I believe I have discovered a great way to teach special relativity:

http://www.everythingimportant.org/relativity

What makes my approach intuitive, easy and interesting is that I derive the Lorentz transformation from the Galilean transformation using magic, elementary algebraic manipulation and a clear definition of time. The charm in my approach is that inattentive readers and inexperienced thinkers who know the difference between Galilean and Einsteinian physics are left wondering why the magic seems to work.

If you understand the magic, then you understand relativity.

Eugene,

This is indeed a great "breakthrough" for mankind's never ending quest for knowledge.
I especially appreciated the "Shubertian Clock" which can be looked at as a Grand-father clock without a pendulum. (or a cabinet either)
Once again, congratulations, I know MY faith will never be the same again!

thanks, Ken

Confessions of an SR Prankster and Special Relativity Rabble-Rouser

Confession Number 1 (relevant to sci.physics.relativity):

I have an inclination to say things as pointedly as possible. I always disappoint myself when I do. It isn't easy to believe that I'm responsible for how people understand my words but I suppose that I am. I should consider how slow people are to understand new ideas.

I remember the time when I stunned Wolfgang Rindler with my approach to deriving SR. (I believe that the most insightful path to special relativity is to derive the Lorentz transformation from the Galilean transformation). I explained to Rindler my definition of time using two lines L and L' and that, indeed, the formula T=(x-x')/ u =T' is an acceptable definition of time for two observers in relative motion. Then, wishing to emphasize the logical fallacy of the all-too-familiar reliance on simultaneity to explain time dilation, i.e., the absurdity of the popular phrase "moving clocks run slow," I pointed to and read this sentence from my first draft:


I thought that sentence was a relevant milestone. Rindler's jaw literally dropped and I felt terribly embarrassed by his very visible show of obvious misunderstanding. (How could any graduate student who, only a few years before, seemed competent and rational in his relativity classes, now be an anti-relativity crackpot?) With a deep sense of heartfelt humility and apology, I then hastily explained that a Galilean synchronization exists between any two frames of reference but not for three simultaneously. That had a calming effect but it didn't come close to repairing the rift that I had created. My purpose in using "shock and awe" was to vividly impress the professor with a very charming and delightful derivation. Instead, I alienated professor Rindler from his usual kind and friendly regards, as if I had purposely fooled him with unethical trickery and deception. Sensing his discomfort that I continue, we exchanged a few irrelevant, uncomfortable and clumsy words and we ended our conversation with surprising abruptness. —That situation felt so awkward (the worse I've ever experienced) that I haven't had the temerity to speak to professor Rindler since.

Here's my complete derivation of the Lorentz transformation equations:

http://www.everythingimportant.org/relativity

Let me see. I start with x'=x-uT, T'=T and I end up with

x'=Y(v)(x-vt)
t'=Y(v)(t-vx/c^2)
Y(v)=1/sqrt(1-v^2/c^2)

Yes indeed. That's a derivation all right.

> You have a transformation.

Yes indeed! I transformed the equations x'=x-uT, T'=T by resetting clocks and I ended up with the Lorentz transformation. It's a transformation through and through.

> What you call "manipulation" is merely transformations so you don't have a derivation.

It's obvious that your claim of "merely transformations" is totally false. There is no isomorphism between the Galilean group of transformations and the Lorentz group. Every child mathematician knows that the Galilean group and the Lorentz group are not isomorphic.

A derivation can have elementary algebraic manipulations / transformations and still be a derivation. It's obvious that I did more than merely adjust time on a Shubertian clock.

Sorry, but you have not accurately identified how I decapitated relativity and then reattached its head by the end of the performance.

Let's see you persuade my critics of the fact and get them to understand it.


Dear Bilge,

If you wish to refute Tom Roberts' understanding of clock synchronization and his testimonials in my favor, perhaps you should demonstrate near asymptotic credibility and write up a scientific paper on the threat I pose to the laws of physics and the universe with my very menacing desynchronization scheme.

If you lack courage in refuting recognized experts like Tom Roberts then I don't believe that you've earned the right to pretend, with elaborate charades, that you've refuted my thesis.

