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

[zonde]

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.

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]

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?

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]

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.

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]

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.

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

This simply follows from direct interpretation of Doppler - they will be slightly more blue shifted.

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

This is consistent with the slower time, obviously.

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.

Measurements by other methods would be expected to generally agree, but not necessarily be exactly the same.

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]

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).

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.

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.

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.

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.

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]

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).

It is a good idea to check your beliefs against observations in real world.
So it might be good to check out about http://en.wikipedia.org/wiki/Shapiro_delay"

 

[Bjarne]

It is a good idea to check your beliefs against observations in real world.
So it might be good to check out about http://en.wikipedia.org/wiki/Shapiro_delay"

I agree gravitational time delay is real.

 

[PAllen]

No



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

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]

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

.

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]

We will call the third observer C.

When C is falling towards the sun and first passing A and next B he would off course accelerate faster (due to acceleration of the Sun) when passing B as he would when passing A.

So for C it would look like B is moving faster away from C than A.

But in fact C is moving relative to A and B, - and not A and B relative to C.

I mean any other observer as C (on the Earth or other places in the Universe) would not see that A or B is moving away from the sun, (or away from each other) but only that C is moving towards the sun.



I can’t see there really is "relative motion" between A and B ?

How can the reality (an illusion) of the third observer C have anything to do with the time-rate for A and B ?

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]

I agree gravitational time delay is real.

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]

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.

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

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.

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.

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.

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 length both places, - can it ?

In GR, C is not accelerating at all.

Notice C is the third observer “invented” by DrGreg ( it is not “c” )
https://www.physicsforums.com/showpost.php?p=3543384&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.

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.

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. ?

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?

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 traveling to A and B is the exactly same.

The ONLY way both A and B can agree that the light was traveling 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]

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 double so much time.

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

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

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]

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.

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 traveling 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?

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.

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..

So what we do next?

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) ?

 

[PAllen]

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

The context was, suppose you don't know you're in a gravitational field, or what consequences that would have. What laws do you apply to your observations? If you apply either pure SR or Galilean physics (even accounting that you know you are accelerating), you would conclude different relative velocity for distant objects than you would if you were not subject to gravity (or subject to less gravity).

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.

You claim to accept gravitation time dilation, per se. The same derivations that lead to it, also lead to gravitational length contraction. The thing that allows all of it to be consistent is that the observer that sees your clock slow and your rulers short also sees light going slower for you. When you put in the actual numbers, this observer 'understands' why you still measure the same value for light speed. (this comment was unrelated to observer C. It was in reference to how the 'outer' of A and B would view the inner. Observer C would be more complex, because they have relative motion to account for).

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 length both places, - can it ?

The point is ultimately related to the fact that only for inertial observers in flat spacetime do you have the nice property that any 'reasonable' way of doing measurements comes out the same. For inertial observers in flat spacetime, radar ranging, parallax distance, luminosity distance, etc. all yield an equivalent distance scale. For either curved spacetime or non-inertial observers (even in flat spacetime), they disagree with each other. You can choose which to favor, getting different answers for where your results are 'unexpected'. My example shows, if you choose to favor radar ranging, you get shorter distances to remote objects, but the same speeds (well, there would be higher order differences, but let's not worry about that) for A and B.

There truly is no unique, preferred answer to large distances in GR (short of choosing a preferred global coordinate system). Actually, there isn't in SR either - distances are observer dependent.

Notice C is the third observer “invented” by DrGreg ( it is not “c” )
https://www.physicsforums.com/showpost.php?p=3543384&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. ?

You are simply wrong here. In GR, all observers agree C is the inertial observer and A and B are the non-inertial observers. ('Accelerating', on the other hand, has very little relevance in GR if it is referring to coordinate acceleration, as you are; proper acceleration, computed in any coordinates, by any observer, says A and B are accelerating and C is not accelerting). On this, there is no 'relativity'. What is describe here is not an illusion at all, but the essence of relativity (note that C sees the distance between A and B shrinking over time; not sure you got that). The point (initially by Dr. Greg) is that the how much of an effect is related to gravity or SR effects is observer dependent. This is fundamental in GR, not an illusion to be ignored. And, in particular, for C, difference between A and B would be primarily the same effect as the SR bell spaceship 'paradox'.

