# Special Relativity - Transformations and Equivalence Principle

1. Feb 26, 2005

### controlfreak

I am gonna try to explain relativity without light or maxwell's equation.

Light or Maxwell's equation or electromagnetism has nothing to do with relativity.

a) The speed of light (and not light itself - note the difference) has something to do with it.
b) The fact that M&M used light to find the speed of ether and failed has something to do with it.
c) The fact that it was observed that Maxwell's equation is not invariant under galliliean transformation has something to do with it.

But conceptually even if there is no electromagnetic force or light in the world, special relativity still holds good and newton's equations are wrong.

Ok what is special relativity?

It hinges on one principle, which we need to take for granted.

The principle of equivalence:

a)There is a train which moving at 50 miles/hr and a physicist is inside this train.
b)There is a train which moving at 40 miles/hr and a physicist is inside this train.
c)There is a kid standing in the platform and is pushing a slab of wood horizontally with constant force. Let us assume no friction.

Both the physicists looks at the slab and works out the laws of physics and they both should come up with the same laws of physics governing the horizontal motion of the slab.

Let me further explain:

We provide the physicists with the some measurements for them to figure out laws of motion.

a) Constant Force of the push acting on the ball - F
b) The path traced by the block is calculated by each physicist by observation from their respective trains.
c) m - Inertial :) Mass of the block before the boy kicked the block.

What was thought before relativity was that both physicists will come up with.

F= d(mv)/dt (Newton's Laws)

where v is the instantaneous velocity calculated from the path of the block by each physicist.

The problem was their measurements were inaccurate. If they had performed a really accurate measurement, the equation which they would have got would have been different from Newton's laws (which I couldnt write here as I dont know how to write equations in this text box). Both of them would have got the same einstein's modified equations.

Question: But we thought and accepted newton's laws as it obeyed equivalence principle.What happened to that? It still obeys equivalence principle, but under galiliean transformation of frames of references.The new Einstein equation doesnt obey the equivalence principle based on galilien transformation, but the one based on lorentz transformation.

Yes.They changed the laws of motion and the equivalence principle at one stroke, but not in that order.So that both again tally.

In elementary school, we would have learnt kinematics and then dynamics.

The galiliean and lorentz transformation belong to kinematics.
The newton's and einstien laws belong to dynamics (which involve force).

So we all learnt wrong kinematics(galileo) and wrong dynamics(newton).But both negatives worked well to safegaurd the equivalence principle.

Now we have the correct kinematics(lorentz) and correct dynamics(einstien).

That is all to it.No Light!!
-------------------------

But then I thought relativity had something to with light???!!!

In the whole argument I havent brought the subject of light at all. Light which in turn pointed to maxwell's equation was the actual percursor for the train physicists of our world to start thinking whether they actually did their motion (kinematics) measurements acurately. Maxwell's equations wasnt invariant under galilean transformation based equivalence principle. This puts newton and maxwell at odds. Who was right? This indirectly put Galileo and Lorentz at odds.Who was right?

Rather the question is which team was right?
(Maxwell and Lorentz) new age team or (Galileo and Newton) old wise men team?

We all know Eienstien judged that the New Age team won with the support of M&M team of experimenters as they proved that an object which moved at the speed of light, moved with the same velocity when observed from both trains. This result is inconsistent with Galilean Kinematics, but worked well with Lorentz Kinematics. Incidentally the object which moved with the speed of light was light itself(photons). The subtle point here is that, it could have been any object and also u didnt need to actually go in the speed of light to find out that galiliean kinematics is wrong and we could have done well with any object which went in a speed atleast close to light (close enough for the measuring instruments to detect the discrepancy).

So maxwell's equations and light were only helpers in finding the basic problem in kinematics and dynamics. They werent necessary as in if we had accurate instruments we could have unravelled this problem without having no knowledge of light or maxwell's equations or for that matter even without knowing the speed of light.

To take it further and bring home my point more. Let us assume maxwell's equations and speed of light were discovered after we discovered special relativity. What would have happened?

The constant in the lorentz transformation and einstien's equation of motion would have been named 'l' (in the name of lorerntz) instead of 'c' :) as no one would have known that light travelled at that speed or no one would have known the constant in maxwell's equations. Then later when they would have discovered laws of electrodynamics, they would recognized that the lorentz constant 'l' actually is the speed of light 'c' or the constant in maxwell's equation 'c' and world would have marvelled at that coincidence :).

My intention: Special Relativity is about the laws of physics which is one layer below the laws of forces or interaction. It is like the stage for dancers(other laws) like electrodynamics and gravitation. Is the shape of the stage, based on the shape of the dancers? This is a profound question, which some answers I would say in general theory of relativity.

A fundamental question I am working now on: Are there any other transformations apart from lorentz, which will satisfies invariancy of both maxwell's equation and einstiens equations and also satisy the velocity measurements (atleast to the level of accuracy we are able to measure now).

2. Feb 26, 2005

### ZapperZ

Staff Emeritus
1. You posted this in the wrong section. If you care to scroll even further down, you'll see a Special and General Relativity section.

2. If this is how you think a physics paper should be, then you haven't been reading proper physics papers.

3. At best, all you're trying to do is offer an "alternative" to current theories. Why would anyone adopt your point of view when you haven't given any kind of improvement, predict how your idea deviate from the established model, and propose new results that can be tested. If all you can do is propose an alternative on something that ALREADY works and already being used, then you haven't proposed anything significant.