But I do thank you for your effort.

Dear David,

Thanks for your reply. Rage Bilge gave me an answer similar to yours and I just laughed saying that he didn't believe in metric spaces. There is nothing about my derivation that requires the use of ordinary materials. The exercise is entirely mathematical. Use ghostly neutrino measuring rods if you like. :-)


The only requirement is that you believe in metric spaces and I doubt that you do. A ruler represents a simple, childlike illustration of a space-measuring device. I do not care about the physics of materials.

I said that the rulers were frictionless. If you search Tobin's Space Catalogue for the physics of incorporeal and ethereal objects, you'll probably find that frictionless rulers are listed. If not, then try to understand that I'm entertaining mathematical axioms that lead to an intuitively simple derivation of the Lorentz transformation. My purpose is not to be bound by the limitations of real measuring devices but to teach special relativity in a clear and understandable way.

http://www.everythingimportant.org/relativity

I have just completed my first pdf version of my relativity paper.

http://www.everythingimportant.org/relativity/special.pdf

Tom Roberts <tjroberts@lucent.com> wrote in message news:<A9Hed.15741$5b1.13208@newssvr17.news.prodigy.com>...
> Eugene Shubert wrote:
> > http://www.everythingimportant.org/relativity/special.pdf

> The quality of a derivation of the equations of SR is usually judged by:
> 1. the simplicity and physical believability of its assumptions, or
> lack thereof.

> and:
> 2. the generality of those assumptions.

I wholeheartedly agree. And by the generality of those assumptions, I assume you mean the value and added clarity that it brings to the subject and to the opening of new questions, vistas and future research. That describes my paper perfectly.

> Your derivation is seriously lacking in both of those aspects:
> 1. On page 2 your assumptions for \mu and \gamma are completely
> unsupported,

My official derivation begins on page 4. The assumption that you refer to (page 2), the principle called change of variables, also called substitution, is one of the clearest and most useful mathematical ideas in high school algebra and baby calculus. What's your dispute with intuitively simple fundamentals? What support do I need and why is it an unwarranted physical assumption if I label the function 1/sqrt(1 -v^2/c^2) with the Greek letter gamma?

> and are not obvious at all -- these are QUITE unusual assumptions,
> to say the least; why should anybody believe them?

Why should anyone believe in the substitution v/c = tanh(theta), which transforms the usual Lorentz transformation to its hyperbolic form? It's just the writing of one parameter in terms of another.

Why is substitution allowable here but not there? Perhaps the difference is that every child mathematician can plod through a difficult mathematical proof, checking each step for logical correctness, whereas mature physicists need their hands held by someone they trust and have their irrational prejudices pacified at every step.

> 2. Your sliding rulers work in 1 spatial dimension,

Thanks for mentioning that. You'd be surprised by the number of physicists and seemingly educated folks who have an emotional difficulty with sliding rulers!

> though you have left a lot out (e.g. how to mark them uniformly;

I suspect that just about all students of algebra at the high school level will assume that the rulers are pre-made and that even middle school students could figure out how "to mark them uniformly."

> how to know they move with uniform velocity);

They're assumed to move with uniform velocity. That translates into equal distances traveled in equal proper times. That's where the constant u comes from in the general two-ruler synchronization:

T = T(x,x') = -x'/u + xi(x)
T' = T'(x,x') = x/u + zeta(x')

> your omissions can be corrected. But it is not at all clear how to
> apply this to an arbitrary relative velocity in 3 spatial dimensions.

My intended audience is second year algebra students in high schools and all backward uneducated folks on the newsgroups. Relativity in 3 spatial dimensions plus 1 time dimension is a college level topic.

> And you have completely left out any mention of isotropy and
> homogeneity, which are important and necessary aspects of inertial
> frames in SR.

Homogeneity and isotropy are geometric ideas of zero or virtually zero importance in 1 spatial dimension.

> This is, of course, related to the omissions I mentioned in #2
> above; but it is not obvious how to resolve this with your
> assumptions, especially isotropy.

