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

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.
...
So now they must both be following the same path.

we do in fact have a dilemma here.

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.

The planet cannot be moving with 2 different speeds at the same time.

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.

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.

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.

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.

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.

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,