) they are more like ghost particles.

Not only that, but as I understand it these "particles" have a squared mass which is negative. I mean that right there tells ME that the hypothesizing of these particles reveals a fundamental flaw in our models rather than an actual possibility of their existence. How can something have an "imaginary mass,' which is EXACTLY what these particles must have? (tell me, what is the square root of negative 1, √(-1)?

Further, if I understand it correctly, these particles have a minimum amount of potential energy (like a pencil balanced on its tip) and then due to quantum fluctuation it will "tip over" gaining energy. But once it gains a minimum amount of energy it is no longer a tachyon anyway, and instead transforms into a "real" particle.



Honestly, my knowledge of these particles comes straight from Brian Greene books and the like, so don't trust me, but to me these "particles" hardly exist even within the model and are really like ghost particles to me. And since they don't transmit information faster than light, they are really not violating SR or GR anyway. That's important.

These particles find a home much more in string theory. If you're interested in tachyons, I recommend you read some books on string theory.

[DontBeAfraid]

What do you mean by "spent" force? I'm not sure what you mean here.I just meant force traded for more speed.

[Cartesiantheater]

I just meant force traded for more speed.

Well, since in relatively low speeds force = mass * acceleration, you must add force to chance speed (which would be acceleration), but other than that, I've got nothing. It's just a relationship.

HOWEVER, maybe you might find some answers in all of this mess?

http://forum.physorg.com/index.php?showtopic=18565&st=0

There are a few guys here qualified to answer the questions that can be answered. Also, maybe you might consider looking into Einstein field equations and their history?

If you want, start a register there and post a thread in the "puzzling questions" section. I'm sure if you're nice enough someone with some decent education will answer some of your questions.

Enjoy.

[TEMELUCHUS]

Wholly crap you folks are like super brains. Now these are the threads that I enjoy reading even though I don't quite get it anymore but sometimes it helps me to remember.
If I could ask a question: An experiment will take place in a few months in Switzerland I believe with the new accelerator. If this succeeds and a minute black hole is formed possibly causing a worm hole, would that be considered faster than light if we are able to move from one existence to another or from one galaxy to another in seconds?

[DontBeAfraid]

Its not the same kind of black hole that most of us are "familiar" with. And nothing will move through it to anywhere for a couple of reasons.... One, it will be incredibly small and two it will be equally incredibly short lived.

[lazserus]

Sorry Cartesiantheater, but that was a HORRIBLE explanation. You explained how it works on a mathematical level and not on a physical level. The issue needs be explored in a light the average person can see, not magic light such as UV or infrared.

Special relativity theory was one that challenged that of ether. Einstein said the speed of light is constant and that should be used as reference, not some imaginary ether that cannot be measured. His conclusion not only stated that the speed of light was constant, but that all observers will measure it the same regardless of relative motion. Hence the name relativity.

The reason nothing can travel at the speed (or beyond) is because of mass. Light, which is constructed of photon, travels at a constant speed and has no mass. In order for a particle with mass to travel at the same speed, it would require an infinite quanity of mass and energy. E=mc^2 means energy equals mass times the speed of light squared. What this simple equations tells us is any object attempting to attain the speed of light must accumulate infinite energy and infinite mass. Mass and energy are directly correlate because mass is but another form of energy.

Experiments have shown in simple forms such as aeronautics that as you attempt to increase velocity (the rate of which an object travels over time) you need more energy. Aeronautics present the best experimental data we have. In order for an aircraft to reach a certain velocity it requires a certain amount of fuel to give it the energy to do so. Using Einstein's equation, electrons have been given extraordinary energy levels in order to reach the speed of light--the expierments always fail. Because the electron has mass, it would take an infinite amount of energy to get it to move at velocities of the photon.

The reason the speed of light cannot be breeched is due to mass and photons have none. If any of you heard of neutrinos, it is the same concept. Neutrinos travel at the same speeds as photons because they have no intrinsic mass.

Imagine making a spit-wad and using a straw to launch it across a classroom. The wad contains mass based on your saliva content and the paper used. The straw is acts a launching device. The heavier the wad is, the more breath required to launch it to the designated target. I'm sure many of you have created spit-wads in class and adjusted the angle in order for it to reach the person you plan spitting. This is the same concept. You have to provide more energy via breath in order to make a heavier wad travel the same distance. The lighter the wad the less breath required. If you take this same example and apply it to particles you reach a similar conclusion; however, that conclusion results in the requirement of infinite energy to make it travel the speed of light.

Special relativity introduces E=mc^2, but takes no position mass. It was not until general relativity that mass was included in the Einstein relativity equations and theory. Special relativity introduced the simple equation but merely focuses on velocity without mass. THat is neither hear nor there. The reason the speed of light cannot be surpassed is because all other particles contain mass.

[Cartesiantheater]

Sorry Cartesiantheater, but that was a HORRIBLE explanation. You explained how it works on a mathematical level and not on a physical level. The issue needs be explored in a light the average person can see, not magic light such as UV or infrared.

Maybe, but doing that will only take a math equation and reduce it to a verbal proportionality, as you have done below.


Special relativity theory was one that challenged that of ether. Einstein said the speed of light is constant

Actually, I'm pretty sure that was determined before Einstein by Maxwell, Lorentz, etc. The equations of special relativity come directly from Lorentz.


and that should be used as reference, not some imaginary ether that cannot be measured. His conclusion not only stated that the speed of light was constant, but that all observers will measure it the same regardless of relative motion. Hence the name relativity.

Well, he wanted invariance, but anyway.


The reason nothing can travel at the speed (or beyond) is because of mass. Light, which is constructed of photon, travels at a constant speed and has no mass. In order for a particle with mass to travel at the same speed, it would require an infinite quanity of mass and energy.

Now you have done nothing but represent a mathematical equation in words. This is not any different then what I did, except you've deleted the math. You simply have a proportionality between mass, energy and velocity, and in order to reach the speed of light you must have infinite energy. This is just another math equation.

Starting from the equation (by the way, this is the "real" "E =mc^2" equation, including motion, whereas plain old E=mc^2 is when v = zero in the equation below)

E = mc^2/√(1 - v^2/c^2)

And solving for v you get:

v = √[c^2 (1 - (m^2c^4)/(E^2)]

And you can easily see why energy must be infinite. In order for v to equal c from this equation, the value (m^2c^2)/(E^2) must equal zero.

In order for that value to equal zero, you must let the denominator approach infinity (remember, the lim of 1/x as x →∞ is zero)

So, in order for v to approach c, E must approach infinity.


Here you have what I said and what you said amounting to exactly the same thing, being equal in explanatory power, but one written in words and one in math.



E=mc^2 means energy equals mass times the speed of light squared. What this simple equations tells us is any object attempting to attain the speed of light must accumulate infinite energy and infinite mass. Mass and energy are directly correlate because mass is but another form of energy.

However, please do not forget to mention that E = mc^2 is only an objects "rest" energy.


Experiments have shown in simple forms such as aeronautics that as you attempt to increase velocity (the rate of which an object travels over time) you need more energy. Aeronautics present the best experimental data we have. In order for an aircraft to reach a certain velocity it requires a certain amount of fuel to give it the energy to do so. Using Einstein's equation, electrons have been given extraordinary energy levels in order to reach the speed of light--the expierments always fail. Because the electron has mass, it would take an infinite amount of energy to get it to move at velocities of the photon.

Yes, this is true. But this is experiment, not theory. The explanation is found in the theory, not the experiment. That's why I think the math is the best way to explain why.


The reason the speed of light cannot be breeched is due to mass and photons have none. If any of you heard of neutrinos, it is the same concept. Neutrinos travel at the same speeds as photons because they have no intrinsic mass.

Then why can't massless particles surpass the speed of light?


Imagine making a spit-wad and using a straw to launch it across a classroom. The wad contains mass based on your saliva content and the paper used. The straw is acts a launching device. The heavier the wad is, the more breath required to launch it to the designated target. I'm sure many of you have created spit-wads in class and adjusted the angle in order for it to reach the person you plan spitting. This is the same concept. You have to provide more energy via breath in order to make a heavier wad travel the same distance. The lighter the wad the less breath required. If you take this same example and apply it to particles you reach a similar conclusion; however, that conclusion results in the requirement of infinite energy to make it travel the speed of light.

And this result is explained as well with the math.


Special relativity introduces E=mc^2, but takes no position mass. It was not until general relativity that mass was included in the Einstein relativity equations and theory. Special relativity introduced the simple equation but merely focuses on velocity without mass. THat is neither hear nor there. The reason the speed of light cannot be surpassed is because all other particles contain mass.

But you see, that is really the EXACT same explanation I gave in this very post using pure math- only without the math.




So I guess my point is, at this point NEITHER explanation explains why this law of nature is what it is. Both only describe the law. I probably shouldn't have said "why" in the title, but rather offered a logical backing to the observed physical law.

[lazserus]

My purpose was not to claim that your explanation was wrong, but to provide an explanation the majority of people can comprehend. Displaying equations teaches few--explaining the phenomena behind the equations is the fruit of knowledge which all can enjoy. I say you explanation is horrible because you explained little. You merely stimulated the knowledge others of your mathematic proficiency. Mathematics supports knowledge...it does not truly explain it.


Actually, I'm pretty sure that was determined before Einstein by Maxwell, Lorentz, etc. The equations of special relativity come directly from Lorentz.
Since we are discussing science, Einstein is accredited with the concept of relativity. In reality, Galileo was the first to introduce relative motion.


Now you have done nothing but represent a mathematical equation in words.
Ah but I have possibly accomplished more than you have using words other than equations. The art of science is not what you know in its intrinsic form, but how you can share it with the rest of the world. Knowledge is absolutely useless if not understood by the world.


However, please do not forget to mention that E = mc^2 is only an objects "rest" energy
I skipped this on purpose. Complicating the theory does not aid in teaching its basic premise. I mention only what is necessary to understand the concept. This is not a physics class, therefore getting into the nasty fabrics of the theory only strays from teaching.


Then why can't massless particles surpass the speed of light?
Modern thinking considers a photon's rest is the speed of light. Being that particles with no mass can only reach the speed of light, massless particles should in no way be considered for surpassing it.

[DontBeAfraid]

Here you have what I said and what you said amounting to exactly the same thing, being equal in explanatory power, but one written in words and one in math.I agree. Ta, you didnt explain it any better or in any more detail than ct.. You just dumbed it down.

[DontBeAfraid]

ok, last night I had somewhat of an epiphany and believe I now understand the mechanism by which an objects mass is seen to increase from the relative perspective of "outside" or "not in motion with" thereby making it need more and more energy for smaller and smaler increases in speed.

It has everything to do with the motion paradox and when I figure out a good way to put it inot words I will.

[lazserus]

In relativity theory there is no paradox when it comes to motion. Cartesiantheater and I explained the same thing in different ways. In his defense, it becomes much more difficult to appreciate and comprehend special relativity without proficiency in the mathematics, which is little more than algebra.

