YEC: can't speed up light, so change time measurement.

[nasor]

The speed of light is constant from any frame of reference, so when you go faster, time slows down so that it's still constant even from your frame of reference. Therefore, if you launch a ship at 0.9c and a laser beam at c, the laserbeam will not appear to be moving at 0.1c from the ship's frame of reference as predicted by Newtonian physics. Instead, time will slow down from the ship's POV so that the light still appears to be moving at c (length also dilates, but let's leave that aside for the moment).

I’ve never taken any classes in relativity, but this explanation does not make sense to me. It implies that time dilation should be linear with velocity, when (according to the time dilation equations) it isn’t.

If, as in your example, I’m moving at .9 C parallel to a light beam then time would have to pass at 1/10 normal speed for me in order for the light beam to continue to travel away from me at C. But in fact if you plug .9C into T=To / (1-V^2/C^2)^.5, time would only pass at a bit less than half for normal speed.
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[drachefly]

If, as in your example, I’m moving at .9 C parallel to a light beam then time would have to pass at 1/10 normal speed for me in order for the light beam to continue to travel away from me at C. But in fact if you plug .9C into T=To / (1-V^2/C^2)^.5, time would only pass at a bit less than half for normal speed.
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Nope. You also need to take length contraction into account, and that handles the rest.

[Darth Wong]

The speed of light is constant from any frame of reference, so when you go faster, time slows down so that it's still constant even from your frame of reference. Therefore, if you launch a ship at 0.9c and a laser beam at c, the laserbeam will not appear to be moving at 0.1c from the ship's frame of reference as predicted by Newtonian physics. Instead, time will slow down from the ship's POV so that the light still appears to be moving at c (length also dilates, but let's leave that aside for the moment).

I’ve never taken any classes in relativity, but this explanation does not make sense to me. It implies that time dilation should be linear with velocity, when (according to the time dilation equations) it isn’t.

If, as in your example, I’m moving at .9 C parallel to a light beam then time would have to pass at 1/10 normal speed for me in order for the light beam to continue to travel away from me at C. But in fact if you plug .9C into T=To / (1-V^2/C^2)^.5, time would only pass at a bit less than half for normal speed.

Oh for fuck's sake, did you completely ignore the part where I acknowledged right up-front that I was oversimplifying, by making reference to length dilation which I would leave aside for now? Or do you think that you get some kind of reputation bonus points on this board for being pedantic? Because I assure you that you don't.

[Wyrm]

I’ve never taken any classes in relativity, but this explanation does not make sense to me. It implies that time dilation should be linear with velocity, when (according to the time dilation equations) it isn’t.

If, as in your example, I’m moving at .9 C parallel to a light beam then time would have to pass at 1/10 normal speed for me in order for the light beam to continue to travel away from me at C. But in fact if you plug .9C into T=To / (1-V^2/C^2)^.5, time would only pass at a bit less than half for normal speed.

Because in the stationary frame of reference, you're traveling forward at .9 c, chasing after a pulse of light going at c, and all the while, I see that your rulers are too short in the direction of travel. When you travel at speed, in my frame of reference (in which you're moving) all your clocks are ticking slowly than mine by a factor of 1/γ (where γ=√(1 - v²/c²) ), and all of your rulers are shorter than mine by a factor of γ, as well as moving forward at v = .9 c.

Suppose that we've synchronized our watches such that a light pulse passes you at (0,0). A second later (t = 1s), you locate the light pulse at x = c(1s). From your frame of reference, the speed of this light pulse is w = c(1s)/1s = c. What is the speed of this pulse from my frame of reference?

The Lorentz transformation for translating between your coordinates (t, x) and mine (t', x') is:

t' = γ(t - vx/c²)
x' = γ(x - vt)

The light pulse passes you at our coordinates (0,0) as well. Our coordinates for the coordinates (c(1s), 1s) in your frame (where the light pulse is after 1s of your time) is (γ(.1s), cγ(.1s)), so w = x'/t' = cγ(.1s)/γ(.1s) = c.

And there you have it. The speed of light is the same from all frames of references. We agree on practically nothing else: we don't agree on the position of the light pulse, we don't agree on the time the light pulse reaches that position, and we don't even agree on the zero axes. (We do agree on the origin, but that's arbitrary anyway.) The Lorentz transformation involves not only a change in time, but also of space, and the moving frame's position. This is why it is not linear.

[Wyrm]

GHETTO EDIT:

When you travel at speed, in my frame of reference (in which you're moving) all your clocks are ticking slowly than mine by a factor of 1/γ (where γ=√(1 - v²/c²) ), and all of your rulers are shorter than mine by a factor of γ, as well as moving forward at v = .9 c.

Messed up there. Usually, γ = 1/√(1 - v²/c²), which makes your rulers shorter than mine by a factor of 1/γ (L = L_0/γ), and your clocks tick slower than mine by a factor of γ (T = T_0 γ).

γ is correctly used in the rest of my message.

[Magnetic]

Is there an Emoticon who's head exploads? There SHOULD be one.

[nasor]

Oh for fuck's sake, did you completely ignore the part where I acknowledged right up-front that I was oversimplifying, by making reference to length dilation which I would leave aside for now? Or do you think that you get some kind of reputation bonus points on this board for being pedantic? Because I assure you that you don't.

