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

by Bjarne
Tags: frames, laws, nature, reference
P: 344
 Quote by darkhorror It IS with respect to something that is one of the basic parts of relativity. To say you are moving at a certain km/s without saying anything else is meaning less. You are saying we are moving at 250 km/s with respect to the center of the MW. This also means the center of the MW is moving at 250km/s with respect to earth. So are you trying to get the results from a frame of reference that is at the center of the MW galaxy?
I have not invented how to calculate the orbit speed of the MW
So how was it done then ?
P: 344
 Quote by zaybu Relativity is a difficult subject. Even simple cases are difficult to tackle. I would suggest that before looking at complex situations, you start looking at simple cases to begin with. Here are two simple cases: 1) Twin paradox. See: http://soi.blogspot.com/2011/09/twin-paradox.html 2) Faster than light violates causality. See http://soi.blogspot.com/2011/09/why-...causality.html

That confusion is not necessary.
General relativity alone is enough.
Don’t make it more complicated as it is.
PF Gold
P: 5,059
 Quote by Bjarne Both the example in the link is about Special relativity. That confusion is not necessary. General relativity alone is enough. Don’t make it more complicated as it is.
General relativity is more complex that special relativity; further all of special relativity is contained in general relativity. Treating GR separately from SR is impossible.
P: 344
 Quote by PAllen General relativity is more complex that special relativity; further all of special relativity is contained in general relativity. Treating GR separately from SR is impossible.
The point is; according to the example (above) the 2 clocks moves with the relative same speed, and is therefore in the same SR-reference frame. (but not same GR-reference frame) Which mean SR is not affecting the 2 clocks, only GR does.
PF Gold
P: 1,376
 Quote by Bjarne First at all I want to say that we can simplify the scenario even more, to avoid confusion. Because we could say that the 2 clocks are following the Sun’s orbit around the Milkyway. (Technical we could say the orbiting clocks have devices (small rockets) on board to counteract the gravity from the Sun. Seen from our perspective both the Sun and the two clocks (all 3 objects) are therefore orbiting the Milkyway in the excact same radius to the center of the Milkyway) . The one clock is 50 billion km. behind the Sun, and the other 150 billion km. This should eliminate he last confusion according to the Special relativity influence, since all relative speed now are the same. Back to yours suggestion; As I understand you now I can only understand it like that speed not is comparable “the same” – which then also mean that also comparable distances not can be the same, - right?
Wrong, distances are the same.
Only clocks tick at different rate. Measuring rods are of the same length.

 Quote by Bjarne I think we have a serious mathematical problem here and wonder how such a simple obviously unsolved mystery possible can have existed the last 100 years without any explanation. ? I mean the math should be simple. We know the 2 relative time rates and I believe we also know the speed, - the logical result (so far I can understand it) hence should be that B impossible can travels the same distance, simple because speed multiplied with time = distance. I mean how difficult can that really be ?
PF Gold
P: 5,059
 Quote by Bjarne The point is; according to the example (above) the 2 clocks moves with the relative same speed, and is therefore in the same SR-reference frame. (but not same GR-reference frame) Which mean SR is not affecting the 2 clocks, only GR does.
In GR, there is really no such thing as a global inertial frame of reference. You are actually trying to selectively use SR for one purpose and GR for another. Specifically, in a situation where you can detect time difference due to gravity, and where inertial paths in spacetime are observed over a whole spiral (that's how an orbit looks in spacetime), you really can't model this in terms of a global inertial frame centered on an orbiting body. Further, to maintain the paths you describe, none of your bodies (except the sun) are following inertial paths.

Next, you should be aware that for both SR and GR it is wrong believe there is equivalence between inertial and non-inertial frames, or between two non-inertial frames (which is what you really have). Acceleration (deviation from inertial path) is an invariant feature, not a relative feature (it is characterized by proper acceleration).

In a nutshell, every aspect of your scenario is ill conceived. The only thing you can actually expect from your scenario is that if all laws are expressed in their general tensor form, then each observer can build a coordinate system in which they are at rest, and use said coordinate system and laws in tensor form to make valid physical predictions.
P: 140
 Quote by Bjarne I have not invented how to calculate the orbit speed of the MW So how was it done then ?
Observations and calculations.

How it was measured has no bearing on what I was talking about.

I am trying to figure out what you mean to say or what you are thinking. Here are a couple questions for you.