Paradoxical motion comes in when using Newtonian motion to describe the motion of extent celestial bodies, such as the much of the outskirts of our own galaxy. Relativity theory does not change Newton's laws of motion. It changes our conception of gravity, time, and mass's correlation to the previous. Special relativity does cap a limit to the velocity of mass. The speed of light is peak because the photon has no mass while particles with mass are incapable of aquiring the energy to reach relative velocity. Some theories conclude that a photon's velocity is directly related to the fact is is massless. IN essence, a photon's rest is 186,000 miles per second and all massless particles (neutrinos) naturally rest at such velocities.

[DontBeAfraid]

In relativity theory there is no paradox when it comes to motion. Simply saying it doesnt make it true. If you think it does then you dont understand the paradox.


which is little more than algebra. When you know me you can talk down to me.



Paradoxical motion comes in when...The correct ending to this sentence is: "when you consider the motion of ANYTHING".


The speed of light is peak because the photon has no mass while particles with mass are incapable of aquiring the energy to reach relative velocity.Again you have managed to state what we already know. You have not explained the how or the why of it.


N essence, a photon's rest is 186,000 miles per second and all massless particles (neutrinos) naturally rest at such velocities. You have still not explained anything with this sentence. You have again rewritten what we have already observed.

So, just to recap what we know; you guys should love this because its about a sentence long:

Objects with mass cannot attain the speed of light because as their relative velocities increase so too does their mass meaning that it takes more energy to propel them.

Now the question I posed was: why does their mass increase with velocity?

The answer to that question is NOT: it takes more energy because their mass increases.

I do believe I have an understanding of the "how" the mass increases and it does pertain to the motion paradox.

edit: Please dont interpret my post as stand offish, its just how I choose to comminucate, continued exchange is the goal.

[lazserus]

Simply saying it doesnt make it true. If you think it does then you dont understand the paradox.
No, I am saying there is no paradox in relativity theory regarding motion. Special relativity is solid when dealing with motion. Maybe you mean something else? Because paradox is the wrong word in this case. There are not contradictory factors in SR that negate it.


Now the question I posed was: why does their mass increase with velocity?
I see what you are asking and it is difficult to explain. Explaining how is easier than why. The eternal philosophical question is why? The question of why can never truly be answered, but how can.

Say you want to throw a football 30 yards. Ignoring wind and gravity you might simply tell yourself you have to throw it x hard. If you want to throw it 70 yards you know you have to throw it harder, right? Energy and mass are interchangeable here. To lug the football farther you have to apply more energy. If you want to move something heavy you must acquire an amount of energy relatively equal to the mass you wish to push.

We've established the concept. The special theory of relativity's focus is on relativity: relative motion.- motion relative to the observer. If you got on a track an ran as fast as you could, reaching a speed close to that of light, you would not notice yourself getting heavier. The person recording your time would be the observer noticing. The point of the theory is partially philosophical in that only observers can measure, not the object itself. With energy and mass being interchangeable, the more mass that increases the more energy and the more energy used the more mass accumulated.

You have to remember that Einstein put SR down on paper and it was not tested for over a decade. It was all upstairs. Maybe a simpler way to think of the concept is through vehicle collisions. If you put a truck in neutral and pushed it, you could only get it so fast due to a limited supply of kinetic energy. If you add 4 friends, the truck will move much faster. The truck weighs the same amount, but once it impacts another object at the velocity you and your friends pushed it, it will impact that object as if it were x times heavier.

I probably didn't answer your question, but I may have answered others'. If you really want to dig deep, check out these sites for better answers. I warn you, they are mathematically heavy.

http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html
http://galileoandeinstein.physics.virginia.edu/lectures/mass_increase.html

The second one has some real-world applications to flesh things out, but I can't safely say they will help.

[DontBeAfraid]

Say you want to throw a football 30 yards. Ignoring wind and gravity you might simply tell yourself you have to throw it x hard. If you want to throw it 70 yards you know you have to throw it harder, right? Energy and mass are interchangeable here. To lug the football farther you have to apply more energy. If you want to move something heavy you must acquire an amount of energy relatively equal to the mass you wish to push.Ignoring wind AND gravity I would not need any more force to throw the ball 1 million miles than I would need to throw it 1 foot. If you understanding of the motion paradox is this profoundly wrong then Im not sure you should be posting "answers" in here, aristotle.


If you got on a track an ran as fast as you could, reaching a speed close to that of light, you would not notice yourself getting heavier. The person recording your time would be the observer noticing. The point of the theory is partially philosophical in that only observers can measure, not the object itself.You like to state what we have already covered...


With energy and mass being interchangeable, the more mass that increases the more energy and the more energy used the more mass accumulated.Now Im almost certain you do not understand the concept. Or maybe you do and you are having as hard a time as I am putting it into owrds.


If you put a truck in neutral and pushed it, you could only get it so fast due to a limited supply of kinetic energy. If you add 4 friends, the truck will move much faster. The truck weighs the same amount, but once it impacts another object at the velocity you and your friends pushed it, it will impact that object as if it were x times heavier.Rolling friction has nothing to do with this conversation. Here, on earth, there is no practical example which can be used to describe physics of an object becoming more massive as its velocity increases.. The only thing on earth that even approaches velocities this high would be a particle zipping around a super collider. It has to be taken into account a little bit when dealing with satellites but not much.

No, me throwing a football or pushing a car, simply has nothing to do with why no object can surpass he speed of light.


I probably didn't answer your question, but I may have answered others'. If you really want to dig deep, check out these sites for better answers. I warn you, they are mathematically heavy.I appreciate your enthusiasm.

[Cartesiantheater]

Okay, this discussion was tactically flawed from the beginning. I had thought that the math itself would be sufficient, however, if I cannot show you how the math is derived from reality, then it is meaningless. But if I CAN show you how the math is derived from reality, then the math can be used as a proof. After spending a bunch of time trying to learn how it was derived (they don't teach you that part in a survey of physics class; had to figure it out on my own time, thus it took forever), I am ready to show where the math comes from, which in turn will show why the speed of light is a necessary speed limit.


HOWEVER, that isn't necessary at all! The only thing necessary is to follow one of the two fundamental assumptions of special relativity to its logical conclusion (however, I really don't believe this first part is satisfying. Read the entire post, especially the part about the math, because I think it is vital).

The two major postulates of special relativity are that:

1- The laws of physics are the same for every inertial frame

2- The speed of light is constant for every inertial (non-accelerating) frame

Number 2 says that the speed of light is constant for every inertial frame, but it does NOT say that it is the FASTEST speed. Experiments (Michelson-Morley, for example) have confirmed that the speed of light is constant for inertial reference frames.

Now, let us follow that to its logical conclusion.


Consider two observers at rest with respect to each other in the same location (ingore the impossibility of two people being at the same point in space). Call them Alice and Bob. Let's say Alice emits a circle of light that propagates out radially at the speed of light. Both Alice and Bob would forever be at the center of the circle of light as it propagates.

However, what if, at the instant that Alice sends out the light signal, Bob begins to move to the right at half the speed of light, but without accelerating. That is, Bob moves at a constant speed with respect to Alice. According to the principle of the constancy of the speed of light (postulate 2), the speed of light must be the same for both Alice and Bob. What this means, if you think about it deeply enough, is that BOTH Alice AND Bob must be in the center of the circle of light as it propagates, even though Bob is moving away from Alice at a constant speed. The only possible way for both Alice and Bob to both be in the center of the circle of light is if space and time distort as they move in just the right way so that both see themselves as being in the center of the circle. (This is where time dilation and length contraction come from- in the thread "The Universe" I gave a decent explanation of how that happens)

But there is one other thing we have yet to consider: If Bob remains in the center of the light circle (from his perspective) despite moving away from Alice at half the speed of light, then with respect to the edge of the circle Bob never "gains any ground." That is, the light is STILL moving away from him at the speed of light, because he remains in the center of the circle.

Ultimately, the assumption that the speed of light is constant for all reference frames caries with it the logical consequence that no observer moving slower than the speed of light can ever reach the speed of light, because in all frames the speed of light is constant, including ones of very high speeds.





Now onto the math. Before you panic, this is juts the Pythagorean theorem, and it will show you what is going on with all of this (including the increase in mass as you approach the speed of light).

What we are dealing with is coordinate transformations. For example, if you are standing on a bus going 40 miles per hour with respect to some observer, and you throw the ball 40 miles per hour from your perspective, then from the perspective of the person at rest, the ball travels 80 miles per hour. We've all experienced something like that. This is a coordinate transformation. In your coordinate system, the ball moves away at 40 miles per hour. However, because your coordinate system is moving with respect to the observer at rest, in his coordinate system the ball is moving away at 80 miles per hour. This is the fundamental issue dealt with in special relativity. Transformation of coordinates from "at rest" systems to "in motion" systems.

The problem, however is that the transformation discussed above (the Galilean Transformation) is inconsistent with the postulate of the constancy of the speed of light (I also discussed this in the Universe post mentioned earlier). If you follow this example it will be easy to see why the transformation isn't identical to the Galilean transformation, and what it implies.


Imagine two observers, each with clocks calibrated exactly. The two clocks work as follows: a beam of light shoots up from one mirror, hits the other mirror, then reflects back down to the original point. Light beam goes up = "tick," light beam goes down = "tock." We will assume that the speed of light is constant for all inertial frames, as per the the postulate of the constancy of the speed of light (and as per experimentation).

Here are the two clocks at rest with respect to each other.

617

Now, imagine that one of the clocks moves away at some speed less than the speed of light. Remember, assume that light travels the same velocity in both frames, since the two are in the same inertial frame (there is no acceleration going on between them- all velocities are constant). You will see that, because the light beam must travel at velocity c in both instances, the light beam travels a longer distance in the moving clock than the stationary clock. Here is an animation of path the light travels in both clocks, one at rest, and one in motion with respect to the other (traveling at some velocity, v).

618

Now, it is easy to see that the path the light follows in the moving clock is a triangle, while the path the light follows in the stationary clock is a straight line. It is also easy to see that in the moving clock, if you draw a perpendicular line from the top of the triangle to the base, that line is the same distance the light travels in the stationary clock. Keep that in mind, because it will be important shortly.

Remember, the speed of light is the same for both observers. And remember that "Distance = rate times time," D = rt. Consider the path the light beams travel. The distance for the clock at rest is shorter than the distance for the clock in motion. Thus, we will define the distance for the clock at rest to be D1 = r1t1. We will then define the distance the beam travels in the clock in motion to be D2 = r2t2.

Again, remember that the speed of light is the same for both clocks. That means that r1 = r2, so now we will rewrite the two distance formulas as D1 = ct1, and D2 = ct2. The rate the beam travels is the same for both clocks- the speed of light.

Now, because the two distances are different, and because the rate the beam travels is the same in both, the times must be different as well. Keep that in mind.

Now, consider the triangle formed by the moving clock, and remember what I said about "the line drawn from the top of the triangle perpendicular to the base is equal to the distance traveled by the beam from the clock at rest." If you draw that line, you split the triangle in half. We will consider this half triangle. The hypotenuse of the triangle is equal to D2, the leg going up is equal to D1, and the leg pointing sideways is equal to another distance, D3. This third distance is the distance the clock travels in time t2. It depends upon how fast the clock is moving, so we will label this third distance D3 = vt2.



