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

by Bjarne
Tags: frames, laws, nature, reference
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P: 15,568
 Quote by Bjarne I wrote comparable difference from the start. It confused me you could misunderstand that so much.
Comparable doesn't have a well-defined meaning in terms of experiment. I.e. there is no experiment called the "comparable" experiment. Writing "comparable" over and over and over was not helpful to the conversation and was one of the main sources of delay. I am not a mind reader to know that by the word "comparable" you meant something like A or D and not something like B or C.

 Quote by Bjarne Good question. I believe it is impossible.
Then there is no use discussing about whether or not lengths change at different locations.

 Quote by Bjarne Already we compare space with a stretching rubber band, - or use the expression "curvature" What does that mean? Can we get closer to an understandable nature of that? What happens with the ruler in such “bended” space? ( what do we know or not know) At least seen from a mathematical perspective, is space stretching like the rubber band?
The word "curvature" does not refer to space stretching like a rubber band. Curvature refers to deviations from (pseudo) Euclidean geometry.

Consider the difference between geometry on a sphere and geometry on a plane. On a plane, two straight lines which are parallel at one point remain parallel and never intersect. On a sphere, two neighboring lattitude lines are straight lines which are parallel at the equator and intersect at the poles. On a plane the sum of the interior angles of a triangle are 180°, but on a sphere the sum of the interior angles of a triangle are greater than 180°. This is the kind of thing that is meant by "curvature".

A rubber band which is stretched into a triangle shape on a flat table still has interior angles which sum to 180°, regardless of the stretching of the band.
P: 344
 Quote by DaleSpam Consider the difference between geometry on a sphere and geometry on a plane. On a plane, two straight lines which are parallel at one point remain parallel and never intersect. On a sphere, two neighboring lattitude lines are straight lines which are parallel at the equator and intersect at the poles. On a plane the sum of the interior angles of a triangle are 180°, but on a sphere the sum of the interior angles of a triangle are greater than 180°. This is the kind of thing that is meant by "curvature". A rubber band which is stretched into a triangle shape on a flat table still has interior angles which sum to 180°, regardless of the stretching of the band.
Sorry, but it is still very difficult for me to understand how, - reality differences’ - at all is possible (in this case) when distances not is affected too.

Let’s return to the example, - the ISS and the Earth orbiting the exact same orbit around the Sun. – And both exactly 1 orbit.
Both places / both observers (A & B) will locally agree that it will take 1 year, - 31536000 second.
They will also agree about their orbit local speed is average exactly 30000 m/s
• I have claimed that distance cannot be the same.
• You have claimed that these 2 observers follows different path.
1. Do you mean these object follows 2 comparable different path?
2. Do you mean these path locally seems to be exactly the same ?
3. Or how would you describe the “different path”?
Because observer A (on the ISS) he will say it took exactly 31536000 ISS-second to complete one orbit, and the ISS-speed was exact averagely 30000m/s

Observer B on the Earth, orbiting the exact same orbit round the Sun will also say that that it took 31536000 earth-second to complete one orbit and the Earth-speed was exact averagely 30000m/s.

But according to the Shapiro delay experiments we know that the comparablespeed between the ISS and the Earth not is the same, - (even though it locally is the same) .
For exsample, - if it was possible for A and B to reflect a light beam on the Sun and get it back, it would take the exact same local time, and the exact same local speed.
But the comparable time and speed would not be the same.

Let us now say that the comparable speed difference is proven to be 50% .

Option 1.
The only way we mathematical can understand what happens here is that distances also must be 50% comparable different.
This is simple logic. Then both local and comparable different reality can both be true at the same time. - (Seen from both observer A+B+E).

Option 2.
is that we from Earth would see the ISS orbiting the Sun double as fast as the Earth (according to the exaggerated exsample) .
That would contradict that an external observer (E) would see both objects moving with the same (his) speed and using the same (his) time to complete one orbit.

If you disagree, to both these options, - can you please be more detailed according to;
• What you mean with that these 2 objects follows a “different path”?
• How is this at all possible without assuming that comparable distance differences also must be a fact.?
This REALLY confuse me. – Sorry that I not is so quick to understand this.
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P: 15,568
 Quote by Bjarne Sorry, but it is still very difficult for me to understand how, - reality differences’ - at all is possible (in this case) when distances not is affected too.
If you cannot come up with an experiment for comparing distances then it doesn't make sense to claim that distances are not affected. You cannot know anything about the distances if you cannot experimentally compare them, so you cannot claim that they are affected and you also cannot claim that they are not affected.

