Is the speed of light infinite?

[barbacamanitu]

I have been reading up on time dilation a bit this morning, and for the first time, I think it really clicked. Its raised some questions that I haven't seen answered anywhere, so I was hoping someone here could help.

As I understand it, and please correct me if I am wrong, the only thing that affects time is our speed relative to other objects. This is why a man traveling much faster will age less from his point of view than he will to others. This is also why you can't exceed the speed of light - because if you get close to it, time slows down for you. You would appear to be traveling near the speed of light to an earthly observer, but would be traveling "slower" than you perceive yourself to be traveling.

This is where I see tons of problems, and I assume its because I don't grasp the concept.

If we cannot ever reach the speed of light, then isn't the speed of light faster than infinite speed? If I have the means to move some mass as fast as I wanted, time would only keep passing slower and slower, and the SOL would always be faster. This means a particle with mass can move infinitely fast, but still be outrun by light, doesn't it?

1. 
   
   How can someone 'approach the speed of light'? If a man moving 99% SOL, according to an observer on Earth, really would age more (and I know this has been proven), then less time really would pass for the traveler. This means that the traveler could, in principal, know that he is traveling slower than his observer on Earth measures. Well, if we use the traveler as the stationary frame of reference, couldn't this exact same effect happen if someone on his rocket built a new rocket, and launched off of it going the same direction, with a velocity proportional to the first rocket leaving Earth? Could this go on forever, with each new rocket observing his own speed to be the same as the first rocket observed his to be? Would any of these velocities be any closer to the speed of light than the other? If not, then how is it that we give the SOL a value at all?
   
   Or is the SOL that we perceive the same SOL that a person moving 100,000,000 km/h would perceive? If that's the case, then I think I get it. But, this would mean that it isn't really a constant, just a constant relative to every possible observer. Wait a minute.. is that sort of the point of relativity?

 

[phinds]

Infinite? No, that's just silly. The speed of light is c.

If you are sitting on Earth and a beam of light hits you from the sun, it is traveling at c.

If you are sitting on Earth and a beam of light that was emitted by a spaceship traveling away from Earth at 99% of c hits you, it will be traveling at c (and it will be red-shifted in frequency)

If you are sitting on Earth and a beam of light that was emitted by a spaceship traveling towards Earth at 99% of c hits you, it will be traveling at c (and it will be blue-shifted in frequency)

Nothing with mass can travel at c.

In your own time frame you age exactly the same regardless of your motion, not more, not less. If you travel along a different world-line than someone else (say you're on a spaceship moving away from Earth and then you come back) then you may age differently than someone who was on Earth the whole time, but that is NOT because your biological processes are different than his, it's just because you were on a different world-line.

Yes, this is very weird but it is what it is. It seems weird to us only because our normal lives and senses are not in a realm where it happens to us (in a noticeable way).

 

[PeterDonis]

As I understand it, and please correct me if I am wrong, the only thing that affects time is our speed relative to other objects.

Basically this is true (at least, it's true as long as gravity is not present or can be neglected, but I assume that case is what you meant to ask about). However, you have to have the proper meaning for "affects time". See below.

This is why a man traveling much faster will age less from his point of view than he will to others.

This is where it becomes important to be precise. "Age less" is ambiguous as it stands. You never perceive yourself to be aging any differently; to you, other people that are moving fast relative to you appear to age more slowly, but to those other people, *you* appear to age more slowly. That often confuses people because they can't see how both of those things can be true. The key is that there is no objective way to determine which of two people is "really" aging less unless they meet up again at some point and compare their clocks.

You might want to check out the Usenet Physics FAQ entry on the twin paradox:

http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

(There are *lots* of discussions of the twin paradox here on PF as well, but I would recommend reading the above FAQ first before diving into them.)

This is also why you can't exceed the speed of light - because if you get close to it, time slows down for you.

Not really. See above.

You would appear to be traveling near the speed of light to an earthly observer, but would be traveling "slower" than you perceive yourself to be traveling.

You never perceive yourself to be "traveling" at all; you always perceive yourself to be at rest. If you got in a rocket and set off from Earth at nearly the speed of light, relative to Earth, then the Earth and the rest of the universe would seem to you to be traveling at nearly the speed of light. You yourself would seem normal and at rest.

I won't comment on the rest of your post because I think you need to reconsider your thinking in the light of the above, but there is one thing at the end:

Or is the SOL that we perceive the same SOL that a person moving 100,000,000 km/h would perceive?