Christ, don't be so fucking defensive. I didn't understand and was asking for more information, not challenging you or saying that you were incorrect. That's why I said that it didn't make sense to me. I'm sorry that I didn't preface my post with something like "This is not to be construed as a challenge to Darth Wong's understanding of relativity," but I didn't know about your policy of assuming that anyone who expresses confusion must necessarily be trying to insult you. I'll try to be more careful of your tender, paranoid ego in the future.

Thanks for actually providing a useful answer, Wyrm. I think I understand now.

[Darth Wong]

Christ, don't be so fucking defensive. I didn't understand and was asking for more information, not challenging you or saying that you were incorrect. That's why I said that it didn't make sense to me. I'm sorry that I didn't preface my post with something like "This is not to be construed as a challenge to Darth Wong's understanding of relativity," but I didn't know about your policy of assuming that anyone who expresses confusion must necessarily be trying to insult you. I'll try to be more careful of your tender, paranoid ego in the future.

If you know the fucking equations of relativistic dilation, you little fucktard, then you already know about length dilation and you are either being deliberately pedantic or you are just being a dishonest little shit. Either that or you're really such a goddamned idiot that you looked up the equations of dilation and couldn't put two and two together to figure out that length dilation might have something to do with it even though I conveniently mentioned it for you.

So forgive me for getting angry and assuming that you were being pedantic instead of assuming that you're a blithering idiot. I keep forgetting how stupid the average Internet user can be.

[nasor]

So forgive me for getting angry and assuming that you were being pedantic instead of assuming that you're a blithering idiot. I keep forgetting how stupid the average Internet user can be.

Yeah, I'm a blithering idiot because I didn't feel like trying to teach myself relativity.

But since you made yourself look like an uptight prick by responding to my statement of "this does not make sense to me" as if I had said something more along the lines of "Darth Wong has a tiny dick," I guess your only option now is to try to continue to act as though my expression of confusion was some sort of personal insult.

[Darth Wong]

So forgive me for getting angry and assuming that you were being pedantic instead of assuming that you're a blithering idiot. I keep forgetting how stupid the average Internet user can be.

Yeah, I'm a blithering idiot because I didn't feel like trying to teach myself relativity.

But you did try to teach yourself relativity, fool. And then you expected people on the Internet to help you because you were too lazy to do it right. Worse yet, you ignored an explanation that was right in front of you until someone spelled it out for you, because you're too fucking stupid to put two and two together on your own.

But since you made yourself look like an uptight prick by responding to my statement of "this does not make sense to me" as if I had said something more along the lines of "Darth Wong has a tiny dick," I guess your only option now is to try to continue to act as though my expression of confusion was some sort of personal insult.

What does my dick have to do with this? Oh yeah, you assume that someone who points out what a moron you are must be suffering from some sort of psychological inadequacy, rather than confronting the fact that he may be right. Grow up, dipshit. Do you really think I'm rattled by this "OMG you are compensating" diversionary bullshit? Is that your answer to any insult? Assume the other guy is suffering from sexual inadequacy? You just figure you'll repeat that generic comeback every time someone flames you?

You're the worst sort of Internet science poser; the imbecile who tries to Google his way to glory and then ask total strangers to help him. Here's a hint: if you're curious about science and relativity, try reading books. Or is that too difficult for you?

[drachefly]

You did tell him to 'set aside' length contraction, which, if one does not understand relativity yet, could reasonably be interpreted to mean that it is not relevant, for whatever reason.

[Darth Wong]

You did tell him to 'set aside' length contraction, which, if one does not understand relativity yet, could reasonably be interpreted to mean that it is not relevant, for whatever reason.

I said "let's leave that aside for the moment". Most normally intelligent people would recognize that this means it's relevant, but I just don't want to get to it quite yet.

[drachefly]

He took the literal interpretation of your statement, which was that time dilation was adequate to maintain the speed of light; while there is this other effect length 'dilation' (contraction) which is not necessary to explain this, because if it were necessary, we wouldn't be leaving it aside, even for now!

That he did not go and stick in the length effect you fairly explicitly told him not to is not, IMO, unreasonable.

Miscommunications happen. No need to call people morons every time, especially when they check the figures they've been given, which is commendable.

[Darth Wong]

He took the literal interpretation of your statement, which was that time dilation was adequate to maintain the speed of light; while there is this other effect length 'dilation' (contraction) which is not necessary to explain this, because if it were necessary, we wouldn't be leaving it aside, even for now!

One would think that such a perfunctory explanation could not possibly be complete, particularly since it did not even come with equations attached. And even a literal interpretation does not lead to his conclusion, since I did say that length does dilate, hence it obviously must be accounted for. It would, in fact, be impossible for length to dilate without having some effect on perception of velocity: something that I would consider obvious.

Miscommunications happen. No need to call people morons every time, especially when they check the figures they've been given, which is commendable.

There is never a "need" to call someone a moron. I do it when I feel like it. And let's face it, while you often like to make excuses for foolishness, someone who doesn't immediately realize that length dilation would have some effect on perceived velocity would have to be a bit of a dim bulb, especially if he's studied the subject enough to collect equations and do calculations.

[General Trelane (Retired)]

Maybe there was a miscommunication, but. . .

I’ve never taken any classes in relativity, but this explanation does not make sense to me. It implies that time dilation should be linear with velocity, when (according to the time dilation equations) it isn’t.

Actually, DW's explanation states that time dilation varies with velocity, but it does not at all imply that the relationship is linear.

So I interpreted the rest of his post exactly the way DW did. . .