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

Bjarne

This is very a general "answer"
I belive 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

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

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

Bjarne

I have not invented how to calculate the orbit speed of the MW
So how was it done then ?

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.

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.

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.

zonde

Wrong, distances are the same.
Only clocks tick at different rate. Measuring rods are of the same length.

PAllen

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

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

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.

The orbit speed round the Milkyway is the same for both observes (A and B).
Hence it doesn’t matter

Bjarne

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.

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).

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

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.

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).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

This is not possible.
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

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

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.

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 ?