Hubble's Law and Exponential Expansion vs Many-Minds Relativity

The Hubble law

• $v=Hx$ 

with $x$ distance to a galaxy with velocity $v=\frac{dx}{dt}$ vs the Earth with $t$ time and $H$ Hubble's constant, is the most celebrated law of cosmology. Solving the equation $\frac{dx}{dt}=Hx$ with $x=1$ for $t=0$, we have

• $x(t)=\exp(Ht)$  and $v(t)=H\exp(Ht)$ for $t\gt 0$. 

The galaxy thus appears to be receding from the Earth with both distance and velocity increasing exponentially in time. The Universe thus appears to be expanding exponentially. What is driving such a violent expansion?

Newton's 2nd Law takes the following form in Many-Minds Relativity MMR:

• $\frac{dv}{dt} = (1+v)F$,

where again $v$ is velocity and $F$ force and mass is normalised. With $F$ a positive constant the solution with $v(0)=0$ for $t=0$ is given by 

•  $v(t)=\exp(Ft)-1$.

We thus see an exponentially increasing velocity from a constant force in MMR. We compare with the standard form of Newtons 2nd law $\frac{dv}{dt}=F$, which gives $v(t)=Ft$  with much slower  linear increase in time in the case of a constant force.

In MMR a constant expansion force thus appears to be compatible with observations of exponential expansion. In a Big Bang scenario it is thinkable that such a constant expansion force was active over an initial period of time resulting in observations of exponential expansion later.  

We thus find exponential expansion in both observations and MMR with constant expansion force. 

Is this a coincidence?

Of course, exponential expansion appears to require massive dark energy, but nobody knows anything about this new form of energy.

In MMR, the exponential expansion appears as an optical effect from using (composite) Doppler shifts to determine velocities, and so the exponential expansion could be more illusion than reality. If so, less dark energy would seem to be needed which could easy the task of finding an explanation of its apparent presence.   

Redshift in SR vs MMR

Recent posts have given evidence that Einstein's special theory of relativity SR is the result of an incorrect contradictory derivation of the Lorentz transformation from the basic physical Postulate of SR, and thus is unphysical. An alternative theory based on the same Postulate using correct logic takes the form of Many-Minds Relativity MMR.

In MMR a light source is connected to a receiver of light by a standing wave satisfying Maxwell's equations in a space-time system with the space axis connecting source to receiver. Shifting amplitude and frequency of the light source will then travel as a disturbance superimposed on the standing wave to be received at the receiver with a time delay given by the speed of light and the distance between source and receiver, and Doppler shift from motion of the source. The description of light in MMR is not as a stream of "photons" as "particles of light", which is unphysical.

Since both SR and MMR differ from Newtonian theory only for very high velocities, it is natural to compare predictions of SR and MMR with observations of large cosmological redshifts $z$ from far away galaxies receding from an observer on the Earth with very high velocity $v$.

According to SR the redshift $z$ is connected to the recession speed $v$ by the formula (with the speed of light = 1):

• $z = \sqrt{\frac{1 + v}{1 − v}}-1$ where $-1\lt v\lt 1$.  

According to Peacock Cosmological Physics p. 72, this is misleading and any such temptation should be avoided. I agree: SR is unphysical and so must a SR redshift be. In particular SR does not allow a recession speed larger than the speed of light.

The accepted way to connect the redshift to the recession velocity is thus not according to SR, but instead by invoking Einstein's general theory of relativity GR to come up with the idea that it is the very "fabric of space" between source and receiver which "stretches" (see picture above) and not really the source that speeds away, which allows recession speeds larger than the speed of light with redshifts bigger than 1. This is referred to cosmological redshift connected with observations of redshifts as large as $z=8$.

In MMR we have (without taking into account the time of travel of a light signal):

•  $1+z = \frac{\lambda_r}{\lambda_s}$ with $z=v$,    

where $\lambda_s$ is the wave-length of the light emitted by the galaxy source and $\lambda_r$ that observed. This is the same as the classical Doppler shift formula, where the increase of wave-length and redshift depends on the motion of the source vs the receiver.  

But MMR is also compatible with the idea of "stretching of space" as simply a different space axis in the same Maxwell's equations with a speed of light = 1 underlying MMR. The observed large cosmological redshifts of far away galaxies thus appear to be compatible with MMR, but not SR.

Note also that it is not natural to invoke GR concerned with gravitation, to handle propagation of light, which is the specialty of special relativity.

Resolution of All the Paradoxes of Special Relativity

• Length contraction and time dilation are ways of regarding things and do not correspond to physical reality. (Max Born)
• There is not a single concept of which I am convinced that it will stand firm, and I feel uncertain whether I am in general on the right track. (Einstein)

The special theory of relativity SR presented by Einstein in one of his five articles from the "miraculous year" 1905, is viewed as a pillar of modern physics introducing new mysterious qualities of "strangeness" in the form of "space contraction" and "time dilation" asking for a fundamental revision of classical Newtonian concepts of space and time, by Einstein excused with: "Newton, forgive me!"

SR emerged from a realisation that there is no "unique aether" as an "absolute space" for the propagation of light. Instead, it appeared that there were "many aethers" as different space coordinate system for the expression of Maxwell's equations describing propagation of electromagnetic waves including light, which could be fixed to different observers/receivers of light moving with respect to each other.      