This is what that "half" triangle looks like.

http://img411.imageshack.us/img411/7153/lighttriangle1zn5.jpg


The hypotenuse is D2, which is the speed of light times t2, the vertical leg is D1, which is the speed of light times t1, and the horizontal leg is D3, which is the velocity of the mirrors, v, times t2.


Now, using algebra, we will divide all three sides by ct1, thereby making the vertical leg equal to 1, the hypotenuse equal to t2/t1, and the horizontal leg equal to t2v/t1c. This gives us the following triangle:

http://img156.imageshack.us/img156/9342/lighttriangle2qg7.jpg

End of part 1.

[Cartesiantheater]

Part 2.

One more algebra step. For simplicity, we will let the value t2/t1 = y. The triangle now looks like this (click on it to make it larger- the site isn't letting me host another image):

619


This is the triangle we will work with. We will now use the Pythagorean theorem to solve for y. The Pythagorean theorem states that the sum of the squares of two legs of a right triangle equals the square of the hypotenuse of that triangle. Therefore:

y^2 = 1^2 + y^2 v^2/c^2

Step by step algebra to solve for y:

y^2 - y^2 v^2/c^2 = 1

y^2 ( 1 - v^2/c^2 ) = 1

y^2 = 1/( 1 - v^2/c^2 )

y = 1 / √( 1 - v^2/c^2 )


There you have it. We have just derived the Lorentz factor. This equation, which is a mathematical description of a real physical relation (the triangle formed by the beam of light in the moving clock), states that it is impossible for the velocity of the moving clock to be equal to or greater than the speed of light. EDIT- The reason the Lorentz factor precludes faster than light travel is, as has been mentioned earlier in this thread, if v >c, then you would have a negative square root, which is nonsense, in a physical sense. Or, you can look at it as a natural consequence of the constancy of the speed of light for all inertial frames, as discussed earlier.




What all this means is that if we assume that the speed of light is constant for all inertial reference frames, then it is impossible for any object to travel faster than the speed of light. Because this assumption (that the speed of light is constant for all inertial frames) is backed up by experimental reality (as discussed earlier), the mathematics are valid for real objects.


Now, what the Lorentz factor, that we have just derived is:

Using those triangles we have derived a scaler factor to be used whenever a reference system is in motion with respect to another. For example, if a ball is being thrown from on a train, in order to find out what that ball's coordinates are with respect to the coordinate system at rest, we would take the Galilean transformation (discussed earlier) and multiply it by the Lorentz scaler factor. The reason we do this is because in our world the speed of light is constant for all inertial frames. Therefore, whenever a frame is in motion with respect to another, we must multiply its coordinates by the Lorentz factor in order to determine where its position is with respect to the stationary coordinate system in a universe in which the speed of light is constant for all inertial frames (a universe like ours).

Another example is that of a moving object's mass. If a massive object is moving with respect to an "at rest" coordinate system, then in order to calculate that objects mass from the perspective of the stationary system, we must use the Lorentz factor, because we live in a world in which the speed of light is constant for all inertial frames- which causes distortions in space and time, which then distorts everything within space and time, including mass. Therefore, to determine the relativistic mass of an object in a moving reference frame, you must multiply that value by the Lorentz factor, which then implies, via the E = mc^2 relation, that an object's relativistic mass will approach infinity as the object's velocity approaches the speed of light (this was discussed earlier in this thread).



The simple matter is that our intuitive notion about coordinate transformations was inconsistent with a universe in which the speed of light is constant for all inertial frames. We do not live in a universe in which the speed of light changes. That was an assumption made by the Galilean transformation. If we are in a universe in which the speed of light is constant for all inertial frames (which we are), then all coordinate transformations must by logical necessity (as derived in this post) use the Lorentz transformation, and NOT the Galilean one alone. Because the Lorentz transformation necessarily implies that we cannot move faster than light, and because we must use this transformation (because we live in a universe in which the speed of light is constant for all inertial frames), it is a natural consequence that faster than light travel is impossible.



I don't know if this is any better than my first post, but at least you now know where the Lorentz transformation comes from. So now, anything this formula suggests to you should no longer seem like magic, but rather a natural geometric consequence of a universe in which the speed of light is constant for all inertial frames.

Is this one any better at all?

[Lightmind]

Not sure on all this math... but to save all our sanity's and CT's time, I'm not gonna contest, and I'm not an expert either.

DBA, you asked why something gains mass as it approaches the speed of light. I'll try;-

All equations MUST balance. Both numerically and units.

AT the speed of light a particle's energy has E=MC^2
C... The speed of light, is a constant, so cannot change. Therefore the only factor that can change is mass.
Disregarding potential energy (gravity) and Kinetic energy (relative motion). As a particle(m) accelerates (v^2) it gains energy E, as in E=mv^2, v here is a variable and so can change. If we substitute E we get mv^2 trying to become MC^2
If v increases, only an increase in M can balance the equation. But because mass is common to both sides m=M, and the energy of the particle, at any one point in time, is constant. Increasing m means reducing v. ie the bigger it gets the more energy required to maintain acceleration.

I'm not sure that there is anything in this equation that points to Infinite energy requirement, but it would certainly take a lot. Like I said, I'm not an expert. Whether it's a "final barrier" or simply a believed one, due to current knowledge I think only time will tell. Similar science was postulated for the speed of sound, and even at the advent of passenger travel in locomotives, i.e. traveling at faster than 30mph, the reduced air pressure would suck the air from our lungs!

There have been postulated other methods of at least data transferal at hyper-light speeds. Specifically Quarks created from the same atom. There is also a thread on here on AO, (though I can't remember it's name), regarding changes in DNA occurring instantaneously, without regard to distance.

One of these days.... who knows, I'm no expert ::):

[serge_regulator]

After reading this thread I have to say....Wow.... Some interesting descriptions of some complex theories.

I wont go into too much detail but there is a legacy of physicists in my family. I had it explained to me this way:

Energy has mass all to itself. Example: A coil spring at rest weighs less than the same spring when compressed and under tension. The only difference is the potential energy. Velocity is also energy. The more velocity an object has, the more it weighs. The more it weighs, the more energy it takes to accelerate it. You need an infinite supply of energy in order to accelerate an infinite mass. It cant be done.

Simple.

[Lightmind]

LOL.... I've been thinking of a way of explaining it in less words....as in "I'll define that principle in two." ::):

Maybe someone can explain why it is proven/assumed that any mass at C must be infinite energy? As C is a quantifiable value.

Secondly, hasn't general (and therefore special) relativity been disproven with the advent of Quantum physics? In that photons, can have the characteristics of particle OR wave, but not both?

[serge_regulator]

Funny you should ask that.... This was the answer I got:

If you are ten feet from a wall and you move exactly half way there on every turn, how many turns will it take you to reach the wall?

[Lightmind]

It was a genuine question....

As E=mv^2 becomes closer to E=MC^2.
There's nothing in E=MC^2 that points to infinite..... just very large.

In fact. If this article (http://www.hno.harvard.edu/gazette/1999/02.18/light.html) has any veracity, it doesn't even look like speed of light is a constant. I'm sure we can all manage E=M(38mph)^2.

It clearly states that this does not rebuff Einsteins Relativity theories, but it does show that once the science can become applied, through technological inovation, our concept of such things as "Absolute Barriers", and constants, can change. We know that light can be bent by gravity, and I seem to remember reading somewhere that it is also slowed by it, a Black hole's event horizon? Is light speed an absolute?

After all, it was an advance in engineering, (and endeavour) to finally prove the theory, that the earth was round.

[serge_regulator]

It was a genuine answer too.... They always made me work for the answers...

If you have an object at a certain mass and you want to accelerate it to a certain velocity you know exactly how much force (energy) you need to impart upon that object to achieve the desired result. However, energy has mass. Because of the energy you apply to that object the mass increases, which means that the amount of energy you need to reach your target velocity has also increased. And it will increase every time you apply more energy. There is no reason to assume these two factors funnel to parity or converge in a manner that resolves the mass/velocity paradox. If these two factors remain parallel the effect is infinite.

The wall is the speed of light. By losing half of the energy to increasing mass I was only taking steps that moved me half way to my goal instead of all the way. No matter how many steps I take, I never get more than half way there....

[Lightmind]

Ok serge.... You've obviously got this one between your teeth ::):

Lightspeed is NOT possible because E=MC^2. The reason you give is.....


If you have an object at a certain mass and you want to accelerate it to a certain velocity you know exactly how much force (energy) you need to impart upon that object to achieve the desired result. However, energy has mass. Because of the energy you apply to that object the mass increases, which means that the amount of energy you need to reach your target velocity has also increased. And it will increase every time you apply more energy. There is no reason to assume these two factors funnel to parity or converge in a manner that resolves the mass/velocity paradox. If these two factors remain parallel the effect is infinite.

Therefore E=MC^2 contains a variable equating to a varaible multiplied by a constant squared.
The only way to balance this equation is E vs M. Any increase in energy will result in an increase in mass. This points to a parrallel path, ie infinite.

However your making two assumptions;-

1) Energy and mass are freely and equally interchangeable.
2) The speed of light is constant, under all conditions.

If C is a merely a maximum speed, rather than a constant, we now have 2 variables balancing one. Which forms one of those "magic triangles" that physics is full of. It also means our equation is now resolvable.

DBA... you got the accepted answer. Sorry mate, now your back to square one again. ::):

If photons have mass, then because of E=MC^2 (http://www.circlon-theory.com/HTML/EmcFallacies.html), C cannot be a constant, under ALL conditions.

[serge_regulator]

Ok serge.... You've obviously got this one between your teeth ::):

I just answered the question...lol




Lightspeed is NOT possible because E=MC^2. The reason you give is....



Therefore E=MC^2 contains a variable equating to a varaible multiplied by a constant squared.
The only way to balance this equation is E vs M. Any increase in energy will result in an increase in mass. This points to a parrallel path, ie infinite.

Correct.



However your making two assumptions;-

1) Energy and mass are freely and equally interchangeable.
2) The speed of light is constant, under all conditions.

If C is a merely a maximum speed, rather than a constant, we now have 2 variables balancing one. Which forms one of those "magic triangles" that physics is full of. It also means our equation is now resolvable.

Here I disagree. C as merely a maximum speed rather than a constant is the assumption.



If photons have mass, then because of E=MC^2 (http://www.circlon-theory.com/HTML/EmcFallacies.html), C cannot be a constant, under ALL conditions.

In order for this to be true you have to prove that the for any given variable the ratio of change in C is not equal to the ratio of change in M. If they are equal then they remain parallel and the effect is still infinite.

Occums Razor: "when you have two competing theories which make exactly the same predictions, the one that is simpler is the better."

In physics we use the razor to cut away metaphysical concepts. The canonical example is Einstein's theory of special relativity compared with Lorentz's theory that ruler's contract and clocks slow down when in motion through the Ether. Einstein's equations for transforming space-time are the same as Lorentz's equations for transforming rulers and clocks, but Einstein and Poincaré recognised that the Ether could not be detected according to the equations of Lorentz and Maxwell. By Occam's razor it had to be eliminated.

