Why is there a universal speed limit, c, and why is it what it is?

[Dmitry67]

SR is a particular case of GR, GR in flat spacetime.
I suggest checking this link:
http://en.wikipedia.org/wiki/Eternalism_(philosophy_of_time)
It explains what is time (based on SR and GR)

 

[nitsuj]

The point of special relativity relies on the notion that c is the same for all observers. You can derive tile dilation from, for example, the famous light-clock diagram.

Ultimately we find t=T*(1-v^2/c^2)^.5 or T*gamma. As v approaches c, gamma approaches 0. So hypothetically, at v=c we have T*gamma = T*0 = 0 = t, which implies that no matter how much time passes for T (the clock according to the observer moving at c), we'll see t's clock frozen in time.

Sorry for the time, but I don't understand equations beyond + - * / = and in that order :) and that's a part of my misunderstanding i'd guess.
I think I got the part that "c" is the same for everyone.

I guess I take the "time stops at "c" too far when I think of someone in a ship traveling at "c" that there is no time passing (and in turn no movement, rulers shrink to nothing ect) being the same as infinity.

 

[bcrowell]

The fundamental question is "Why does nature rotate the X1 axis like this?" (The rotations are described mathematically by Lorentz transformations).
[...]
Of course, bcrowell had it right when he advised us to first choose the postulates. I have not formalized my statements of postulates well.

I would say that if you take postulates P1+P2 from #3, then x1 has to rotate because the transformation has to be linear (due to the homogeneity of space) and has to leave the x1=x4 diagonal fixed (due to P2).

If you prefer (as I do) the symmetry-based postulates in the systems referenced in #3, then there are three cases, in which x1 rotates clockwise, counterclockwise, or not at all. The counterclockwise case violates causality. The nonrotating case is Galilean relativity. You need a postulate to say that you want the clockwise case rather than the nonrotating one; this postulate is strongly motivated because we observe that time is not absolute, e.g., in the Hafele-Keating experiment. Given that postulate, you can then prove as a theorem that there is some velocity that is the same for all observers (because if x1 rotates clockwise and x4 counterclockwise, and the transformation is linear, there must be some line that doesn't rotate at all).

 

[Quickless]

1. e = mc(squared) - c(squared) is the rate at which matter is transformed into energy.

2. What constrains c - c is a function of the electric and magnetic fields - Maxwell

3. For c a. velocity is constant b. acceleration is equal to zero (This is more interesting than the value of c).


a. It was never established ex ante that a = o for c. It was just assumed.
b. It is very convenient to have a=0 for c. Lots of equations just disappear.
c. The constant velocity of c with respect to all regimes both real and imagined suggests that the wave/particle conception is flawed. Constant velocity pertains more to the properties of a field than a wave/particle.

I just made all this up but I had fun.

Q

 

[bobc2]

I would say that if you take postulates P1+P2 from #3, then x1 has to rotate because the transformation has to be linear (due to the homogeneity of space) and has to leave the x1=x4 diagonal fixed (due to P2).

If you prefer (as I do) the symmetry-based postulates in the systems referenced in #3, then there are three cases, in which x1 rotates clockwise, counterclockwise, or not at all. The counterclockwise case violates causality. The nonrotating case is Galilean relativity. You need a postulate to say that you want the clockwise case rather than the nonrotating one; this postulate is strongly motivated because we observe that time is not absolute, e.g., in the Hafele-Keating experiment. Given that postulate, you can then prove as a theorem that there is some velocity that is the same for all observers (because if x1 rotates clockwise and x4 counterclockwise, and the transformation is linear, there must be some line that doesn't rotate at all).

Good job as usual, bcrowell. Thanks.

 

[bcrowell]

1. e = mc(squared) - c(squared) is the rate at which matter is transformed into energy.

This is incorrect.

The constant velocity of c with respect to all regimes both real and imagined suggests that the wave/particle conception is flawed.

No, special relativity is a classical theory. It can also be extended to quantum field theory, and QFT does not, as you seem to imagine, harbor deep logical flaws (presumably covered up by a vast conspiracy among physicists world-wide?). You haven't defined what you mean by "regimes real and imagined."

I can't make out what you mean by your remarks about acceleration equaling zero.

 

[Quickless]

1. Incorrect? How so? If you attach actual units to the 3 variables, c(squared) is the only unit with a time dimension.

2. Constant velocity implies acceleration is zero.

 

[bobc2]

1. e = mc(squared) - c(squared) is the rate at which matter is transformed into energy.