But SR is filled with paradoxes or contradictions: Ladder Paradox, Bug-Rivet Paradox, Cooling Paradox, Twin Paradox, Trouton-Noble Paradox,  Ehrenfest Paradox, Detonator Paradox,  Falling Rod Paradox,  Bar/Ring Paradox,...and many more. The most famous paradox is the Twin Paradox about two twins both ageing slower than the other according to SR, which has been subject to heated debate over more than 100 years without any real resolution, with only a proclaimed "consensus" that the paradox is just an "apparent paradox" resolved since long, since in fact only one of the twins is ageing slower than the other, then in contradiction to SR as an expression of an inevitable most real "strangeness" of modern physics.

In a series of posts and the book Many-Minds Relativity MMR I have analysed SR to find the true root of the paradoxes, because it is not easy to find in the literature.

Let me now present the result of the analysis in easily understandable concise form, which you can go through in a couple of minutes. That is, if you want to understand that the "strangeness" of modern physics based on SR is the result of a logical mistake by Einstein, which when removed allows rational progress without "strangeness".  If you are happy with the consensus of "strangeness" as an ultimate expression of the victory of modern physics, you can stop reading.

The basic question to be answered is thus: From where do all the paradoxes of SR come?

SR concerns observations of different observers $X$ using different space-time coordinate systems $(x,t)$ with space axes moving with constant velocity with respect to each other, with $x$ a Euclidean space coordinate, here for simplicity 1d, and $t$ a time coordinate, which are referred to as inertial systems. 

Einstein assumes all observers in SR to use identical  standard "rigid rods" to measure distance in space and identical standard clocks to measure progress of time. An observer $X$ equipped with an $(x,t)$-system thus scales the $x$-axis using a standard rigid rod and a standard clock to scale the $t$-axis. So far no paradox.

Einstein formulated the following basic Postulate of SR:

• All observers $X$ observe light signals to travel (in vacuum) with speed 1 (normalised) along the observer's $x$-axis independent of the movement of the source of light on the $x$-axis.

Or in the exact wording of the 1905 article:

• Light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body.

We see that the Postulate of SR allows a light source to be moving. But it says nothing about an observers motion, which can only be interpreted as implicitly requiring the observer to be at rest in the observer's system when receiving/observing the arrival of a light signal sent from some possibly moving source.

More precisely, allowing the observer to move in the observer's system would contradict the basic set-up of equipping each observer $X$ with an individual $(x,t)$-system. If observation by moving observers was included in the Postulate of SR, then it would be enough with just one inertial system, which could then act as an "absolute space" in contradiction to the basic motivation to develop SR as physics beyond Newtonian physics supposed to require some "absolute space" (cf. PS4 below).

An observer $X$ at rest in the observer's $(x,t)$-system can thus observe the propagation of light by receiving/observing light signals at different space locations emitted by possibly moving light sources at other locations on the $x$-axis.

The Postulate of SR takes the more precise form:

• All observers $X$ at rest on the observer's $x$-axis observe light signals to travel with speed 1 along the $x$-axis independent of the movement of the source of light on the $x$-axis. 

In particular, an observer $X$ will in the observer's $(x,t)$ system observe a light signal emitted at $x=0$ at time $t=0$ to follow the trajectory $x=t$. Another observer $X^\prime$ will in the observer's $(x^\prime ,t^\prime )$ system observe a light signal emitted at $x^\prime =0$ at time $t^\prime =0$ to follow the trajectory $x^\prime =t^\prime $. In the Postulate of SR there is no connection between signals in different systems. Even though the coordinates of emission $(x,t)=(0,0)$ and $(x^\prime ,t^\prime )=(0,0)$ are the same, the light signals will be different, one traveling in the $(x,t)$-system and another in the $(x^\prime ,t^\prime )$-system.

Note that the Postulate of SR is compatible with the null result of the Michelson-Morley experiment by allowing light signals to travel the same way independent of the motion/orientation of the arms.

Analogy can be made with elastic waves traveling in two identical parallel elastic beams moving with respect to each other, where it is evident that the waves are not the same even if launched the same way when the beams overlap. Each beam then represents a space axis, with the beams/axes moving with respect to each other. So far no paradox.

In Einstein's illustration with a stationary observer $X$ on a train embankment and another observer $X^\prime$ traveling inside a moving train with windows covered, the Postulate of SR does not admit $X$ on the embankment to observe light signals inside the train, nor $X^\prime$ inside the train to observe light signals in the system of the embankment outside the train. This is a key point!

Connecting to Maxwell's equations the Postulate of SR can be expressed in the form:

• All observers $X$ assume light propagates according to Maxwell's equations with speed of light normalised to 1 in a $(x,t)$-system in which $X$ is at rest. If the light source is moving on the $x$-axis with velocity $-1\lt v\lt 1$, then the frequency of received light signals is subject to a Doppler shift of $\frac{1}{1+v}$. 

This is also the basic Postulate of MMR. The "rigid rod" as measure of distance can then be replaced with the 1983 SI standard of defining meter as a certain fraction of light-second as the distance of light traveled in 1 second. So far no paradox.

Now we come the critical point concerning the origin of all the paradoxes of SR. This is the very  starting point for Einstein in his pursuit of SR considering two observers $X$ and $X^\prime$ using $(x,t)$ and $(x^\prime ,t^\prime )$-systems with space axes moving with respect to each other, in the form of the following question:

• What is the observation by $X^\prime$ of a light signal in the $(x,t)$ system? 