Yes, the speed of light is the same for every observer.

 

[barbacamanitu]

After reading more and discussing this with a friend for a few hours, I think I understand it. The faster you travel, the slower time passes, relative to something slower than you. So light will always move at the speed of light, whether its coming from your flashlight or someone slower than you. The difference is in how time passes for you.

I imagine it like two people shooting guns. Both guns shoot at 100m/s. Steve shoots his gun standing still, but Jack shoots his while running 90 m/s. If this really happened, then Jack's bullet would be traveling at 190 m/s relative to Steve. However, if time passed 10x slower for Jack, and his gun still shot at 100 m/s away from him, to Steve it would only be traveling 10 m/s faster than Jack, which is still 100m/s. Steve's bullet, according to jack, would be traveling at 10 m/s unless time dilation was factored in. In reality, it would also move at 100m/s.

This means that no matter how fast you go, the change in the progression in time will always equate with the speed of light. The difference is in "how long" it takes a second to tick, for lack of better words.

 

[barbacamanitu]

Thank you Peter, it clicked. Correct me if I'm wrong, but trying to exceed the speed of light is a little bit like trying to drive faster than a bullet fired from your car. In space.

Edit: Actually, its more like everyone has a stopwatch that has a normal second hand on the front, but the second hand on the back slows down proportionally to the speed its traveling away from whoever is looking at it. You can only see the front of the watch, and other people can only see the back, and according to everybody's watch light travels at 299,792,458 m/s.

Edit 2: The experiments done with clocks moving at different speeds verify that the passage of time varies with velocity. However, this doesn't imply that light travels at a constant speed. I don't see a reason that the two must go hand in hand really, unless c has been observed while traveling at various speeds. I've looked for some experimental proof of this, but all I'm finding is people saying that "x wouldn't work without c being constant". To me, it seems like there should be a better answer than this. A moving observer should also be able to measure the light from a stationary (relative to the Earth, or whatever other reference frame used) light source and get the same results as if he measures the light from a light source moving the same velocity as him. Has this been done? Or, we could reflect the light from objects in space which are moving away from us, and measure the speed of this light.

tl;dr - Are there any experiments which verify that c is a constant?

 

[PeterDonis]

The faster you travel, the slower time passes, relative to something slower than you.

"Faster" and "slower" are frame-dependent. To you, the other object is traveling faster than you are, since to you, you are always at rest.

So light will always move at the speed of light, whether its coming from your flashlight or someone slower than you.

This is true, but I'm not sure how it follows logically from what you said before.

I imagine it like two people shooting guns. Both guns shoot at 100m/s. Steve shoots his gun standing still, but Jack shoots his while running 90 m/s. If this really happened, then Jack's bullet would be traveling at 190 m/s relative to Steve. However, if time passed 10x slower for Jack, and his gun still shot at 100 m/s away from him, to Steve it would only be traveling 10 m/s faster than Jack, which is still 100m/s. Steve's bullet, according to jack, would be traveling at 10 m/s unless time dilation was factored in. In reality, it would also move at 100m/s.

This doesn't look like a good analogy to me. For one thing, I don't see how any of this matches up with how SR actually models time dilation and relative velocity mathematically. Have you looked at the actual math?

For another thing, you have ignored the fact that in relativity, velocities don't add linearly the way you have assumed here. Suppose the guns fired bullets moving at 0.9c. Steve fires his gun "standing still" (note that this implies a choice of reference frame, in this case Steve's rest frame--it's not a frame-independent objective fact), and Jack fires his gun while moving at 0.8c relative to Steve. The relativistic velocity addition formula is

$$v' = \frac{u + v}{1 + uv / c^2}$$

where $u$ is the relative velocity of the two observers, one who sees an object moving at $v$ and the other who sees that object moving at $v'$. For Jack's bullet moving relative to Steve, we have $u = 0.8c$ and $v = 0.9c$, so $v' = 0.99c$; Steve will see Jack's bullet moving at 0.99c relative to him, not 1.7c. For Steve's bullet moving relative to Jack, we have $u = - 0.8c$ and $v = 0.9c$, so $v' = 0.36c$; Jack will see Steve's bullet moving past him at 0.36c, not 0.1c.

Correct me if I'm wrong, but trying to exceed the speed of light is a little bit like trying to drive faster than a bullet fired from your car. In space.

I don't really see this analogy either. Again, have you looked at the actual math?