 

[zonde]

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 traveling 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?

This is different from how Shapiro experiment was performed.
There is only one observer who is sending radar signals so that sometimes they are passing close to the Sun and sometimes far from the Sun. When you make a correction for time delay depending on signal's closest passing distance from the Sun you can consistently describe orbit of observed object (Venus).
In your case speed of light is always the same because proportion "m/s" does not change.

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..

From Wikipedia about http://en.wikipedia.org/wiki/Shapiro_delay" :
"The time delay effect was first noticed in 1964, by Irwin I. Shapiro. Shapiro proposed an observational test of his prediction: bounce radar beams off the surface of Venus and Mercury, and measure the round trip travel time. When the Earth, Sun, and Venus are most favorably aligned, Shapiro showed that the expected time delay, due to the presence of the Sun, of a radar signal traveling from the Earth to Venus and back, would be about 200 microseconds,[1] well within the limitations of 1960s era technology.

The first tests, performed in 1966 and 1967 using the MIT Haystack radar antenna, were successful, matching the predicted amount of time delay.[2] The experiments have been repeated many times since then, with increasing accuracy."

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) ?

First of all speed of light globally is not the same everywhere.
Statement that "laws of physics are the same in all inertial reference frames" means that local experiments will give the same results. But global observations can be different.

 

[PAllen]

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 length both places, - can it ?

I realize I didn't directly answer this question. In theory, a meter stick by your feet would be slight shorter than one by your head (not longer as you have argued several times). Light would be slower at your feet compared to your head. Clocks would be slower at your feet than your head. The only one of these that has been experimentally verified is the clocks, because they have reached the precision to detect differences over 6 feet in the Earth's field. The others will not be observable in the foreseeable future (of course, unforeseeable future could be only a few years away; never know when there is a breakthrough).

None of this is relates at all to the issue I was presenting (measuring distance over tens of thousands of light years using radar ranging distance as your definition, with other measuring methods calibrated to match). Especially because your own scenario had these measurements being done from lab held stationary (by thrust) with respect to the sun. Also, of course, there are no astronomic measurement that could be made at a precision where it mattered whether they were done at your head or your feet.

 

[Passionflower]

In theory, a meter stick by your feet would be slight shorter than one by your head (not longer as you have argued several times).

Your claim that meter sticks are shorter closer to the EH, could you back it up with some math or at least a reference? And shorter tangentially or radially, or perhaps both?

What I can show you mathematically is that both the volume and radial distance between two shells is more than we would suspect if we would calculate it based on their areas. And the discrepancy increases for lower r-values closer to the EH.

 

[PAllen]

Your claim that meter sticks are shorter closer to the EH, could you back it up with some math or at least a reference? And shorter tangentially or radially, or perhaps both?

What I can show you mathematically is that both the volume and radial distance between two shells is more than we would suspect if we would calculate it based on their areas. And the discrepancy increases for lower r-values closer to the EH.

Ah, but if delta r represents distance as perceived by an observer at infinity, and a local, stationary observer computes a proper distance (with their t=0 simultaneity) of something greater, that implies the local rulers look short to the observer at infinity (in the radial direction).

I've only seen this contraction discussed radially. Two references validating its existence (but not deriving it) are (search for contraction on of these pages):

http://www.upscale.utoronto.ca/PVB/Harrison/GenRel/GenRel.html

http://www.mathpages.com/rr/s6-01/6-01.htm

 

[Passionflower]

Ah, but if delta r represents distance as perceived by an observer at infinity

1. How do you conclude that delta r is distance as perceived by an observer at infinity.
2. If so, how do you conclude that the observer at infinity has the ultimate saying about what the real length is?

r simply represents the, so called, reduced circumference and directly relates to the circumference and area of resp. a circle and sphere.

Are you perhaps saying that the increase in radius and volume between shells of lower r-values over the expected Euclidean values is not due to the fact that space is no longer Euclidean but due to the fact that rulers shrink?

, and a local, stationary observer computes a proper distance (with their t=0 simultaneity) of something greater, that implies the local rulers look short to the observer at infinity (in the radial direction).