Does it matter what frame of reference you are talking about when you say earth is moving at 250km/s? Or are we simply moving at that velocity no matter what frame of reference we take?
P: 344
 Quote by darkhorror Observations and calculations. How it was measured has no bearing on what I was talking about.
So how would A and B measure the distance of the Milky way ?
We can say A is you and B have a slower ticking clock, due to gravity, we could say that A live in a skyscraper, and B in a cellar etc. Or we can use the example above.

 I am trying to figure out what you mean to say or what you are thinking. Here are a couple questions for you. Does it matter what frame of reference you are talking about when you say earth is moving at 250km/s? Or are we simply moving at that velocity no matter what frame of reference we take?
The orbit speed round the Milkyway is the same for both observes (A and B).
Hence it doesn’t matter
P: 344
 Quote by PAllen In GR, there is really no such thing as a global inertial frame of reference.
I have heard that before, but it is irrelevant according to the example, since this is not what the example conclude. All questions are open. So far there are no mathematical / logical explanations.

 You are actually trying to selectively use SR for one purpose and GR for another.
No, - I am only distinguishing between the cause of time-difference between the 2 observers, and whether the cause is SR or GR.

The scenarios I have shown SR do not apply since speed of both observers is the same.
Both clocks orbit the MW in the same radius.
The cause of time difference between the 2 observers is in this case is only caused due to gravity (GR) (General Relativity).

 Specifically, in a situation where you can detect time difference due to gravity, and where inertial paths in spacetime are observed over a whole spiral (that's how an orbit looks in spacetime), you really can't model this in terms of a global inertial frame centered on an orbiting body.
I am not suggesting "a global inertial frame" but only asking simple questions.

We can assume that A’s reality is exact the same as ours.
Hence we know everything about A’s reality, as well how A has come to all his conclusions, - for example the circumstance of the Milkyway etc..

But when a clock is ticking slower due to the gravity of the Sun, for another observer (we call that observer B,) - then it is simple calculation that A’s reality cannot be valid for B.

The answer must be that A‘s reality must be exactly so real as B’s, and therefore we also must know how is comparable distances speed etc or B.

For example;
How is speed for B ?
How is comparable speed between A and B ?
What is the distance of the MW-orbit for B ?
How is the comparable distance between of the MW orbit for A and B ?
Is B's meter stick comparable smaller than A's – or longer – or the same length ?
Is a meter stick comparable smaller – or longer – or the same length, at the surface of the Sun compared to 100 billion km away, - du to gravity (GR) ?
seen from B’s reality

 Further to, maintain the paths you describe, none of your bodies (except the sun) are following inertial paths.
I do not understand , above I wrote that we assume these clock's does, we assume these have small rocket engines on board and therefore counteracts the gravity of the Sun, - (but not counteract the time difference). and therefore orbits the MW without getting attracted to the Sun.

Hence 2 clocks orbit the Milkyway exactly as the Sun does.

The difference is that one clock (B) is closer to the sun and therefore ticking slower than the other clock (A).

This certainly , logically and mathematical MUST have SIMPLE consequence(s), since 1 complete orbit round the Milkyway take less time for B as it does for A.

Time multiplied with speed = distance.

There must certainly be “consequences” of time dilation.

There are no reasons to make the simple scenario more difficult or impossible as necessary.

 In a nutshell, every aspect of your scenario is ill conceived.
Then the Universe must also be such ill place, since time really is ticking slower due to gravity and that must have consequences .

“If you can't explain it simply, you don't understand it well enough”.
Albert Einstein
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P: 1,847
Asking for an answer in terms of GR-without-SR is meaningless. No such theory exists. The only theories available are either SR alone (without gravity), or else GR+SR (with gravity).
 Quote by Bjarne The scenarios I have shown SR do not apply since speed of both observers is the same.
This is not something that all observers agree to.

According to each of your two observers, the velocity of the other observer is zero. But according to a third observer who is falling freely directly towards the Sun, the two observers are not a fixed distance apart. According to this third observer, who within GR is an inertial observer (and the other two are not inertial), Lorentz contraction causes their distance to keep changing, i.e. they are not both moving at the same speed according to the third observer. According to this 3rd observer, this relative motion is the cause of the time dilation between the first two observers.
PF Gold
P: 5,059
 Quote by Bjarne No, - I am only distinguishing between the cause of time-difference between the 2 observers, and whether the cause is SR or GR.
This is not possible.
 Quote by Bjarne I am not suggesting "a global inertial frame" but only asking simple questions.
Yes, you are asking about global coordinates but you don't realize it.