Einstein was quick in his 1905 article to point out that there was something contradictory in his preparation of SR, but then reassured himself that it was only an apparent contradiction ("another postulate, which is only apparently irreconcilable with the former").

In any case the question is really contradictory, because observations are assumed to be made by observers at rest on their respective space-axis, and so $X^\prime$ cannot observe light signals on the $x$-axis because $X^\prime$ is at rest on the $x^\prime$-axis, but not on the $x$-axis.

Einstein thus poses a question which is contradictory and thus can only have a contradictory answer, but Einstein nevertheless seeks to give an answer, in a heroic attempt to reveal new strange physics of space and time.

In Einstein's train example the question reflects breaking the Postulate of SR by asking $X$ on the embankment to observe light signals in the inside system of the train and $X^\prime$ inside the train to observe light signals in the embankment system outside the train, both involving moving receivers/observers. This is the origin of all the paradoxes.

To get around the contradiction of the Postulate of SR asking observation of real light signals by moving observers,  Einstein engaged in his famous "thought experiments" to replace real experiments, thus allowing $X$ on the embankment to peek into the train and there observe not real but imagined light signals in the system inside the train, or $X^\prime$ inside the train to peek through closed windows to observe light signals in the system of the embankment. Of course a train driver is able to observe a light signal emitted from a source on the embankment, but then at rest on a space axis on which the the light source is moving.

Einstein's answer to the contradictory question is the Lorentz transformation supposedly opening $X^\prime$ to observations in the $(x,t)$-system mediated by the coordinate transformation:

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

supposing that the $x^\prime$-axis of $X^\prime$ moves with velocity $0\lt v\lt 1$ with respect to the $x$-axis, so that the origin $x^\prime =0$ follows the trajectory $x=vt$ in the $(x,t)$-system.  

$X^\prime$ is thus invited "to observe" the light signal in the $(x,t)$-system in terms of $(x^\prime ,t^\prime )$-coordinates connected to the $(x,t)$-coordinates by the Lorentz transformation. This is in contradiction to the assumption that $X^\prime$ can observe only light signals in the $(x^\prime ,t^\prime )$-system. Nevertheless, the light signal in the $(x,t)$ system when transformed into the $(x^\prime ,t^\prime )$-coordinates according to the Lorentz transformation by Einstein is required to be a light signal in the $(x^\prime ,t^\prime )$-system represented by a trajectory $x^\prime =t^\prime$. 

Einstein thus derives the Lorentz transformation by requiring a light signal in a $(x,t)$-system to be observed by an observer $X^\prime$ using different $(x^\prime ,t^\prime )$-coordinates as a light signal in the $(x^\prime ,t^\prime )$-system. This forces $X^\prime$ to use different measures of space and time when "viewing" the light signal in the $(x,t)$-system,  than the rigid rods and clock belonging to $X^\prime$.

SR as based on the Lorentz transformation according to Einstein thus boils down to twisting the brains of an observer $X^\prime$ with an $(x^\prime ,t^\prime )$-system "to view" a light signal in another $(x,t)$-system with the $x^\prime$-axis moving with respect to the $x$-axis, as a light signal in the system of $(x^\prime ,t^\prime )$. The twisting involves forcing $X^\prime$ to use different measures of space and time when "viewing" a light signal belonging to a different $(x,t)$-system.

The necessity of twisting the brains of $X^\prime$ when "viewing"  light signals in the $(x,t)$ system, is seen in the basic example of a light signal in the $(x,t)$ system emitted at $x=0$ at time $t=0$, which at time $t=1$ can be observed by $X$ at $x=1$ as having traveled the distance 1 with respect to the $x$-axis but only the distance $1-v$ with respect to the $x^\prime$-axis moving with velocity $v$ with respect to the $x$-axis, which requires  $X^\prime$ to reset time to "observe" a speed of light of 1.

The difference between Einstein and Lorentz who wrote down his transformation before Einstein picked it up, is that Lorentz does not consider the transformed coordinates $(x^\prime ,t^\prime )$ to represent physical coordinates, only some form of "local (unphysical) coordinates". Lorentz thus does not consider the light signal in the $(x,t)$-system as "viewed" by $X^\prime$ to be a physical light signal in the $(x^\prime ,t^\prime )$-system. It was Einstein who took this step in contradiction to the Postulate of SR and then leading into the bushes of non-physics.

Without twisting of brains the truth buried in the Postulate of SR is that all observers use the same measures of space and time, which means that the coordinates between moving systems are connected by the Galilean transformation:

• $x^\prime =x -vt$,  $t^\prime =t$.

With a Galilean transformation the Postulate of SR carries no contradictions or paradoxes, and the consequences are explored in MMR. In a Galilean transformation there is no "space contraction" or "time dilation" and no "strangeness". 

Summary: All paradoxes of SR result from Einstein's question of asking for the view of an observer of the propagation of light in a system in which the observer is not at rest, which is contradictory because the Postulate of SR requires observations to be made at rest in the system for observation.

Einstein's question expresses a form of logical contradiction, in the sense of asking for something which is forbidden in the Postulate of SR. From one logical contradiction infinitely many contradictions can be derived, which is seen in the many paradoxes of SR.

The Postulate of SR is physical and without contradiction, but the contradiction of the Postulate as the Lorentz transformation is unphysical. Einstein's SR is thus unphysical.

