# Laws of physics are the same

1. Aug 24, 2010

### Myslius

How do you prove that the laws of physics are the same in all inertial frames of reference?

2. Aug 24, 2010

### JustinLevy

A quick comment first: the laws of physics are the same in all inertial frames of reference of the same handedness.
http://en.wikipedia.org/wiki/Inertial_frame_of_reference

-- Define an inertial coordinate system. Deduce the most general coordinate transformations between such frames allowed by the definition. Now choose an inertial coordinate system to map out your surroundings and experimentally determine the laws of physics in that frame. Now mathematically check if applying the general inertial coordinate transformation to these laws of physics leaves the laws the same.

Historically, this actually happenned the other way around. We had a rough idea of an inertial frame, but found the physics had a different symmetry. This caused a lot of confusion at first, but eventually realized our approach to inertial coordinate systems was incorrect (the Newtonian concept of absolute time). Now that we have the concept of a spacetime, most definitions of an inertial frame essentialy are just defining what the metric for flat spacetime should be in such a coordinate system. We can then deduce the most general coordinate transformations preserving those metric components (lorentz boosts, rotations, translations, etc.) and check if the physics we measure is invariant under these coordinant transformations.

So when you here about an experimentalist seaching for "lorentz violating dynamics/processes/etc", they are testing the principle you asked about.

3. Aug 24, 2010

### nismaratwork

Length contraction, Time dilation, and other Relativistic effects go a long way towards to showing the invariance of the laws of physics across IRFs. Essentially, every proof for SR/GR is a proof of that postulate.

4. Aug 24, 2010

### jcsd

You don't is the answer, it's a postulate. Special relatvity is designed to preserve the laws of physics in different inertial frames, so any argument that it proves this statement is circular. If you like an inertial frame by definition is a frame belonging to a certain class of frames where the laws of physics and the speed of light are invariant (and constant) under transfomations between frames belonging to this class.

Postulates are generally speaking inferred emprically, i.e. from experiment. The success of special relatvity for describing certain physical phenomena can be taken as 'proof' of it's postulates.

You could use a different set of postulates which allow you to derive the postulates of special relativity. I still think that's a bit circular as essentiallly you're still setting out to create a theory which includes the postulates of SR.

5. Aug 24, 2010

### JesseM

But it would certainly be possible to falsify the postulate experimentally, so it is testable in that sense. Basically I think the idea is that you can determine the correct equations that govern the dynamical behavior of particles/fields in the lab frame (like finding that charged particles obey Maxwell's laws in the lab-frame), and then if the equations are written in terms of x,y,z,t, you can see what happens when you use the Lorentz transformation to perform a substitution in your equations:

x' = gamma*(x - vt)
t' = gamma*(t - vx/c^2)
y' = y
z' = z
(with gamma = 1/sqrt(1 - v^2/c^2))

If the equations after the substitution can be reduced to a form that looks identical to the original equations before the substitution (but with x' in place of x, t' in place of t, etc.), then the equations are Lorentz-invariant. It's logically possible that we might instead discover that the equations that give correct predictions in the lab frame do not have this property, which would falsify relativity unless we could show that the equations could be viewed as approximations to some other Lorentz-invariant equations which were consistent with all our experimental results.

6. Aug 24, 2010

### nismaratwork

As I said, support for Relativity = support for its postulates, but theories aren't "proven" in physics; they're used, improved, and eventually discarded. I haven't seen any wrong answers to the OP's question in this thread, just differing approaches.

7. Aug 25, 2010

### bcrowell

Staff Emeritus
To prove that it's true, you would need to start with a set of assumptions and then carry out some logical reasoning. What set of assumptions do you have in mind?

To prove that it's not true, you would need to find an experiment that comes out different when you do it in different inertial frames of reference. For example, if the Michelson-Morley experiment had come out with a positive result instead of a negative one, it would have disproved your statement.

The two possibilities --- proof and disproof --- are totally asymmetrical. One experiment can disprove a theory. No number of experiments can prove a theory.

8. Aug 25, 2010

### Myslius

An experiment, let's take a satellite orbiting around the Earth as FOR. The Earth moves so time on Earth should go slower (SR, time dilation).
In reality time goes slower for satellites.

9. Aug 25, 2010

### starthaus

This is due to the difference in gravitational potential. You need to take it in consideration in your calculations. See http://relativity.livingreviews.org/Articles/lrr-2003-1/ [Broken].

Last edited by a moderator: May 4, 2017
10. Aug 25, 2010

### Ich

Myslius, please explain what you think "inertial" means in a SR context.

11. Aug 25, 2010

### atyy

12. Aug 25, 2010

### Myslius

My understanding about "inertial" was wrong. Inertial in SR context means that is it not affected by any force, and goes at a constant speed in the straight line.
Satellite is affected by Earth's gravity. So it can't be FOR. Right?

Actually, none object with mass can be inertial FOR.

13. Aug 25, 2010

### Myslius

What observations conflict with relativity? As far as i know, relativity does not work at extremums: blackholes, beggining of the big bang etc.