Edit: Actually, its more like everyone has a stopwatch that has a normal second hand on the front, but the second hand on the back slows down proportionally to the speed its traveling away from whoever is looking at it. You can only see the front of the watch, and other people can only see the back, and according to everybody's watch light travels at 299,792,458 m/s.

This might be ok if you could specify, mathematically, how the reading of the second hand on the back of the watch is determined. "Slows down proportionally" isn't quite right.

Edit 2: The experiments done with clocks moving at different speeds verify that the passage of time varies with velocity.

They verify a lot more than that: they verify the specific mathematical formula that SR uses to predict exactly *how* the passage of time varies with (relative) velocity.

However, this doesn't imply that light travels at a constant speed.

It does when you look at the mathematical formula that has actually been verified by these experiments, since that formula requires that light travel at a constant speed.

Are there any experiments which verify that c is a constant?

It's not as simple as that, because in order to measure the speed of light the way you are describing, you would have to take measurements in various states of motion and then compare them. But how do you compare them without knowing how the rate of time flow varies with your state of motion? And how do you know how the rate of time flow varies with your state of motion, if you don't make some assumption about how the speed of light behaves? There's a chicken and egg problem here.

The best we can do is to to test for indirect effects that we would expect to occur if the speed of light were variable. An example of such an experiment is the classical Michelson-Morley experiment:

http://en.wikipedia.org/wiki/Michelson–Morley_experiment

In the end, the best argument for the speed of light being constant is that we can make very accurate predictions by assuming that it is in our theory, whereas nobody has come up with an equally accurate theory that has a variable speed of light in it.

 

[phinds]

... The difference is in how time passes for you.

I addition to all the good info Peter gave you, I would emphasize that this particular statement is incorrect. Time passes for you at exactly the same rate regardless of your speed relative to other things (and all speed is relative). In your frame of reference, you are not moving and time passes for you at one second per second.

 

[barbacamanitu]

No, i have not looked into the math. I really just read about time dilation and how time can pass differently for different objects, and sort of figured out the rest. I didn't expect the math to line up with Einstein's, I was just trying to grasp the concept of time being dependent on relative velocities, and if the only argument against my analogy is that my numbers are wrong, then I think the analogy is a fine one.

Why would you expect the numbers in an analogy to be correct anyway? Then it stops being an analogy and starts being an example.

With the gun analogy, I was just assuming the field that the field they were standing on was the reference frame. This would be the same as Steve's point of view. I understand that there is no "faster" and "slower" in the absolute sense.

 

[barbacamanitu]

I addition to all the good info Peter gave you, I would emphasize that this particular statement is incorrect. Time passes for you at exactly the same rate regardless of your speed relative to other things (and all speed is relative). In your frame of reference, you are not moving and time passes for you at one second per second.

True. The difference is in how time would seem to pass for you according to another observer, right?

 

[PeterDonis]

No, i have not looked into the math. I really just read about time dilation and how time can pass differently for different objects, and sort of figured out the rest.

This doesn't strike me as a good approach, for the reasons I give below.

I didn't expect the math to line up with Einstein's, I was just trying to grasp the concept of time being dependent on relative velocities

But the concept depends on the math. By "the math" I don't mean the specific numbers; I mean the equations and the terms in them and what they mean physically.

and if the only argument against my analogy is that my numbers are wrong, then I think the analogy is a fine one.

It's not a matter of the numbers being wrong; it's a matter of the concepts you use in your analogy not mapping in any recognizable way to the terms in the equations. If you would actually look at the math you would see this.

 

[phinds]

True. The difference is in how time would seem to pass for you according to another observer, right?

That is an artifact of how someone else sees you moving from their frame of reference, yes. Just don't get confused as to whether or not it has to do directly with how you measure the speed of light.

You are moving right now as you read this, relative to SOME frame of reference, at every possible speed up to but not including c so how you measure the speed of light hitting you cannot possibly be a function of how fast you are moving relative to someone else.

 

[barbacamanitu]

That is an artifact of how someone else sees you moving from their frame of reference, yes. Just don't get confused as to whether or not it has to do directly with how you measure the speed of light.

You are moving right now as you read this, relative to SOME frame of reference, at every possible speed up to but not including c so how you measure the speed of light hitting you cannot possibly be a function of how fast you are moving relative to someone else.

Right. However, only by already knowing c was constant would you understand that how you measure light couldn't be a function of how fast you are moving relative to someone else. If did not know that c was a constant regardless of relative motion, then this would definitely be something worth testing.

 

[barbacamanitu]

But the concept depends on the math. By "the math" I don't mean the specific numbers; I mean the equations and the terms in them and what they mean physically.