The "consensus" of modern physicists seems to be that despite its logical contradiction from start and the resulting infinitely many paradoxes, Einstein's SR represents an advancement of physics of a magnitude never seen before with Newton's mechanics only a bleak incorrect first step.

The crisis of modern physics witnessed by so many in recent times can be seen as a consequence of the contradictions of SR.  To get out of this trauma blocking progress, a revision of SR is needed. Today professional physicists pay lip service to SR, while viewing SR as a dead subject of interest only to cranks presenting ever new resolutions of the paradoxes in fruitless attempts to come to grips with the "strangeness" of SR.

PS1 More aspects are found under the tag special theory of relativity.

PS2 The Postulate of SR in particular expresses that emission and reception/observation of a light signal is coupled process where the observer is connected to the emitter through a space coordinate system in which the observer is at rest.  The connection can be seen as being established by a standing wave satisfying Maxwell's equations with the light signal as a superimposed traveling wave.

PS3 The Postulate of SR is not compatible with light as a stream of "particles" or "photons", which is anyway unphysical.

PS4 The Postulate of SR is in some texts stated as allowing not only emitter but also receiver to be moving in the space system of observation, but Einstein did not include receiver and doing so does not make any sense as argued above.

• But one thing is the thought, another thing is the deed, and another thing is the idea of the deed. The wheel of causality doth not roll between them. Friedrich Nietzsche, Thus Spoke Zarathustra
• What I wanted to say was just this: In the present circumstances, the only profession I would choose would be one where earning a living had nothing to do with the search for knowledge. (Einstein’s last letter to Born)
• The question whether the Lorentz contraction does or does not exist is confusing. It does not really exist in so far as it does not exist for an observer who moves (with the rod); it really exists, however, in the sense that it can as a matter of principle be demonstrated by a resting observer. (Einstein 1911)
• But no Anglo-Saxon can understand relativity. Said at a dinner in 1910, teasing Ernest Rutherford, who replied: No, they have too much sense.

In the footsteps of Greta...

1. Read the analysis by Czech Ex-President Vaclac Klaus: In the footsteps of Greta, on the road to slavery.

2. Watch the speech by Greta to world leaders at UN Climate Action Summit: How dare you? You have stolen my childhood and my dreams with your empty words. 

3. Think for a moment yourself!

Compare with The Times.

Special Relativity as Unphysical Views on Views

The conclusion of the last sequence of posts on Einstein's Special Theory of Relativity SR is:

• SR is an unphysical theory about views on views, not a physical theory about views on physics.

In SR the views of two different observers, $X$ using a $(x,t)$-space-time system and $X^\prime$ a $(x^\prime ,t^\prime )$-system, are demanded to be related by the Lorentz transformation connecting the coordinates in the two systems.  Through the Lorentz transformation the view of $X^\prime$ in the $(x^\prime ,t^\prime )$-system is coordinated with the view of $X$ in the $(x,t)$ on a light signal propagating in the $(x,t)$ system with speed 1. 

SR thus prescribes the view of $X^\prime$ in the $(x^\prime ,t^\prime )$-system on the view of $X$ on a light signal in the $(x,t)$-system, under the condition that $X^\prime$ is denied the possibility to directly observe the light signal in the $(x,t)$-system, while $X$ can view it to travel with speed 1 (and $X^\prime$ views an independent light signal in the $x^\prime ,t^\prime )$-system to travel with speed 1).

SR is a theory about the view of $X^\prime$ on the view of $X$ on physics in the form of a light signal traveling with speed 1 in the $(x,t)$-system, and vice versa!

SR is a theory about views on views on physics, where the views on physics are reduced to a light signal traveling with speed 1. 

SR with one observer with one view on physics is Galilean physics of light traveling with speed 1.

SR with several observers is non-physics of views on views. All the paradoxes of SR result from confusing non-physics with physics. 

The physics of SR is simple and clear in the form of light signals propagating with speed 1 in all inertial systems. The non-physics of SR with views on views is confusing and paradoxical from physical point of view, since it leads to an infinite loop of views on views on views ... into a nightmare of repeated space contractions and time dilations without physical meaning. 

The insight that SR is epistemology without ontology of physics was clear to the physics community when Einstein presented SR in 1905. This was the reason Einstein abandoned SR in 1907 to never return.

Recall that Lorentz said that the view of $X^\prime$ on the view of $X$ on physics, is not physics.
In particular the transformed time $t^\prime$ is not real time only "local time", and that it was Einstein who took the step to proclaim the local time = real time, against Lorentz.

Recall that SR boils down to the Lorentz transformation supposedly derived by identifying two different light signals in two different systems to be the same light signal, which is unphysical and the origin to all the physics paradoxes carried by SR.

The confusion of two signals into one was made possible with the invention by Einstein of the new concept of event as "something" which can be labeled with coordinates $(\bar x,\bar t)$ in an $(x,t)$-system, however without any physics specified. This made it possible for Einstein to remove the physics of launching two different light signals in two $(x,t)$ and $(x^\prime ,t^\prime )$-systems into two events with the same coordinates $(0,0)$ in the two systems, and identify the two events without physics to be the same event without physics, and then finally reintroducing physics by claiming the two different light signals are one and the same light signal since the originate from what is viewed to be one and the same event. Thus from physics to events without physics and then back to physics. Einstein was a master of this form of deceitful unscientific reasoning switching between ill-defined concepts and so created a new standard of modern physics.    

It is a mystery that SR has survived into our time as a foundation of modern physics, although SR is no longer part of the education of a modern physicist because there are no longer any professors in SR able to teach the subject.

