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

[Bjarne]

We don't know the speed. We measure speed i.e we make some observations and then come up with some number.
Two observers will come up with different numbers from their respective observations. Just because these numbers are different doesn't mean that they live in different worlds. It just means that they use different units for their measurements. In particular case it is time unit that is different.

If speed is different for the 2 observers, - classic laws of gravity would not (as I see it) be the same. - I mean how could these?

Or the gravity of the galaxy would not be the same for the 2 observers. That too would sound absurd.

What should possible cause two different speed, or different influence of gravity?

 

[darkhorror]

If speed is different for the 2 observers, - classic laws of gravity would not (as I see it) be the same. - I mean how could these?

Or the gravity of the galaxy would not be the same for the 2 observers. That too would sound absurd.

What should possible cause two different speed, or different influence of gravity?

Lets say we are both on earth. I decide that a foot is 24 inches. You come along and ask for 2 feet of lumber. I cut to me what is 2 feet of lumber. Now to you a foot is 12 inches. You measure the lumber i just cut(with a foot being 12 inches), and you tell me it's too long and that it's 4 feet. I say no it's clearly 2 feet. Is the lumber really 4 feet and 2 feet at the same time? Yes it just depends on which foot measurement you use.

That isn't really a good example but it might help you see the point people are trying to make.

 

[Bjarne]

Lets say we are both on earth. I decide that a foot is 24 inches. You come along and ask for 2 feet of lumber. I cut to me what is 2 feet of lumber. Now to you a foot is 12 inches. You measure the lumber i just cut(with a foot being 12 inches), and you tell me it's too long and that it's 4 feet. I say no it's clearly 2 feet. Is the lumber really 4 feet and 2 feet at the same time? Yes it just depends on which foot measurement you use.

That isn't really a good example but it might help you see the point people are trying to make.

So what you are saying is; if observer A and B would compare their meter sticks, the size must be different and therefore they also measure different distance?

So when time shrink, the meter stick extend?
And this explains that the math is correctm, - for both, - when 1 orbit of the MilkyWay is completed?

 

[JordanL]

Ah, alright. I just went back and reread how this thread began:

Bjarne: The answer is yes, the laws of nature would be found the same in all reference frames. However, the measurements taken of your surroundings, and thus your inputs into your equations, would be different. Because the measurement is different, your receive a different answer for your reference frame. However, because of your different reference frame, you received the right answer for you.

That was actually the point of the idea... that we had spent hundreds of years making equations and laws that only worked for Earth and our reference frame. GR and SR together were a set of rules that would give the right answer even if your measurements turned out different.

 

[Bjarne]

Ah, alright. I just went back and reread how this thread began:

Bjarne: The answer is yes, the laws of nature would be found the same in all reference frames. However, the measurements taken of your surroundings, and thus your inputs into your equations, would be different. Because the measurement is different, your receive a different answer for your reference frame. However, because of your different reference frame, you received the right answer for you.

That was actually the point of the idea... that we had spent hundreds of years making equations and laws that only worked for Earth and our reference frame. GR and SR together were a set of rules that would give the right answer even if your measurements turned out different.

Try to be more exact.
We can very simple multiply speed and time and get the result = distance

Why can a "stranger" living in a different space-time (caused by GR) - according to the mentioned example, not do the exact same as we can ?

Why seems reality to be limit to a certain place on Earth. ?

WHAT exactly should a observer that not shares our time-rate then exactly do if he also want to make such speed * time calculations. ?

How are the rules for him?

Shall he just pretend he is moving faster as us, even though there are absolutely no reason to believe so ?

Is his meter sticks really longer than ours and distance therefore shorter for him?

WHAT exactly would you tell him?.

I mean not only words, but how are the rules / law exactly according to the examples I have mentioned?

How can such relative huge dilemma have surveyed in 100 years without anyone have wonder; what happens here?

I believe we have no clue how to explain that, right ?

This could be a bad sign.

 

[russ_watters]

The rules for another observer are exactly the same as for us. No pretending needed and no issue of who's measurement is "really" right - the whole point of Relativity is that both measurements are right.

 

[Bjarne]

The rules for another observer are exactly the same as for us. No pretending needed and no issue of who's measurement is "really" right - the whole point of Relativity is that both measurements are right.

