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The Essential History of Special Relativity


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The genesis of the theory of relativity was a long process that involved three major players and their critical reactions to the electrodynamics of moving bodies.

 

Lorentz made a key step when he sought to develop a mechanics that would obey the principle of relativity and Maxwell's equations. Lorentz exploited the invariance properties of the fundamental equations for the interaction between electrons and fields, and thus accounted for the absence of effects of the motion of the earth through the ether, but only to a certain approximation.

 

Poincaré made this absence of effects a general postulate and elevated the principle of relativity even higher than Lorentz did. He put the Lorentz transformations into a perfect form, discovered their group properties and gave them a physical interpretation. He used these transformation equations to reveal the perfect invariance of the electromagnetic equations and to create a Lorentz-invariant theory of gravity.

 

Einstein made Poincaré's theory completely symmetric by putting space and time in any two inertial systems on exactly the same footing. He also simplified relativity by eliminating the ether and by declaring two previously accepted results were fundamental postulates. From the two postulates, Einstein derived the Lorentz transformation.

 

Special Relativity Directory - Everything Important

 

The next significant development in the history of relativity occurred when I eliminated everything from relativity that was not amenable to experimental verification. This was achieved by specifying an irreducible axiom set that produces the least confusion for beginners, which is the set of absolute minimum requirements for a relativistic theory to exist. My theory derives the Lorentz transformation without using Einstein's first or second postulate.

 

The Axiomatization of Physics - Step 1

 

The reductions and simplifications created in this theory are both dramatic and unpleasant. The consequences are severe in that the whole edifice of special relativity has been reduced to a near tautology, which requires more work. The theory states that all the laws of physics may be divided into two distinct categories. There are physical laws that are the same in all inertial frames of reference and there may be laws that aren't.

 

Shubee

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The next significant development in the history of relativity occurred when I eliminated everything from relativity that was not amenable to experimental verification.

 

What part of relativity do you believe is outside the scope of experimental verification?

 

This was achieved by specifying an irreducible axiom set that produces the least confusion for beginners, which is the set of absolute minimum requirements for a relativistic theory to exist. My theory derives the Lorentz transformation without using Einstein's first or second postulate.

 

I haven't read you paper and I don't know of what method you speak. But, I would agree there are alternatives in deriving the Lorentz transformations to Einstein's method. Erik Christopher Zeeman has done so starting with the principle of causality. Can you tell us what postulates you start with?

 

The reductions and simplifications created in this theory are both dramatic and unpleasant. The consequences are severe in that the whole edifice of special relativity has been reduced to a near tautology, which requires more work. The theory states that all the laws of physics may be divided into two distinct categories. There are physical laws that are the same in all inertial frames of reference and there may be laws that aren't.

 

Shubee

 

Which laws are different in differing inertial frames? And, what makes them different?

 

-modest

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What part of relativity do you believe is outside the scope of experimental verification?

A fundamental pillar in special relativity is that no absolute frame of reference exists. I believe that assumption can never be proved true empirically.

 

I haven't read you paper and I don't know of what method you speak. But, I would agree there are alternatives in deriving the Lorentz transformations to Einstein's method. Erik Christopher Zeeman has done so starting with the principle of causality. Can you tell us what postulates you start with?

 

Yes. My fundamental axioms are:

 

1. Newton's first law of motion.

2. There is a simple definition of clock time for each point in an inertial frame of reference. (i) This time is mathematically well-defined. (ii) Time is defined the same way in all inertial frames of reference.

 

Which laws are different in differing inertial frames? And, what makes them different?

 

I didn’t specify any. I was merely elaborating on the logical consequences of my fundamental axioms.

 

Shubee

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Apparently not. I responded to your questions but, upon hitting the reply button, got a screen message that said that the post had to be approved by the administrator first.

:)

 

Shubee,

 

An upgrade to the latest vBulletin software may have some associated bugs. The developers are working on the issue. Rest assured you have done nothing wrong. The message you received was unintentional as it is not site practice to approve a user's post before it is posted.

 

You can message me or any other moderator or administrator if you have continued trouble posting.

 

-modest

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I see where you're coming from Shubee. I looked over your paper and found it very interesting. I plan to look closer at your derivation when time permits.

 

I also looked closer at the oxford author we mentioned before and found a book that is VERY related to your paper and interests: "Physical Relativity: Space-time Structure from a Dynamical Perspective" published in 2005.

 

I've been looking at what is available at Google Book's preview and found interesting and related information. The type of derivation you're doing was done by Jean-Marc Lévy-Leblond in 1976. The results are called Ignatowski transformations in honor of the first to do so.