I encourage students to try to break the no-nonlinearity postulate of SR and construct all the Shubertian clocks possible that are unauthorized and frowned upon in conventional physics. I advise that students and researchers only do so for purely mathematical reasons so that no sacred traditions are violated and that the sacrilege is not to be flaunted.

http://www.everythingimportant.org/SDA/viewtopic.php?t=221
http://www.everythingimportant.org/relativity/generalized.htm

> A better approach, IMHO, is to use group theory: given sufficient
> postulates to establish isotropy and homogeneity of the coordinates,

Homogeneity and isotropy are mathematical terms that describe a geometry, not coordinates. You are perfectly free to break with standard mathematical convention and define what you mean by homogeneous and isotropic coordinates but I've never seen you do that. I've seen you presupposing that space and time together is a geometry called spacetime and that the homogeneity and isotropy of spacetime automatically implies that coordinate transformations are linear.

The problem with your approach to SR is that you don't define what a geometry is so it's impossible to really understand the implications of homogeneity and isotropy in your vague, meaningless and nebulous terms. I don't mean to discourage you from pursuing a geometric derivation. It's just that the fallacy of supposed linearity of coordinate transformations is easily refuted by simply defining geometry according to Klein's Erlanger Program:

"Every geometry is defined by a group of transformations, and the goal of every geometry is to study invariants of this group." Klein, Erlanger Program.

"Each type of geometry is the study of the invariants of a group of transformations; that is, the symmetry transformation of some chosen space." Stewart and Golubitsky 1993, p. 44.

"A geometry is defined by a group of transformations, and investigates everything that is invariant under the transformations of this given group." Weyl 1952, p. 133.

"The geometry of Minkowski space is defined by the Poincaré group." [1].
Here's the critical point. It's easy for any child mathematician like myself to show that the nonlinear transformation group of exercises 1 and 2 of http://www.everythingimportant.org/relativity/generalized.htm is isomorphic to the Poincaré group. That means that their respective geometries are isomorphic, i.e., indistinguishable. Thus, it's impossible to prove linearity of coordinate transformations from homogeneity and isotropy alone. If Minkowski space is isotropic and homogeneous, then so is the geometry defined by my wildly nonlinear transformation group.

> group theory constrains the transforms to 3 groups:
> The Euclid group in 4 dimensions
> The Galileo group in 3 dimensions
> The Lorentz group in (3+1) dimensions
> The first has grossly unphysical consequences, and the second does not
> agree with basic observations about the world, such as the simple fact
> that pion beams exist. But the Lorentz group works, and is the basis of SR.
>
> Evaluated on the basis of those above criteria, this approach is VASTLY
> simpler and more general than yours.

My approach is obviously more general and informative. The Shubertian clock is the discovery I used to correctly understand and properly interpret the first counterexample to Einstein's thoroughly misguided no-nonlinearity postulate of special relativity. That's a new result.

When you remove the nonsense argument about homogeneity and isotropy implies linearity, your approach will be simple. But I use group theory also and you should notice that I begin with the greatest conceivable nonlinearity possible and then I quickly and honestly simplify the problem to linear mathematics, two unknown functions and an easily invertible matrix. What I've done is spend a lot of time explaining an intuitively simple and straightforward definition of time—the Shubertian clock. That's to my credit.

> It was already old when I first saw it ~1972.

What you have is just a slight rewrite of the findings of Ignatowsky, Frank and Rothe in papers written between 1910 and 1912. [2].

> [I posted a version of this some 15-20 years ago, but realize
> my ancient presentation has some major flaws (which can be
> corrected).]

> Tom Roberts tjroberts@lucent.com

Eugene Shubert
http://www.everythingimportant.org/relativity/special.pdf

Tom Roberts wrote
>>> The quality of a derivation of the equations of SR is usually
>>> judged by: 1. the simplicity and physical believability of its
>>> assumptions, or lack thereof.
>>> and: 2. the generality of those assumptions.
>>
>> I wholeheartedly agree. And by the generality of those assumptions,
>> I assume you mean the value and added clarity that it brings to the
>> subject and to the opening of new questions, vistas and future
>> research.
>
> No. Perhaps you too should learn how to read.