[Lightmind]

In physics we use the razor to cut away metaphysical concepts. The canonical example is Einstein's theory of special relativity compared with Lorentz's theory that ruler's contract and clocks slow down when in motion through the Ether. Einstein's equations for transforming space-time are the same as Lorentz's equations for transforming rulers and clocks, but Einstein and Poincaré recognised that the Ether could not be detected according to the equations of Lorentz and Maxwell. By Occam's razor it had to be eliminated.

Unfortunately, you are applying a double standard.

A


Therefore E=MC^2 contains a variable equating to a varaible multiplied by a constant squared.
The only way to balance this equation is E vs M. Any increase in energy will result in an increase in mass. This points to a parrallel path, ie infinite.

In this you agree..... "correct"

Whereas....

B


However your making two assumptions;-

1) Energy and mass are freely and equally interchangeable.
2) The speed of light is constant, under all conditions.

If C is a merely a maximum speed, rather than a constant, we now have 2 variables balancing one. Which forms one of those "magic triangles" that physics is full of. It also means our equation is now resolvable.

You challenge.... "Here I disagree. C as merely a maximum speed rather than a constant is the assumption."

Which you qualify by....


If photons have mass, then because of E=MC^2, C cannot be a constant, under ALL conditions.

"In order for this to be true you have to prove that the for any given variable the ratio of change in C is not equal to the ratio of change in M. If they are equal then they remain parallel and the effect is still infinite."


In B you ask me to prove that the rate of change of C(^2) is not equal to the rate of change of M, but I've already shown you an article (http://www.circlon-theory.com/HTML/EmcFallacies.html) oultlining some common misconceptions about Special Relativity, and also an article (http://www.hno.harvard.edu/gazette/1999/02.18/light.html) showing that, under certain circumstances, the speed of light can be slowed.

However, you offer 3 examples to support A....


Energy has mass all to itself. Example: A coil spring at rest weighs less than the same spring when compressed and under tension. The only difference is the potential energy. Velocity is also energy. The more velocity an object has, the more it weighs. The more it weighs, the more energy it takes to accelerate it. You need an infinite supply of energy in order to accelerate an infinite mass. It cant be done.


If you are ten feet from a wall and you move exactly half way there on every turn, how many turns will it take you to reach the wall?....
The wall is the speed of light. By losing half of the energy to increasing mass I was only taking steps that moved me half way to my goal instead of all the way. No matter how many steps I take, I never get more than half way there....


If you have an object at a certain mass and you want to accelerate it to a certain velocity you know exactly how much force (energy) you need to impart upon that object to achieve the desired result. However, energy has mass. Because of the energy you apply to that object the mass increases, which means that the amount of energy you need to reach your target velocity has also increased. And it will increase every time you apply more energy. There is no reason to assume these two factors funnel to parity or converge in a manner that resolves the mass/velocity paradox. If these two factors remain parallel the effect is infinite.

You've yet to support the notion that, because C is a constant, there must be a free, equal AND linear exchange between Energy and Mass, and that by compressing a spring, somehow it's mass increases.

Occums Razor: "when you have two competing theories which make exactly the same predictions, the one that is simpler is the better." ....Not always.

Apples do not always fall downwards.

[serge_regulator]

Thats not a double standard. (I didnt right that, I quoted an article that summed it up nicely) But its true according to Occum's razor. The ether is an extra element added to the equation that cant be measured and therefore has to be eliminated.

True, the article does imply that the speed of light can be slowed. However, it does not indicate whether the increase in mass slows in equal proportion to the decrease in velocity or not. If it does then the effect is still infinite. Again, per Occum's razor, the simpler theory is to assume it is equal unless there is a reason to suspect otherwise. The burder of proof is on your end. :-)

The theory with the coil spring is simple. The only difference is the addition of potential energy. Its the same with photons. Photons have no 'rest' mass but do have mass when in motion. The only difference is the addition of energy. If you could build a sensitive enough scale you could measure the difference but for now it exists only in theory.

I dont know if I would describe the interaction between mass and energy as a free, equal and linear exchange or more of a cause and effect relationship. The mass in question could not be measured were it not for the application of energy.

I'm getting a headache and my dog wont play with me any more....

[Lightmind]

True, the article does imply that the speed of light can be slowed. However, it does not indicate whether the increase in mass slows in equal proportion to the decrease in velocity or not. If it does then the effect is still infinite. Again, per Occum's razor, the simpler theory is to assume it is equal unless there is a reason to suspect otherwise. The burder of proof is on your end. :-)

The Bose-Einstein Chanber works by reducing the energy of light E, so slowing the "constant" C. Mass remians the same.

But to avoid pain to your head, and your dogs heart :-)

My point is;-
Special relativity is over 100 years old.
General relativity, a revised more complicated equation, is over 90 years old.
Long before we ever split the atom, went into space, developed computers, cyclotrons, quantum physics, and genetically engineered apples. I'm not refuting it, and no one else is. I'm simply saying, that we cannot hold to it as "Universal" when today we simply know better. I think even Einstein would agree here.

Wanna argue time as a constant? ::):

[serge_regulator]

These ideas arent new. That much is certain. I guess I should look closer at the new toys kids are playing with these days before arguing that the old days are better... :-)

[Lightmind]

::):
I'm not a physist, not even anything to do with academia. I do know a guy, American kid doing a PHd in Physics. He went home this summer to help out in an experiment at MIT, I believe. They're using, really high current, electro magnets, to levitate frogs! :Llol:

Man is doing some incredible stuff.

The title of this post... "Why the speed of light cannot be exceeded according to Special Relativity." is correct. It doesn't mean we'll never do it though.

[Cartesiantheater]

No, no, no. Not to be a jerk, but E=mc^2 is NOT why. Look at the equation. You will see an E for energy, an m for mass, a c for the speed of light, but no v for the velocity of the object itself. There's a reason for ths: The E=mc^2 is for an object AT REST with respect to the observer. The correct energy/mass equation for an object in motion- the one that relates energy, mass, the speed of light, and the objects velocity- is E=mc^2 times the Lorentz factor(well, to be more precice, the relation is more often written as E^2 = m^2 c^4 + p^2 c^2, where p is momentum, which is algebraically equivelant). You will notice that there is a v for velocity of the object in the Lorentz factor (while there isn't a v in plain old E=mc^2 [the AT REST version]). You CANNOT forget the Lorentz factor when dealing with relative motion. There are two huge posts discussing where the Lorentz factor comes from. I suggest a more careful reading (the only math you need is basic algebra and a little right-triangle geometry. The hard part is getting to the triangle, but the only math used for that is the distance formula everyone knows. If you take your time, the math really isn't so bad- there's no math passed the 10th grade in that post. It's deriving the math [the physics] that's challenging). I cannot emphesize it enough: coordinate transformations are the key to special relativity (and the constany of the speed of light). The Galilean transformation is incompatible with the postulate that the speed of light is constant for all inertial frames. We must use the Lorentz transformation (as shown earlier), and most of the "quirks" of special relativity follow from this. *this post was made with a Wii remote, thus the potential errors...

[Cartesiantheater]

LOL.... I've been thinking of a way of explaining it in less words....as in "I'll define that principle in two." ::):

Maybe someone can explain why it is proven/assumed that any mass at C must be infinite energy? As C is a quantifiable value.

Secondly, hasn't general (and therefore special) relativity been disproven with the advent of Quantum physics? In that photons, can have the characteristics of particle OR wave, but not both?

The reason the need for infinite energy is elluding you is that you are not using the entire equation (you're forgetting the Lorentz factor). The correct equation is E=mc^2 DIVIDED BY the square root of 1 - v^2/c^2. Looking at the correct equation, it is clear that as v approaches c, E approaches infinity (as v gets bigger, the denominator approaches zero. When the denominator = 0, you are at infinity [you can't divide by zero, remember?]). Go ahead. Insert various ever increasing values for v. You should see the relationship.

As for the second question- no, quantum mechanics has not disproved special or general relativity. In fact, special relativity is already unified with QM in the Standard model. GR is as yet not unified with QM, but it is not disproven by it.

You are right about photons. Exactly right.



Hope that helps. I'm no expert eithet, so double check anything I say, but I'm pretty sure this all correct... :D



*another Wii post...

[Lightmind]

Hi CT
Yes.... I'm not disagreeing with you....
You cannot attain the speed of light according to special relativity.
I didn't even want to bring in relative velocity.
My point is.... Much like the speed of sound.... The speed of light is NOT a constant.... Photons DO have mass.

[Cartesiantheater]

Hi CT
Yes.... I'm not disagreeing with you....
You cannot attain the speed of light according to special relativity.
I didn't even want to bring in relative velocity.
My point is.... Much like the speed of sound.... The speed of light is NOT a constant.... Photons DO have mass.

The speed of light is always constant within any given inertial reference frame. You can "slow" the speed of light, but everything else within that reference frame is slowed as well.

And you MUST bring in relative velocity when speaking of motion approaching the speed of light. Otherwise your calculations will be off. Ignoring the Lorentz factor when discussing velocities approaching the speed of light is incorrect.

Photons do not have mass in the sense we have been discussing. They have relativistic momentum, but this is NOT because they are made of electrons, protons and nuetrons. I'm sure you're aware of this.

As far as the validity of special relativity:

Special relativity is exactly correct for all inertial frames. Maybe you have heard otherwise, but I have not. As long as we are discussing inertial frames, special relativity matches reality, as far as I have seen.

If you have sources to the contrary, please post them. In fact, if you want you could give that subject its own thread (it's certainly big enough a subject).

[Lightmind]

"The speed of light is always constant within any given Inertial reference frame (http://en.wikipedia.org/wiki/Inertial_frame_of_reference)"......."An inertial frame of reference is one in which the motion of a particle not subject to forces is a straight line."

> Whats this got to do with depriving a particle of energy?

"You can "slow" the speed of light, but everything else within that reference frame is slowed as well."

> A Neutrino passing through a Bose-Einstein condensate is unlikely to be slowed, even though photons are. At this point, by it's own "frame of reference", it is travelling at 20 million times the speed of light.

"Photons (http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/photon_mass.html) do not have mass in the sense we have been discussing. They have relativistic momentum, but this is NOT because they are made of electrons, protons and nuetrons. I'm sure you're aware of this."

> "It is almost certainly impossible to do any experiment that would establish the photon rest mass to be exactly zero. The best we can hope to do is place limits on it. A non-zero rest mass would introduce a small damping factor in the inverse square Coulomb law of electrostatic forces. That means the electrostatic force would be weaker over very large distances."

"Special relativity is exactly correct for all inertial frames. Maybe you have heard otherwise, but I have not. As long as we are discussing inertial frames, special relativity matches reality, as far as I have seen."

> Unfortunately "all inertial frames" is a pure theoretical concept, not reality. Which is why Einstein spent another 12 years developing Special Relativity into General Relativity.


*** Blinks... Wondering why someone is working so hard to disagree with someone who is agreeing with them. ***

[Cartesiantheater]

"The speed of light is always constant within any given Inertial reference frame....

