Is time universal? NO (and its proof)

Aer:

Pete's right about that.

Take a moving spaceship which accelerates while watching a clock on the Earth's surface.

One way to explain what the spaceship sees is to consider the spaceship as changing inertial references frames (passing through many "infinitessimal" inertial frames) as it accelerates. That's an SR picture.

Another way to explain the same thing is to consider the spaceship as being in a single non-inertial reference for the whole accelerating period. This is the GR picture. In such a frame, there is a gravitational field in the spaceship's frame which accounts for the observed time dilation of the Earth clock.

Both methods produce the same results if you do the quantitative calculations correctly.

 

Pete:

I'm assuming you mean that the satellite-stationary clock (for example) is at the same height as the satellite but not orbiting the Earth.

In which frame? And are we including gravity or not?

Once you answer that, I'll move on to the following questions.

 

Aer:

Tell me what the difference is between a "true gravity field" and a "pseudo-gravity field", and then I might be able to tell you whether or not I agree with your reference sources.

 

Pete:

Ok, ignoring GR effects (i.e. pretending the Earth has no mass for the moment):

In the Earth-centre frame, let's assume they are.

No. In the Earth-centre frame that is true. In the satellite-stationary frame (which is the same) that is true. But in the satellite frame the satellite-stationary clock ticks slower than the satellite clock.

(What "ratio" are you talking about?)

No. My answer is similar to my answer to my answer to (2).

 

I'm talking to Pete, MacM. I'm not interested in re-hashing this with you yet again. Go away.

 

If the satellite clock moves in a circle to come back to its starting point, then it has accelerated, while the stationary-satellite clock did not. My first thought is that I would expect its clock to display less elapsed time than the stationary clock, after the entire trip. This effect would not be symmetrical, since the stationary clock is in an inertial reference frame the whole time while the satellite is not.

This probably means I need to revise my previous statement, doesn't it?

BUT... hang on a minute. This is difficult, because if I think of the problem from a GR perspective the "gravitational field" experienced by the satellite constantly changes direction relative to the stationary-satellite clock, and I'm not sure if or how this affects the timing.

I suspect an easier analysis would involve the Sagnac effect, but I'm not an expert on that...

This is why this GPS stuff is harder than it seems at first glance. MacM thinks he has it all figured out. I think he doesn't realise all the complicating factors. Certainly the GPS literature says you need to include things like the Sagnac effect to make the system work.

So, where do we go from here?

 

MacM:

No. What I mean is "Questions I have answered before in considerable detail go away." I have no interest in having a discussion in which I have no chance of learning anything, or of teaching anything.

I started off knowing little other than that GPS had to make relativistic corrections, and the general nature of the corrections needed. I have learnt a little more about the system - most of it from my own reading on the web, a little from 2inquisitive's posts, and, as far as I can tell, nothing at all from you.

Probably you did. I'm sure you didn't explain any of it. In fact, I'm sure you can't give a good description of the Sagnac effect now, either. (And I think it's relevant to the discussion I'm having with Pete.)

I don't need to argue this. The evidence is all over the forum for all to see.

I'm talking to Pete about a situation with no gravity. A real orbit is inertial. This orbit is not, because gravity is not the cause of the orbit we're discussing. We're talking about a flat-space problem here. Since this is probably beyond you, why don't you stay out of the conversation?

The only reason you think I am inconsistent, MacM, is that you don't understand my posts. I am careful to explain clearly what I mean. I sometimes make mistakes, and I'm happy to admit it when I am wrong. But I do not deliberately lie about things, as you claim. And in your particular case, your accusations that I change from one view to another as is convenient stem from your inability to appreciate subtle differences between different situations, or perhaps just a laziness on your part. You simply look for any opportunity to attack me. Instead of reading the entire argument and getting up to speed, you pick on a single point in a single post, make an unwarranted assumption, and fire away. That's why I don't engage with you any more.