Is the speed of light infinite?

[PeterDonis]

are you saying that when traveling quickly relative to another object, distance changes too?

Yes. It's called "length contraction", and it's usually discussed in SR textbooks along with time dilation.

 

[barbacamanitu]

See that's where I was thinking differently. Since time is always the same for you to you, I don't see why the light would ever take 2 seconds instead of one. Our scenario is something like this:

Object A: Stationary with respect to the emitter and detector.

Object B: Traveling away from Object A at a fast enough rate for his seconds to appear twice as long to Object A.

This means that B would also perceive A's second to be twice as long as his own. A turns on the emitter and turns his stopwatch on. B also turns on his stopwatch when he sees the light leave the emitter. It takes 1 second from A's perspective. This means that from A's perspective, it would take 0.5 'B seconds' for the light to make the trip, since B's clocks spin twice as slow. The same is true for B. He sees the light make the trip in one second, but thinks that A must have counted only .5 seconds. When they meet and exchange data, they both have one second. It should have nothing to do with distance as far as I understand it.

Edit: Actually, from ones perspective, it would appear that the other should measure it taking 2 seconds, not .5. I think.

 

[barbacamanitu]

Light will always travel at at c, and a light second will always take 1 'my second' for light to travel. Why does the distance need to contract for this to be true? The only differences in the amount of time it takes for the beam to make the journey are from me applying my seconds to some other object, but we know that's not right. If I gave the traveler my watch, and he timed it, he would clock it at one second. The difference is that when he came back and showed me the results, I would have experienced more time than him.

Edit:This is not contradictory, because even while he was traveling fast relative to me I could see his watch, and see that it was moving slower than mine. I wrongfully may assume that he is measuring the length of time differently since in one second here only half a second elapsed there, but I have to remember that he will perceive the light 'slower' so that it matches up with one second on his watch too. He won't notice it move slower, but since his time passed differently, his entire universe would operate slower than mine. Therefore, my assumption that only half a second has elapsed is mixing my view with his.

What's wrong with this interpretation?

P.S. I appreciate the patience, Peter. I'm learning quite a lot. You are much nicer and more helpful than I originally assumed. And trust me, I plan on learning the math behind it too;I start on my physics schooling this summer.

 

[barbacamanitu]

Only if you also look at length contraction as well as time dilation. Two observers in relative motion both see the same light beam traveling between a source and a detector. One observer says it takes 1 second for the beam to travel from the source to the detector; the other observer says it takes 2 seconds, because of the difference in rate of time flow between the two. The only way to reconcile that with a constant speed of light is for the two observers to also measure the distance between source and detector differently: the first observer says the distance is 1 light-second (300,000 km); the second says it is 2 light-seconds (600,000 km). This is fine, but it only works if you include both distance and time in your analysis; just looking at time by itself won't work.

I have read this over and over, and I swear its contradictory. I could easily be wrong though. If light travels at a constant rate according to the observer, this means that the timing device must be at rest with the observer.

"because of the difference in rate of time flow between the two" seems to imply that the time flow of A is somehow more special than the time flow of B because it is at rest with the light emitter. What I don't get is how this is any different than A and B both moving at equal speeds away from the light emitter, but retaining the same relative motion. Now, neither one is at rest with the emitter. The reason it shouldn't be any different:

This constancy of the speed of light means, counter to intuition, that speeds of material objects and light are not additive. It is not possible to make the speed of light appear greater by approaching at speed towards the material source that is emitting light. It is not possible to make the speed of light appear less by receding from the source at speed.

If you can't make the speed of light appear greater or less by moving, then why does A or B's relative motion to the emitter matter? It seems like it shouldn't matter whether A is moving away from the direction of the light, sitting on the light source, or following the light; it still travels in all directions with equal speed relative to A. If it doesn't matter for A, then it doesn't matter for B. Thus, there is no reason to say that B would clock the light moving any differently than A would.

 

[PeterDonis]

Object A: Stationary with respect to the emitter and detector.

Object B: Traveling away from Object A at a fast enough rate for his seconds to appear twice as long to Object A.

Ok.

This means that B would also perceive A's second to be twice as long as his own.

Yes, but now you're leaving out the relativity of simultaneity. B and A perceive different pairs of events to be simultaneous, and you have to take that into account when figuring the times they perceive as elapsing between events. See further comments below.

A turns on the emitter and turns his stopwatch on. B also turns on his stopwatch when he sees the light leave the emitter.

Where is B when he sees the light leave the emitter? Is he co-located with the emitter? If not, there will be a time delay involved between A turning on the emitter and B seeing the emitter turned on and starting his stopwatch. I assume you didn't intend that, so I assume B is co-located with the emitter when it turns on (i.e., he is just flying past A and the emitter when A turns on the emitter).

It takes 1 second from A's perspective. This means that from A's perspective, it would take 0.5 'B seconds' for the light to make the trip, since B's clocks spin twice as slow.

More precisely, from A's perspective, only 0.5 seconds elapse on B's clock during the light's trip.

The same is true for B. He sees the light make the trip in one second, but thinks that A must have counted only .5 seconds.

No, this is not correct. B is moving relative to the emitter and detector and A is not. This means the situation is not symmetric between them.

When they meet and exchange data, they both have one second.

No, this is not correct. See below.

Light will always travel at at c, and a light second will always take 1 'my second' for light to travel. Why does the distance need to contract for this to be true?

Light always takes 1 second to travel 1 light-second, yes. But in the scenario just discussed above, A observes the light to take 1 second to travel, but B does not; he only observes it to take 0.5 seconds. So for the speed of light to be constant, B must see the distance as contracted to 0.5 light-second.

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.

The difference is that when he came back and showed me the results, I would have experienced more time than him.

But that means the watch, moving with him, would have experienced less time than you, just as the traveler did. The watch and the traveler experience time at the same rate if they are traveling together.

What's wrong with this interpretation?

The basic problem you are having is that you are still trying to reason about space and time separately, instead of reasoning about spacetime as a unified whole. See further comments below.

If light travels at a constant rate according to the observer, this means that the timing device must be at rest with the observer.

Yes, this is true for each observer; the timing device they are using to measure the speed of light is at rest relative to them.

The diagram you have drawn is only valid for A; it is drawn with respect to A's reference frame, not B's. What you really need to draw is a *spacetime* diagram, with time on the vertical axis and space on the horizontal axis (you only need one dimension of space, assuming that B is moving relative to A in the same direction as the light beam travels). If you're not familiar with spacetime diagrams, I strongly recommend learning them; many relativity puzzles become a *lot* easier to figure out if you use them. You could try the Wikipedia page for a start:

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

A spacetime diagram will also make it clearer how relativity of simultaneity comes into the picture.

"because of the difference in rate of time flow between the two" seems to imply that the time flow of A is somehow more special than the time flow of B because it is at rest with the light emitter.

It's not that A's time flow is "more special"; but it is true that A will perceive the light beam to take *more* time to travel (and therefore to cover more distance) than any other observer, because A is at rest relative to the emitter and the detector.

If you can't make the speed of light appear greater or less by moving, then why does A or B's relative motion to the emitter matter?

It doesn't matter for determining the *speed* of light; but it *does* matter for determining how much time the light takes and how much distance it covers. Speed is only the ratio of time and distance; speed can be constant while time and distance vary.

Once again, I strongly recommend learning about spacetime diagrams (if you haven't already done so), and then drawing a spacetime diagram of your scenario, before trying to analyze it any further.

 

[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.