PS The get perspective on the above concept of "a view on a view" as non-physics, consider the following examples:

• $X$ viewing/experiencing a definite pain in the neck goes to doctor $X^\prime$, who takes a view on this view of $X$. Even if $X^\prime$ is capable of some empathy, does it mean that $X^\prime$ also experiences pain in the neck, or can it even be that $X$ views the view of $X^\prime$ to be a simulation and not real pain?
• View your arm when lifting it in front of a mirror, and then view the same thing when looking into the mirror and note that the person in the mirror lifts her/his right arm.          

Quantum Mechanics Not Understood by Physicists

Sean Carroll promotes his upcoming new book Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime by an article i NYT with the catching title:

• Even Physicists Don’t Understand Quantum Mechanics.
• Worse, they don’t seem to want to understand it.

and conclusion

• What’s surprising is that physicists seem to be O.K. with not understanding the most important theory they have.
• Physicists don’t understand their own theory any better than a typical smartphone user understands what’s going on inside the device.

The article exposes the crisis of modern physics resulting from the acknowledged accepted intrinsic incomprehensibility of its pillars in the form of quantum mechanics (and relativity theory). 

Shocking! But of course modern physics led by Lubos on The Reference Frame counters by assuring that:

• Actual physicists do understand quantum mechanics rather well – it has really been understood for over 90 years – and they are using it as rock-solid foundations to discover increasingly amazing things about the physical world.

while those who do not understand "rather well" are simply crackpots, including all the big names in physics except Lubos.

If you think that a new approach is needed take a look at Real Quantum Mechanics.

The Special Relativity of Swedish Society

Einstein's special theory of relativity SR is so strange that it is difficult to comprehend how strange it is, since that requires first to comprehend what the theory is all about, and secondly to comprehend that it is nonsense.

Let me make an effort to explain SR in the setting of an analogy with Swedish Society SS, to see how absurd SR is.

Let me then recall that SR/SS is concerned with the coordination of views of different observer/citizens $X$ each using a space-time coordinate system/value system  $(x,t)$ with $x$ space and $t$ time in the SR setting. SR/SS is based on the following postulate:

• The speed of light is equal to 1 as measured by all observers. (SR)
• The speed of the Swedish Society is optimal equal to 1 as measured by all citizens. (SS)

It is also acknowledged that observers/citizens move with constant speed $0\le v\lt 1$ with respect to each other.

Consider now any two observers/citizens $X$ using an $(x,t)$-system and $X^\prime$ using an $(x^\prime ,t^\prime )$-system. Suppose now that $X^\prime$ as viewed by $X$ in the $(x,t)$-system moves with (constant) velocity $v$. Then $X$ has reason to predict that the speed of light/SS for $X^\prime$ should be $1-v$ as the relative velocity in the $(x,t)$-system. But that conflicts with the postulate that $X^\prime$ must measure the speed of light/SS to be 1. How to handle this conflict between the views of $X$ and $X^\prime$? 

Einstein's idea is to to ask $X^\prime$ to put on special glasses (in the form of the Lorentz transformation) connecting the $(x^\prime ,t^\prime)$-system to the $(x,t)$-system, allowing $X^\prime$ to look into the $(x,t)$ system and then see that the speed of light/SS in the $(x^\prime ,t^\prime )$-system indeed is the postulated 1, and not the $1-v$ as predicted (but not really observed) by $X$. It is no problem to construct such glasses (Lorentz transformation) by suitably distorting the view of $X^\prime$ when looking into the system of $X$ as the fellow citizen of $X^\prime$. 

An effect of the distorting glasses is that $X^\prime$ views $X$ to be smaller (space contraction) and slower (time dilation). And by symmetry this view is shared by $X$ vs $X^\prime$. 

Summary 1: All observers/citizens are thus equal and all measure the same optimal speed of light/SS equal to 1 in their respective system, as the basic postulate.

Any observer/citizen $X$ using an $(x,t)$-system views any other $X^\prime$ moving with speed $v$ relative to $X$ to have a relative speed $1-v$ in $(x,t)$-system, while with special glasses $X^\prime$ views the speed to be 1 in conformity with the basic postulate, special glasses which make $X$ appear to be both smaller and slower to $X^\prime$.

Summary 2: All observers are equal but everybody views the other to truly be inferior.

Is this the essence of Swedish Society and SR? Is it good physics/society or just nonsense?

Summary 3: Note that the view of the other as being smaller is not considered to correspond to viewing a person at distance, which can give the impression that the person is smaller than you, which we all know is just an illusion and not any real shrinking by distance. If you don't understand that, you are in trouble, and if you do, then SR will mean trouble to you.

Compare with  Many-Minds Relativity where all observers are equal and there are no distorting glasses forcing everybody to see the same thing, while moving with different speeds.

SR concerns the view of one observer on the view of another observer with the views demanded to be connected by the Lorentz transformation. SR does not compare the independent views of different observers, which is pointless since the views are supposed to be the same. SR is thus a theory about views on views and not about views on physical phenomena.

MMR compares different independent views of different observers on physical phenomena and seeks common aspects.

SR is a form of command physics dictating that measurements of the speed of light must give the same value in all inertial systems independent of translation with constant velocity. The dictate is fulfilled by dictating that space-time coordinates in different systems to be connected by the Lorentz transformation. But you cannot dictate physics. Physics concerns "what is" and not "what must be seen". In the same way real politics is about "what is and can be done" and not "what must be".