According to last the mentioned exsample;

• We know observer B’s clock is "losing" 6 earth-years relative to A’s clock. after one Milkyway orbit,
• We also know that both clocks’ orbits the milkyway (MW) the same radius from the center of the MW.
• And we know that both clocks complete an orbit of the MW in the same period.
• Both clocks follows the Sun, - The only difference that counts is that B is closer to the Sun as A is , hence B is stronger affected by gravity from the Sun as A, - ( none of the clocks are orbiting the Sun, and none on board of a planet).

Questions

1. So is the speed of observer B the same as the speed of A( 250 km/s) ?
2. Does both observer A and B agree the speed is the same ?
3. Are A's and B's meter-stick comparable the same ?
4. Will both observer A and B agree about how long the circumstance of the Milkyway is ?
5. If both observer A and B agree that speed and distance is the same for both (but the time rate not) , how can it be that speed multiplied with time not would show the same result for observer B as it would for observer A ?

It seems to be that we say that our reality is more real than these”out there”
I mean this is also how science was in the Middle Ages, - something must have change since.
I am not satisfied with words, but to know WHAT exactly is going on here.

 

[darkhorror]

You are getting caught up in time, speeds, distances being absolute. You have to do the calculations with respect to each "observer." So you say you are moving at 250k/s you have to ask with respect to what. In your own frame of reference you aren't moving at all. In the Earth's you are moving at one speed, sun another,...

 

[russ_watters]

*So is the speed of observer B the same as the speed of A( 250 km/s) ?

As you must know, this question is incomplete. Speed is measured between two points and you've only listed one point for each of the two speeds you are looking for. You need to specify what you are measuring the speeds relative to and who is doing the measuring. Don't bother fixing this question, though - I'm not interested in playing games with made-up/impossible numbers and it really isn't important to your original point.

[*]Does both observer A and B agree the speed is the same ?

Maybe. But again, this isn't really all that important. What is important is this:

If both observers faithfully follow the principle of Relativity as stated in your title and, as it requires, ensure they are clear and consistent about what frames of reference they are doing the measurements from, or measure from one and properly transform to the other, they will agree on what is happening.

[*]Are A's and B's meter-stick comparable the same ?

Again: If they follow the principle of Relativity and are clear on the choices of reference frames (and the definition of a "meter") they most certainly will. They might say: "From here, your meter looks smaller than mine, but since I know our relative speeds, I calculate that if I was to go over to you and measure your meter it would be the same as mine."

[*]Will both observer A and B agree about how long the circumstance of the Milkyway is ?

Same answer as above.

[*]If both observer A and B agree that speed and distance is the same for both (but the time rate not) , how can it be that speed multiplied with time not would show the same result for observer B as it would for observer A ?

The wording of the question violates Relativity by mixing and matching observations from different reference frames without properly accounting for the differences. So we can answer this way: if A and B don't properly apply the principle of relativity, they may not believe that the laws of the universe are the same in all reference frames. Or put another way: if a person doesn't understand how to use a law, they will misuse it and may assume that the law is wrong when, in fact, it was just their use of the law that was wrong. That appears to be the basis of your issues with Relativity.

 

[Bjarne]

As you must know, this question is incomplete.
Speed is measured between two points and you've only listed one point for each of the two speeds you are looking for.

We have “two point”...
We have a orbit and thereby a circumstance of the milkyway (MW).
You can bend the orbit to a straight line.
So you do have “two points”.
A staring point that also is the final point when the orbit is completed.

You need to specify what you are measuring the speeds relative to and who is doing the measuring.

This is done too.
The Sun travels relative to a points of no motion, which is the center of the Milkyway.
The 2 clocks are according to the example mentioned above following the exact same orbit as the Sun.

Bjarne
Does both observer A and B agree the speed is the same ?
Maybe. But again, this isn't really all that important. What is important is this:
Russ
If both observers faithfully follow the principle of Relativity as stated in your title and, as it requires, ensure they are clear and consistent about what frames of reference they are doing the measurements from, or measure from one and properly transform to the other, they will agree on what is happening.