What kind of computation did you have in mind?

wrt the first reference, I am sorry I must be slow but I do not see where it states anything that is relevant to what you said, could you tell me exactly what you think shows the reference that rulers shrink.

wrt to the second reference I am also at a loss, where exactly is this pointed out that rulers shrink?

 

[PAllen]

1. How do you conclude that delta r is distance as perceived by an observer at infinity.
2. If so, how do you conclude that the observer at infinity has the ultimate saying about what the real length is?

r simply represents the, so called, reduced circumference and directly relates to the circumference and area of resp. a circle and sphere.

Are you perhaps saying that the increase in radius and volume between shells of lower r-values over the expected Euclidean values is not due to the fact that space is no longer Euclidean but due to the fact that rulers shrink?What kind of computation did you have in mind?

wrt the first reference, I am sorry I must be slow but I do not see where it states anything that is relevant to what you said, could you tell me exactly what you think shows the reference that rulers shrink.

wrt to the second reference I am also at a loss, where exactly is this pointed out that rulers shrink?

With regard to the first reference, the following is said:

"Gravitational Length Contraction

Lengths of objects in gravitational fields are contracted according to the theory. The prediction has never been tested. For the keen, you may wish to derive this prediction using the same techniques used in the previous sub-section to derive gravitational time dilation. "

With regard to the second reference, there is the following:

"The factor of 2 relative to the equation of 1911 arises because in the full theory there is gravitational length contraction as well as time dilation. Of course, the length contraction doesn’t affect the gravitational redshift, which is purely a function of the time dilation, so the redshift prediction of 1911 remains valid"

Here is another discussion, but it is not at all rigorous:

http://www.relativity.li/en/epstein2/read/g0_en/g4_en/

"The smaller r is, the longer a segment in the radial direction will be when measured with local yardsticks. As seen from OFF: yardsticks shorten in the radial direction with increasing strength of the gravitational field! Thus, for the thickness of a spherical shell around M, a local surveyor determines a larger value than an observer in OFF. "

[EDIT: found better discussion of this:

http://www.mathpages.com/rr/s7-03/7-03.htm ]

 

[Bjarne]

First of all speed of light globally is not the same everywhere.
Statement that "laws of physics are the same in all inertial reference frames" means that local experiments will give the same results. But global observations can be different.

I guess the different speed of light happens doesn’t matter whether the length of the rulers always is comparable the same or not.

 

[Bjarne]

With regard to the first reference, the following is said:

"Gravitational Length Contraction

Lengths of objects in gravitational fields are contracted according to the theory.

Right
I agree (and "disagree").
Notice Observer “Ex” (external) will not see any length contraction.
Seen from the perspective of "Ex" the distance of the Milkyway would be the same for both A and B.

B is deeper inside the gravitionel field of the Sun. He will complete 1 orbit in less time as A.

If B shall have the right to claim that the orbit of the MW is shorter (length contraction), it is only possible if B’s ruler is comparable longer than A’s.

Do you understand that point? – It seems like a contradiction but it is not, but rather a mathematical necessity that B’s meter stick must be longer than A’s.
(You must also respect the mathematical reality of observer Ex, - Observer Ex must also have the possibility to understand other realities - relative to his own )


B and A’s perception of speed can also not possible be the same, simply because B’s clock is ticking slower.

We should not be allowed to mix realities, hence also not to force our (A’s) perception of speed into B’s reality.

So since B’s time-rate is ticking slower, - that alone should mean that B moves FASTER than A, - but because B’s ruler (seen from a mathematical point of view) must be longer the speed is the “same” – but not comparable the same.

Notice A and B will agree to complete the orbit of the MW in the exact same period, but they can impossible agree about distance / circumstance / time / rulers.

I appreciate your contribution to the thread and I understand most of what you have explained, but still I wish there was a simpler way to understand and compare how B's reality really is, as well as understand how would B’s ruler would be compared to A’s.

I think there still is more to discover to make that simpler, straight and logical.

 

[zonde]

I guess the different speed of light happens doesn’t matter whether the length of the rulers always is comparable the same or not.

It matters. Length of rulers is related to local speed of light and local rate of clocks.

 

[A.T.]

Are you perhaps saying that the increase in radius and volume between shells of lower r-values over the expected Euclidean values is not due to the fact that space is no longer Euclidean but due to the fact that rulers shrink?

