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

[Dale]

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.

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.

 

[Bjarne]

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.

 

[Dale]

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.

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.

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.

 

[Bjarne]

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