Perhaps you should learn how to listen. Mathematicians speak of the generality of a certain idea, axiom or technique and they mean something capable of being generalized and having the richness to yield fruitful, far-reaching consequences, i.e., having usefulness in many situations as opposed to a highly specialized trick that only works in a single unique instance.

> By "the generality of those assumptions" I means precisely that:
> how generally valid the assumptions are. Yours, of course, aren't
> generally valid at all, as they only apply to 1+1 dimensions.

You're ignoring the power of my approach in that it has created a clearer understanding and new results. It refutes a confused understanding that many relativists have, even in 1+1 dimensions. You're also ignoring the sheer entertainment value of being able to derive the Lorentz transformation from the Galilean transformation.

> > The assumption that you refer to (page 2), the principle called
>> change of variables, [...]
>
> So change variables using any other functions, and get equally well
> supported results.

Does that concept trouble you?

> For the result of a derivation to be believable, it
> must rest on believable postulates. You gave no
> reason whatsoever why your postulates should
> be believed.

The actual computations that you are whining about on page 2 were rendered invisible in my official derivation on pages 4-6. I added the computational details of page 2 and 3 because the furious physicist Rage Bilge didn't have a clue about how to reset a Shubertian clock. He calls my derivation (pages 4-6) symbol manipulation.

>> What's your dispute with intuitively simple fundamentals?
>
> If you want anybody to believe you, you need a physical justification
> for the equations you plucked from the air.

Real mathematicians are qualified to pluck equations out of the air. They do it all the time. And those skilled in mathematics are absolutely clear about when they can do this to construct a logical proof. Proof by mathematical induction is a perfect example.

All logical proofs are believable. My postulates are practically invisible on pages 4-6. Does that give them a lesser or greater magical appearance?

>>> and are not obvious at all -- these are QUITE unusual assumptions,
>>> to say the least; why should anybody believe them?

> > Why should anyone believe in the substitution v/c = tanh(theta),
> > which transforms the usual Lorentz transformation to its hyperbolic
> > form?
>
> Because that is not an ASSUMPTION, it is a CONCLUSION.

There are plenty of derivations of the Lorentz Transformation equations that don't define theta. Take Einstein's tortured derivation for example (Dover, The Principle of Relativity). And try to find a mathematician who isn't going to laugh at you. If theta isn't defined anywhere in a derivation, then you are perfectly free to let theta be anything that pleases you at any step in a derivation. And even if a simple substitution/transformation doesn't please some physicists, it still has every mathematical right to exist.

There is no physical assumption in the mathematical substitution u=v/sqrt(1 –v^2/c^2).

>> Eric Gisse wrote:
>> > you make huge gaping errors in mathematical logic.
>>
>> What error did I make using the principle called, change
>> of variables? What assumption is made in the substitution,
>> u=v/sqrt(1 -v^2/c^2)?
>> http://www.everythingimportant.org/relativity/special.pdf

> Read the following for comprehension:
>
> Your math is fine. Technically it is correct, but it is not a proper
> derivation in any sense of the word.

You're not qualified to make that judgment. You're a beginning physics student, not a math major. Isn't that right?

> The assumption you make in the substitution is that the proper
> form of the equation is v/sqrt(1-v^2/c^2). You do not derive
> gamma anywhere, you assume it.
>
> Do you understand what I said?

I understand your claim. You don't understand my assertion. You also lack experience with mathematical proofs to know that mathematicians command great power and often pull things out of the air. You also don't see that my official derivation on pages 4 to 6 doesn't depend on this little tidbit that you're objecting to on page 2. You also failed to notice my insistence that my definition of v and gamma works perfectly well in a Galilean universe. You seem to believe that I assumed something Einsteinian. If so, then construct a gedanken experiment in a Galilean universe and reach a contradiction.