The typical reaction by a professional modern physicist on the many mysteries of SR, is that the "strangeness" of SR is a true expression of the fact that "physics is strange", or more precisely, "the stranger the better". Like Swedish Society?

Addition of Velocities in Special Relativity?

The formula for relativistic addition of two (1d constant) velocities $u$ and $v$ in Einstein's special theory of relativity SR, reads

• $\frac{u+v}{1+uv}$    (1)

to be compared with addition in Galilean relativity:

• $u+v$.

To give meaning and prove (1) two inertial frames $(x,t)$ and $(x^\prime ,t^\prime )$ are introduced connected by the Lorentz transformation

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

where $v$ with $\vert v\vert \lt 1$ is the relative velocity between the two systems, $u=\frac{dx}{dt}$ is the velocity of an object $O$ as measured by an observer $X$ in the unprimed system, while (1) is supposed to give the velocity of $O$ for an observer $X^\prime$ in the primed system as the result of relativistic addition of velocities.

To prove (1) the standard argument is to differentiate (2) with respect to $t$ to get  

• $dx^\prime =\gamma (\frac{dx}{dt}+v)dt$, 
• $dt^\prime=\gamma (1+v\frac{dx}{dt})dt$,

and so by division with $u=\frac{dx}{dt}$ obtain 

• $\frac{dx^\prime }{dt^\prime}=\frac{u+v}{1+uv}$,

which is (1). 

We thus see that the Galilean sum $u+v$, which is valid in any chosen single inertial frame,  in SR is replaced by $\frac{u+v}{1+uv}$ as the result of introducing two inertial systems connected by the Lorentz transformation. 

The key point is that the sum of two velocities $u$ and $v$ in SR is made in two steps with $u$ the velocity of an object $O$ with respect to the unprimed system (as viewed by $X$) and $v$ the relative velocity between the systems, with the sum supposed to be the velocity in the primed system (as viewed by $X^\prime$). 

In particular, $X^\prime$ is denied the possibility of directly observing the object $O$ in the primed system and determining its velocity in that system. One may ask why? In any case, $X^\prime$ is instead referred to an observation of $O$ made by $X$ in the unprimed system, which is then transferred to the primed system by the Lorentz transformation and finally combined with the motion between the systems to serve as the observation by $X^\prime$. 

The two step procedure is used to bring in two inertial systems connected by the Lorentz transformation. Of course, to describe the motion of an object it suffices in principle with just one inertial system, where the motion is followed in space and time. But in a SR with just one inertial system there is no Lorentz transformation and thus no content beyond what can be given to any inertial system such as Galilean relativity.  

This connects to the previous post making the point that SR in just one chosen frame without any Lorentz transformation appears to be empty of content. 

The above analysis poses more questions concerning the physics of the Lorentz transformation: 

• Why cannot $X^\prime$ observe $O$ in the $(x^\prime ,t^\prime )$-system?
• Why can the motion of $O$ as viewed by $X$ be transferred to be the view of $X^\prime$ by the Lorentz transformation, when the transformation was derived to match light signals and not general motion? 

We compare with addition of velocities in MMR given by (modulo signs)

• $u+v+uv$, 

as a result of composite Doppler shifts in a case where $X^\prime$ cannot directly observe $O$ and so is referred to a Doppler shift observation by $X$, which is transferred by another Doppler shift to $X^\prime$ as a consequence composite shifts with  

•  $\frac{1}{1+u}\frac{1}{1+v}=\frac{1}{1+u+v+uv}$.  

There may thus be some rationale to view addition of velocities as composition of observations in  

different inertial systems by composite Doppler effects, but building the composition on the Lorentz transformation lacks physics since the Lorentz transformation itself so does.   

What Is Special Relativity without the Lorentz Transformation?

Many-Minds Relativity MMR is an alternative to Einstein's Special Theory of Relativity SR. Let us bring out the essential difference between MMR and SR.

Let us start noting that MMR and SR share the same basic Postulate:

• The speed of light is the same in all internal systems.

An inertial system is a spatial Euclidean coordinate system with space coordinate $x$ combined with a time coordinate $t$ into a space-time system with coordinates $(x,t)$. Inertial systems move with constant velocity with respect to each other.

The set-up in MMR is a collection of observers $X$ equipped with inertial systems with space-time meter-second scales set by the 1983 SI standard with meter defined as a certain fraction of a lightsecond and second defined by a standard cesium clock. The light speed will then be the same in all inertial systems. 

MMR studies the relation between descriptions of physics by different observes using different inertial systems in which the observer is stationary. MMR contains in particular physics which can be expressed in one privileged system in which the observer is stationary (like an Earth based observatory).

The set-up in SR is different. In basic form SR boils down to the Lorentz transformation as a coordinate transformation connecting coordinates in different inertial systems, which is supposed to be a consequence of the Postulate.  SR is thus empty of content in the case of one privileged system since the Lorentz transformation involves two systems. In the case of two systems with two observers $X$ using an $(x,t)$-system and $X^\prime$ an $(x^\prime ,t^\prime )$-system, SR dictates that an event labeled $(x,t)$ to $X$ will have to be labeled $(x^\prime ,t^\prime )$ to $X^\prime$ by the Lorentz transformation. The effect is that $X^\prime$ will see effects of space contraction and time dilation in the $(x,t)$-system vs her/his own system, and vice versa. In particular, $X^\prime $ will see a slowing down of the clock/time of $X$, and vice versa.  