> Whats this got to do with depriving a particle of energy?
Huh? I'm simply pointing out thar SR is correct when used in the correct arena. Please elaborate.
You cannot define a moving particle's energy with E=mc^2 alone. That is why I am responding to you.

"You can "slow" the speed of light, but everything else within that reference frame is slowed as well."
> A Neutrino passing through a Bose-Einstein condensate is unlikely to be slowed, even though photons are. At this point, by it's own "frame of reference", it is travelling at 20 million times the speed of light.Okay, but the light interacts with the matter, while nuetrinos hardly interact. In every single "empty" space between "pieces of matter light travels at c, faster than nuetrinos. You bringing this up will confuse people who don't know better. If the nuetrino also interacted with matter, it would move slower. When a photon hits an electro, it is absorbed and energizes the electron. The electron then moves at the speed of an electron, until it releases the energy as a photon-whih travels at c until it interacts with another piece of matter.
Photons do not have mass in the sense we have been discussing. They have relativistic momentum, but this is NOT because they are made of electrons, protons and nuetrons. I'm sure you're aware of this."> "It is almost certainly impossible to do any experiment that would establish the photon rest mass to be exactly zero. The best we can hope to do is place limits on it[...]QM puts that sort of limit on everything. We had a nice discussion on the limits of what we can measure in the universe thread.
Why am I arguing? Because I don't want you to confuse people. You were incorrect about E=mc^2 having to do with motion so regardless if we agree that SR is incomplete, I fear you will confuse people like you did Serge.

[Cartesiantheater]

Also, I was responding to your question about why infinite energy is needed to accelerate an object with proper mass to c. The answer is within the correct energy-mass relation - the one derived for an object in motion.

And whether or not a photon will, through some quantum fluctuation, have a rest mass (even though photons are never at rest), you would still discuss a moving object's energy using the "in motion" energy relation, not the "at rest" one.
Looking at E=mc^2, where is the variable for the object's velocity? No where. There IS no v because that equation does not describe an object in motion. The "in motion" equation has a v for the object's velocity. Do you agree with this or no?

[serge_regulator]

OK....y'all need another hobby....may I suggest women? They are infinitely more complex than any theories being discussed here, but if you even come close to figuring one out the results are far more rewarding....

I gonna go spend some time with the wife.... :-)

Just a bit of humor....nothing personal....
(the wife said someone may be insulted by that comment.... :-)

[Lightmind]

CT.

There is an underlying question on this thread, going back to post #2, that for all it's complexity and accuracy of the mathematics, has never been answered to the satisfaction, or understanding, of the questioner:-


hmm.... CT, you explained how the math of the equation works but you did not put into words WHY a thing cant possibly go faster than light.... Einstien didnt start with the equation, he started with the observation and wrote the equation to fit it. So, and I really am curious as this is still kinda shady to me, why is it that as matter approaches the speed of light that it takes more and more energy to increase its speed? Why does that energy needed increase exponentially while the speed increases linearly? Or hell, maybe even logarithmically(sp).

I understand it has something to do with "mass increasing"?

The only reason I first posted on this thread, was to try to explain it, using nothing other than the equation itself, in simple mathematical terms, Post #22;-


All equations MUST balance. Both numerically and units.

AT the speed of light a particle's energy has E=MC^2
C... The speed of light, is a constant, so cannot change. Therefore the only factor that can change is mass.
Disregarding potential energy (gravity) and Kinetic energy (relative motion). As a particle(m) accelerates (v^2) it gains energy E, as in E=mv^2, v here is a variable and so can change. If we substitute E we get mv^2 trying to become MC^2
If v increases, only an increase in M can balance the equation. But because mass is common to both sides m=M, and the energy of the particle, at any one point in time, is constant. Increasing m means reducing v. ie the bigger it gets the more energy required to maintain acceleration.

If C is a constant, then E must always balance M.......Yo! Serge, *** Hi-5*** I define that principle in one!!! ::):

Notice, I do say... "Disregarding potential energy (gravity) and Kinetic energy (relative motion).".... Which are the limitations of special relativity, (SR?)


Why am I arguing? Because I don't want you to confuse people. You were incorrect about E=mc^2 having to do with motion so regardless if we agree that SR is incomplete, I fear you will confuse people like you did Serge.

I understand about the Lorentz factor, but to include it, for the sake of accuracy, simply complicates basic understanding. Not just for DBA, but for any body else who seeks basic understanding. As Ta'Nahir has already pointed out;-


Sorry Cartesiantheater, but that was a HORRIBLE explanation. You explained how it works on a mathematical level and not on a physical level. The issue needs be explored in a light the average person can see, not magic light such as UV or infrared.

I, personally believe, science should never appear mystical. Was I "incorrect about E=MC^2 having to do with motion?"


Special relativity introduces E=mc^2, but takes no position mass. It was not until general relativity that mass was included in the Einstein relativity equations and theory. Special relativity introduced the simple equation but merely focuses on velocity without mass. THat is neither hear nor there. The reason the speed of light cannot be surpassed is because all other particles contain mass.

There is a v in E=MC^2.....v=d/t..... the unit of C.

Its perfectly correct, mathematically, to write E=Mv^2 or even E=M((d/t)^2). Whether it's correct to, is case specific. As I was never seeking, technical accuracy, merely mathematical understanding, of a theoretical equation. I think a substitution, for the sake of example, is valid.

Much like women, d and debatably t should never be treated as a constant. If we can slow time down, would that not speed up light?.... Not sure, I'm not an expert. Hence the second half of my original post.


I'm not sure that there is anything in this equation that points to Infinite energy requirement, but it would certainly take a lot. Like I said, I'm not an expert. Whether it's a "final barrier" or simply a believed one, due to current knowledge I think only time will tell. Similar science was postulated for the speed of sound, and even at the advent of passenger travel in locomotives, i.e. traveling at faster than 30mph, the reduced air pressure would suck the air from our lungs!

There have been postulated other methods of at least data transferal at hyper-light speeds. Specifically Quarks created from the same atom. There is also a thread on here on AO, (though I can't remember it's name), regarding changes in DNA occurring instantaneously, without regard to distance.

Just because we can't currently accelerate a mass beyond lightspeed, does not mean that we will never travel faster than light. That's simply dogma, and leads to fallacy (http://home.att.net/~numericana/answer/record.htm#quotations).

"History is full of scientific custard pies."..... Albert Einstein. (I believe)

You like to challenge accuracy, I like to challenge Dogma, none of us are experts, and humour is always welcome.

Serge HAS to spend some time with his wife.... I'm afraid THAT will always be a constant. ::):

[Cartesiantheater]

2 things:
1.) At the time of post two, I had no idea where the Lorentz factor came from. I might has well have pulled it from the sky. In post 20 I finally figured it out and explained where it came from in detail. This is important because the mathematical answer to both DBA's question and yours is answered by it (why everyone talks of infinite energy). Plug in c for v (let v approach c, so you get a term of c/c in the denominator) into the Lorentz factor and see what you get.
2.) There is no relation of E=mv^2(I will give the pre relativity relation of KE =1/2 mv^2, but that eqation is only approximat for slow speeds). The c in E=mc^2 is not the object's velocity. It is just a scalor. The reason we know it is not a vector value but a scalor is because energy isn't a vector quantity and neither is mass. The entire purpose of the Lorentz factor is to include the object's velocity. E=mc^2 isn't enough. The c has nothing at all to do with the object's velocity.
I'm all for simple answers- but I'm all about making things "as simple as possible, but not simpler," to quote Einstein. As far as I can tell, you can't really get simpler than coordinate transformations and still be correct.
3.) As far as cutting edge physics go, those who really want to understand should hold up untill they really get this more fundamental stuff.

Besides, the jump from E=mc^2 to E=mc^2 times 1/(1 - v^2/c^2)^(1/2) isn't that big. It's still only algebra. I'd prefer to encourage someone to stretch themselves than to simplify too much. Better not to give math at all than to give incorrect or misleading math.

I promise that anyone who is patient, has passed high school math, and really wants to learn it will eventually do so. But not if they are sent down an inaccurate path. Make it as simple as possible, but not simpler. I know you're just trying to make it easier to understand, but I don't think you give the average person enough credit.

[Lightmind]

2.) There is no relation of E=mv^2 (I will give the pre relativity relation of KE =1/2 mv^2, but that eqation is only approximat for slow speeds). The c in E=mc^2 is not the object's velocity. It is just a scalor. The reason we know it is not a vector value but a scalor is because energy isn't a vector quantity and neither is mass. The entire purpose of the Lorentz factor is to include the object's velocity. E=mc^2 isn't enough. The c has nothing at all to do with the object's velocity.

That's the best explanation I've seen so far, thanks


I'm all for simple answers- but I'm all about making things "as simple as possible, but not simpler," to quote Einstein. As far as I can tell, you can't really get simpler than coordinate transformations and still be correct.

I promise that anyone who is patient, has passed high school math, and really wants to learn it will eventually do so. But not if they are sent down an inaccurate path. Make it as simple as possible, but not simpler.

Different approaches to the same solution, neither are wrong, and sometimes neither are right.

You sure this about flat Earth (http://forums.armageddononline.org/world_flat-t14300.html) thing though? ::):

[serge_regulator]

Relativity works....here is proof....

Look at this image....

http://i301.photobucket.com/albums/nn51/serge_regulator/EINSTEIN.jpg

Now back up about 15 feet and look at it again....

[Lightmind]

lol.... It certainly does depend on your frame of reference.
Though I did have to lose energy in backing up...... But it doesn't matter! ::):

[serge_regulator]

I couldnt pass that one up. It had to be done...lol

[Cartesiantheater]

That's the best explanation I've seen so far, thanks



Different approaches to the same solution, neither are wrong, and sometimes neither are right.

Well, I would disagree, but then again, special relativity is just a limited condition within general relativity (kind of like Newton's laws of motion are limited conditions within special relativity).

And in all likelihood, general relativity is just a limited condition within the eventual "Theory of Everything." But within their respective arenas they are correct.


You sure this about flat Earth (http://forums.armageddononline.org/world_flat-t14300.html) thing though? ::):

Nah, that's all bs (obviously). But you got to admit, the pictures are hilarious. The secret is that the whole premise is based upon slight distortions of legit theory :D

I guess it makes the point that hearing about theories isn't enough. You've got to really understand them, as much as possible.

[Cartesiantheater]

Coordinate transformations. This might help. No math whatsoever.

http://www.youtube.com/watch?v=C2VMO7pcWhg&feature=related

[DontBeAfraid]

Lightmind, saying: "all equations must balance" does in no way shape or form answer the question as to why inertial mass increases with relative velocity. The equations were derived from intuition and the observation that the speed of light is constant from all frames of reference. CT thanks for showing me exactly where the scaler comes from but Im not sure it really answered my question... It did change it for me though. The more proper question should be: by what means is light able to always have the same speed from all frames of reference.... and what are the implications for black holes.

[Cartesiantheater]

1.) It turns out that my "derivation" for the Lorentz factor is far from a mathematical proof. It is merely an intuitive realization of the result of the constany of the speed of light. It is not complete because it fails to take into account the other postulate of special relativity, that the laws of physics are the same regardless of your relative inertial motion to another frame. However, I will rectify this later today or tomorrow, using a more mathematically rigorous method that uses both major postulates of special relativity.