 Quote by Bjarne Let’s return to the example, - the ISS and the Earth orbiting the exact same orbit around the Sun. – And both exactly 1 orbit. Both places / both observers (A & B) will locally agree that it will take 1 year, - 31536000 second.
No, this is option D from my post 151. They will measure 1 astronomical year to be a different number of seconds.

 Quote by Bjarne They will also agree about their orbit local speed is average exactly 30000 m/s
How does each measure that?

 Quote by Bjarne I have claimed that distance cannot be the same. You have claimed that these 2 observers follows different path.
These claims do not contradict each other.

 Quote by Bjarne Do you mean these object follows 2 comparable different path? Do you mean these path locally seems to be exactly the same ? Or how would you describe the “different path”?
You like to put the word "comparable" in bold as though somehow putting it in bold magically helps give it some meaning. What is a "comparable different path"? I have never heard the term and as far as I know it has no meaning.

As far as how I would describe the different paths, I would use a 4D coordinate system. I would then write the different paths in terms of parameterized worldlines in the coordinate system. Probably the ecliptic coordinate system with the GPS time coordinate would be the easiest.

 Quote by Bjarne But according to the Shapiro delay experiments we know that the comparablespeed between the ISS and the Earth not is the same, - (even though it locally is the same) .
How do you experimentally compare speeds?

If you write "comparable time" then I know what you mean since we already discussed it. But we have not discusses "comparable distances" nor "comparable speeds", so don't bother to use those terms when you have not defined them. When you say "comparable speed" what experiment are you thinking about performing to compare the speed?

 Quote by Bjarne For exsample, - if it was possible for A and B to reflect a light beam on the Sun and get it back, it would take the exact same local time
No, this is not correct. This is known as Shapiro delay.

 Quote by Bjarne and the exact same local speed.
This is true, the local speed of the light beam is c.

 Quote by Bjarne But the comparable time and speed would not be the same. Let us now say that the comparable speed difference is proven to be 50% .
Again, please define the experiment for comparing speeds.

 Quote by Bjarne Option 1. The only way we mathematical can understand what happens here is that distances also must be 50% comparable different.
Again, what experiment are you using to compare distances?

 Quote by Bjarne Option 2. is that we from Earth would see the ISS orbiting the Sun double as fast as the Earth (according to the exaggerated exsample) . That would contradict that an external observer (E) would see both objects moving with the same (his) speed and using the same (his) time to complete one orbit.
How would we measure the speed of the ISS and how would the external observer measure both the Earth speed and the ISS speed?

 Quote by Bjarne If you disagree, to both these options
Neither of the options is clear enough for me to either agree or disagree with them.

 Quote by Bjarne What you mean with that these 2 objects follows a “different path”? How is this at all possible without assuming that comparable distance differences also must be a fact.? This REALLY confuse me. – Sorry that I not is so quick to understand this.
They follow different paths because the coordinates of their path are different in any coordinate system you might choose.

Again, you put an undefined term in bold as though that helps to convey meaning. It does not, it is simply irritating. What is a "comparable distance difference" and how would you measure it?

Please do not use the word "comparable" or any related word in our further discussions unless you have clearly defined the experiment you would perform to make the comparison.
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 Dalespam They will measure 1 astronomical year to be a different number of seconds.
Yes off course, this was a blunder..

 If you cannot come up with an experiment for comparing distances then it doesn't make sense to claim that distances are not affected. You cannot know anything about the distances if you cannot experimentally compare them, so you cannot claim that they are affected and you also cannot claim that they are not affected.
Ok so this is then still an open question. This is what confused me.
The conclusion is then, - it seems more to discover, - but whether it is possible, is then a different question.

Thanks’ a lot for your patience, and detailed explanation.
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P: 15,568
 Quote by Bjarne Ok so this is then still an open question.
I wouldn't even call it an open question yet. I would call it an undefined term. Until you have defined all of the terms you don't even have a properly formed question.

 Quote by Bjarne Thanks’ a lot for your patience, and detailed explanation.
You are welcome. I will be glad to continue the discussion if needed.
P: 344
 Quote by DaleSpam I wouldn't even call it an open question yet. I would call it an undefined term. Until you have defined all of the terms you don't even have a properly formed question..
Since we know the comparable length of one second is relative stretching or shrinking in different spacetime, for exsample relative to one of ours seconds, we know 1 of 3 factors.