MMR studies the same physics as experienced by different observers in different inertial systems. MMR is meaningful with just one observer. MMR is compatible with the 1983 SI standard.

SR assumes that observations by different observers in different systems are identical, as an expression of relativity according to Einstein. Instead SR is concerned with the view of one observer on the observations by another observer in another system. SR has no meaning for just one observer, does not compare the observations of different observers in different systems (because they are supposed to be identical), and is concerned instead with the view of one observer on something described in another system than her/his own. This connects to Matthew 7:3:

• Why do you look at the speck of sawdust in your brother's eye and pay no attention to the plank in your own eye?

SR also has a most unclear relation to the SI standard.

In MMR each observer makes observations in her/his own system, and compares with that of other observers in other systems if there are more than one.

In SR each observer focusses interest not on observations in her/his own system, but on observations made in other systems, and so has nothing of interest to say alone from observations in her/his system. 

Hopefully this discussion can help to clarify what SR is about, which is truely mysterious as witnessed by all leading physicists as a wonderful new aspect of modern physics, which however connects back to the Dark Age rather than Enlightenment.

PS The basic theories of physics take the form of physical laws expressed as differential equations such as Newton's 2nd law and law of gravitation, Euler's equations for fluid mechanics, Boltzmann's equations for gas dynamics, Maxwell's equations for electromagnetics, Schrödinger's equation for atom physics, and even Einstein's field equations. SR does not have this form, but is instead basically a coordinate transformation. There is no other theory of physics which has this form. Can a coordinate transformation contain any physics? Does a transformation from meter to yard bring in any physics? 

Einstein Did Not Understand the Idea of Relativity

Continuing the previous post on the unphysical nature of the Lorentz transformation as derived by Einstein based on unclear physics of light signals, let us seek some clarification, because from shoddy waters muddy fish can be drawn.

We start noting that a light signal needs both a source for emission and an observer for receiving/recording. In the simplest model the signal propagates in time $t$ (as measured by a standard clock) with velocity 1 along a spatial 1d $x$-axis from a source and is recorded by an omni-present observer $X$, who is stationary with respect to the $x$-axis, which then acts as an "aether" for propagation of light with $(x,t)$ a corresponding space-time system. The source can be moving with (constant) velocity $v$ with respect to the $x$-axis with a corresponding Doppler shift of $\frac{1}{1+v}$ of the signal received by a stationary observer, assuming $\vert v\vert \lt 1$.

This is the set-up in Many-Minds Relativity MMR with several observers $X$ with spatial $x$-axes moving with respect to each other with constant velocity, each observer $X$ establishing a source-receiver relation on the $x$-axis in which $X$ is stationary, all observers using the same standard clock for measuring time $t$.

Each observer $X$ thus uses a $(x,t)$-system with $X$ stationary with respect to the $x$-axis together with a standard clock for measuring time $t$.  The basic question in MMR is then to what degree different observers can agree on the physics of light propagation (or more generally on other aspects).

Note that MMR directly reflects the 1983 SI meter standard as a certain fraction of a lightsecond which can be used to separately establish the length standard in each inertial system, using a standard cesium clock to set the time scale.

Note as a key point that it is natural to assume an observer $X$ to be stationary at whatever point on the observers $x$-axis signal reception is made, rather than making the source stationary.  This is because it is the reception of a signal which can recorded, but not in the same way the sending of a signal. We shall see below that allowing $X$ to move is the source of confusion in SR, and so in MMR we stay away from this option without real loss of generality.

In MMR there are thus as many "aethers" as spatial coordinate axes, with each coordinate axis "dragging" its own "aether" along with light signals propagating with velocity 1. This can be seen as an expression of a maximal form of relativity with no privileged observer or $x$-axis. It is compatible with the Michelson-Morley experiment supposed to give evidence that "there is no unique aether", by offering the possibility of "there are many non-unique aethers" (as an alternative to Einstein's "there is no aether at all").

But Einstein was not happy with (maximal) relativity without any privileged observer, and so set out to find a common ground for any two observers $X$ and $X^\prime$ with $X$ using a $(x,t)$-system and $X^\prime$ using a $(x^\prime ,t^\prime )$-system supposed to move with constant velocity $v$ with respect to each other. The common ground showed to take the form of a coordinate transformation, the Lorentz transformation, which Einstein established by asking for the view of $X^\prime$ on light propagation in $(x,t)$ in addition to $(x^\prime ,t^\prime )$.

To form the common ground Einstein started by introducing the origin $x^\prime =0$ in the $x^\prime$-system into the $(x,t)$-system to follow the trajectory $x=vt$ reflecting that the  $x^\prime$-axis is supposed to move with velocity $v$ with respect to the $x$-axis, or at least its origin $x^\prime =0$.