I think these are just two different ways to say the same thing:

- The space in not Euclidean, so rulers measure more radius than expected based on the circumference, so the rulers appear to be shrunk when compared to identical rulers placed around the circumference.

This is equivalent to:

- The space-time in not Euclidean, so clocks measure less time than expected, so the clocks appear to be slowed down when compared to identical clocks placed around the circumference.

 

[PAllen]

Right
I agree (and "disagree").
Notice Observer “Ex” (external) will not see any length contraction.
Seen from the perspective of "Ex" the distance of the Milkyway would be the same for both A and B.

Correct, some observer floating away from the milkyway would see these distances the same.

B is deeper inside the gravitionel field of the Sun. He will complete 1 orbit in less time as A.

If B shall have the right to claim that the orbit of the MW is shorter (length contraction), it is only possible if B’s ruler is comparable longer than A’s.

Do you understand that point? – It seems like a contradiction but it is not, but rather a mathematical necessity that B’s meter stick must be longer than A’s.
(You must also respect the mathematical reality of observer Ex, - Observer Ex must also have the possibility to understand other realities - relative to his own )

Here, you have confused several things. The length contraction I described had to do with local rulers as perceived by a distant observer. However, I never proposed a way to use local ruler measure for astronomic distances (it is possible, building a ladder of distances).

Totally independent of the issue of local rulers perceived from a distant free fall observer, I proposed a different, simple convention for astronomic distances (radar ranging, using local time, and assumption speed of light is isotropically c. It is only using this convention (rather than local rulers) that you end up with shorter distances to distant objects, and thus the same speed measured by A and B.

Note that whatever definitions are used, some measurements by A and B will differ (assuming each uses the same definitions). This is not unexpected or inconsistent with invariance of laws of physics.

Let's state what is really claimed by different relativity principles:

1) Galilean relativity: All laws take the same, simplest, form in any inertial frame. Note, this never meant that measurements are the same, only laws (equations) relating measurments. The main thing wrong with this was that its law for velocity transformation between inertial observers turned out to be experimentally incorrect. Between observers with relative acceleration, there is no simple relativity, and laws take more complex form.

2) Special relativity: Same principle as above, except the transformation law between different frames is different and consistent with experiment. In particular, there is no 'relativity' between observers undergoing relative acceleration.

3) General relativity gives you both less and more. The laws of special relativity only apply locally, for inertial observers, defined as those in free fall. There is no unique answer at all to such things as long distances or velocity of a distant object (whether for inertial observers or non-inertial observers). Instead there are only useful conventions you may choose, and procedures for making valid physical predictions based on whatever conventions you choose. There is a general formulation of laws such that whatever conventions are used by any observer, the laws in this form apply (but measurements are not the same). However, the same conventionality of coordinates means, in practice, you use transformation rules to convert your measurements to the most convenient coordinates for calculation.

Based on (3), your A and B observes each know they are non-inertial; they know the magnitude of their acceleration. Seeing the sun, and making measurements, they can determine the quali-local structure of spacetime. What each does, in practice, is convert their local measurements, using the predictions of GR to accomplish this, to milkyway center coordinates (each able to determine a different required clock adjustment, for example). They compute distances, speeds, etc. in this frame. Each one doing this ends up with the same predictions and values. This is all that is expected, and found to be true.

B and A’s perception of speed can also not possible be the same, simply because B’s clock is ticking slower.

You cannot make such a blanket statement. It depends on measurement conventions. I have shown that there exists a simple convention that has the property that A and B differ on distances and times such that speeds of distant objects come out essentially identical. Other equally valid measurement conventions will lead to different results. However, GR provides the precise rules allowing A and B to make the same physical predictions whatever consistent conventions they use, and compare results, as long as each knows the other's conventions. The requirement on consistency here are very broad (one-one mapping of spacetime, continuity conditions, etc.).

We should not be allowed to mix realities, hence also not to force our (A’s) perception of speed into B’s reality.

There is really one reality in GR - the spacetime manifold. There are many ways to label events in it, and many different physical processes for taking measurements, that can be used at different places, times, instrument speed etc. GR allows any of these to be used to probe the underlying reality. However, the underlying reality does not include statements such as a unique valid distance between distant objects, nor a unique valid relative speed between distant objects.