"The justification of page 2 and 3 is extraordinarily easy. Let 1/c be any real number. Try to argue how the substitution u=v/sqrt(1 -v^2/c^2) could be false in a Galilean universe or in any other universe that begins with an undeclared symbol v. Understand that I started my paper by defining u, not v. I never gave v a physical meaning. So where's the contradiction? Devise a gedanken experiment in a Galilean universe to prove that this substitution leads to contradictory results. It's impossible. Inconceivable! It can't even be imagined to be false. So it's true without any effort. It's just one step in a powerful magic trick." http://www.everythingimportant.org/relativity/special.pdf

> If you truly have a [degree] in mathematics, this would
> be patently obvious to you.

It's improper for you to speak for mathematicians.

> Why should u = v/sqrt(1-v^2/c^2)?

Because it's vacuously true in every conceivable universe.

> You assume what you wish to derive!

Since there is no conceivable universe where that substitution is false, it is then always true, even in a Galilean universe.

> But you ASSUME u=v/sqrt(1-v^2/c^2)!
> You ASSUME u=v/sqrt(1-v^2/c^2)!

You have no proof that my change of variables is a physical assumption. You are merely arguing out of blind and bigoted ignorance. The onus is on you. Magicians aren't expected to justify waving their magic wands or their use of the word, abracadabra. Those are just props used to invoke a sense of mystery in some and to entertain others. The challenge is for you to prove that my steps violate some law of physics in some conceivable universe. Suppose universe X and real numbers u and 1/c. How does writing u=v/sqrt(1 -v^2/c^2) violate the laws of physics in that universe?

Thanks for stating the issue so clearly. Perhaps Tom Roberts et al will be helped by it.

The Nature of Mathematics - a plea for help

I have a trivial question concerning mathematics and logic and I would like to receive a resounding answer that is both unanimous and clear from practicing mathematicians and logicians. The cross-posting is for the benefit of the physicists who have read my paper http://www.everythingimportant.org/relativity/special.pdf and are stumbling over its elementary logic. Here's the logic that the physicists find troubling. Suppose you begin a derivation by assigning a clear and undisputed physical meaning to real parameters x, x', T,T', and a real constant u. From that reasonable starting point, I claim it's legitimate to pick a real number 1/c and then define a new quantity v by the equation u=v/sqrt(1 -v^2/c^2). The point is to then write everything in the ensuing derivation in terms of v and not u. I also believe it's legitimate to define, without any justification whatsoever, the function gamma(v) = 1/sqrt(1 -v^2/c^2).

What troubles the physicists is the appearance of magic. I'm just magically pulling definitions out of the air. Are these steps—to demonstrate that we may arrive at a conclusion with fewer assumptions than previously thought possible—mathematically and logically admissible?

This is your condemnation:

You are confident that Gene Ward Smith and Will Twentyman failed to answer my opening question. And you believe that you're handling the evidence honestly.

"Tom Roberts" <tjroberts@lucent.com> wrote in message news:npIpd.32646$Qv5.9901@newssvr33.news.prodigy.com...
> Eugene Shubert wrote:
>> A Magical Derivation of the Lorentz Transformation
>> http://www.everythingimportant.org/relativity/special.pdf
>
> Your insistence on your peculiar "magic" makes this more complicated
> than it really is, and less related to the underlying assumptions you
> actually make.

My aim was to derive the Lorentz transformation from the Galilean transformation in the most plausible, instructive and entertaining way possible. I believe that I've achieved my objective.

> I grant you that your "Shubertian clock" is new and unique (AFAIK).
> But your insistence on using it obfuscates your "derivation".

The Shubertian clock gives a very precise definition of time and provides the physical motivation and concrete interpretation for the equations that follow. The difficulty that physicists have displayed in their inability to interpret my elementary equations is faithfully recorded in the google archives. I believe it's clear that their silly rants are based on the collective ignorance of professional physicists generally for mathematical clocks and how to reset them, not on my tangible model of spacetime.

> And the fact that your "Shubertian clock" cannot be applied to 3+1
> dimensions makes it irrelevant to the world we actually inhabit.