I, and any other physicist, would agree with bcrowell. That is incorrect.

3. For c a. velocity is constant b. acceleration is equal to zero (This is more interesting than the value of c).

a. It was never established ex ante that a = o for c. It was just assumed.
b. It is very convenient to have a=0 for c. Lots of equations just disappear.

Again, I'm with brcrowell on this. We all know the relationship between velocity and acceleration. But, the implications you seem to be getting out of this seem muddled and incoherent to me. I really can't make any sense out of it.

c. The constant velocity of c with respect to all regimes both real and imagined suggests that the wave/particle conception is flawed. Constant velocity pertains more to the properties of a field than a wave/particle.

What? This is not making sense.

I just made all this up but I had fun.

Q

Are you trolling?

 

[bcrowell]

1. Incorrect? How so? If you attach actual units to the 3 variables, c(squared) is the only unit with a time dimension.

The units are the same on both sides of the equation, so if there is a time unit on the right when you break it down into the fundamental SI units (kg, m, s), then there must be one on the left as well. And there is: a joule is 1 kg^.m²/s². In any case, this has no logical relationship to your incorrect interpretation of the equation.

2. Constant velocity implies acceleration is zero.

This doesn't clarify anything for me.

 

[thetexan]

I have given this a lot of thought and this is why I think it is...because, so far, light is the fastest thing upon which information can be transfered. So far. That doesn't mean there isn't something out there faster.

For example. Let's say that something out there travels faster than light. The fastest we could receive information about that object would be at c. Any information beyond that would be hidden by the light equivalent of a sonic bow wave. For example, two people are standing next to each other at an airshow; one blind the other sighted. A Blue Angle F18 comes by at mach 2. Each person is asked to point at where he believes the jet is. The sighted person points at the jet itself. The blind person points to where he hears the jet, which is considerably behind where the jet actually is. The difference is that the two observers are limited to how they each receive information about the jet, one by light, one by sound. To the blind man, the fastest speed in the universe is the speed of sound. To the sighted man, the fastest speed is that of light. To the blind man, no matter how fast something moves, the information about that object will only arrive to him at the maximum speed of sound. Thus he is convinced that the speed of sound is the universal speed limit, and to him it is. In fact, when you ask him about light, he has no idea what you are talking about.

What if there were discovered a faster informational mode? Imagine if, say, mental thought traveled at 100 times the speed of light and we learned how to utilize this mode. Now information about what is going on inside a spacecraft traveling at 10c could be transfered. To the mental telepath the 10c spacecraft is quite discernable, to the rest of us the spacecraft appears to be limited to c because our ability to obtain information about the spacecraft is limited to c.

Why is the speed of light the universal speed limit? Let's ask the blind man why the speed of sound is the fastest speed in the universe..."because it, it...just is! Everybody knows that!"

By the way, if you ask the blind man how much energy it would take to push the jet beyond the speed of sound he would conclude an infinite amount since the jet can't travel faster than the speed of sound. Consequently, he would be forced to create new math and physics to explain the phenomena and contain it within his world which is limited by what he perceives is a universal constant. New math and physics, by the way, which, to the sighted man, would seem ignorant and naive, however much he might symathize with how and why the blind man might have arrived at it...and believed in it.

So, I believe the speed of light is the universal limit only because it is possible we may all be blind men living in a sighted man's world...and just don't know it yet.

Or maybe not. But here is the quetion. Can we prove that a faster medium cannot exist?

 

[Dale]

Hi thetexan, the analogy is not very useful at all because the speed of sound is not frame invariant. The important thing about c is not that it is the speed of information (as you mention information often travels much slower), but the important thing about c is that it is frame invariant. A blind man measuring the speed of sound would not claim that it was frame invariant and would therefore not claim that it would take an infinite amount of energy to exceed the speed of sound.

 

[bobc2]

Welcome, thetexan. What part of Texas? That was very creative thinking. I liked your light and sound idea. But, DaleSpam had the perfect answer (as you will find he often does here) and is of course quite correct.

 

[atomthick]

Sure you can travel faster than light, the only thing is that you don't have enough time. It's like trying to do a job that takes 25 hours in a single day.

 

[thetexan]

Dalespam,

I understand about frame invariance, and that light has it and sound doesnt. But the point of the analogy is to show that whatever 'thing' one uses to obtain his information about the universe is the determiner of the fastest speed limit...to that person. This even has a rough analogy to the frame of reference issue of light...that is...it depends on your point of view. From the point of view of the blind man, he lives in a world where everything he knows came to him at the speed of sound. An even courser analogy would be the pony express. Imagine you are bed ridden and you want position reports on a fast railroad train. The only way you can get those is by a pony express rider. You will always be behind in knowing the true location (and thus the capability of calculating distance traveled compared to time) because of the limited speed of the horse. The only way you can keep up in real time with the train is to have some form of communication concerning the position of the train that is at least as fast as the train.