Does it matter if I know whether or not I know how to calculate the volume of a sphere when all I want to know is if dropping the sphere in a bathtub will cause the water level to rise?

I started today having no idea what relativity meant. I now understand that when an object moves relative to another object, the time which each one experiences is different, even though no difference is noticed by the object itself. This is why nothing can exceed the speed of light, you can only approach it from the point of view of another object which would appear to you to be approaching the speed of light as well.

Seriously, if you have any interest in getting people interested in physics then your approach is terrible.

 

[nuby]

If there was a 'space' or universe with just one electron. What would prevent the electron from traveling from one side to the other faster than c?

 

[barbacamanitu]

How fast would you know how fast it was going if there was nothing to compare it to? Thinking about space and time as absolutes are what I think most people do. Your speed is always 0 to you. Compared to the universe would imply that there were two things: the electron and the bounds of the container it was inside.

No matter how fast the electron travel led (which already doesn't make sense, because there is no reference frame), it would still see the speed of light the same way that you do.

 

[WannabeNewton]

This is why nothing can exceed the speed of light...

How does this follow as a logical consequence of what you said right before it? That there is a finite upper bound for the speeds of massive objects is a postulate of SR. Also, there is no need to go start insulting Peter Donis. He knows what he's doing and he's successfully educated many people on the forum. Getting interested in physics entails getting interested in the math behind it, otherwise you just start spouting random jargon.

 

[nuby]

How fast would you know how fast it was going if there was nothing to compare it to? Thinking about space and time as absolutes are what I think most people do. Your speed is always 0 to you. Compared to the universe would imply that there were two things: the electron and the bounds of the container it was inside.

No matter how fast the electron travel led (which already doesn't make sense, because there is no reference frame), it would still see the speed of light the same way that you do.

The reference point could be the center of the 'space'.

 

[PeterDonis]

I started today having no idea what relativity meant. I now understand that when an object moves relative to another object, the time which each one experiences is different, even though no difference is noticed by the object itself.

Yes, this is correct.

This is why nothing can exceed the speed of light

But I don't see how this follows from it.

Seriously, if you have any interest in getting people interested in physics then your approach is terrible.

Well, you started the thread because you were already interested, correct? If you weren't you wouldn't have bothered posting.

But you also saw some issues with the way you were conceptualizing relativity. That's why you posted. So I would assume that, if I continue to see issues with the way you're conceptualizing relativity, you would want me to say so. That's what I'm doing.

 

[barbacamanitu]

So only physicists can be interested in physics. I completely understand how important math is, and to fully understand anything in physics I know that it must be described mathematically.

Yes, what I said doesn't follow logically. One could never deduce that the speed of light was the upper limit by what I know about SR so far. I don't understand why its the limit, I just understand that it is the limit that SR gives to objects.

What would follow, however, is grasping the idea that there could be an upper limit to speed, and it exists because as our relative speed increases, our relative time slows down. Why light speed is the upper limit is another thing to learn, but understanding that time is not static is absolutely necessary first.

 

[PeterDonis]

So only physicists can be interested in physics.

How do you figure that?

One could never deduce that the speed of light was the upper limit by what I know about SR so far.

That's right. The constancy of the speed of light is a *postulate* of SR. It's not something that gets deduced from other things; it's something the theory assumes at the outset.

What would follow, however, is grasping the idea that there could be an upper limit to speed, and it exists because as our relative speed increases, our relative time slows down.

And this is the part I don't understand. Can you expand on this argument?

 

[barbacamanitu]

Peter, I do want my mistakes to be corrected, which is why I posted here. I make an analogy to try to grasp the concept of time not being this static ticking thing that everyone usually assumes is true, and you tell me that I clearly don't understand because I used the numbers 1 and 9, or that because the function isn't linear like I said it was. Clearly I wasn't trying to be even remotely close to accurate with the analogy. I wasn't showing that I knew how time changed, just that I now realize that time changes because of relative velocity.

 

[PeterDonis]

I wasn't showing that I knew how time changed, just that I now realize that time changes because of relative velocity.

Yes, that part's fine, but I don't see how you go from that to the fact that there must be a finite upper limit to speed. That's the part I've been trying to get you to expand on.

 

[barbacamanitu]

How do you figure that?



That's right. The constancy of the speed of light is a *postulate* of SR. It's not something that gets deduced from other things; it's something the theory assumes at the outset.



And this is the part I don't understand. Can you expand on this argument?

