Are laws of nature really the same in all reference frames?

zonde

It is possible to take gravitational time dilation as experimentally verified physical fact without any reference to SR or GR.

Nobody is doing it like you describe. This is simply crap.
Orbital speed can be calculated by simple formula when ellipticity is zero (circular orbit).

Why are you inventing problems that are not there? Are you trying to confuse Bjarne? Why?

PAllen

But that's not relevant to how I understand the Bjarne's confusion. In fact, he understands that and that is source of his confusion: "How come A and B, using their raw measurements, come up with different results? Aren't they supposed to be the same? " He is questioning in what sense there is 'relativity' between A and B, where each can directly use their measurements and find equivalent results.
I agree nobody would actually do it like that (as I described in another post). However, this is the only sense in which one can talk about applying the same laws to the raw measurements by A and B. I was trying to get across that in going from 'free falling enclosed labs' to global measurements by non-inertial observers, the statement the 'laws of physics are the same for all observers' takes on a more complex, less useful form. The same laws apply only if expressed in general tensor form. Otherwise, in practice, you correct measurements to do computations in a convenient coordinate system where the expression of the laws is simplest.
No, I am trying to directly address where I think his confusion is leading to incorrect expectations.

zonde

Ok, how the question went?

First, the setup for consideration is such that we can investigate gravitational time dilation with other things unchanged.
Yes we can do that in physically meaningful way exactly as Bjarne described. And that's the right approach to understand something. Isolate that one factor as much as possible. That is exactly the thing that you do in real experiments.

Second, observers make astronomical observations about their movement relative to the center of MW and the distance to the center of MW.
Again, yes we can do that and we don't have to factor out anything related to our gravitational acceleration.
Astronomers on surface of Earth (gravitationally accelerated frame) perform observations all the time and the only thing they factor out is aberration but that's velocity not acceleration effect.

Third, we compare results for two observers.


So far question (actually background for question) is formulated in physically meaningful way. Do you agree with that?

PAllen

No, not completely. My understanding of Bjarne's issue is that time measurements will be different (they set up the idea that they were sensitive to the time difference between their A and B). So measurements sensitive to time will be different. At this level of sensitivity, doppler measurements will also be affected. Then, of course, aberration will apply (angles, as I called it in one of my posts). My understanding of Bjarne's thesis was that all of this violated the idea of laws being the same for different observers. If you used these measurements to directly compute a distant velocity, it would come out different.

I wanted to focus on this being a false expectation. That it is expected that different observer's measurements may differ. And that for arbitrary observer's, the only form 'laws being the same' that you can expect is if they are expressed in general tensor form.

Bjarne

All what we can be 100 % sure about is;

1. That the 2 clock will tick different, - experience shows this.
2. Both clocks will complete the orbit of the Milkyway in the exact same period (according to the scenario mention above).
3. And because of that either speed or distance must be different from the perspective of A as it is for B.

I see no reason to complicate that more than this.

I believe we first at all only need to look at this purely / simple mathematical.

Speed multiplied with time = distance, - this must be true both for A as well for B, - since there is no reason to believe that only our ( or A’s) reality is more true like others.

This leaves us with 2 simple mathematical options;

Option 1.
The orbit speed for the 2 clocks (and the Sun) must seen from the perspective of observer B be faster as for observer A. - (I don’t believe in that option, - since A and B do not change distance between them).

Option 2
B's meter stick is longer and therefore distances shorter. - This is the only explanation I can accept so far.

As I understand relativity; - there are no certain reality (also not ours), since time (and probably also “size / distance”) not is comparable the same.
I think before accelerating the speculation into too much complexity we should try to look at the must simple level, as just shown, and finish here first.

PAllen

It is easy to see that the most direct interpretation is that speed of distant objects will be greater for the one closer to the sun. This simply follows from direct interpretation of doppler - they will be slightly more blue shifted. Thus, if interpreted without adjustment, distant objects should be viewed as going slightly faster than the 'further from sun' observer would conclude. This is consistent with the slower time, obviously. Measurements by other methods would be expected to generally agree, but not necessarily be exactly the same. One key point is that it is only in flat spacetime, for inertial frames, that all reasonable ways of measuring a distant velocity or large distance will agree. For your observers (non inertial, curvature present), if they interpret their measurements as if they were inertial, Minkowski, observers, different measurement methods for distant observations will disagree.

Bjarne

No
According to the example the 2 clock counteracts gravity from the Sun, - (they have small racket engine on board).

No there will be no Doppler effect due to speed difference of the 2 clocks; both clocks orbit with the exact same orbit-speed as the Sun, and with the exact same radius to the center of the Milkyway


You may have misunderstood that both clocks follows the orbit of the Sun, and is not approaching the Sun due to the gravity of the Sun, - because that gravity attraction is counteracted (by small rockets on board on the 2 clocks) . Therefore both clocks and the sun move in the exact same orbit around the Milky Way.

The 2 clocks (observers) are certainly meassuring different time-rate and can't therefore agree how distance (or speed) around the Milkyway.

All other observers (in the Universe) will observe that the Sun and the 2 clocks are completing 1 orbit of the Milkyway in the exact same period of (their) time.
This will not affect the motion (or time-rate) of the 2 clocks..

zonde

Certainly different time rate will affect measurements. And that's the point of example.
I think that aberration can be factored out if both observers translate their observations to rest frame of MW mass center. After they do that they should point in the same direction as where is MW mass center.

Well, yes, there are problems Bjarne's position but my point was that you where adding confusion to the problem and not making it clearer.

Generalized form might not be the best starting point for clearing confusions. Special simplified cases where you can replace tensors with simple specific transformations might be better.

zonde

It is a good idea to check your beliefs against observations in real world.
So it might be good to check out about Shapiro delay

Bjarne

I agree gravitational time delay is real.