EDIT: Done. http://forums.armageddononline.org/deriving_lorentz_transformation-t15578.html?p=219640

2.) DBA:



by what means is light able to always have the same speed from all frames of reference

I don't have the details on this question yet, but I know the answer lies in the field of electromagnetism. It has to do with Maxwell's equations, and the principle of relativity (the laws of physics are the same regardless of relative inertial movement), and the phenomenon of induced emf (http://en.wikipedia.org/wiki/Electromagnetic_induction).


.... and what are the implications for black holes.

I have no idea about this one, because it involves general relativity.

One thing I want to bring up though. You said, "by what means is light able to always have the same speed from all frames of reference," but I do not think this is accurate (if by "speed" you mean "velocity."). In non-inertial frames, there are gravitational fields, and gravitational fields cause light to follow a curved path. This by definition implies that the velocity is not constant (a particle following a curved path is always accelerating).

As I understand it, the postulates of special relativity hold in general relativity for small stretches of space or time- that is, they are limiting aspects of general relativity. Kind of like if you take a curved line and zoom in to a point, the closer you get to the point, the closer the path on the curve approaches a straight line (for shits and giggles (http://www.themathpage.com/aCalc/derivative.htm) -For the curious who wish to learn, you should probably start at lesson 1 (http://www.themathpage.com/aCalc/continuous.htm)). In the same way, special realtivity is accurate within the context of general relativity if you look at a sufficiently small region of spacetime.

However, any large area of spacetime, because invariably there are gravitational fields (and hense curvature), requires an entirely different mathematical basis, and I've got nothing on that at this point. Black holes would be the most curved areas of spacetime in the universe, so I'm pretty sure that aspects of special relativity do not hold there. (but I could be mistaken, as that is over my head)

[DontBeAfraid]

I chose the word speed for that reason CT. I do like your eagerness to educate on this topic though.... And dont think that I have not learned anything from you. Far from it in fact.

[Cartesiantheater]

Thanks. I try to educate on it because that's how you learn it, you know? And this subject has been my obsession for a few months.

Anyway, how about this. A guy at physorg asked a similar question, and I like the answer that was given.

The original question was "Why can't we move faster than light?" and the answer was, "the speed of light is constant for all inertial frames," which has the logical consequence of the Lorentz factor (which makes the speed of light the maximum speed).

This leads to the next question, "why is the speed of light constant for all inertial frames?" and I think this is a good answer.

http://www.physforum.com/index.php?showtopic=21977

Look at post two, by Good Elf.

[DontBeAfraid]

Wow... good elf spent a lot of time explaining red shift and almost none answering the question. His answer to the actual question though was circular in that he used time dilation to explain why the speed of light is constant(the same) in all frames of reference... yet time dilation is the logical consequence of the speed of light being the same for all frames of reference.

To make clear what I understand: Time must be percieved as passing more slowly for an observer moving at high velocity in order for light "emitted" from the observers frame of reference to be percieved as moving away from it at the known constant speed of light....

INteresting tangent: The faster something moves, the longer it takes to decay. Black holes: matter which is accellerated into the singularity percieves itself as being immediately evaporated back out of it at some time in the very very distant future.

[Cartesiantheater]

Wow... good elf spent a lot of time explaining red shift and almost none answering the question. His answer to the actual question though was circular in that he used time dilation to explain why the speed of light is constant(the same) in all frames of reference... yet time dilation is the logical consequence of the speed of light being the same for all frames of reference.

I liked the "light can't get a push" thing, but I guess that would only push the question back further.


To make clear what I understand: Time must be percieved as passing more slowly for an observer moving at high velocity in order for light "emitted" from the observers frame of reference to be percieved as moving away from it at the known constant speed of light....

I think that's right. But I believe there is more to it. Also, Minkowski space must be considered. Course, I know jack about that.


INteresting tangent: The faster something moves, the longer it takes to decay. Black holes: matter which is accellerated into the singularity percieves itself as being immediately evaporated back out of it at some time in the very very distant future.

Hmm... How so? Via Hawking radiation?

[DontBeAfraid]

Hmm... How so? Via Hawking radiation?Ya. The particle is accellerated to almost the speed of light and so time "within" it slows down and cannot return to normal until it is out of the hole.

[Cartesiantheater]

Yeah, that makes sense. I'm pretty sure that Einstein said that the observer who experienced the most acceleration experienced the least amount of time.

One question I have though is, if you can't feel length contraction or time dilation when moving with a high velocity, why do you feel the curving of space (via gravity) and thus why will you be ripped to shreds as you enter a black hole?

I'd like to think that space-time for you simply changes, and that you wouldn't be able to tell except visually (like with length contraction, time dilation, etc).



Of course, obviously there is a fundamental difference between accelerating and uniform motion, since you can feel the former.

[DontBeAfraid]

One question I have though is, if you can't feel length contraction or time dilation when moving with a high velocity, why do you feel the curving of space (via gravity) and thus why will you be ripped to shreds as you enter a black hole?My guess would be that we dont come in small enough discreet packets...


I'm pretty sure that Einstein said that the observer who experienced the most acceleration experienced the least amount of time.Ya... and that is basically(exactly) what you just explained to us.

[Cartesiantheater]

Ya... and that is basically(exactly) what you just explained to us.

Well, except what I've tried to explain (and learn) here neglects all considerations of accelerations/gravitational fields.

But yeah, you're right. Thing is, until I can at least partially wrap my mind around the math of the GR theory, it just doesn't mean as much to me. To be honest, I don't even know what the math of GR even looks like (I guess I've seen it before, but it is just gibberish to me at this point).

EDIT- Ok, it looks like this:

http://en.wikipedia.org/wiki/Mathematics_of_general_relativity

Looks a bit too much to dream about...

[Cartesiantheater]

By the way, it looks like the constancy of the speed of light actually comes from Maxwell's equations, not Einstein. Turns out Einstein was merely trying to UNIFY Maxwell's equations (which predict electromagnetic phenomena with unreasonable accuracy) with the principle of relativity (all laws of physics are the same in inertial frames), thus came special relativity. And so, it's "off to a more detailed understanding of pre-Einstein electromagnetic theory.................. AWAAAAAAAAYYYYY!!!!!!!!!!!!!!!!!!!!!!!!!"

[Cartesiantheater]

Turns out if you write Faraday's law of induction and the Maxwell-Ampère law in one dimension, and then differentiate them twice and substitute them into each other, you get two wave equations with a very special velocity (I believe this is how Maxwell predicted that electricity, light and magnetism have wave qualities).

Preliminaries:

(1.) Faraday's law of induction describes how an EMF (old lingo: electromotive force) can be generated by a change in magnetic flux.

(2.) The Maxwell-Ampère law describes how a moving current produces a magnetic field.


So these two relate the circumstance of magnets creating electricity and electricity creating magnetic fields. I believe a relationship to special relativity can be made here. The following is my own speculation.








Anyway, here goes (for the slightly mathematically inclined poster).

Faraday's law of induction and the Maxwell-Ampère law in empty space (these are supposed to be closed integrals, but I don't know how to type them):


∫ E ds = - dΦB/dt



∫ B ds = με dΦE/dt

*μ = permeability of free space = 4 π x 10^-7 T m/A

*ε = permittivity of free space = 8.854 x 10 ^-12 C^2/Nm^2

Which, from my text book, you can derive these two relationships:


∂E/∂x = - ∂B/∂t

and

∂B/∂x = - με ∂E/∂t







Taking the second partial derivative with respect to x, and then substituting in the appropriate one of these two equations:

∂^2E/∂x^2 = ∂/∂x (- ∂B/∂t) = - ∂/∂t (∂B/∂x) = - ∂/∂t (- με ∂E/∂t)

==> ∂^2E/∂x^2 = με ∂^2E/∂t^2


And

∂^2B/∂x^2 = ∂/∂x (- με ∂E/∂t) = ∂/∂t (- με ∂E/∂x) = - ∂/∂t (με - ∂B/∂t)

==> ∂^2B/∂x^2 = με ∂^2B/∂t^2







Since both of these equations look like the standard wave equation,

∂^2y/∂x^2 = (1/v^2) ∂^2y/∂t^2

could we not take either one of them, with με = (1/v^2), and then solve for v,

v = 1/√(με) = 2.998 X 10^8 m/s (obviously the speed of light).




And then, considering that BOTH equations have the same value for 1/v^2, and considering, if I understand it correctly, each of these can refer to the same induced emf = rate of change of magnetic flux/ or the same magnetic field produced by some current flowing through a loop, could that not be in some way connected to the postulate of the constancy of the speed of light in inertial frames? That is (and I am likely wrong, as I barely have an elementary understanding of this), couldn't we describe the exact same event using either law depending on which part is "at rest" and which is "in motion? (using Faraday's law if we assume that an emf is made by change in magnetic flux, and alternatively using the Maxwell-Ampère law if we assume the magnetic field is created by current changing to describe the same event depending on which frame we designate as "at rest?")

Obviously (since it is probably wrong), this is a step my textbook doesn't take. But, I find it very interesting that the velocity is the exact same for both Faraday's law and the Maxwell-Ampère law. As I understand it, this means that if you move a magnet through some loop of current carrying wire (wire at rest), the speed given in the wave equation describing this event is identical to the speed describing the magnet at rest and the loop moving. If you are "the magnet," this seems to mean to me that the speed of light is the same whether you are moving or whether you are at rest- that is, for any inertial movement relative to the loop of wire. This makes me wonder if it is in part these two laws that predict that the speed of light is constant regardless of inertial motion.




Now, as I understand it, this result (or one like it) was considered to be only true with respect to the hypothesized luminiferous ether. After the Michelson-Morley experiment (and duplications of it) however, it seemed that the result was true regardless of relative motion. If this is right, you can neatly see how special relativity relates to electromagnetic theory. As to where Maxwell's equations come from, well, these come from experience. Experiment, that is. The very valuable work of people like Faraday, Ampère, Gauss, Tesla, etc.


Does this enrich anyone's understanding any? It certainly is fascinating to me. I just hope the connection turns out to be correct (I don't think I'll cover Maxwell's equations in depth until next year. Ive got a long slate of basic quantum mechanics coming up this semester, and only a brief introduction into special relativity).

[nuke]

I have a few questions:

1. The speed of light is constant for all observers in all inertial frames. So what happens in an accelerating frame? Does the speed of light change, or is there simply a rate of change in time dilation and length contraction?

2. There was movie a ways back with Kevin Spacey, KPax - he's basically an alien in a mental patients body. He makes a statement that Einsteins laws only apply to objects with velocities below the speed of light, but does not say anything about objects already travelling FASTER than the speed of light. Is this simply Hollywood non-sense, or does physics allow for some particles to travel faster than the speed of light?

