The special theory of relativity is defined by the Lorentz transformation between two systems of of space-time coordinates $S:(x,t)$ and $S^\prime :(x^\prime ,t^\prime )$ defined by (normalizing the speed of light to 1):

$x^\prime = \gamma (x -vt)$ , $t^\prime = \gamma (t -vx)$ , $\gamma =\frac{1}{\sqrt{1-v^2}}$ .

This transformation is supposed to connect observations in two coordinate systems with space-axes moving with velocity $v$ with respect to each other as indicated in the above figure typically presented in a book on the special theory of relativity.

However, the figure is misleading: The $x^\prime$ -axis defined by $t^\prime =0$ is not parallel to the $x$ -axis, since it is given by the line $t=vx$ which is tilted with respect to the $x$ -axis.

The Lorentz transformation thus does not describe the physics of two observers moving with constant velocity with respect to each other, each equipped with a space axis, but is instead a non-physical coordinate transformation mixing space and time with the sole purpose of conserving the same speed of light.

Einstein viewed the Lorentz transformation both as a definition and as a physical reality, and physicists have followed in his footsteps with a firm belief that the constancy of the speed of light in vacuum is both a definition (in operation today since now the length unit is defined as a certain fraction of a lightsecond) and a true physical fact.

But this is against the first principle of real science of not viewing a definition (which is true by its construction) as a statement about reality which may be true or false. In other words, physicists of today are not making a clear distinction between science (which may be true or false) and pseudo-science (true by definition). This means a collapse into irrationality and mysticism, in full glory present in the theory of relativity.

In general relativity the principle of equivalence (of heavy and inertial mass) is similarly used both as a definition and physical fact.

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Richard T. Fowler
January 16, 2012

“Cogito ergo sum.”

This is all very interesting, as I noted on your previous post. One thing though, Claes. I do not agree with your suggestions on this post and the previous one that there is no place in science for any expressions of certainty. There is a question of reasonability.

In my mind, I conceive of what I could call “the ideal reasoner” or “the perfectly reasonable person”. This is the person who has no flaws whatsoever in his capacity of reason.

We cannot necessarily always know what this person would think of a given proposition. But we can know that if, upon consideration of the evidence and the argument for it, he would have no doubt about its truth, then it would be unreasonable (a.k.a. unscientific) for us to have any doubt about it.

We are called on — as both scientists and as human beings generally — to do our utmost to follow in the footsteps of the ideal reasoner. This means first accepting that there are some propositions which can be known for certain, and that if, after all due diligence, we have no doubt that we have found such a proposition, then we are ethically required to declare our certainty about it, and to declare that, to us, it is proven.

At the same time, we recognize our fallibility as men and women — we recognize that while there is an “ideal reasoner”, we are not that person, and thus it is sometimes possible for us to reason in error. But we also recognize that it is possible, on some occasions, for our experience (including our observations) to be so compelling that it overwhelms all possibility of erroroneous reasoning on a particular question, and thus on those particular occasions it is possible for us to temporarily equal the logical capacity of the ideal reasoner and, thereby, be certain. We, of course, cannot do this solely on our own merit. The accomplishment is a function of the ability of experience to temporarily overwhelm the corrupting influence of our own imperfect reasoning capacity.

As proof of the foregoing, recall Descartes and his “I think, therefore I am.” This statement is an excellent example of those which it would be inherently unreasonable to express any doubt about. Notice that Descartes did not say, “I think, therefore I think I am.” Thus, the statement was one of certainty, and not mere ordinary belief, which contains doubt. There is ordinary belief, and there is extra-ordinary (i.e. beyond ordinary) belief. The latter is synonymous with knowledge.

And there are other propositions that follow directly from that one of Descartes. Those propositions must also be accepted with certainty by the ideal reasoner.

As further proof, I offer the following as an example.

This is taken from the following blog page (from a blog which I am not associated with, and do not agree with everything found there):

http://fellowshipofminds.wordpress.com/2012/01/14/you-just-cant-make-this-stuff-up/

The excerpt is claimed to be a quote from a book entitled “Disorder in the American Courts” and is reportedly an actual exchange that happened in a U.S. courtroom.

——-
ATTORNEY: Doctor, before you performed the autopsy, did you check for a pulse?
WITNESS: No.
ATTORNEY: Did you check for blood pressure?
WITNESS: No.
ATTORNEY: Did you check for breathing?
WITNESS: No..
ATTORNEY: So, then it is possible that the patient was alive when you began the autopsy?
WITNESS: No.
ATTORNEY: How can you be so sure, Doctor?
WITNESS: Because his brain was sitting on my desk in a jar.
ATTORNEY: I see, but could the patient have still been alive, nevertheless?
WITNESS: Yes, it is possible that he could have been alive and practicing law.
——-

The doctor is joking, of course. Clearly he does not believe that it was possible that the “patient” was alive (according to the accepted definition of “alive” for this context) when he, the doctor, began the autopsy. But the doctor makes an excellent point … namely, that in considering the seemingly brainless nature of the attorney questioning him, that, in the practice of a “science” that contains no possibility of certainty about anything, the “scientist” would be ethically required to conclude that it really is possible that the attorney questioning him has his brain, not in his head at the moment, but rather in a jar on someone’s desk!

Is that a scientific conclusion? If not — and if you can say that with certainty, with no doubt whatsoever in your mind — then the true science must be as I have described it above.

– Richard

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Philippe
January 20, 2012

However, the figure is misileading: The -x’ axis defined by t’=0 is not parallel to the x -axis, since it is given by the line t=v.x which is tilted with respect to the x-axis.

This is nonsense squared.
There are so many things wrong in a single sentence that one doesn’t know where to begin.

1) x’ axis is not defined by t’=0. x’ axis is defined by whatever orientation the observer O’ in S’ chooses at any t’

2) S and S’ may be considered with no relative movement (O=O’ and v = 0) . In this case obviously Ox’ can be chosen such as O’x’=Ox while t=t’=0. This is how one gets synchronisation of clocks and definition of spatial orientations.

3) t = v.x is only a “line” in t,x coordinates. As the figures shows spatial coordinates (x,y,z) it is trivial that neither x nor x’ is “tilted” with regard to each other

4) If O in S observes that O’ in S’ moves with a velocity (v,0,0) expressed in his S coordinates then O’ in S’ observes that O in S moves with a velocity (-v,0,0) expressed in his S’ coordinates. This is what the Lorentz transformation shows. Besides one can trivially notice that, indeed, x and x’ are parallel because they are both parallel to v – a known result of geometry familiar already to ancient Greeks 🙂

5) The Lorentz transformation just says that for any S and S’ (not accelerating and not in a gravitational field) : (x,t) = M.(x’,t’) where M is a 2×2 matrix with coefficients given by the Lorentz transformation.
This is basic algebra.
What is original and physical inside is the value of the 4 coefficients of M.
The value of these coefficients has been experimentally verified during a century with an extremely high accuracy and fully agrees with the Lorentz transformation (=SR).
The whole of SR and its physical consequences on energy, momentum etc is completely contained in the above equation and in the value of the 4 coefficients of M (or 16 if we consider that the orientation of the S and S’ spatial axis is random)

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claesjohnson
January 20, 2012

Lorentz insisted that the transformed time t’ is not to be considered as physical time, but Einstein did not listen and twisted the Lorentz transformation into a relation between physical coordinates. It was Lorentz who introduced the Lorentz transformation in full awareness of its physical meaning and I argue that is more reasonable to listen to Lorentz than to Einstein.

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