Hence the options are whether speed and /or distance does "the same", and whether that happens proportional.

Which is the most likely option.
• Is it that only speed follows the relative (proportional) stretch of time (and hence relative slowing or speeding)?
• Or is distance also involved in the same relative proportional change?
Of course there could be other combination, according to what these 2 other factors does or not does, - but I think these 2 are the most likely.

I know you twist these words, - but I also think you know what i mean.
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 Quote by Bjarne I know you twist these words, - but I also think you know what i mean.
It is hard to claim that someone is twisting words which are undefined. I certainly do not know what you mean. In fact, I believe that you do not know what you mean either.

Note, this is not a personal criticism, this is a common problem when you are learning a new and difficult subject, the concepts are not clear and words often have subtly different meanings in the new context. It is just a simple fact that you need to be aware of and have patience with. People will be willing to help you, but you need to recognize that communication about this topic is inherently difficult. You need to ask people to define terms when you are confused and you need to be willing to define terms when asked.

GR is mathematically guaranteed to be a self-consistent framework. So, any time that you use an English description and come up with some inconsistency you immediately know that you are not correctly translating between the math and the English. That is typically due to using a poorly defined term or due to making a statement which is well defined and gramatically correct in English but is not mathematically correct.

Here, we have the first case. You use words like "comparable", "the same", "stretch", etc. but without a rigorous definition. Any inconsistencies you come up with are due to that, not due to the theory.
 P: 344 On the one hand I have heard that when people not get confused first time they hear about reality they haven’t understood it, so I am maybe legally excused (even though it is not first time). On the other hand it must also be possible to explain it to grandmother according to Einstein. I think I begin to understand a lot more, especially what we don't know. Still I would be happy to hear some ideas / opinions (if any) about how the third factor, “distance” in space time, and whether these too possible can be a changing factor too (in the same way as time) I mean how this factor most likely can be globally understood, - there must at last have been speculations about it, what is the opinion of the majority, - are there different theories, etc.. or is that what we don’t know a dead end. If possible explained in a “grandmother adaptable language” first at all, then later I believe it is easier to understand the math behind, if any.
P: 344
 Quote by DaleSpam Bjarne Wrote Either speed, distance and/or the definition of 1 second can then not be the same. It is a simple mathematical necessity. I haven't got an excact answer where the "camel is buried" I am just asking the simple question; - how would these space time realities look like (what would be the comparable difference) if I could jump between them, and see the differences? I am not an expert in his field, but it is easy to see that the full story can’t have been told so far. I also did not got the answer (yes or no) to whether the orbit circumference for example of the Earth really can be 2 different sizes, (the same orbit), according to the example mentioned above.. And if this is so, how can the law of gravity apply for both without contradictions. DaleSpam Wrote The two paths are not the same, so the answer is "yes, two different paths may have different lengths". Each path is a 1D line (a helix) in a 4D curved spacetime. You can easily come up with coordinate systems where the two paths have two coordinates which are identical and constant, and you can parameterize the paths by one of the remaining coordinates, but they will always be different in at least the final coordinate. They are simply different paths with different lengths, no contradictions nor confusions. You certainly haven't demonstrated any conflict with the law of gravity. I don't even know what you think would be contradicted here.
Let’s say observer ‘A’ and ‘B’ live in a high-rise flat.
'A' at 1st. floor and 'B' at 10th.
Between the Sun and the Earth there is a measurement tape.
Because time is ticking different for ‘A’ and ‘B’ they cannot agree about the speed and /or the distance to the Sun (the circumstance).
Because ‘A’ and ‘B’ live at the same planet they cannot be travelling with different speed.
Because ‘A’ and ‘B’ both can see the same measurement tape (between the Sun and the Earth) the distance (circumstance) of the Sun can also not be different. Because time multiplied with speed = distance (circumstance) we do in fact have a dilemma here.
So now they must both be following the same path.
The only logical possible explanation is that ‘A’ relative to ‘B’ lives in a completely transformed reality.
This mean when time is stretching, then distances and speed is doing the same.
Or ?
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Hi Bjarne, welcome back! It has been quite a while.

 Quote by Bjarne Let’s say observer ‘A’ and ‘B’ live in a high-rise flat. 'A' at 1st. floor and 'B' at 10th. ... So now they must both be following the same path.
These two statements are mutually contradictory. If they are following the same path in spacetime then one cannot be on the 1st floor at the same time that the other is on the 10th floor. I.e. as described their spacetime paths are different by approximately 30 m or so, therefore they are not following the same path in spacetime.

