Einstein's 1905 derivation of his Transformations of Coordinates and Times

[HannonRJ]

Einstein first derived his transformations of coordinates and times in section I-3 of ON THE ELECTRODYNAMICS OF MOVING BODIES. The physical predicates of that derivation were his two Postulates, which Einstein believed were "only apparently irreconcilable". The implicit purpose of all that follows was to remove that irreconcilability.

 

Einstein's First Postulate: "...to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good*i.e. to the first approximation."

 

Einstein's Second Postulate: "...that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body."

 

Bearing in mind that in his subsequent analysis, Einstein treats his "ray of light" as a point that moves along his coincident xi and x axes, is there actually a conflict between his two postulates?

 

What is the physical meaning of Einstein's Second Posulate?

 

It is unfortunate that Einstein did not provide a diagram of his kinematic model, but relied on a verbal description that is open to interpretation

[ajb]

Mathematically it means that Maxwell's equations are not invariant under the Galilean group (which is compact with parameter v, meaning particles can travel at v ) but it is invariant under the Lorentz group which is non-compact with parameter c. This means that nothing massive can reach the speed c.

[HannonRJ]

Mathematically it means that Maxwell's equations are not invariant under the Galilean group (which is compact with parameter v, meaning particles can travel at v ) but it is invariant under the Lorentz group which is non-compact with parameter c. This means that nothing massive can reach the speed c.

 

HannonRJ ASKS: What has this to do with my questions?

[swansont]

Einstein's First Postulate: "...to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good*i.e. to the first approximation."

 

You have improperly quoted this, and changed the meaning by doing so.

 

The actual quote is

"They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good."

 

There is no caveat of "to the first approximation" implied in that postulate.

 

What is the physical meaning of Einstein's Second Posulate?

 

It is unfortunate that Einstein did not provide a diagram of his kinematic model, but relied on a verbal description that is open to interpretation

 

Try reading the rest of the paper. He does math that does not rely on a verbal description.

[ajb]

HannonRJ ASKS: What has this to do with my questions?

 

Everything.

 

From a modern perspective Einstein's postulates "translate" into the (local) invariance under the Lorentz group. This is the physical/mathematical statement that under pins SR.

[HannonRJ]

I see that I made a mistake. Strike "i.e. to the first approximation".

 

I have read the first three sections of OEMB at least a huindred times over the last 18 years. Einstein's model is kinematic, and it has only a verbal description which is open to interpretation. I have learned this fact through many discussions of those sections of OEMB with many other people who have also read them. That will become apparent as discussion of section I-3 unfolds. The mathematics is purportedly an algebraic-correct description of Einstein kinematic model.

 

"Modern perspectives" are irrelevant to what Einstein said in 1905. In his 1915 derivation, he doesn't mention his Second Postulate, per se. In his 1912 derivation, he abandoned the Second Postulate.

 

Since you raise "the Lorentz Group", by which I assume you mean "the Lorentz transformation", have you ever seen an article by H.A. Lorentz in which he details his derivation of the transformation equations that now bear his name? If you know of such an article, please tell me how I can obtain a copy. A few years ago, I tried to find one, enlisting the aid of the US Library of Congress. They could'nt find it. No, it is not in his 1904 article in which he propounds his "contraction". By chance, I did find what was purported to be Lorentz's own derivation of those equations in a book by Sir Edumund Whittaker, who did not cite a source. I did a step-by step analysis of that derivation, that was published as THE MYSTERIES OF THE LORENTZ TRANSFORMATION in Galiliean Electrodynamics, Vol 15, No. 3 (2004).

[insane_alien]

do think maybe the only reason you think it is only a verbal description is because you are only looking at a small part of the whole? the maths comes in the later sections.

[HannonRJ]

My interpretation of Einstein's Second Postulate is that light behaves as if its emitting body has no state of motion at the instant it emits light. Since an instant has no duration, a moving body has no motion at any instant.

[insane_alien]

only in a reference frame where it is not moving does your statement make any sense whatsoever. which is what the postulate is all about.

 

in a frame where the object is moving, an outside observer will see the light moving off the leading edge with a velocity c-v and the trailing edge velocity of c+v relative to the object in question.

 

basically, what you said is that a non moving body has no motion.

