Is the speed of light infinite?

[barbacamanitu]

This is the main thing that gets me

If I gave the traveler my watch, and he timed it, he would clock it at one second.

Why do you say that? The watch will appear to you to tick at a slower rate if it is moving relative to you.

Yes, B's clock will appear to tick at a slower rate if it is moving relative to A. That is only according to A though. That isn't B telling A that it took one second, that is A looking at B's watch and deducing that B must say that it took one second. The thing is, while A perceives B's clock ticking .5 seconds, A is effectively viewing a clock which he knows to tick twice as slowly as his. This means that time passes more slowly for B than A. I'm thinking that he would also perceive the light as traveling slower, but since his time passes slower at the same rate, he notices no difference in the time taken to travel. When he looks at A's watch, he will also only see .5 seconds ticking during the time it takes for the light to make the journey. This seems like the obvious explanation to me, not that it takes two seconds to go twice as far. I know there is evidence of length contraction too, and I'm not just calling all of physics wrong, just trying to wrap my head around why this isn't the case.

Also, I don't see why it matters where B is with respect to A when the light leave the emitter. The length of time it takes to make the journey shouldn't depend on when B sees it leave. Even if it takes the light 100 seconds to reach B according to A, the journey could still take 1s from the emitter to the detector.

I am going to do some reading into what you've suggested, thanks.

 

[PeterDonis]

Yes, B's clock will appear to tick at a slower rate if it is moving relative to A. That is only according to A though. That isn't B telling A that it took one second, that is A looking at B's watch and deducing that B must say that it took one second.

This is OK as far as it goes, but it implies that A would say it took two seconds, not one.

When he looks at A's watch, he will also only see .5 seconds ticking during the time it takes for the light to make the journey.

You're leaving out relativity of simultaneity. Also, you're continuing to try to split up space and time instead of looking at spacetime as a unified whole. Once again, before trying to analyze this scenario any further, I strongly recommend learning about spacetime diagrams and drawing one of the scenario. The same comment applies to the rest of your post.

 

[barbacamanitu]

This is OK as far as it goes, but it implies that A would say it took two seconds, not one.



You're leaving out relativity of simultaneity. Also, you're continuing to try to split up space and time instead of looking at spacetime as a unified whole. Once again, before trying to analyze this scenario any further, I strongly recommend learning about spacetime diagrams and drawing one of the scenario. The same comment applies to the rest of your post.

I think I get it. Our concept of spacetime never changes for us. If we assume c is constant, then distance must always depend on the passage of time. If a second is different for me than it is for you, then a meter is different also.

In the analogy, B views the emitter and detector as traveling at some fraction of the speed of light. However, if c is constant, then B knows that A sees c the same exact way. If B's clock is ticking at half the speed of A's clock, but B still sees the same light-speed, then B's distance measurements must change also. That's why the emitter and detector would be twice as far away from each other for B as they were for A. They aren't "really" a light second apart, just a light second apart according to A.

Does this mean that it doesn't matter what direction the light leaves the emitter at with respect to B?

 

[PeterDonis]

I think I get it. Our concept of spacetime never changes for us. If we assume c is constant, then distance must always depend on the passage of time. If a second is different for me than it is for you, then a meter is different also.

Yes.

In the analogy, B views the emitter and detector as traveling at some fraction of the speed of light. However, if c is constant, then B knows that A sees c the same exact way. If B's clock is ticking at half the speed of A's clock, but B still sees the same light-speed, then B's distance measurements must change also.

Yes, exactly.

That's why the emitter and detector would be twice as far away from each other for B as they were for A.

Actually they would be *half* as far apart for B as they were for A (since A is the one at rest relative to the emitter and detector, and B is the one that's moving relative to them).

They aren't "really" a light second apart, just a light second apart according to A.

Yes; distance is frame-dependent, so you have to specify "according to whom" when you give a distance.

Does this mean that it doesn't matter what direction the light leaves the emitter at with respect to B?

No. Everything I've said so far assumes that B is moving in the same direction as the light beam from the emitter to the detector. If we allow the directions to be different, the math gets considerably more complicated. The basic effects are still there, but the exact details will change.

 

[barbacamanitu]

I'm guessing that's because of the Doppler effect?

 

[PeterDonis]

I'm guessing that's because of the Doppler effect?

What are you guessing is because of the Doppler effect? The Doppler effect is separate from everything we've talked about thus far; it affects the frequency (or wavelength) of the light, not its speed or the time or distance it is perceived to cover. (The Doppler factor for a given relative velocity is not the same as the time dilation or length contraction factor for that velocity.)