First at all notice we are only speaking about influence due to gravity (GR) not about SR
The orbits of the 2 clock’s are exactly the same (for all observers).
Observer A and B are doing the measurement from their own reference frame.
B's clock is really ticking slower as A's clock - because B is closer to the Sun as A and therefore comparable slower as A's clock.

Nothing prevent that A and B can compare time differences.
Think about; how do we determinate how long 1 meter is or what the speed of light.
Both obersver A and B would determinate that the exact same way, wouldn’t they?

Again: If they follow the principle of Relativity and are clear on the choices of reference frames (and the definition of a "meter") they most certainly will.
They might say: "From here, your meter looks smaller than mine,

If A's meter-stick is comparable shorter as B's it will not only "look" shorter.
B's reality is real, as well as A's (or our) reality also are real.
Therefore B's meter stick will really be shorter.
We are not speaking about "illusion" but about realities.

but since I know our relative speeds, I calculate that if I was to go over to you and measure your meter it would be the same as mine."

Now you are speaking SR
Both A and B is according to the example in the same SR-reference frame, since both exactly follows the motion of the Sun, hence SR do not apply, - only GR does.

Let me ask more simple and all-round.
Imaging you was orbiting the Sun with a meter stick 50 billion km from the Sun.
I was orbiting 150 billion km from the Sun also carry a meter stick.
Would both meter sticks comparable be the same length? .
What I am asking is 1 meter the exact same length if a observer far away ( not affected by gravity of the Sun) could se both meter stick and also was able to compare if our meter stick did have the exact same length, so long we are different places in the gravitational field of the Sun ?

Now let say that time in your orbit is 1 billion part slower for you, compared to my time rate.
Would your meter stick then proportional to that be 1 billion-part longer ? (or shorter ) – or exactly the same as mine, - still seen from a observer C far away and not affected by the gravity of the Sun.

The wording of the question violates Relativity by mixing and matching observations from different reference frames without properly accounting for the differences.

Comparing relative differences, doesn’t matter whether we speak about time rate, speed or length, - is not necessary mixing these, and this is also not what I have done at all.

I am not mixing anything but asking what is the speed and distance /B] difference between A’s and B’s reality according to the example, - if any ?
There must be a very simple answer to that question.

If you would say there is no difference between the reality of A and B (accept time), simple math would show you a mathematical contradiction, since time multiplied with speed can impossible result to the same distance for A and B. (since time for B is shorter)

So I am in fact trying to separate relative differences.

Mathematical either speed or distance cannot comparable be the same.
So what is the mathematical answer here?
Is speed comparable larger - or is it distance that is proportional and comparable shorter (and therefore the meter -stick propositional longer) ?

If nothing proves that (comparable) speed is affected (and hence comparable different), and you multiply less time (for B) with the same (comparable ) speed that is valid for A, - you will get a shorter distances for B.

So if you have no objection that we assume that speed is (comparable) the same for A and B, - then it is mathematical proven that distance (circumstance of the MW) for A and B NOT is comparable the same for A.

If you do not agree speed is comparable the same, what is the correct comparable speed for B, ?.

Yours assumption that I am mixing realities is not true. – I am ONLY comparing realities, and do in fact try to keep factors separated, by asking what the differences except time .

Is speed and / or distance comparable different according to the very simple example mentioned?

Please try to keep it simple.

 

[Bjarne]

You are getting caught up in time, speeds, distances being absolute. You have to do the calculations with respect to each "observer." So you say you are moving at 250k/s you have to ask with respect to what. In your own frame of reference you aren't moving at all. In the Earth's you are moving at one speed, sun another,...

No both clocks are moving 250 km/s as well as the Sun
Both clocks’ follows the Sun
SR does not apply to the mentioned scenario.
So this is not the correct answer either.

 

[darkhorror]

No both clocks is moving 250 km/s as well as the Sun
Both clocks’ follows the Sun
SR does not apply to the mentioned scenario.
So this is not the correct answer either.

250 km/s with respect to what?

 

[Bjarne]

250 km/s with respect to what?

I geusss the same way how we measure speed in space.
That must be valid for us but also for an observer with a slow ticking clock.

 

[darkhorror]

I geusss the same way how we measure speed in space.
That must be valid for us but also for an observer with a slow ticking clock.