So since B’s time-rate is ticking slower, - that alone should mean that B moves FASTER than A, - but because B’s ruler (seen from a mathematical point of view) must be longer the speed is the “same” – but not comparable the same.

Notice A and B will agree to complete the orbit of the MW in the exact same period, but they can impossible agree about distance / circumstance / time / rulers.

That all depends on how they take and interpret measurements. Using raw local measurements, some of these must disagree (but not necessarily all of them, and many choices about which differ). However, if each converts their measurements to an agreed common coordinate convention, using the predictions of GR, they will agree on everything.

I appreciate your contribution to the thread and I understand most of what you have explained, but still I wish there was a simpler way to understand and compare how B's reality really is, as well as understand how would B’s ruler would be compared to A’s.

I think there still is more to discover to make that simpler, straight and logical.

 

[Bjarne]

Here, you have confused several things. The length contraction I described had to do with local rulers as perceived by a distant observer.

My point is imaging you could jump between A and B’s reality, which difference would there be , except time ?

Well I have come to a new simpler conclusion.
When I would jump from A’s to B’s reality, I would see the exact same Universe.
The distance between the Earth and the Moon, or any other distance would be exact the same everywhere.

But if we compare these 2 realities, - B’s reality would be a bit smaller. - Everything would be a bit smaller, also the ruler.
That could then also explain the cause of the Shapiro delay http://en.wikipedia.org/wiki/Shapiro_delay
Because speed of light must then be measured in the local surroundings.

Edit
No
I change my mind
This can't be true because then there would be no Shapiro delay, but rather opposite

PS
Any idea what is causing the Shapiro delay ?

 

[Bjarne]

Let's say the International Space station (ISS) was orbiting the Sun in the exact same orbit as the Earth.

A clock on board the ISS and the Earth would now tick different due to different gravity.

This mean that the laws of orbit gravity can't be the same these 2 places, simply because the time consumption to complete one orbit for both objects, - is larger for the ISS

So what is wrong?

I mean the law of nature must be the same everywhere, or ?

Is the answer that; - the length of one second not is the same both places , - or in other words that one second is "stretching" on board the Earth (compared to one second on board the ISS) and therefore longer compared to one second at the ISS ?

I mean the time to complete one orbit must be the same on board at both objects, but a clock on board the 2 objects would not show this.

There must be a simple way, basic to explain which factor(s) is (are) changing

 

[ghwellsjr]

Let's say the International Space station (ISS) was orbiting the Sun in the exact same orbit as the Earth.

A clock on board the ISS and the Earth would now tick different due to different gravity.

This mean that the laws of orbit gravity can't be the same these 2 places, simply because the time consumption to complete one orbit for both objects, - is larger for the ISS

So what is wrong?

I mean the law of nature must be the same everywhere, or ?

Is the answer that; - the length of one second not is the same both places , - or in other words that one second is "stretching" on board the Earth (compared to one second on board the ISS) and therefore longer compared to one second at the ISS ?

I mean the time to complete one orbit must be the same on board at both objects, but a clock on board the 2 objects would not show this.

There must be a simple way, basic to explain which factor(s) is (are) changing

You don't have to use the example of the ISS in the same orbit as Earth but far removed to make your point. You can use the simple fact that atomic clocks near sea level at Greenwich tick at a different rate than identical atomic clocks at Boulder Colorado at an elevation of one mile. They would each say that the orbit of Earth around the sun takes a different amount of time based on their own coordinate system.

But what is important is that they both measure the same value for the speed of light and in order to do that, they must use the time from their local clock, not some other time such as from GPS which gives the same time for every point on earth.

 

[Dale]

A clock on board the ISS and the Earth would now tick different due to different gravity.

Yes.

This mean that the laws of orbit gravity can't be the same these 2 places, simply because the time consumption to complete one orbit for both objects, - is larger for the ISS

How do you get from the above correct statement to this incorrect conclusion? The law of physics which pertains to this situation is GR. What makes you think that GR states that both clocks should measure the same time?

 

[Bjarne]

You don't have to use the example of the ISS in the same orbit as Earth but far removed to make your point. You can use the simple fact that atomic clocks near sea level at Greenwich tick at a different rate than identical atomic clocks at Boulder Colorado at an elevation of one mile. They would each say that the orbit of Earth around the sun takes a different amount of time based on their own coordinate system.