To expand on the blind man analogy...as he points at the jet as it travels from his right to left, he is pointing at the place where the sound tells him it is. You could never convince him that the jet was a quarter mile farther to his left. He would say that's impossible! "Im pointing at the jet now!" He would be forced to conclude that as the jet approached the speed of sound it could get closer and closer to it but never exceed it. And in a way that would be true from his viewpoint. Even if the jet exceeded the speed of sound the information about it would lag and never get to him faster than the speed of sound. He would therefore always be 'observing' a limited transfer of information about the jet which would never allow him to hear the jet traveling faster than that speed. He is convinced and you can't tell him otherwise because observation proves it to him.

Right now, knowledge of anything about anything is limited by the speed of photons. If there were a particle that traveled faster and was emitted or reflected by everything at all times, similar to a photon, then the fastest anything could appear to move would be at the much higher speed of these 'bizarrons'. Better stated, there might even be something faster than bizarrons but we could never know it because, like photons now, our ability to detect that faster speed is limited to how fast the position of the object can be transmitted to us by bizarrons. This would have the effect of convincing us that nothing can travel faster than bizarrons. Just like the blind man is convinced that nothing can travel faster than the speed of sound, or grandma in her bed is convinced that the train cannot travel faster than the horse.

And just like most other theories down thru history, we tend to create theories that explain what we observe. This works great right up until we observe something different. The theory of relativity works great to explain and justify the idea that photons are the reigning speedsters and transmitters of information.

My question and puzzlement is this. Are we not and were we not predisposed by logic to assume that the speed of light is the fastest limit? Wouldnt the blind man first assume that the speed of sound is the limit because his sense of hearing is the 'fastest' sense he has? What if taste traveled faster? Then the taste of things would be the fastest limit. Light is the fastest limit because we have a sense called sight. And if you tried to explain to the blind man that there is something called light that is faster wouldn't he say 'prove it', already being convinced by his own theories and calculations that that was impossible? Of all of our senses, the one that receives something that is really fast is sight (Im just talking about humans and can include any other receiver of electro magnetic waves like a radio). The minute someone invents a bizarron receiver our observations will change.

Again, here is my question. Why can't there be something faster that we have yet to discover that would have it's own speed limit? And if it did, wouldn't that throw a monkey wrench into present day physics?

tex

Longview, Texas

 

[OnlyMe]

But here is the quetion. Can we prove that a faster medium cannot exist?

The question is one that has been put to bed so to speak and yet is a good question.

Current theory is that there is no light medium. In the late 1800s Michelson & Morley carried out experiments to detect the luminiferous aether, the light medium. The experiments as designed were sensitive enough that had there been an aether wind it should have been detected. They found nothing. The experiments have been reproduced several times, even into the 20th century.

Light as a universal constant was introduced by Einstein in a single sentence in his 1905 paper introducing Special Relativity. "In agreement with experience we further assume the quantity 2AB/(t'-t)=c to be a universal constant--the velocity of light in empty space."

The experience that he was referring to was:

• The speed of light in vacuum, which had been repeatedly measured experimentally.

• The speed of light in vacuum was the same no matter who measured it, without being affected by the relative velocity of the light source and the observer.

• And experimental observations were consistent with Maxwell's findings, as he developed electrodynamics.

Einstein's assumption was that "empty space" and a vacuum are equivalent, as far as the propagation of light is concerned.

The conclusions drawn from special relativity have been supported by observation. For light itself, those observations are theory dependent. We cannot test the equvalence of "empty space" and a vacuum, as in intergalactic empty space, locally. However, there is strong evidence in the radio and radar bands.

Is it possible that the speed of light is different somewhere in the depths of intergalactic space? Since we are unable to conduct experiments "there" the answer has to be yes and yet..., from everything we do know and observe experimentally, c, the speed of light in vacuum and locally empty space, is the same for all observers. It is observed to be a "speed limit".

So to answer your question. If a light medium exists, it lies beyond our ability to measure and define it and it appears to us as equivalent to a vacuum..., "empty space".

 

[1994Bhaskar]

It is experimental.it is postulated to explain lorentz experiment's where first effect's of relativity were observed.just like coulomb's law.