The way we measure speed in space is we see how fast we are going with respect to something else. If I am in space with respect to me my velocity is 0. With respect to the Earth it might be .5c. With respect to something else it might be 250km/s.

Saying something is moving 250km/s is meaningless unless you say what it is with respect to.

 

[zaybu]

Now you confuse me.
My concern is mainly if ALL laws of nature (equations) ALWAYS the same for all observer.
OR is (for example) gravity - and here I mean G (the gravity constant) an exception´.
Above you wrote; "G", does not change due to any local considerations"
I am now not sure what you really mean, - Is "G" ALWAY constant. - Yes or no ?

A consequence of Relativity is that we seek laws that are Lorentz invariant: meaning, if we have an equation A = BC + D in one frame of reference, then using the lorentz transformation laws to another frame of reference, we get A' = B'C' + D'. Note that not all equations will have this property, and certainly not certain observables. That's why we have time dilation, length contraction or that if two events are simultaneous in one frame, they might not be silmutaneous in a different frame. Now there are constants that are taken to be the same in every frame, that is, Lorentz invariant, notably the speed of light c, Planck's constant h-bar, and G -- Newton's constant in his law of universal gravitation.

Hope this helps.

 

[Bjarne]

The way we measure speed in space is we see how fast we are going with respect to something else. If I am in space with respect to me my velocity is 0. With respect to the Earth it might be .5c. With respect to something else it might be 250km/s.

Saying something is moving 250km/s is meaningless unless you say what it is with respect to.

250 km/s is the speed of the Sun's motion orbiting the MW
I don’t know how they did that measurement.
It is not with respect to “something” I believe, - but only to the center of the MW, where you have relative no motion.
If we can do such measurement, other observers in the Solar system can also. But I am not sure the result for a different space-time observer would be the same.

 

[Bjarne]

A consequence of Relativity is that we seek laws that are Lorentz invariant: meaning, if we have an equation A = BC + D in one frame of reference, then using the lorentz transformation laws to another frame of reference, we get A' = B'C' + D'. Note that not all equations will have this property, and certainly not certain observables. That's why we have time dilation, length contraction or that if two events are simultaneous in one frame, they might not be silmutaneous in a different frame. Now there are constants that are taken to be the same in every frame, that is, Lorentz invariant, notably the speed of light c, Planck's constant h-bar, and G -- Newton's constant in his law of universal gravitation.
Hope this helps.

This is very a general "answer"
I believe many really are confused.
I am not sure that the right answer exsist ?

Try to be more specific and if you can try to answer some of all the questions.
I seem that many have mysophobia to answer concrete, for example show the simple content of the equation for B

Alle the content of the equation for A we can say we know, - A could share the same time rate as here on Earth, so it is only the stranger B, - that is the problem / challenge.

• 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) ?

We are only discussion GR not SR

 

[darkhorror]

250 km/s is the speed of the Sun's motion orbiting the MW
I don’t know how they did that measurement.
It is not with respect to “something” I believe, - but only to the center of the MW, where you have relative no motion.
If we can do such measurement, other observers in the Solar system can also. But I am not sure the result for a different space-time observer would be the same.

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?

 

[zaybu]

This is very a general "answer"
I believe many really are confused.
I am not sure that the right answer exsist ?

Try to be more specific and if you can try to answer some of all the questions.
I seem that many have mysophobia to answer concrete, for example show the simple content of the equation for B

Alle the content of the equation for A we can say we know, - A could share the same time rate as here on Earth, so it is only the stranger B, - that is the problem / challenge.

• 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) ?

We are only discussion GR not SR

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-ftl-violates-causality.html

 

[Bjarne]

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 ?

 

[Bjarne]

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-ftl-violates-causality.html

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.

 

[PAllen]

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.

 

[Bjarne]

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.

 

[zonde]

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.

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 ?

 

[PAllen]

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.

 

[darkhorror]

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?

 

[Bjarne]

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

 

[Bjarne]

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.

Try instead exactly to answer some or all the questions.
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

 

[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).

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.

 

[PAllen]

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.

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.

 

[Bjarne]

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"

 

[PAllen]

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. ]

 

[Bjarne]

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 ?

 

[zonde]

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.

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).

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?

 

[PAllen]

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.

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.

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.