[stingray78]

There's no misinterpretation. Einstein theory is pretty clear for anyone with some physics education. The second postulates means that the speed of light is the same if you measure it from the earth than if you measure it from a super sonic airship. Maybe this relativity video can help:

http://www.tubepolis.com/play.php?q=relativity&title=Simultaneity%2B-%2BAlbert%2BEinstein%2Band%2Bthe%2BTheory%2Bof%2BRelativity&engine=1&id=wteiuxyqtoM&img=http%253A%252F%252Fi.ytimg.com%252Fvi%252FwteiuxyqtoM%252Fdefault.jpg

[ajb]

 

"Modern perspectives" are irrelevant to what Einstein said in 1905. In his 1915 derivation, he doesn't mention his Second Postulate, per se. In his 1912 derivation, he abandoned the Second Postulate.

 

OK, you are interested in an historical account. That is fine, it is important to have some understanding of the original arguments. I respect that.

 

Since you raise "the Lorentz Group", by which I assume you mean "the Lorentz transformation", have you ever seen an article by H.A. Lorentz in which he details his derivation of the transformation equations that now bear his name?

 

Well, I did mean the Lorentz group, which consists of all Lorentz transformations. So we do mean the same thing really.

 

If you know of such an article, please tell me how I can obtain a copy. A few years ago, I tried to find one, enlisting the aid of the US Library of Congress. They could'nt find it. No, it is not in his 1904 article in which he propounds his "contraction". By chance, I did find what was purported to be Lorentz's own derivation of those equations in a book by Sir Edumund Whittaker, who did not cite a source. I did a step-by step analysis of that derivation, that was published as THE MYSTERIES OF THE LORENTZ TRANSFORMATION in Galiliean Electrodynamics, Vol 15, No. 3 (2004).

 

I don't know where you can find the original papers. There are some of Einstein's original papers at Chronology of Milestone Events in Particle Physics web site. (You have these, but other people may also wish to have a copy).

 

Am I right in assuming that you are trying to understand the original motivations for special relativity? I gather, you are not fully familiar with the modern ideas of relativity (viz you remark on the Lorentz group). If you are trying to learn relativity from the original papers, then I can assure you that this is not the best way to start out. Either way, whatever it is you want to learn and from what ever perspective, best of luck.

[Klaynos]

# ^ The reference is within the following paper: Poincaré, Henri (1905), "Sur la dynamique de l'électron", Comptes Rendues 140: 1504-1508

# ^ Larmor, J. (1897), "Upon a dynamical theory of the electric and luminiferous medium", Philosophical Transactions of the Royal Society 190: 205-300

# ^ Lorentz, Hendrik Antoon (1899), "Simplified theory of electrical and optical phenomena in moving systems", Proc. Acad. Science Amsterdam I: 427-443 ; and Lorentz, Hendrik Antoon (1904), "Electromagnetic phenomena in a system moving with any velocity less than that of light", Proc. Acad. Science Amsterdam IV: 669-678

 

 

The above are 3 references, the first is when the Lorentz transforms are first called that, the second two are the first derivations of them (the second being the Lorentz paper on them).

 

Einstein derived them himself under Lorentz covariance and that c=constant.

[HannonRJ]

The actual derivation of Einstein's transformation is in section I-3 of OEMB. The previous sections are preparatory. The following sections are applications of thos transformations.

 

There are no "reference frames" or "systems of coordinates" in Einstein's second postulate

 

STRINGRAY78, Are you questioning my education?

Are you familiar with Section I-3 of OEMB? If you are, you would not make such a statement. If you aren't you will not be able to follow this discussion

 

To ajb.

I have been intensively studying SR for about 18 years. If the original premises were invalid, all that follows from them cannot be valid. Einstein was a relative newcomer to the subject, but he is credited as its originator. Whatever later physicists may have contributed, we still represent SR as the equations now known as "the Lorentz transformation".

 

In my studies, I learned that later contributors to SR were more concerned with rationalizing what Einstein said, or interpreting what he said. Too often Einstein is misquoted or misinterpreted. Only Minkowski attempted something different, but that is not my current subject.

 

My objective in starting this thread was to obtain the views of others regarding the mathematical and logical validity of Einstein's 1905 derivation of his transformations of coordinates and times. There are aspects of that derivation that are open to interpretation, and some which seem to me to be invalid.