4. There are several misconception of what SR is in your essay. I mean "light" and "speed of light"? You should go back and try to understand it. Maxwell equations have been reformulated to be covariant under Lorentz transformation. You should also go back and read all the postulates of SR.

5. Unless you have completely missed how things are done here in PF, I'm guessing you should expect this thread to be moved to the TD section.

Zz.

3. Feb 26, 2005

### controlfreak

Zapper,
>>2. If this is how you think a physics paper should be, then you haven't been reading proper physics papers.

U got me wrong... I was not writing a paper here.. I was just blogging my thoughts on something wellunderstood without adding any thing new.

>>3. At best, all you're trying to do is offer an "alternative" to current theories. Why would anyone adopt your point of view when you haven't given any kind of improvement, predict how your idea deviate from the established model, and propose new results that can be tested. If all you can do is propose an alternative on something that ALREADY works and already being used, then you haven't proposed anything significant.

Cool down. I am not proposing anything ground breaking here or I am saying so also. I am just blogging my thoughts on something everbody knows and I am not even adding any new information. But then this is my perspective (which is also not new). What I expect from this forum is a discussion, discussion this view point.

>>I mean "light" and "speed of light"? You should go back and try to understand it. >>Maxwell equations have been reformulated to be covariant under Lorentz >>transformation. You should also go back and read all the postulates of SR.

Is there no distinction between light and speed of light?

>>5. Unless you have completely missed how things are done here in PF, I'm guessing >>you should expect this thread to be moved to the TD section.

I am kind of new here so dont know the rules! out here. So please tell me whether this blog should be in Relativity section or TD section? I am not developing any theory though.. I am just blogging my thoughts. Is that allowed here in this forum?

CF

4. Feb 26, 2005

### ZapperZ

Staff Emeritus
Then use the JOURNALS section. If people want to read your "thoughts", then they can go there. That's what that section is for!

Zz.

5. Feb 26, 2005

### controlfreak

I do not intend to write a journal, but want to start a discussion which can be more effectively done in posting in these sections than in journals which nobody will look at (atleast for an unknown person like me), so that I can learn more based on the different viewpoints of different members in the group.

This is a forum for discussion and I suppose people read these threads and those who want to comment on it can comment on the same.If someone wants to point some mistakes in one's point of view it is more than welcome as that is how people learn. This process increases interaction, online discussion on ideas on physics and in turn help everyone including me in understanding more and helps in correcting mistakes in undersanding.

I do not have direct exposure to physicists on a daily basis for the above process and this is an online forum which I would like to use to do that.

Hope that answers your question. I intend to move this to special relativity section. Can I do that or should the moderator do that?

I repeat my question:
Is there no distinction between light and speed of light? Please elaborate your comment so that I can understand where I am making a mistake.

6. Feb 26, 2005

### Integral

Staff Emeritus
I have moved this to the Relativity forum, but it is not clear that is even where it belongs. Let's see were it goes.

7. Feb 26, 2005

### controlfreak

Thanks a lot. I hope it is retained in a place (whichever is appropriate) where people can look at it and find mistakes with my point of view and post on the same. That way I can learn from other's knowledge and enhance mine, which is my main objective in joining this forum!

8. Feb 26, 2005

### Integral

Staff Emeritus
How do you make measurements without knowledge or use of light or some form of electromagnetic interaction? Seems to me that just because you ignore it in your set of assumptions does not mean that it is not the significant factor.

9. Feb 26, 2005

### controlfreak

Very Very Valid Point. I thought of this very much.

I decided that there should be some measurement/experiement which proves special relativity that doesnt involve light or electromagnetism or rather Is it possible to prove relativity without the use of any kind of help from electromagentism even in experiments. That may be is a wrong assumption.

10. Feb 27, 2005

### cronxeh

I actually thought about a similar thing, but related to the uncertainty principle.

In making measurements you bounce off a photon, perturbing the system. Essentially I was thinking about other possible ways to measure the particle's position and momentum simultaneously and precisely. If a particle resonated the space time and you could detect the tiny ripples and fluctuations then you could find its momentum. However I dont know any theory or even thought experiment that allows for such a thing. Any takes?

11. Jan 9, 2010

### toomajj

Relativity without light is in fact an attempt to show that principles of relativity can be derived even if there weren't any electromagnetic waves, including light. A paper is written on the subject by David Mermin in the American Journal of Physics, 1984, vol 52, page 119-124, showing that if we assume that all laws of physics are the same in all inertial frames of reference, and space behaves the same in all directions (isotropic and homogeneous), then basic formulations of relativity can be derived. In these formulations there exists a limiting speed, which in the case of our universe would be c, the speed of light. I haven't read the article fully, but I've gone through it. So it is nothing new to show that relativity would exist without light.

12. Jan 9, 2010

### bcrowell

Staff Emeritus
Yes, it is possible to develop the whole theory of special relativity without mentioning light or Maxwell's equations. In addition to the paper toomajj listed, here are some more such treatments that I know of:

Rindler, Essential Relativity: Special, General, and Cosmological, 1979, p. 51

Morin, Introduction to Classical Mechanics, Cambridge, 1st ed., 2008, Appendix I

http://www.lightandmatter.com/html_books/6mr/ch01/ch01.html [Broken]

The last one is my own. As far as I know it is the only such treatment that's available online for free. It's aimed at a lower level than the others, but that shouldn't be taken as indicating that the idea can't be developed mathematically and rigorously. Rindler's treatment is very rigorous and mathematical.

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