Wait, I think I see what you are saying. Knowing that time changes with speed doesn't tell you that there is an upper limit. It does tell you that moving faster than another object can cause you to perceive the passage of time differently than that object. No upper limit has to follow from this, but this difference in the passage of time is what allows there to be a limit which is also a constant to every observer, regardless of any relative motion. Does that make more sense?

Edit: Replacing the speed of light with an arbitrary number like 1,000 m/s really helped me understand the non-sequitur I was making. The limit can only be proven by observing the speed of something always traveling at the same rate relative to you, or by seeing how exactly time dilates (if that's the proper way of saying it) and deriving a formula to calculate apparent time passage differences between two objects at various relative velocities. Then, I imagine its just a matter of seeing at what point this formula would break down, and voila, limit found.

 

[PeterDonis]

No upper limit has to follow from this, but this difference in the passage of time is what allows there to be a limit which is also a constant to every observer, regardless of any relative motion. Does that make more sense?

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.

 

[barbacamanitu]

The reference point could be the center of the 'space'.

Looking at space as a reference frame is sort of the problem, if I'm not mistaken. Even if there were an immaterial grid in space that we could use to measure distance, we still couldn't exceed the speed of light, according to SR. This hypothetical grid would effectively be another object though, since it would appear to be moving to the traveler.

If I'm understanding correctly, SR is just the opposite. The only way to measure speed is with two objects. How would you know that you were moving through the universe in your question? That would only be possible by observing the electron move, or by being the electron and observing your surroundings moving.

The simple answer is that the speed of light is c. If you are alone in a void, its still c. How do you speed up when you have no intrinsic speed? Are you at rest in this universe to begin with? Prove it. Now prove that you are moving.

Time doesn't change with speed, it is just different for two objects which are moving relative to one another.

A second is always a second to you. A meter is always a meter to you. 1 m/s away from you is always 1 m/s away from you. A car traveling at 100 m/s relative to a street will still have a speed of 1 m/s away from you if you are going 99 m/s relative to the street.

Exceeding the speed of light is sort of like going faster than 10 m/s away from yourself. It isn't that its fast, its that time it has a constant speed, but your speed depends on another object. From your vantage point, you can never get closer to the speed of light than 0. According to you, other objects can go faster than 0 m/s, but from their frame of reference, they are sationary and you are the one moving slightly closer to light speed.

 

[barbacamanitu]

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.

If they are both moving only with respect to each other, then wouldn't the difference in the flow of the rate of time occur in each one, but only perceived by the other? I'm not seeing how you can say that one counts one second but the other counts two seconds when they are just moving apart from each other. How do you decide which object gets to experience more time than the other?

Using a light second seems like circular reason when you are measuring light speed. Measuring the distance something travels with a unit of measure based on how fast it should go, then deducing how fast its going from that. Or are you saying that when traveling quickly relative to another object, distance changes too?

 

[PeterDonis]

The reference point could be the center of the 'space'.

How do you know the space even has a "center"? How would you define it if the space doesn't contain anything except a single electron?

 

[barbacamanitu]

How do you know the space even has a "center"? How would you define it if the space doesn't contain anything except a single electron?

"If an electron falls in the middle of a void, but nobody is around to see it, does it have a velocity?"

 

[PeterDonis]

If they are both moving only with respect to each other, then wouldn't the difference in the flow of the rate of time occur in each one, but only perceived by the other?

Each one perceives his own time to flow at one second per second, so to speak; but that's not the same as saying that each one perceives the same physical process (in this case, the light traveling from a given source to a given detector) to occur in the same amount of time. See further comments below.

I'm not seeing how you can say that one counts one second but the other counts two seconds when they are just moving apart from each other. How do you decide which object gets to experience more time than the other?

Because there are other objects in the scenario besides the two observers: there's a light source and a light detector. Suppose (which I should have said before) that the source and detector are at rest relative to each other. Then at most one of the two observers in relative motion can be at rest relative to the source and detector; suppose that the second observer, who sees the light taking two seconds to travel, is that observer. Then the other observer *must* be moving relative to the source and detector, and will therefore see the physical process of light traveling between them as proceeding more slowly; with the numbers I gave, he will see it as taking only one second instead of two, indicating a time dilation factor of 2, or a relative velocity of the source and detector with respect to him of 0.866c.

 

[PeterDonis]

"If an electron falls in the middle of a void, but nobody is around to see it, does it have a velocity?"

Or, "what is the sound of one electron clapping?"

 

[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.