It's obvious to me that the Shubertian clock can be extended to 3+1 dimensions. I believe that it's easy for any mathematician to imagine ghostly Euclidean 3-spaces passing through each other. Truthfully, I believe that children can conceptualize that.

> When you say: "Now let's assume that when we multiply two matrices of
> this form, then the product matrix will be of the same form [...]" you
> are really applying group theory, but don't seem to realize it.

My math degree is from the University of California, San Diego. I graduated summa cum laude. I also pursued advanced degrees in math and physics. I'm not aware of any respectable undergraduate mathematics program anywhere where math majors are permitted to escape the study of group theory.

My intention was to demonstrate that understanding the essence of special relativity at a very deep level is really just elementary high school mathematics.

> Standard and well-known derivations of the Lorentz transform are based
> on the following assumptions/postulates/techniques:
> 1. The Principle of Relativity (Einstein's version)
> 2. Definition of inertial frames
> 3. Application of group theory
> 4. A basic experimental observation, such as the existence of
> pion beams
>
> Your "derivation" implicitly assumes 1, 2, and 3, but you don't bother
> to mention them,

1. My derivation does not assume Einstein's Principle of Relativity. I assumed a much weaker formulation. My physical postulates are two: Time can be defined with moving rulers. The relative "proper velocity" between any two observers is equal in magnitude and opposite in direction. If you believe that I assumed anything else, either you misunderstand or I was cheating. :-)
2. I refer to sliding rulers. That's a good enough mention of inertial frames for high school students.
3. I'm not aware of any magic that comes about by using the words "group theory."

> and your "magic" is really mere omission on your part[#].
> [#] While such omissions are an essential part of a stage
> magician's illusions, in a paper purporting to be a
> mathematical derivation they are cause for rejection.

My magic is based on full disclosure and that's a mystery to physicists because they are so deeply believing in tradition and I derive special relativity in an irreverent, nontraditional way. The only omission of any relevance is the lack of objectivity and professionalism by physicists when they hear of an upstart claiming that the Lorentz transformation can be derived from the Galilean transformation.

> Your omission of 4 (or any such observation) makes your
> "derivation" unrelated to the world we inhabit, which is an
> important aspect of physics.

My aim was to interpret the Lorentz transformation as a colossal, universal, everywhere present clock. My goal was to derive the Lorentz transformation in a way that explains and validates this new model of spacetime.

> I put "derivation" in quotation marks, because in normal
> usage that word means a mathematical demonstration of the
> conclusion from stated postulates. As you don't actually
> state your postulates, but "magically" introduce them
> whenever the mood strikes you, your paper is not really a
> derivation.

It's unreasonable to dismiss a valid argument by whining about the precise sequence and procedure in which a mathematician/magician decapitates relativity and then reattaches its head by the end of the performance.

> Moreover there is a glaring omission in your paper: you fail to consider
> the situation when k=0 or k<0. Had you done so you would find that your
> method cannot rule out either the Galilean transform or the Euclidean
> transform.

The meaning of k=0 is obvious in my derivation. I did refer to the case k<0 in the first draft of my paper but I now think it's best to leave it as an elementary exercise. If you check you'll see that my transformations for the case k<0 fail to be a mathematical group.

> Bottom line: your claim that "many physicists have dogmatically
> declared that it is impossible" is based on your own limitations
> and inexperience, not any fault of "physicists".

I will leave it to future historians to judge the senseless opposition to my physics from all that's recorded in the google archives. I believe that the scholarly consensus will be, in their judgment of the incredible bigotry and blindness, that all my detractors with degrees in physics are practically indistinguishable from the rest of the ignorant newsgroup rabble.

> You confuse "dogmatism" with the desire that such
> a paper be complete and logically well-formed.
> Yours isn't.

For the record, you're saying that physicists are obviously confused by my failure to mention the consequences of k=0, k<0 and their inability to recognize my assumptions. That's very amusing.

I have a question for you Eugene. Why are you so convinced that you can derive SR from a Galillean transformation and math alone when so many smart people (who have physics training) have told you that you cannot?