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


by Bjarne
Tags: frames, laws, nature, reference
Bjarne
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Oct8-11, 02:43 PM
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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
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Oct8-11, 03:17 PM
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Quote Quote by Bjarne View Post
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
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Oct9-11, 02:28 AM
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Quote Quote by PAllen View Post
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
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Oct9-11, 03:19 AM
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Quote Quote by PAllen View Post
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.

Quote Quote by PAllen View Post
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.

Quote Quote by PAllen View Post
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
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Oct9-11, 05:44 AM
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Quote Quote by Bjarne View Post
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 dont 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 Shapiro delay
Bjarne
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Oct9-11, 06:11 AM
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Quote Quote by zonde View Post
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
I agree gravitational time delay is real.
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Oct9-11, 08:04 AM
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Quote Quote by Bjarne View Post
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.
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Oct9-11, 08:12 AM
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Quote Quote by Bjarne View Post
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.
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Oct9-11, 10:55 AM
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Quote Quote by Bjarne View Post
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 cant 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
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Oct10-11, 03:23 AM
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Quote Quote by Bjarne View Post
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
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Oct10-11, 05:04 AM
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Quote Quote by PAllen View Post
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.

[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.

Quote Quote by PAllen View Post
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 lenght both places, - can it ?

Quote Quote by PAllen View Post
In GR, C is not accelerating at all.
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.

Quote Quote by PAllen View Post
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. ?

Quote Quote by zonde View Post
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 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
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Oct10-11, 07:18 AM
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Quote Quote by Bjarne View Post
Good exercise.
Let us now say that Bs clock tick half so fast like As (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 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 Bs meter-stick is comparable double so long as As 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
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Oct10-11, 12:46 PM
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Quote Quote by zonde View Post
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 travelling is 300,000 km ...
BUT I do not agree it took one second, - my clock shows it only took 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
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Oct10-11, 12:55 PM
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Quote Quote by Bjarne View Post
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).
Quote Quote by Bjarne View Post
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).
Quote Quote by Bjarne View Post
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 ?
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.
Quote Quote by Bjarne View Post

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. ?
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
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Oct11-11, 01:23 AM
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Quote Quote by Bjarne View Post
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 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.

Quote Quote by Bjarne View Post
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 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."

Quote Quote by Bjarne View Post
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
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Oct11-11, 06:28 PM
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Quote Quote by Bjarne View Post
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 ?
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.
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Quote Quote by PAllen View Post
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.
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Quote Quote by Passionflower View Post
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/H...el/GenRel.html

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


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