Correct
But the example of the ISS and the Earth orbiting the exact same orbit is at least for me easier to handle, because both such observers (these places) must be right, which mean the time one orbit takes can't be the same.

Hence there is a problem since the gravity-orbit-equations a ISS inhabitant and a Earth inhabitant will use, - will not give the same result.
For exsample to determinate their speed or orbit size.

So whos calculation will be wrong?
The Earth observer or the ISS observer?

Option 1 is the definition of 1 second cannot be universal.
Option 2, - this is what wrote about above, ( but now I have change my mind) and believe option 1 must be correct.

You don't have to use the example of the ISS in the same orbit as Earth but far removed to make your point. You can use the simple fact that atomic clocks near sea level at Greenwich tick at a different rate than identical atomic clocks at Boulder Colorado at an elevation of one mile. They would each say that the orbit of Earth around the sun takes a different amount of time based on their own coordinate system..

It is the same kind of problem, 2 observers (on the Earth), -one living in a cellar and another one in a skyscraper, - both would not be able to agree how long time it takes the light (e.g; from the sun) to reach a certain point of the earth.
So what is wrong, - which simple factor(s) must be flexible?

Is it the definition of how long 1 second is from place to place, - or is it distances or/and speed that not are the same in such 2 observer realities. ?

As I wrote I believe it is “one second” that cannot have a universal definition.
If that should be wrong WHAT is hen the correct answer?

The answer must as I see it be simple, logical and understandable - since we are discussion simple math, >> time multiplied with speed must = distance ( and not for exsample distances)

 

[Bjarne]

How do you get from the above correct statement to this incorrect conclusion? The law of physics which pertains to this situation is GR. What makes you think that GR states that both clocks should measure the same time?

Because ………….
Let say one (atomic) clock is on board at the ISS and another on board of the Earth, both objects orbit the Sun in the exact same orbit.

Let’s say the clock on board the ISS ticks double so fast compared to a clock at the Earth (due to different gravity)
And exactly this is the problem, - because time is different these 2 places.

Hence many laws / equations cannot give the same result.
1 orbit of the Sun cannot at the same time be both 500 million km and also 250 million km.
This should be pretty simple, at least so long time multiplied with speed must = distance.
Due to time is not the same even in the same orbit, we have such principle problem (just not so exaggerated as the example shows,).

This means that either equation-constants, distances and/or speed, - or the definition of 1 second cannot be the same in different space-time realities.
Does the stable nailed definition of one second mean that we are mixing ingredients of different space-time realities?
As I see the difination of "one-second" cannot be universal, and if it really should be how can we know it is so?

It seems that “our definition” of 1 second simple cannot be used in other space-time realities..
I know this will confuse you, - but the point is that yes a process in a different space time reality can be either faster or slower as here at the planet.

How can equation and laws of gravity be exactly the same everywhere, something must give and take. Why doesn’t it seem to be answer to these questions?

Shortly spoken, let say 1 second is the same length everywhere, - but the process responsible for the definition of 1 second is not the same. Is that possible?

 

[Dale]

Hence there is a problem since the gravity-orbit-equations a ISS inhabitant and a Earth inhabitant will use, - will not give the same result.
For exsample to determinate their speed or orbit size.

So whos calculation will be wrong?
The Earth observer or the ISS observer?

Why should either one be wrong? If the ISS and the Earth observers both use GR then the ISS observer can calculate what both he and the Earth observer can measure, and likewise with the Earth observer. Then they can each perform the measurements and see if they agree with the predictions. If they each do the math correctly then the ISS observer can calculate what the Earth observer will measure and vice versa. Assuming they mach with the observations, then in what way is anyone wrong?

 

[Dale]

Hence many laws / equations cannot give the same result.

Please be specific. The relevant law is GR, so what is the specific difference between the Earth GR and the ISS GR? In what way is GR at all modified between the two frames?

Simply because two different observers measure something different does not mean that the law governing the measurement is different. For example, due to Doppler shift two different observers will measure different frequencies for a given light source, but that by itself does not imply that Maxwell's equations are different.