 

[barbacamanitu]

Scratch that. Calling it the doppler effect really wasn't what I meant to say. If we are talking about a single photon, then if B were moving the opposite direction of the light, and A was a rest with the emitter, then from A's perspective:

After 1 second passed, A would be 1 light second away from the photon, but B would be even further away from the photon then that. A might say that B would see a photon leaving him that was "faster than the speed of light", but to B, it would still be c. I won't attempt the math, because I don't grasp it yet. I do have one more question though.

Please tell me if I have this right: The reason that time slows down when objects are in relative motion is that our clocks are based on electromagnetism. This includes our biological clocks, atoms, and everything with rest mass. Since c is always c, then no matter how 'fast' we are moving with respect to each other, the 'slowed down' speed of light also slows down how we perceive time, thus "speeding it back up" according to us.

This may be totally wrong, but if it is, I think I still understand that spacetime changes due to relative motion, just now why or how.

 

[PeterDonis]

After 1 second passed, A would be 1 light second away from the photon, but B would be even further away from the photon then that. A might say that B would see a photon leaving him that was "faster than the speed of light", but to B, it would still be c.

Yes.

Please tell me if I have this right: The reason that time slows down when objects are in relative motion is that our clocks are based on electromagnetism.

This is what many physicists thought in the early years of relativity; Lorentz, for example, thought this. It's not wrong, exactly, but I would say that it is an interpretation of relativity, and not the only possible one.

One thing we know that physicists then did not is that there are other forces in nature besides electromagnetism, and they are all relativistically invariant in the same way; so what we call "the speed of light" is really better termed "the invariant maximum speed", since other things besides light in vacuum also travel at that speed, and the relativistic laws that have length contraction and time dilation as consequences apply to all forces, not just electromagnetism. (This includes gravity, btw, to the extent that gravity can be viewed as a "force" like the others.)

These other forces are not esoteric, btw. The strong nuclear force is what holds atomic nuclei together; without it, hydrogen would be the only chemical element. The weak force is usually thought of as the force that mediates radioactive decays, but it turns out to also play a key role in the reactions that generate energy in stars like the Sun.

 

[barbacamanitu]

Yes.



This is what many physicists thought in the early years of relativity; Lorentz, for example, thought this. It's not wrong, exactly, but I would say that it is an interpretation of relativity, and not the only possible one.

One thing we know that physicists then did not is that there are other forces in nature besides electromagnetism, and they are all relativistically invariant in the same way; so what we call "the speed of light" is really better termed "the invariant maximum speed", since other things besides light in vacuum also travel at that speed, and the relativistic laws that have length contraction and time dilation as consequences apply to all forces, not just electromagnetism. (This includes gravity, btw, to the extent that gravity can be viewed as a "force" like the others.)

These other forces are not esoteric, btw. The strong nuclear force is what holds atomic nuclei together; without it, hydrogen would be the only chemical element. The weak force is usually thought of as the force that mediates radioactive decays, but it turns out to also play a key role in the reactions that generate energy in stars like the Sun.

That makes perfect sense now. So the strong and weak force propagate at c also, huh? Since all of the forces that we know of move at the same invariant speed, then every conceivable time keeper must slow down by the same factor when in relative motion.

Can you recommend a good book where I can build on what I've learned so far on this subject?

 

[rbj]

That makes perfect sense now. So the strong and weak force propagate at c also, huh? Since all of the forces that we know of move at the same invariant speed, then every conceivable time keeper must slow down by the same factor when in relative motion.

i thought that the weak force was slower than c. the carrier particles, W^± and Z⁰ bosons, have non-zero "rest mass" or invariant mass. so these carriers cannot move at the speed of c from anyone's reference frame.

 

[PeterDonis]

So the strong and weak force propagate at c also, huh?

The strong force does since gluons have zero rest mass. As rbj pointed out, the weak force carrier particles have nonzero rest mass, so the weak force does not propagate at c.

Can you recommend a good book where I can build on what I've learned so far on this subject?

If you mean all the stuff about the different forces and the particles that carry them, I'm not sure what a good book would be. For one thing, it would depend on how much math you want to get into. You might try posting in the quantum physics or particle physics forum, since people there are more familiar with the subject.

 

[PeterDonis]

i thought that the weak force was slower than c. the carrier particles, W^± and Z⁰ bosons, have non-zero "rest mass" or invariant mass. so these carriers cannot move at the speed of c from anyone's reference frame.

You're correct. See my previous post.

 

[barbacamanitu]

I was referring to books on special relativity, Peter. I want to get into as much math as I can.

 

[PeterDonis]

I was referring to books on special relativity, Peter. I want to get into as much math as I can.

I learned SR from Taylor & Wheeler's Spacetime Physics. However, that was the 1st edition, and the current edition is the 2nd edition, which appears to have changed significantly from the 1st. Some people think the changes are not for the better. I still think it's worth a try, though.