Not only are the paths approximately 30 m different, but that 30 m is a significant difference since there is a measurable amount of time dilation between the two paths.

 Quote by Bjarne we do in fact have a dilemma here.
Agreed. Which of the two mutually contradictory premises do you wish to keep?
P: 344
 Quote by DaleSpam Hi Bjarne, welcome back! It has been quite a while. These two statements are mutually contradictory. If they are following the same path in spacetime then one cannot be on the 1st floor at the same time that the other is on the 10th floor. I.e. as described their spacetime paths are different by approximately 30 m or so, therefore they are not following the same path in spacetime. Not only are the paths approximately 30 m different, but that 30 m is a significant difference since there is, according to you, a measurable amount of time dilation between the two paths. Agreed. Which of the two mutually contradictory premises do you wish to keep?
The observers are following different paths, yes, - but the observed, - the orbit of the Earth is not following 2 different paths..
Let’s say ‘A' and 'B' live at the North Pole i the same high-rise flat
Hence speed and orbit distance of the Earth, - must be the same for both observers.
Speed of the Earth must be the same, since both are at the same planet. The planet cannot be moving with 2 different speeds at the same time.
Distance is also the same.. The measurement tape between the Sun and the Earth would prove for both A and B, that distance is the same.
This means ‘A’ and ‘B’ cannot say that these factors are different.
Hence still the conclusion mentioned above, - that both speed and distance transform proportional with time, - seems to be the most and only logical.
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 Quote by Bjarne The observers are following different paths, yes, - but the observed, - the orbit of the Earth is not following 2 different paths.
That isn't how clocks work. They only measure the length of their own path through spacetime, not some other objects path. A's clock measures the length of A's path through spacetime, not the length of B's path nor the length of Earth's path. Similarly for B.

Also, since Earth is not a point like object in this scenario, the Earth does not have a single path through spacetime unless you define one specific point as the reference point.

 Quote by Bjarne The planet cannot be moving with 2 different speeds at the same time.
Why not? Speed is a frame variant quantity, so it can have as many different values at the same time as you have reference frames.

For instance, suppose one police officer is on the side of the road and another is driving on the road and suppose that they each measure the speed of the same car at the same time. One may get 100 km/h and the other may get 0 km/h. Both are valid measurements of the speed of the car, but in different frames.
P: 344
 Quote by DaleSpam That isn't how clocks work. They only measure the length of their own path through spacetime, not some other objects path. A's clock measures the length of A's path through spacetime, not the length of B's path nor the length of Earth's path. Similarly for B.
Let's say it really was possible to tie a tape measure to the North Pole of the Sun and to the North Pole of the Earth in the other end.
A and B is in this example only observers to the Earth orbiting the Sun.
Both can see the radius / circumstance of the orbit of the Earth and both agree that the orbit of the Earth (as just defined) really is the same for both observers, - simple because both can observe this is how the tape measure proves it to be.
So both must agree that distance / circumstance of the radius/orbit of the Earth, is observed from both observers perspective to be the same.

 Why not? Speed is a frame variant quantity, so it can have as many different values at the same time as you have reference frames. For instance, suppose one police officer is on the side of the road and another is driving on the road and suppose that they each measure the speed of the same car at the same time. One may get 100 km/h and the other may get 0 km/h. Both are valid measurements of the speed of the car, but in different frames.
A and B live at the North Pole in the same building ( ‘A’ at 1st and ‘B’ at 10th floor) . They are not moving relative to each other and also not relative to the Earth.
A and B and the Earth is all exactly following the same orbit, and hence in the same frame.

We could also say that also at the North Pole of the Sun there was a similar building, and from each floor a tape measure to the building / same floors at Earth's North Pole.
A and B would agree that all tape measure was the same length.

How can you then say they are in different frames / moving relative to each other?
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 Quote by Bjarne Let's say it really was possible to tie a tape measure to the North Pole of the Sun and to the North Pole of the Earth in the other end. A and B is in this example only observers to the Earth orbiting the Sun. Both can see the radius / circumstance of the orbit of the Earth and both agree that the orbit of the Earth (as just defined) really is the same for both observers, - simple because both can observe this is how the tape measure proves it to be.
I agree. By the way, I really like how you not only specified what you wanted to measure, but also the experiment to measure it.