 

[OnlyMe]

Again, here is my question. Why can't there be something faster that we have yet to discover that would have it's own speed limit? And if it did, wouldn't that throw a monkey wrench into present day physics?

Yes, it is possible that there is something beyond our ability to perceive that travels faster than c and no it would not throw a monkey wrench into present-day physics. Instead, it would open up whole new areas of research and potential. It would be very exciting.

Einstein's field equations did not falsify Newton's. They expanded the scope and application of our understanding of gravity. Some new faster than light wave or particle would be the same. Expand our understanding.

 

[Dale]

I understand about frame invariance, and that light has it and sound doesnt. But the point of the analogy is to show that whatever 'thing' one uses to obtain his information about the universe is the determiner of the fastest speed limit...to that person.

No, this is incorrect. The fastest speed limit is determined by the invariant speed, not the speed of information.

Imagine you are bed ridden and you want position reports on a fast railroad train. The only way you can get those is by a pony express rider. You will always be behind in knowing the true location (and thus the capability of calculating distance traveled compared to time) because of the limited speed of the horse.

This is true, but it does not imply that the speed of the train is limited to the pony speed, nor does it imply that you could not use the pony express to determine the speed of the train. Specifically, consider two neighboring pony express stations, as the train passes each station a rider sets out. Given that we know the distance between the stations and the time that each pony express route takes to reach my bed I can subtract off the delay time and divide by the distance to get the train speed, which may well be greater than the pony speed.

To expand on the blind man analogy...as he points at the jet as it travels from his right to left, he is pointing at the place where the sound tells him it is. You could never convince him that the jet was a quarter mile farther to his left. He would say that's impossible! "Im pointing at the jet now!"

In SR we assume that all observers are intelligent, meaning that they do not make the mistake that this blind man is making. We realize that we are pointing at where the jet was and, given knowledge of the speed of information travel and the distance, we can determine exactly when the jet was at the location we are pointing at. Similarly, if we see a star go supernova now and it is 1000 ly away in our frame, then we understand that the supernova happened 1000 years ago.

Again, here is my question. Why can't there be something faster that we have yet to discover that would have it's own speed limit? And if it did, wouldn't that throw a monkey wrench into present day physics?

If tachyons were discovered then they would necessarily either violate relativity or causality. Either one would be a monkey wrench indeed, but the speed limit would still apply for massive particles as it is determined by the invariant speed and not the speed of information.

 

[nitsuj]

Sure you can travel faster than light, the only thing is that you don't have enough time.

I think that is well said. (and/or space)

 

[Doc Al]

Sure you can travel faster than light, the only thing is that you don't have enough time.

Not really. Even with infinite time you might approach the speed of light, but not exceed it.

 

[nitsuj]

Not really. Even with infinite time you might approach the speed of light, but not exceed it.

As in an infinite amount of time is still, not enough time? Hmmm...

j/k I get ya, it's that something can't go faster and your saying it is not a consiquence of there not being enough time. 6 of one half a dozen the other from my wrong perspective.

 

[atomthick]

Not really. Even with infinite time you might approach the speed of light, but not exceed it.

That's true it's an asymptotic curve that never reaches c. The analogy was with someone trying to do a 25 hours job in 24 hours. The 24 hour should be read as the infinite time required to get to c.

One way to do a 25 hours job in 24 hours would be to work 24 hours and then go back in time and work another hour.

 

[Archybaldy]

Hey new person here! and this thread is frankly incredible. Thought id throw in my two pence.


After reading this entire thread it seems that the limit of speed is the limit of time.

Firstly Speed is a measurement distance + time.

In bobc's diagrams it showed that the distance and time seemed to join together. So the distance was being limited by the time. So is is no longer possible for any more distance to be gained.

Also with our observation of time being were moving through it. So we have to think of time as traveling at its own "speed". One moment to the next moment has its own finite "speed" as we observe it.

So the reason there is a universal speed limit is, the speed of light is limited by the "speed" of time.

So to go faster then the speed of light it would require modifying the "speed of time" itself.

Hopefully i can get some feedback on how I am picturing it and any problems.

also i only used the "speed of time" referance because i don't know if there's any specific term for how quickly one moment is happening to the next.