You are asking about analyzing the motion of the MW center from A or B point of view. This requires two global coordinate systems. Each of these coordinate systems is built from a non-inertial frame because thrust would be required to hold A and B in position against the Sun's gravity. They are different non-inertial frames because each would require a different amount of thrust.

Further, from A and B point of view the laws to be applied would be determining the elliptical motion of MW center around each of them. For each, this would be a complex application of GR field equations in a rather complex coordinate system. They would still find that their application GR would be successful.

You can pretend the problem is simple only by ignoring its essential features, and misapplying relativity.

Einstein also said: be as simple as possible, but no simpler.
P: 344
 Quote by PAllen Yes, you are asking about global coordinates but you don't realize it. You are asking about analyzing the motion of the MW center from A or B point of view. This requires two global coordinate systems. Each of these coordinate systems is built from a non-inertial frame because thrust would be required to hold A and B in position against the Sun's gravity. They are different non-inertial frames because each would require a different amount of thrust. .

Right, - I remember
We will call the third observer C
The problem that C also cannot agree how "comparable distances" (between A and B) is doesn’t make the problem smaller, does it?
Still we have time rate difference, that must mean 2 (real) and different realities.
The many questions (concerning A and B) mentioned above is still unanswered.
Answering these must be possible also even though SR and GR are "connected"
 Sci Advisor PF Gold P: 5,059 Well, the reality is roughly as follows. We don't have to verify physical predictions in A coordinates and B coordinates would come out the same because this follows purely from mathematical definitions and theorems. However, doing physical computations in these coordinates would be a bummer (the metric tensor would have a very complex form). So, confident of pure math, A and B would each translate their local measurements to a convenient coordinate system (MW central frame, presumably). This translation would be based on relativity. They would have to translate locally measured times, distances, angles, and red/blueshift. Once they translated their local measurements, they would compute in the MW center frame. And no, I have no interest in carrying this out with your numbers. [Addendum: A and B can determine how to transform their local measurements with local measurements plus GR. They measure their proper acceleration with an accelerometer. This along with a bunch of local redshift and other astronomic measurements give enough information. ]
P: 344
 Quote by DrGreg Asking for an answer in terms of GR-without-SR is meaningless. No such theory exists. The only theories available are either SR alone (without gravity), or else GR+SR (with gravity).This is not something that all observers agree to. According to each of your two observers, the velocity of the other observer is zero. But according to a third observer who is falling freely directly towards the Sun, the two observers are not a fixed distance apart. According to this third observer, who within GR is an inertial observer (and the other two are not inertial), Lorentz contraction causes their distance to keep changing, i.e. they are not both moving at the same speed according to the third observer. .

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.

 According to this 3rd observer, this relative motion is the cause of the time dilation between the first two observers
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 ?
PF Gold
P: 1,376
Quote by PAllen
 Quote by Bjarne No, - I am only distinguishing between the cause of time-difference between the 2 observers, and whether the cause is SR or GR.
This is not possible.
It is possible to take gravitational time dilation as experimentally verified physical fact without any reference to SR or GR.

 Quote by PAllen You are asking about analyzing the motion of the MW center from A or B point of view. This requires two global coordinate systems. Each of these coordinate systems is built from a non-inertial frame because thrust would be required to hold A and B in position against the Sun's gravity. They are different non-inertial frames because each would require a different amount of thrust. Further, from A and B point of view the laws to be applied would be determining the elliptical motion of MW center around each of them. For each, this would be a complex application of GR field equations in a rather complex coordinate system. They would still find that their application GR would be successful.
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).

 Quote by PAllen You can pretend the problem is simple only by ignoring its essential features, and misapplying relativity.
Why are you inventing problems that are not there? Are you trying to confuse Bjarne? Why?
PF Gold
P: 5,059
 Quote by zonde It is possible to take gravitational time dilation as experimentally verified physical fact without any reference to SR or GR.
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.
 Quote by zonde 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).
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.
 Quote by zonde Why are you inventing problems that are not there? Are you trying to confuse Bjarne? Why?
No, I am trying to directly address where I think his confusion is leading to incorrect expectations.
PF Gold
P: 1,376
 Quote by 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.
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?