 Quote by Bjarne They are not moving relative to each other and also not relative to the Earth. A and B and the Earth is all exactly following the same orbit, and hence in the same frame.
That would be true if spacetime were flat. I.e. in flat spacetime A not moving relative to B implies that A and B are at rest in the same frame. However, the spacetime is not flat, but is curved, and in curved spacetimes reference frames are local. For example, although the distance wrt each other is not changing (an indicator of the same frame in flat spacetime), signals from A are redshifted when received by B (an indicator of different frames in flat spacetime). So A and B are not considered to be using the same reference frame despite the fact that they are not moving relative to each other.

Besides, haven't you been assuming that A and B are different reference frames and therefore claiming that the laws of physics are different in different reference frames? It seems strange for you to change your position on this topic after this long when it hasn't been a point of disagreement until now.
P: 344
 Quote by DaleSpam That would be true if spacetime were flat. I.e. in flat spacetime A not moving relative to B implies that A and B are at rest in the same frame. However, the spacetime is not flat, but is curved, and in curved spacetimes reference frames are local. For example, although the distance wrt each other is not changing (an indicator of the same frame in flat spacetime), signals from A are redshifted when received by B (an indicator of different frames in flat spacetime). So A and B are not considered to be using the same reference frame despite the fact that they are not moving relative to each other.
I understand this.
I also understand that A and B could move with different speed, - but since there is a different option, (mentioned above) that also can be true - it seems there is a chose between two options.
I mean, we know that both time and speed is comparable different factors, but the fact that we don't know whether also distance are affected or not, must mean the complete picture still is an open question.

 Besides, haven't you been assuming that A and B are different reference frames and therefore claiming that the laws of physics are different in different reference frames?
Did I ? - if so it was not my intention.
I mean I believe that the laws of nature are the same in all space time reference frames. I am just wondering which possible changing (with distance and speed) possible can ‘follow’ time dilation.

 It seems strange for you to change your position on this topic after this long when it hasn't been a point of disagreement until now.
I think we don't disagree about anything, - if it is correct understood that we both agree, that what happen with speed and distance, in different space-time not is fully understood / proven.

And this is really what confuses me. - If that was clearer, I think it would be much easier to understand general relativity.
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 Quote by Bjarne I understand this. I also understand that A and B could move with different speed, - but since there is a different option, (mentioned above) that also can be true - it seems there is a chose between two options.
Actually, there are an infinite number of possible coordinate systems, and therefore an infinite number of choices, not just two. Any of them is valid.

 Quote by Bjarne I mean, we know that both time and speed is comparable different factors, but the fact that we don't know whether also distance are affected or not, must mean the complete picture still is an open question.
Well, the reason that it was still open is that we hadn't defined a measure of distance. If you use your ruler-based measurement of distance then distance is frame-invariant.

That is why it is so important to specify the experiment you are using to perform a measurement. If you are sufficiently clear about what it is that you are measuring then you can get a complete picture of that scenario, it is only when you ask ambiguous questions that you get ambiguous answers.

 Quote by Bjarne I think we don't disagree about anything, - if it is correct understood that we both agree, that what happen with speed and distance, in different space-time not is fully understood / proven.
What happens according to the theory is fully understood, and many aspects (though not all) are also experimentally proven. However, because of the nature of GR it is very important to ask well-defined questions, and that is what can seem like it is not fully understood. I.e. it is not the theory but the question which is not fully understood.

If you get into the habit of thinking about how you can measure a quantity of interest then you will generally be able to ask better questions and get better answers.
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 Quote by DaleSpam What happens according to the theory is fully understood,
Right
But still relativity and the fact that space curves is really strange.
I mean our immediate understanding is that space is nothing
How can nothing curve?
And how can we know whether or not something happens to distances too, and if so what happens to distances, - and to the ruler?
You say that speed is different seen from the perspective of A and B.
But if distance also is a proportional variant still speed would be different, but the whole concept would too.

What I am trying to say, - we cannot cut a piece of “curved space” in cardboard and say , - This is like it really and objective looks like, this is how we can imagine what we are talking about.

The nature of "curvature of space" is a difficult to relate to, even in our fantasy. It doesn’t make it easier when we cannot know for sure whether distances and the ruler not is affected or could be.
So how sure can we be that "the theory" "is it", - or whether there is more to come ?

I think many do have a problem to accept what seems to be huge contradiction, for example that A and B is moving with different speed. Even though eveybody can see this is not the case, since they live in the same building at the Noth Pole. Is our understanding really complete?

The opposite of a fact is falsehood, but the opposite of one profound truth may very well be another profound truth.” Niels Bohr

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