PAllen

Doppler may not have been the best word choice. I meant gravitational blue shift (sloppily, I sometimes use doppler for all kinds of frequency shift). All distant objects will appear slightly more blue shifted to the observer closer to the sun.

PAllen

Actually, along with gravitational time dilation, there is also gravitational length contraction. According to the 'further from sun' observer, the closer observer's rulers are slightly short, rather than long.

Be that as it may, there is straightforward way the two can observers agree on their speed relative to the milky way center. Suppose each adopts as their distance standard (converting other ways of measuring distance to far away object to match this standard) c times light round trip time to object as they measure it. Then the closer to sun observer thinks the MW center is closer (less time for the round trip). They then figure a smaller circumference for the orbit. They divide the smaller circumference by the shorter time, and come up with the same speed as the 'further from sun' observer.

PAllen

In GR, C is not accelerating at all. C is the inertial observer. A and B are accelerating at slightly different rates, as seen by C, their distance is shrinking over time (per C), they have a relative speed (per C). These are facts computable in special relativity alone (treating C as inertial, as required, and treating A and B as accelerating so as to keep distance constant per A. You can read all about this under the Bell spaceship 'paradox'. That A and B are the non-inertial observers is an objective, invariant fact - they experience a force that can be measured by an accelerometer, locally. C feels no force, therefore is inertial.

This concretely explains the idea that, within GR, there is no objective meaning to an SR effect versus a GR effect. Almost always, you can validly treat some effect as different mix of SR vs. gravitation effect by choosing different observers or coordinates.

There is yet another way to choose to treat gravitational time dilation as kinematic rather than gravitational (involving parallel transport of 4-vectors). However, I don't think you have the background for that.

zonde

Shapiro delay does not measure time delay. It measures changes in coordinate speed of light.
To make some statements about time delay in context of Shapiro delay you have to make some assumption about distance measurements. And this assumption is that distances stay the same. When you assume this then Shapiro delay agrees with expected time delay.

Or looking at this from another side. From Shapiro delay we find out that coordinate speed of light is different at different gravitational potentials.
Now if local speed standard (c) is different for two observers then speed measurements for the same (global) physical situation should be different for two observers. Just like it is with time.

You can try to make prediction for coordinate speed of light using your Option 2 (B's meter stick is longer and therefore distances shorter). What it will be?

Bjarne

Gravitionel blue shift yes, but it has nothing with speed to do.

[QUOTE=PAllen;3548070]Actually, along with gravitational time dilation, there is also gravitational length contraction. According to the 'further from sun' observer, the closer observer's rulers are slightly short, rather than long.

I can only understand it like that; if time is ticking slower, the meter stick must be proportional longer (for B) and distances hence seen from the perspective of B – shorter. But seen from a “outsider” distances is the same. Remember both observers complete the “same distance” seen from the perspective of observer C.

Right but keep in mind that reality by your feet is not the same as by your head.
The meter stick cannot be the same comparable lenght both places, - can it ?

Notice C is the third observer “invented” by DrGreg ( it is not “c” )
http://www.physicsforums.com/showpos...4&postcount=64
C is; “a third observer who is falling freely directly towards the Sun”. Off course C is then accelerating, due to acceleration due to gravity.

As I see it and hopefully any other observer in the Universe, - C is really acceleration towards the Sun.
A and B is not affected due to the fact that C can have the illusion that it is A and B that is moving opposite.
I don’t understand the point.
C’s reality and the illusion that A and B is moving opposite, is not real for anyone else than C.
Why make a big point out of what only is an illusion. ?

Good exercise.
Let us now say that B’s clock tick half so fast like A’s (for simplicity reasons) - (still according to the example above) .
A and B would send a light beam to the same planet .
The light beam would reflect and return.
After the exact same period of time (seen by any external third observer “EX”) the light beam would return to both A and B.
Observer A would now say it took 1 (earth)-year, (31536000 s.)
But B would say it took half so much time.

Seen from observer EX perspective the distance the light was travelling to A and B is the exactly same.

The ONLY way both A and B can agree that the light was travelling with the “same” speed, is when B’s meter-stick is comparable double so long as A’s meterstick.
So simple is that.

This mean that speed is really “c” (300,000 km/h) seen from both the perspective of observer A , as well as from B’s reality.

BUT when you would compare the speed it would be a different history.

The only solution to that (as I can see) is that we cannot mix realities, but are forces to separate these.

And as I wrote this must mean a different comparable meter stick – that’s all, and the only simple mathematical solution.

Why not keep things simple, when they are simple?

zonde

Yes, that's correct.

The only problem is that if we would make prediction for Shapiro time delay it would be zero because coordinate speed of light does not change in your case.
And yet we observe slowing down of coordinate speed of light when signal passes gravitating object at close distance. So your model does not agree with observations.

So what we do next?

Bjarne

Right
Now we assume the meter stick always is comparable the exact same for both A and B.
Observer A and B will now in a certain period measure a photon traveling a certain distance (300,000 km).
Both observers agrees that this is what really happen.

Based on this observer A would say that the speed of light is exactly 300,000 km in one (of his) second.

But observer B would say OK I agree the distance the photon was travelling is 300,000 km ...
BUT I do not agree it took one second, - my clock shows it only took ½ second, so here the speed of light is 600,00km/s
Do you prefer that solution?
Hmmm… So what we do next?

I have never heard about Shapiro time delay. If it really is certain and confirmed knowledge, and not something only at a test level, - yes we have a one more problem/challenge..

Hmmm speculate, but not too loud, suggestion could be wrong, and we would look stupid.
What do you think the answer is (except that distances / the meter stick always are comparable the same lenght) ?