Why does time slow down as you approach C?

[ghwellsjr]

But, assuming that you did the calculation correctly, you could also say that from a reference frame in which B is at rest, A and the Earth-Sun system are moving away at 0.9999c and when B will have aged 10 years, A's clock will have accumulated only about 51 days and 15 hours and the Earth will have only progressed about 1/7 of a revolution around the Sun.

I assume you're talking about what B would see and not what actually is the case, because if B is moving away from the Earth-Sun system and A at .9999c, then during the interval that B's clock goes from 0 to 10 years, then the Earth would have gone around the sun 707 times. But yes I understand that B would see the Earth as only having progressed about 1/7 of a revolution around the Sun when he (B) marks that his clock has accumulated 10 years.

No, I was not talking about what B would see and there is no "what actually is the case", unless you consider what each person sees as "what actually is the case". I discussed this back in post #21 where I said:

"...each observer will read the other one's clock as ticking slower by exactly the same amount but here we are not talking about time dilation, we are talking about Relativistic Doppler which is what each observer actually sees of the other one's clock. The amount of slowdown that they see is not the amount of time dilation."​

The formula for the Relativistic Doppler Factor for observers moving away from each other is:

√[(1-ß)/(1+ß)]

Since ß = 0.9999, we can calculate the factor as:

√[(1-0.9999)/(1+0.9999)]
√[(0.0001)/(1.9999)]
√[(0.0001)/(1.9999)]
√[(0.00005)]
0.00707

You said back in post #30:

Like say A is on Earth, so he's stationary wrt the Earth, and B is moving at .9999c wrt A and the Earth. Ok, so when the Earth-Sun system marks 10 years, then A will have aged 10 years and A's clock will have accumulated 10 years, but B will have aged (and B's clock will have accumulated) only about 51 days and 15 hours.​

Here you were talking about time dilation based on an Earth-Sun reference frame. But this is not what A will see of B's clock after 10 years. Instead A will see B's clock to have advanced only 0.00707 times 10 years or .0707 years or 25.8 days, roughly half of the time dilation.

And, by the same token, during the time that B's clock has advanced 10 years, B will see the Earth as having gone only 1/14 of its way around the sun, the same 25.8 days that A sees of B (except, of course, there's no solar system at B, but he does see his clock and keep track of the days).

Remember two important things about what each observer sees of the other one's clock: It has nothing to do with any specific theory or any particular frame of reference, and, secondly, it's a combination of time dilation and the propagation of light. That's why it's different than just time dilation.

The reason I framed the scenario the way I did was to illustrate the expected reality of a situation where A is stationary on the surface of the Earth and B is moving at .9999c wrt A and the Earth (because akshayxyz seemed concerned with the physical reality of the situation and not just how things might appear to A and B).

What each person sees is physical reality.

akshayxyz specified that A is "stationary". But stationary wrt what, I wondered. Then, reading a bit further, he mentioned "from a neutral perspective", and I supposed that he meant some referent, like say, the Earth, wrt which A is at rest and wrt which B is moving at .9999c. In which case, B would be aging considerably slower than A.

It's perfectly OK to say that A is "stationary" and that B is moving with respect to A. You don't need to have a solar system nearby to validate A's situation.

But yes I understand what you're saying about the notion of a "neutral perspective", and I don't really know what that might refer to wrt the discussion in this thread. I agree with your statement that wrt SR the term "neutral perspective" is essentially meaningless, but I don't think that it's necessarily a euphemism for "preferred reference frame". At least I don't think that that's what akshayxyz meant by it. Hence my conjecture, in the absence of input from akshayxyz, regarding what might contribute to furthering his understanding of differential aging, as he seems to be having some difficulty understanding that it's a prediction of SR and a pretty well established experimental fact.

It's not just in the context of SR that a "neutral perspective" is meaningless, that also is a well established experimental fact.

Or you could pick a Frame of Reference midway between A and B such that both of them are traveling at exactly the same speed in opposite directions and in which they both age at the same rate. Why wouldn't this FoR be a better "neutral perspective" than one in which either A or B was at rest?

Because it wouldn't illustrate differential aging, which is what akshayxyz seemed to me to be concerned about, and which I take to be the basic theme of this thread (ie., a discussion about the relationship between speed and timekeeping/aging).

Differential aging is what happens after the two observers with their clocks are reunited. Until that happens, you either talk about what each observer sees of the other one's clock (Relativistic Doppler which is symmetrical while they continue to move apart), or time dilation based on an arbitrary Frame of Reference and it doesn't matter which Frame of Reference you use, but most will have a non-symmetrical time dilation.

So let me repeat so you don't miss this very important point: any Frame of Reference will illustrate the exact same differential aging as any other Frame of Reference.

And there are a gizzilion other Frames of Reference that establish totally different accumulated times on A's and B's clocks, none of which can be called a "neutral perspective".

Yes, point taken. So I just specified a common referent, the Earth. I thought it would then be clear(er) to akshayxyz that as long as A was at rest wrt the Earth and B was moving at .9999c wrt the Earth, then B would be aging, and his clock accumulating time, slower than A by a factor 70.7

That's true but it's only a half-truth as I hope you are well aware of by now because you can equally establish B as the "neutral perspective", if by that you merely mean a reference frame, but you seem to think the Earth makes one reference frame more significant than some other reference frame.

That's just a euphemism for "preferred reference frame" of which there are none.

Maybe that's how some people use the term "neutral perspective" in these sorts of discussions. I don't know. But, as I mentioned above, I don't think that "preferred reference frame" was what akshayxyz was referring to wrt his use of the term "neutral perspective".

And as I stated in post #31, you could use an imaginary point midway between A and B as the basis for your reference frame and it would give both of them the same time dilation. Why wouldn't this one be the neutral perspective?

 

[ThomasT]

...each observer will read the other one's clock as ticking slower by exactly the same amount but here we are not talking about time dilation, we are talking about Relativistic Doppler which is what each observer actually sees of the other one's clock. The amount of slowdown that they see is not the amount of time dilation.

Ok, thanks ghwellsjr. This corrects part of my thinking on this. I'll get up to speed on it, eventually.

There are some other things you mentioned that I might want to nitpick from your post #36. But I'll have to do it this evening or later.