 

Google Book's preview is here: Physical Relativity: Space-time ... - Google Book Search

 

And a similar derivation is done here: http://philsci-archive.pitt.edu/archive/00003660/01/Tirp.rtwa4.pdf

 

This shows how both the Galilei and Lorentz transformations may be derived from the relativity principle on the basis of certain elementary assumptions regarding time. I then reflect on the implications of this derivation for understanding proper time and the clock hypothesis.

 

I applaud you for your work on this Shubee, this is very interesting.

 

-modest

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I see where you're coming from Shubee. I looked over your paper and found it very interesting.

 

At the present time it’s just an unassailable foundation. I hope to add more interesting stuff later on. I currently have 4 more sections in my mind that I need to write out in this order:

 

Time Dilation

Time Travel

Faster Than Light Transformations

The Spherical Toy Universe

 

Although the group theoretic approach makes no appeal to the rods and clocks that feature in Harvey Brown’s operationalist approach —and indeed HB does not seem to regard the group theoretic approach as very instructive pedagogically— some of the tentative conclusions I reached were nonetheless quite similar to his. —Richard T. W. Arthur, Time, Inertia and the Relativity Principle, p. 1.

 

I agree wholeheartedly that deriving the Lorentz transformation group by assuming a group structure is terribly unenlightening. I don’t go that route and that’s why my approach can’t be compared to the derivations of Ignatowski, Frank, P. and Rothe, Lee and Kalotas, Mermin, N. David, and Jean-Marc Lévy-Leblond.

 

I am going to assume the linearity of these transformations; this follows from the homogeneity of spacetime. HB himself outlines two different ways of proving linearity from homogeneity (26-28), one of which is given a general treatment in Lévy-Leblond (1976). —Richard T. W. Arthur, Time, Inertia and the Relativity Principle, p. 10.

 

That’s a very widely held misconception and I plan to refute the notion by computing time dilation with a general set of nonlinear transformations, getting familiar results, and also show by a direct argument why my Lorentz-equivalent nonlinear transformations are physically indistinguishable from the Lorentz group. See exercise 1 and 2 in my brief notes on Generalized Lorentz Transformations.

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Very Interesting

 

I enjoyed reading the axiomatization of physics.

 

I look forward to further posts.

 

I often wondered whether it was possible to build a spacetime with a recursive nature maybe you can answer that question sometime..

 

Thanks again

 

Peace

:)

 

My very conventional solution of the equations for the three frame universe [imath]\Xi_3[/imath] assumed that those equations were functional equations with independent velocity variables. I didn’t have to assume mathematical simplicity; I believe it’s obvious that infinity many other solutions also exist. If I had decided against finding a simple answer, then I would only be left with an extraordinarily complicated solution strategy. If I had pursued that rebellious strategy, which would only be regarded as being mischievous, then the construction of [imath]\Xi_4[/imath] and all higher order universes would involve a recursive process that would depend on the previous steps taken.

 

To give you an idea of what some of those universes look like, begin with generalizing the Lorentz transformation written in terms of rapidity [imath]\theta[/imath]. Assume the more general form:

 

[math]x' =x\cosh\sigma(\theta) -t\sinh\sigma(\theta)[/math]

 

[math]t'=-x\sinh\sigma(\theta) +t\cosh\sigma(\theta)[/math]

 

Next, suppose that a set of transformations of this type satisfy the properties of a mathematical group and conclude immediately that

 

[math] \sigma (\theta + \phi)= \sigma (\theta) + \sigma (\phi) [/math]

 

Nontrivial solutions to this equation exist, but they all require the Axiom of Choice. The only continuous solutions are of the form [imath]\sigma(\theta)= \alpha \theta [/imath] where [imath]\alpha[/imath] is a constant. The nontrivial solutions are discontinuous at every point.

 

Shubee

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The type of derivation you're doing was done by Jean-Marc Lévy-Leblond in 1976.

The clearest reason this is impossible is that Jean-Marc Lévy-Leblond and I come up with different conclusions. Please note this claim by Richard T. W. Arthur and his alleged agreement with Harvey R. Brown and Lévy-Leblond:

 

I am going to assume the linearity of these transformations; this follows from the homogeneity of spacetime. HB himself outlines two different ways of proving linearity from homogeneity (26-28), one of which is given a general treatment in Lévy-Leblond (1976). —Richard T. W. Arthur, Time, Inertia and the Relativity Principle, p. 10.

 

In my paper, The Axiomatization of Physics - Step 1, it’s already clear from the fundamental equations of [imath]\Xi_2[/imath] that the most complete description of the simplest spacetime imaginable is given by nonlinear transformation equations.

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I'm looking at Brown's book:

 

pages 26-27

 

and he seems to make a good case for linearity.

 

I'll have to find Lévy-Leblond's work on it and go back to your paper to make any kind of intelligent comment. The only derivation I've ever done is Einstein's special relativity and that was some time ago. So, this may take some time for me to properly follow.

 

-modest

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