14. Aug 25, 2010

### Ich

In the context of SR, right.
In this context, you'd find not a single exact inertial frame. But there are many situations where you can simply neglect the deviations, and where SR calculations are sufficient.
For example, the lab frame in a circular particle accelerator is inertial enough for all practical purposes.
The frame of a particle there can be approximated by an inertial frame, but only for a few meters - as long as their path looks almost straight.
Things that go in circles definitely do not qualify as inertial in SR.

15. Aug 25, 2010

### Passionflower

Satellite clocks go faster not slower with respect to a clock on earth.

16. Aug 26, 2010

### JesseM

If you're considering only gravitational time dilation that'd be true, but for satellites in orbit around Earth I think velocity-based time dilation would have a larger effect, causing them to have elapsed less time on each successive orbit when they pass near an Earth-based clock (and if you're imagining a purely SR analysis of satellites where they are traveling in a circle in flat spacetime, which is what Ich was talking about with the comment 'In the context of SR', there would be no gravitational time dilation)

17. Aug 26, 2010

### Passionflower

That is not my impression, I thought that the gravitational "part" was stronger than the SR "part".

But we should consult the literature. I have a paper by Richard Shiffman with the exact calculations that seem to agree with me. But I am not sure if this paper is published in a serious magazine and peer reviewed. Wikipedia also seems to agree with me but Wikipedia cannot always be relied on. There is Neil Ashby's document in Living Reviews but I browsed it and could not find any place where "the rubber meets the road" where it said unequivocally that one is slower or faster than the other one.

By the way, contexts or not, do you agree there is only one valid answer whether the clocks go faster of slower?

Edited: I checked the http://relativity.livingreviews.org/Articles/lrr-2003-1/" [Broken] article again and I think you want to take a look at Eq. 35, the satellite clock goes faster.

Last edited by a moderator: May 4, 2017
18. Aug 26, 2010

### starthaus

No, the effect is about 6 times smaller.

The gravitational effects heavily dominate the effects due to relative motion by a factor of +46us/day vs -8us/day, so, the terrestrial clocks lag the satellite clocks by a net of +38us/day. See here..
In order to compensate for this effect, the frequency of the atomic clocks is adjusted down at launch, making it one of the most direct tests for relativistic time dilation.

Last edited: Aug 26, 2010
19. Aug 26, 2010

### starthaus

Yes, you were correct all along, by 38us day. This is why the frequency is adjusted down at launch (to make it count the same amount of units of time as the terrestrial clocks) The gravitational effects dominate the speed effects by a factor of 6.

Last edited by a moderator: May 4, 2017
20. Aug 26, 2010

### Ich

Neither JesseM nor Myslius were talking especially about GPS satellites. Satellite clocks "go slower" for low earth orbits, like Space shuttles, ISS, and most satellites. Mostly communication satellites (incuding GPS) are in higher orbits, with "faster" clocks.

21. Aug 26, 2010

### JesseM

Yes, you're correct, I misremembered. In an earlier post I had used some equations posted by kev to figure out that for a circular orbit, velocity-based time dilation would only be larger than gravitational time dilation for an orbit less than double the Schwarzschild radius (assuming all the mass was concentrated at a radius smaller than this, which isn't true for the Earth).

Still, when discussing the subject with beginners it may be better to consider a simplified case where we treat an orbit as a circular path in flat spacetime, as Ich did. In that case there is only velocity-based time dilation, and a circular path is non-inertial so a clock on that path will elapse less time than a clock at rest relative to the center of the "orbit".

Last edited by a moderator: May 4, 2017
22. Aug 26, 2010

### starthaus

The above cannot possibly be right since it is falsified by experiment. In the Hafele-Keating experiment one of the atomic clocks lagged behind the ground clock while the other was ahead. So, something is wrong in kev's computations.

23. Aug 26, 2010

### JesseM

kev's calculation was only for comparing proper time on a clock moving in a circular orbit with coordinate time in Schwarzschild coordinates (which matches up to proper time for a clock at infinity).

24. Aug 26, 2010

### starthaus

Even that seems wrong since $$\frac{d\tau}{dt}<1$$ for any value of the Schwarzschild coordinate $$r$$ for the case of objects in circular orbits around a massive object like the Earth.
If you point to the exact post, I will be able to point out the error in kev's calculations. Did you check kev's calculations for correctness?

Last edited: Aug 26, 2010
25. Aug 26, 2010

### JesseM

Why do you think it seems wrong? Do you understand that the clock on Earth is moving in Schwarzschild coordinates due to the Earth's rotation, and that the plane that flies in the direction opposite to the rotation of the Earth would have a smaller speed in Schwarzschild coordinates than the clock on the ground?
See pervect's post here where he calculates time dilation as a function of coordinate velocity in Schwarzschild coordinates--kev's calculation is just a slight modification where he substitutes the local velocity (velocity in a locally inertial frame instantaneously at rest in Schwarzschild coordinates) for the Schwarzschild coordinate velocity, see this post or this one. I remember now that we already discussed pervect's calculations on this thread where you raised a lot of spurious objections and wouldn't give straight answers to the questions I and others asked you, let's not have a repeat of that please (I will only agree to discuss this again if you agree in advance to give definite answers to any questions asked of you).