3. Premise: space ship travelling at .99c around the earth. From a practical point of view:

a) say through a telescope, or whatever, how would someone on the earth "see" someone on the spaceship? Would the person in the spaceship appear to be doing everything more slowly than someone doing the same thing on earth? So say an observer on earth saw someone brushing his teeth on the spaceship - it would appear in slow motion, such that for the person on the earth, it would take years for the spaceship dweller to finish brushing his teeth?

b) how does someone on the spaceship see someone on earth? Would everyone be in "fast forward" to the person on the spaceship? So whole decades might pass on the earth in the time it takes the spaceship dweller to have a shower?

c) would communication be possible between someone on the earth and someone on the ship? Say light beam morse code or something? Would a message from earth be time dilated to the person on the spaceship, such that a reply from someone on the spaceship would take a "long period of time" for the person on the earth?

[Cartesiantheater]

I have a few questions:

1. The speed of light is constant for all observers in all inertial frames. So what happens in an accelerating frame?

Special relativity can deal with accelerating frames, but accelerating frames aren't all equivalent. In General relativity, however, accerating frames are all equivalent, with the addition of gravitational fields.


-as far as I know!


Does the speed of light change, or is there simply a rate of change in time dilation and length contraction?

1.) The speed of light is always constant according to local clocks and measuring rods. That's all I can personally tell you right now. Try posting the question on a physics forum.

2.) There is a gravitational/acceleration time dilation and length contraction, in addition to the time dilation and length contraction found in special relativity. This also has been experimentally verified.




2. There was movie a ways back with Kevin Spacey, KPax - he's basically an alien in a mental patients body. He makes a statement that Einsteins laws only apply to objects with velocities below the speed of light, but does not say anything about objects already travelling FASTER than the speed of light. Is this simply Hollywood non-sense, or does physics allow for some particles to travel faster than the speed of light?

No, this is right. Tachyons, for example, are theoretical particles that fit the description- but what they actually are is really subtle. However, it's not that Einstein's laws only apply to objects with mass. It's that Einstein's laws predict that objects with mass or objects traveling slower than the speed of light cannot reach the speed of light.

wiki article:

http://en.wikipedia.org/wiki/Tachyon



3. Premise: space ship travelling at .99c around the earth. From a practical point of view:

a) say through a telescope, or whatever, how would someone on the earth "see" someone on the spaceship?

It depends on which way the spaceship is moving. If it is moving towards the earth, the observer will see them blue shifted (a yellow dude would look more green than normal; basically the faster the source is coming toward you the bluer the object will appear). If it is moving away from the earth, they will see them red shifted (yellow dude looks orange; faster they are moving way the more red they will look).




Would the person in the spaceship appear to be doing everything more slowly than someone doing the same thing on earth? So say an observer on earth saw someone brushing his teeth on the spaceship - it would appear in slow motion, such that for the person on the earth, it would take years for the spaceship dweller to finish brushing his teeth?

As I understand it, yes (maybe not years though. Distance would play a part too, I think).




b) how does someone on the spaceship see someone on earth? Would everyone be in "fast forward" to the person on the spaceship? So whole decades might pass on the earth in the time it takes the spaceship dweller to have a shower?

They would see the exact same thing the Earth people see (spaceship sees the earth move slow and blue or red shifted)- UNLESS the ship came from the Earth, then turned around and went back to the earth. If there was a break in symmetry (that is, if there was some duration in which the observers were NOT moving uniformly with respect to each other), then one will age less than the other. Otherwise, both will see the other with slow clocks.

Here is a very good explanation of this from wiki.

http://en.wikipedia.org/wiki/Twin_paradox#Resolution_of_the_paradox_in_special_ relativity





c) would communication be possible between someone on the earth and someone on the ship? Say light beam morse code or something? Would a message from earth be time dilated to the person on the spaceship, such that a reply from someone on the spaceship would take a "long period of time" for the person on the earth?


This is a tricky question. I don't know if I'm right here, so again, you might want to post this on a physics forum.

But, as I understand it, YES communication would be possible between two observers moving less than c because c is constant for both observers. However, as long as symmetry is not broken (as long as the space ship hasn't turned around yet), assuming both observers sent the other a signal telling what time it was in their respective present, both observers would get the same message. They would each get a message from the other suggesting that the other's clock was moving slow (because either one can be considered at rest, with the other moving at v or -v. So in either case the distance between the two when the message is sent will be larger when the message is recieved).

Yes, this seems like a paradox. In fact, that is why it's called the twin paradox.
The thing to keep in mind is the idea of "frame of reference." It's not that one clock REALLY is going slower than the other (when things remain symmetrical), it's that from some reference point one thing is observed, and from another something else is observed.





Do NOT take my word on this though. The only thing I remotely understand is some of the basic math involved. I am just presently learning the actual meanings of all of it in a class I'm enrolled in now- and it's way confusing at this point.

Here is a good discussion from a few years back at a physics forum, and maybe a good place for you to post your questions:

http://www.physicsforums.com/showthread.php?t=29674

[Reef Badlaw]

A golf-ball approaches the hole at an angle... but it intersects with the circular lip-of-the-hole, travels a few degrees along the rim-arc, then is 'repelled' back-onto the green's surface at a somewhat greater speed than it was originally travelling.

Can a beam of light gain speed around a black hole?


you may've already answered, but I didn't recognize it...

[Cartesiantheater]

A golf-ball approaches the hole at an angle... but it intersects with the circular lip-of-the-hole, travels a few degrees along the rim-arc, then is 'repelled' back-onto the green's surface at a somewhat greater speed than it was originally travelling.

Can a beam of light gain speed around a black hole?

That question is not a special relativity question. It is a general relativity question, and to be honest I am not really familiar with the intricacies of general relativity (it is usually a graduate level course).

You see, special relativity is relegated to inertial frames- i.e. frames are essentially free from noticeable gravitational influences and that are not rotating or accelerating in any way.

Clearly a black hole involves very large gravitational fields.



But I think the distinction between speed and velocity should be made. According to special relativity (and measurements) the speed of light, that is, the absolute value of the velocity of light, is the same in all frames. But the velocity is not necessarily, because if the trajectory of a light beam changes, then by definition it's velocity has changed, even if it's speed has not. A light beam being bent by a black hole has a changing velocity, since it's trajectory is not constant.

Anyway, I would say that at least in most cases the speed of light does not change, but the velocity does. But the important thing to consider is that this is not because of a property of light, but instead is a property of the geometry of space-time.

However, again, things are a lot trickery in general relativity, because things like 'distance,' 'time' and 'speed' are not so easily defined, because space-time itself is warped. In general relativity you are not dealing with Euclidean geometry (the geometry you learned in high school).


I suppose I should try to show an example of what I mean by that. Here is a link to a post that gives a little explanation for why we need a new geometry and why this new geometry should involve bent space.

http://forums.armageddononline.org/showpost.php?p=311969&postcount=17








So in a nut shell, I am pretty sure that if you personally measured the speed of light in a reference frame, you will get c. But someone watching you do it from a far away location may not get the same answer, because presumably s/he would see you you move in slow motion and see your distances to be different than what you do. But that is speculation. What I am sure of is that the velocity of light will change when accelerated even if the speed does not.

[Sirius]

∫ E ds = - dΦB/dt



∫ B ds = με dΦE/dt

*μ = permeability of free space = 4 π x 10^-7 T m/A

*ε = permittivity of free space = 8.854 x 10 ^-12 C^2/Nm^2

Which, from my text book, you can derive these two relationships:


∂E/∂x = - ∂B/∂t

and

∂B/∂x = - με ∂E/∂t







Taking the second partial derivative with respect to x, and then substituting in the appropriate one of these two equations:

∂^2E/∂x^2 = ∂/∂x (- ∂B/∂t) = - ∂/∂t (∂B/∂x) = - ∂/∂t (- με ∂E/∂t)

==> ∂^2E/∂x^2 = με ∂^2E/∂t^2


And

∂^2B/∂x^2 = ∂/∂x (- με ∂E/∂t) = ∂/∂t (- με ∂E/∂x) = - ∂/∂t (με - ∂B/∂t)

==> ∂^2B/∂x^2 = με ∂^2B/∂t^2







Since both of these equations look like the standard wave equation,

∂^2y/∂x^2 = (1/v^2) ∂^2y/∂t^2

could we not take either one of them, with με = (1/v^2), and then solve for v,

v = 1/√(με) = 2.998 X 10^8 m/s (obviously the speed of light).



Yikes. I think my brain farted.

Seriously though, i'm not good at math, or anything that comes after math. I do remember reading this article and wonder what you think about it.
http://www.cbsnews.com/stories/2000/07/19/tech/main216905.shtml

[Reef Badlaw]

Thanks for the answer and the link, Cartesian. You've answered it perfectly, I believe. -By introducing 'velocity'.

Yes, a new form of geometry will be needed, especially when science evolves-to researching vacuumological-properties. I don't think we've discovered a neutron-star cluster, but we've discovered 'gas bridges'. Both of which add obscure clues to the particle/wave-acceleration puzzle.

[Red Shift]

Dunno if this counts, but if a worm hole were possible and it were possible for light to travel through it....

Light could travel to a point far faster than it would be able to linearly, i know i know this isn't actually increasing the speed of light but decreasing the distance the light would need to travel.

How is that perceived in the scientific world? The light will have travelled from point A to point B in a much quicker time without actually changing speed..

Just thinking out loud here ::p:

[Mezurashi]

Dunno if this counts, but if a worm hole were possible and it were possible for light to travel through it....

Light could travel to a point far faster than it would be able to linearly, i know i know this isn't actually increasing the speed of light but decreasing the distance the light would need to travel.

How is that perceived in the scientific world? The light will have travelled from point A to point B in a much quicker time without actually changing speed..

Just thinking out loud here ::p:

they would treat the energy of the 'light' the same as a 'spaceship' doing the same thing - cheating Einsteinian Relativity by going around the distance rather than through it.


A golf-ball approaches the hole at an angle... but it intersects with the circular lip-of-the-hole, travels a few degrees along the rim-arc, then is 'repelled' back-onto the green's surface at a somewhat greater speed than it was originally travelling.

Can a beam of light gain speed around a black hole?

according to the 'stuff' I'm familiar with the light does not increase in velocity but gains energy, thus 'red' light being slingshotted around a black hole would emerge as a higher frequency of light. add enough energy and you can generate a butt-load of high energy nastiness, like X-rays and gamma rays.

theoretically (and I mean Really Theoretically) a black hole should be producing tachyons as well, but we can't detect them so ...

anyhow, me throwing my hat into the fray ... please correct me as necessary.

[GamerGal]

Dunno if this counts, but if a worm hole were possible and it were possible for light to travel through it....

Light could travel to a point far faster than it would be able to linearly, i know i know this isn't actually increasing the speed of light but decreasing the distance the light would need to travel.

How is that perceived in the scientific world? The light will have travelled from point A to point B in a much quicker time without actually changing speed..

Just thinking out loud here ::p:

First, headache.

Second, that is impossible. Wormholes, as we know them, are impossible. But... what about teleportation? Right now they only move atoms that way, but how do they do it, and could they do it too light, and would the light move slower or the same speed as it was being teleported?

[DontBeAfraid]

Right now they only move atoms that wayNo they dont.

[Reef Badlaw]

Outside of Special Relativity...