 

[1994Bhaskar]

AS ONE APPROACHES 'c' THE MASS OF GIVEN PARTICLE START'S INCREASING, GIVEN BY:
M=M_rest/(sqrt(1-(v²/c²)))
SO AS ONE APPROACHES c, v²/c² INCREASES & WILL TEND M TO INFINITY.SO THIS IS THE SIMPLEST REASON WHY ONE CANNOT MATCH 'c' WITHOUT HAVING INFINITE ENERGY(WHICH IS NOT POSSIBLE).PARTICLE ACCELERATOR'S HAVE GONE TO "0.99c" (WITH SMALL PARTICLES LIKE ELECTRON) BUT NOT 'c'.

 

[atomthick]

AS ONE APPROACHES 'c' THE MASS OF GIVEN PARTICLE START'S INCREASING, GIVEN BY:
M=M_rest/(sqrt(1-(v²/c²)))
SO AS ONE APPROACHES c, v²/c² INCREASES & WILL TEND M TO INFINITY.SO THIS IS THE SIMPLEST REASON WHY ONE CANNOT MATCH 'c' WITHOUT HAVING INFINITE ENERGY(WHICH IS NOT POSSIBLE).PARTICLE ACCELERATOR'S HAVE GONE TO "0.99c" (WITH SMALL PARTICLES LIKE ELECTRON) BUT NOT 'c'.

We all undrestand this, the problem is that the formula you have used is a result of the postulate that c is the speed limit. The question was: why the speed limit is c ? and you shouldn't try to answer it by using the fact that c is the speed limit...

 

[1994Bhaskar]

THANKS atomthick.
I think einstein did all this just to back michelson-morley experimental data.Only EXPERIMENTS can give evidence concerning true properties of space & time.Maybe we should not break our head on an experimental fact.It's just like to think that why gravitation is ATTRACTIVE & not REPULSIVE!

 

[Dale]

Bhaskar, please turn off all caps. It is considered "shouting".

 

[1994Bhaskar]

so sorry about that.I'm quite new to this forum.

 

[Dale]

No worries, thanks for going back and editing. I was not expecting you to do that, but that is especially considerate!

 

[Quickless]

Some may find this link interesting - http://www.phys.unsw.edu.au/einsteinlight/jw/module3_Maxwell.htm#light

Take this brother and may it serve you well,

Q

 

[zyap]

Hi all,

On the moment I'm learning about special relativity in College and there is a fairly
good explanation for the cosmic speed limit, indeed caused by causality (which comes from second law of thermodynamics). I included 3 photo copies of my textbook that explain the relevant part.

After reading i think you will understand why nothing can travel faster than the speed of light, and so why it is the cosmic speed limit.

On the other hand there is one thing i don't understand, and that is why we would not be able to travel at the speed of light, since the book tells we can only travel at near the speed of light and only information can travel at the speed of light. But on the otherhand it says that we could be the information.

If somebody understand out of this text why we cannot travel at the speed of light, please post.

The page come from Six ideas that shaped physics Unit R by T.A. moore
Very good step by step explanation of special relativity.

happy reading,

Thanks.

 

[harrylin]

Hi all,

On the moment I'm learning about special relativity in College and there is a fairly
good explanation for the cosmic speed limit, indeed caused by causality (which comes from second law of thermodynamics). I included 3 photo copies of my textbook that explain the relevant part.

After reading i think you will understand why nothing can travel faster than the speed of light, and so why it is the cosmic speed limit.

On the other hand there is one thing i don't understand, and that is why we would not be able to travel at the speed of light, since the book tells we can only travel at near the speed of light and only information can travel at the speed of light. But on the otherhand it says that we could be the information.

If somebody understand out of this text why we cannot travel at the speed of light, please post.

The page come from Six ideas that shaped physics Unit R by T.A. moore
Very good step by step explanation of special relativity.

happy reading,

Thanks.

Thanks, it's a nice text; but as you already discovered, one weakness is that it fails to explain why we cannot travel at the speed of light. For that you need to look at other, more physical explanations - and probably that has already been done earlier in this thread.

Harald

 

[sahil_time]

Light is Electromagnetic so if light travels at diffrent speeds in different frames then Laws of Electromagnetism will also vary giving different results in different frames..but that's not possible so c is constant!

 

[HallsofIvy]

Light is Electromagnetic so if light travels at diffrent speeds in different frames then Laws of Electromagnetism will also vary giving different results in different frames..but that's not possible so c is constant!

Okay, so no explain why it is trivial (more obvious than the fact that c is constant) that the Laws of Electromagnetism can NOT give different results in different frames.

 

[bobc2]

Light is Electromagnetic so if light travels at diffrent speeds in different frames then Laws of Electromagnetism will also vary giving different results in different frames..but that's not possible so c is constant!

sahil_time, why is that not possible?