 

To KLAYNOS: Thanks, but I am looking for an article by H.A. Lorentz himself in which he performs the complete derivation of what is now known as "the Lorentz transformation". It is not in Lorentz's 1904 article that you cited. I will attempt to find a copy of the 1899 article. Derivations by others are numerous, but there must be a reason why the equations bear Lorentz's name.

[ajb]

 

To ajb.

I have been intensively studying SR for about 18 years. If the original premises were invalid' date=' all that follows from them cannot be valid. Einstein was a relative newcomer to the subject, but he is credited as its originator. Whatever later physicists may have contributed, we still represent SR as the equations now known as "the Lorentz transformation".

 

In my studies, I learned that later contributors to SR were more concerned with rationalizing what Einstein said, or interpreting what he said. Too often Einstein is misquoted or misinterpreted. Only Minkowski attempted something different, but that is not my current subject.

 

My objective in starting this thread was to obtain the views of others regarding the mathematical and logical validity of Einstein's 1905 derivation of his transformations of coordinates and times. There are aspects of that derivation that are open to interpretation, and some which seem to me to be invalid.

[/quote']

 

It is conceivable that some of Einstein's original thoughts and derivations are not quite correct. But as we have had 100 years now to reformulate and correct these ideas I would not question the validity of special relativity.

 

As you say, it was not just Einstein who was working on similar ideas.

 

Good luck with your reading.

[Klaynos]

To KLAYNOS: Thanks, but I am looking for an article by H.A. Lorentz himself in which he performs the complete derivation of what is now known as "the Lorentz transformation". It is not in Lorentz's 1904 article that you cited. I will attempt to find a copy of the 1899 article. Derivations by others are numerous, but there must be a reason why the equations bear Lorentz's name.

 

I believe the naming is explained in my first reference, IIRC the Larmor paper actually derives one of the the Lorentz transformations (but not the others) before Lorentz, and it is only luck really that they are not known as Larmor Transformations

 

The idea of SR was on the horizon for a few years when Einstein wrote his paper on it, imo not the best of the 3 papers he published that year and not the one he got a noble prize for. I think the 1899 paper will be your best bet. There's also:

 

^ Lorentz, Hendrik Antoon (1895), Versuch einer theorie der electrischen und optischen erscheinungen bewegten koerpern, Leiden

 

And the original assumptions have been examined alot, most UG phycists are taught them, and tend not to keep their lack of faith.

 

You may also like:

 

http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000069000010001044000001&idtype=cvips&gifs=yes

 

http://www.historyofscience.nl/search/detail.cfm?pubid=209&view=image&startrow=1

 

Would appear to be the 1899 Lorentz paper.

[HannonRJ]

To KLAYNOS. Thanks for the links! The 1899 article appears (at first glance) to be the predecessor of the 1904 article. The earliest contributor to "relativity" I have found, so far, is Woldemar Voigt. He published something similar to the Lorenta transformation in 1887.

[pioneer]

Doesn't Einstein's second postulate suggest a constant zero reference where light is created by matter. Regardless of the moving reference, light touches bases with that zero reference allowing it to propagate consistently, ignoring finite reference. This sort of suggests a paradox of extremes, with two constants, i.e., 0,C. Matter stays >0 and <C, relative to this absolute reference scale.

 

The actual quote is

"They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good."

 

Since that time, haven't more equations, based on virtual probability, which were not included in Einstein's knowledge of mechanics, been added. The mechanics of his day were more based on math logic. But with statistics there is no probability of 1, which is what logic needs to function properly. One can reason only if x=y. If it doesn't, according to statistics, after so many logic steps, it predicts logic will break down. How many pages of logic before it is chaos? These two approaches are mutually exclusive since reasoning with less than 1, makes all logical extrapolations increasingly fuzzy with compounding error subject to the laws of chaos.

 

The question is, do the probability laws become subject to increasing chaos depending on the reference? I can see relativistic mass increasing. This is sort of virtual and not particle tangible, since it doesn't remain after we take away velocity. Does more of it increasingly become affected by chaos. Or does even random and chaos follow a smooth curve? Einstein didn't have worry about this because it was added later, without checking to see if this contradicts or whether even chaos follows a smooth curve, sort of contradicting itself.

[Klaynos]

No the postulate does not imply an absolute frame.

[Norman Albers]

Empty space is that in the neighborhood of the observer and considered with no relative velocity. I enjoyed reading the original statement of "...to first orders and small quantities"...