186,000 miles-per-second vs. 282,000 miles-per-second... dammit, we humans are way too unadvanced.

-Kinda like Lucian Of Samosata (125AD-to-180?AD), who speculated that a ship could sail across the Atlantic and reach the Moon in 8 days, I'm convinced that superconducted magnetic-propulsion can exceed lightspeed, but I can only find data that calculates-to achieving less than 1% of 186,000 mps.

[Mezurashi]

186,000 miles-per-second vs. 282,000 miles-per-second... dammit, we humans are way too unadvanced.

I thknk you're mixing up Imperial and Metric here because 182 000 mps works out as approx 300 000 kmps and these are, well, if not Absolute then they are pretty much the closest thing we have to it.

but yeah, we are way too unadvanced in so many ways it can stagger the mind ... lucky my unadvanced brain can fall back on random spirituality when the world of quantum realities gets too hazy for my liking (Thank You Metaphysics!)


-Kinda like Lucian Of Samosata (125AD-to-180?AD), who speculated that a ship could sail across the Atlantic and reach the Moon in 8 days, I'm convinced that superconducted magnetic-propulsion can exceed lightspeed, but I can only find data that calculates-to achieving less than 1% of 186,000 mps.

magnetic propulsion can only go as fast as the Maximum propogation of the magnetic field lines themselves.

any sort of Propulsion is limited to the 'exit speed' of the 'thrust' or whatever.

magetic force does not exceed the speed of light - we know this because we've measured it. therefore if magnetic force cannot exceed C then an object being propelled by it cannot exceed C in the same way that a Space Shuttle cannot exceed a certain velocity beyond the thrust velocity produced by it's engines.

to get even close to C one must develop an engine that thrusts at that velocity - chemical rockets don't come anywhere close. Ion propulsion is theoretically capable of accelerating an object to C but the fuel needed for such a lengthy acceleration would be huge and the acceleration itself is so minimal that it would take 10 000 years for the engine to get up to C.

however, SF is a gold mine of speculation on this - look up things like the Bussard Ramjet, Project Orion from the 1960's (not the current Project Orion which is part of the Constellation Back To The Moon thing) and Laser Drives.

and failing that, we can always ask advice from Marvin the Martian ... maybe he's figured out something we haven't ...

[Tired Old Man]

Hey I do good to balance my check book. But I did find this thread an interesting read.
The two things I see in here are relative and constant. I'm not even sure where to go with that.
But you did make me look up basic algebra. Thanks for the headache.

2 + 3 x 7 in my world equals 35. But it would seem you have this thing called BODMAS.

So 3 x 7 = 21 + 2 = 23. No wonder I skipped school and went fishing.

[olddragon]

No wonder I skipped school and went fishing.

So what did you catch?

http://i246.photobucket.com/albums/gg103/o1ddragon/Catfish.jpg

[3rDShifT]

Is that Jake on the left?

[Reef Badlaw]

First, Nessie's a hoax, and now Benson bought a flight-ticket. The UK's going-to run out of mythological monstrosities pretty soon.




Thanks, Mezurashi... I was scoping the following website to try to advance my superconductor-idea...
http://science.howstuffworks.com/electromagnetic-propulsion.htm

-specifically, part-2 of the article; 'Jolting Into Space'.


'n with Niven in your sig, I was wondering if the Bussard-ramjet would do-a-cameo here...

[Tired Old Man]

Hey I do good to balance my check book. But I did find this thread an interesting read.
The two things I see in here are relative and constant. I'm not even sure where to go with that.
But you did make me look up basic algebra. Thanks for the headache.

2 + 3 x 7 in my world equals 35. But it would seem you have this thing called BODMAS.

So 3 x 7 = 21 + 2 = 23. No wonder I skipped school and went fishing.

You know I had to go back and rethink this BS. 2 + 3 x 7 = 35. This is basic math.
So when my teacher asked this question to me and said it equaled 23 I should have said she was on drugs.
No wonder I went fishing....

Egg heads....I'm not trying to be rude here, like I even need to. Back to the speed of light.
All that you know is based upon science as we understand it today. One tin solider walks away.....
CT I'll ask you this....Do you follow the path that is given to you or question it . I'm sure you have questioned it.
And when you was shot down did you just walk away.

The speed of light is NOT as we think it is..........

[Cartesiantheater]

[...]
CT I'll ask you this....Do you follow the path that is given to you or question it . I'm sure you have questioned it.
And when you was shot down did you just walk away.

Everything you see in this thread that I posted was derived from scratch by me, with the two basic assumptions that I made (that the speed of light is constant in all inertial frames and that the laws of physics are the same in all inertial frames).

This is exactly what Einstein did originally, although his mathematical formation is more advanced (he uses more than basic algebra, especially for his derivation of the relativistic momentum and energy equations).

The point, of course, is that aside from the initial starting assumptions, what I have posted here is not only right, it is an original derivation. i.e. NO I did not just "accept what someone told me."

In fact, the very reason I spent an entire summer trying to figure out how to derive the Lorentz transformation equations from scratch was so that I would know that logically if the speed of light is the same in all inertial frames that the wacky stuff predicted by special relativity would be true. So basically, the only reason this thread (and the Lorentz transformation thread) exists is because I "questioned what I was taught," and then after months of mathematical struggle on my own I ended up coming to the conclusion that was presented to me in Introduction to Physics.


That answer the question?


btw- here is a derivation that requires no calculus

http://forums.armageddononline.org/showpost.php?p=312749&postcount=3


The speed of light is NOT as we think it is..........


That is the lone "problem" with all the crap I've posted. I have not personally measured the constancy of the speed of light in inertial frames. However, I have reason to believe that "what they tell me" about physics is correct.



(1)- It is all mathematically consistent

(2)- I've seen several experiments myself in the first place that back up "what they tell me." (probably the most notable one I have preformed myself in a lab is the one that shows that light has both a wave and a particle nature).


Further, there is no reason to assume that I won't ever have the opportunity to test the invariance of the speed of light myself in grad school, when I have access to the required equipment.


But that, of course, does not matter. The bottom line is that if we assume that the speed of light is constant in all inertial frames, I have personally derived the math by myself that shows that the necessary logical conclusion is that nothing can travel faster than the speed of light. Therefore I know personally that it is true, given the starting assumptions (i.e. I am not just "accepting what they tell me").


And further, through more mathematical excursions, I have seen first hand (i.e. derived) that momentum as defined as mv is NOT conserved under the Lorentz transformation; however if momentum is redefined to be ymv, where y is the Lorentz factor, then momentum IS conserved under the Lorentz transformation (I know this means gibbrish to you, but hang with me). But, using that NEW definition of momentum, I can mathematically derive from scratch (and I have done it here on the forums, somewhere...) the mathematical relation between energy and mass (E = mc^2 for a particle at rest, etc). And from THAT equation (the NON-rest equation), I can once again clearly see that if you increase an object's velocity to near the speed of light, the energy required for that increase approaches infinity. i.e. infinite energy is needed to accelerate to c.

The point of that tirade is to point out that I take NONE of special relativity by faith, because I can derive it all myself from scratch. The ONLY parts I take by faith are the two initial assumptions:



(1) The laws of physics are the same in all inertial frames

(2) The speed of light is the same in all inertial frames





But in fact, I don't even have to take (2) by faith!

Because I know Maxwell's equations work (at least to a first approximation), because I've tested them in labs (again, to a first approximation). And as I have derived here on the forums before, Maxwell's equations predict that electromagnetic waves travel at velocity c, but they do not specify with respect to what (i.e. there is a wave equation that propagates at c which relates electric fields and magnetic fields). Which begs the question. And of course, meshes well with the assumption that electromagnetic waves propagate at c with respect to everything (in inertial frames, that is).


Which would mean the only thing I am taking by faith is that the laws of physics are the same in all inertial frames. Although that can't be tested experimentally (we can't physically measure the laws of physics everywhere in the universe), it seems to agree with all of my experience thus far in my life. "What goes up must come down" seems to apply everywhere, all things being equal. Etc.



So basically, no, I don't really take it by faith.




(And neither do you have to, if you would take the time to learn the required math and then follow along on this thread and the Lorentz transformation thread. Because it is in black in white mathematics, and if you know the math, you can follow it plain as day. We are starting with an initial assumption. After that, it is all self evident through the math.)

[DontBeAfraid]

You know I had to go back and rethink this BS. 2 + 3 x 7 = 35. This is basic math.There is an order of operations ToM. Multiplying and dividing are done before adding and subtracting... even if they arent written first.

[Tired Old Man]

There is an order of operations ToM. Multiplying and dividing are done before adding and subtracting... even if they arent written first.

I understand that part now DBA. And CT that was one hell of an answer.
A damn good one at that. So unless something changes, the speed of light is what it is. And if it ever does change it will be because someone like you questioned it and found something different.

Hey what do I know I drive a truck. Thanks......

[Cartesiantheater]

Let me say one thing about "questioning" what someone tells you. Simply disagreeing with someone because you don't like or understand what they tell you is simply NOT good enough. "Questioning" something is more than just not agreeing. It is examining what you are told critically and testing it to see if it is logically consistent and useful in practice, etc. When you question something, if you then reason that what you are told is BS, it is because you have found a BETTER formation or explanation than what you were given, or you have found that the formation or explanation you were given is logically inconsistent.

What would happen ToM, if we used YOUR version of math? 2 + 3 x 7 = 35. Hmm, that would be all well and good, but what about this?

2 + 3 x 6 + 2 x 8 x 9 + 55 - 34 x (-28) + 25^ (2 + 3 x 4 x 1)?

And then what if I chose that 3 x 6 is really just 3 x 2 + 2 x 4? Or what if I randomly chose any other convention?



Well, you end up with problems of inconsistency. You have to have a convention that everyone agrees upon to attack these situations. Just like you have to speak the same language in order to communicate ideas. If you decide that you are going to replace every verb in the English language with random nouns that you have decided are better (i.e. instead of "I ran to the store" you'll have "I dog to the store"), how the funk are you going to communicate with anyone?

But by your logic, simply choosing to replace every verb with a noun that you chose is completely acceptable, because you are "questioning" the English language. Yet if you did that no one would ever know what the hell you are talking about.


Same thing with math. The world over has agreed upon the convention that the symbols 2 + 3 x 7 mean 2 + (3 x 7), which equals 23. If everyone decided to use their own convention, it would be impossible to communicate on matters that involve math, for the exact same reason it would be impossible to communicate if everyone decided to pick and chose their own words to replace verbs with nouns.



Therefore your argument is only valid in your mind because you have not reasoned it through enough to see the flaws within it.



Thus, I have "questioned" your reasoning and presented a counter example that shows that your reasoning is faulty. :D lolololol


Even so, mathematical relations are true regardless of the formalization we use. If I SAY, "What is two plus three times seven," you can either hear it as "two plus three, and that result times seven," or "two plus the result of three times seven," unless the ambiguity is addressed.

However, the ambiguity HAS been addressed. A very long time ago. Thus our current mathematical conventions. However, what you should consider is that that ambiguity DOES NOT ARISE from MATHEMATICS! It arises from VOCALIZATION of mathematics! That, is the important part.