The $(x,t)$ system would then carry two types of motion: light signals propagating with speed 1 following $x=t$ and the origin $x^\prime =0$ moving with speed $v$ following $x=vt$. Einstein then established a connection between the coordinates in the $(x,t)$ and $(x^\prime ,t^\prime )$-systems through the following steps:

1. Make the Ansatz $x^\prime =\gamma (x-vt)$ with $\gamma$ a positive constant, to account for the motion of the origin $x^\prime =0$ in the $(x,t)$-system. 
2. Send a light signal in the $(x,t)$ system from $x=0$ at $t=0$ to be observed by $X$ as following the trajectory $x=t$. 
3. Identify this signal with a light signal in the $(x^\prime ,t^\prime )$-system sent from $x^\prime =0$ at $t^\prime =0$ to be observed by $X^\prime$ as following the trajectory $x^\prime =t^\prime$.  
4. From the identification connect $x=t$ to $x^\prime =t^\prime$ and conclude that $t^\prime =\gamma (t-vx)$ and then that $\gamma =\frac{1}{\sqrt{1-v^2}}$ as the Lorentz transformation $x^\prime =\gamma (x-vt)$ and $t^\prime =\gamma (t-vx)$, or the other way around as $x =\gamma (x^\prime +vt^\prime )$ and $t =\gamma (t^\prime +vx^\prime )$,

The Lorentz transformation connects the $(x,t)$ and $(x^\prime ,t^\prime )$-coordinates through a simple linear transformation by making an identification of two light signals in the two systems. According to Einstein (but not Lorentz) the transformation expresses space contraction and time dilation as true physical phenomena.

In the previous post we questioned the identification on physical grounds, and so also the Lorentz transformation and so the very essence of Einstein's special theory of relativity SR. The questioning thus concerns the capability of $X^\prime$ to properly record the light signal in the $(x,t)$-system although $X^\prime$ has not established a sender-receiver relation along the $x$-axis, because $X^\prime$ is moving with respect to this axis.

This is the key point noted above. The crucial point is thus the perception by $X^\prime$ of a light signal along the $x$-axis traveling with velocity 1, while $X^\prime$ is moving along the $x$-axis with velocity $v$, thus with relativity velocity $1-v$. How can this perception be harmonised with the postulate that light travels with velocity 1 with respect to all observers/inertial systems?

Einstein's answer is: Deny $X^\prime$ the possibility of making direct observations of the light signal in the $(x,t)$-system with manifest relative velocity is $1-v$, because that would be in conflict with light velocity 1,  and instead refer $X^\prime$ to follow the same light signal by identifying it with a light signal in the $x^\prime$ system traveling with velocity 1, which boils down to the Lorentz transformation with its change of space and time scales. The conflict between light velocity 1 and relative velocity $1-v$ of $X^\prime$ in the $(x,t)$-system, is thus circumvented by referring $X^\prime$ to make observations only in the $(x^\prime ,t^\prime )$-system with then a change of scale of space and time handling the conflict.

Let me give further perspective: The only physics expressed in the Postulates of SR is that light signals propagates with constant velocity 1 in all inertial systems. From this sole physics input a connection between coordinates in different inertial systems in the form of the Lorentz transformation is established, a connection which Einstein took as evidence of deep new physics of space and time, not only light signals. We thus go from simple input in the form of light signals propagating with velocity 1 in different inertial systems without connection, to a very precise connection between coordinates in different systems including completely new physical phenomena of space contraction and time dilation. This is viewed to be a result of the genius of Einstein as the ability like nobody else (e.g. Lorentz) to derive mind-boggling (but contradictory) conclusions about the deep real physics of space and time from almost no physics assumptions at all. This puts further doubt on the key step of identifying two light signals in two different inertial systems to be one and the same light signal. It is an unphysical assumption which leads to unphysical consequences.

It is a tragedy that modern physicists have closed their minds to questioning anything Einstein said about relativity, even when it is contradictory, including his derivation of the Lorentz transformation. Note that it is up to anyone believing that the space contraction and time dilation of the Lorentz transformation represent true physics, to show that its derivation is correct including the identification of the two light signals.

The above Einstein quote shows that Einstein himself had little confidence that his mathematical derivation of the Lorentz transformation was correct. So how confident can then followers to Einstein be?

With the Lorentz transformation as a travesty SR is reduces to nil, and what remains is then MMR. Try it out!

SR was by Einstein described as a "no-aether"-theory with the Lorentz transformation acting to unite observations of of different observers into one (privileged) common ground without relativity, to be compared with the full relativity of the "many-aethers"-theory of MMR with no privileged view.

As must be obvious to any physicist with connection to any physics reality, a "no aether"-theory is absurd by not offering any coordinate system for the expression of Maxwell's equations for the propagation of electromagnetic waves in the form of light.

PS1 Ian McCausland writes in The Dingle Affair: An Unresolved Scientific Controversy (1977);

• If scientists are content to turn a blind eye to illogical arguments, and are concerned only that the "right" conclusion is reached but do not care how it is reached, then they are subscribing to dogma instead of searching for truth.
• As we approach the centenary of Einstein's birth (March 14, 1979) there is a new motivation to assess the value of his life's work, a value that would still be enormous even if the special theory had to be abandoned. If the scientific world commemorates this centenary without expressing any concern about the unsatisfactory way in which criticisms of special relativity have been treated, then I think it will be fair to suggest that the scientific world is more interested in hero-worship than in the objective pursuit of truth.

40 years later the controversy is still unresolved, and the dogma has an even tighter grip on the physics community.

PS2 Recall the Einstein introduced the concept of event as some unspecified physics which can be labeled with a space-time coordinate $(x,t)$. The two light signals in the derivation of the Lorentz transformation thus were labeled $(0,0)$ in both the $(x,t)$ and the $(x^\prime ,t^\prime )$-systems, which was taken as evidence that the light signals could be identified.  But with the physics unspecified identifying two events lacks rationale.

It connects to the claimed experimental recording of gravitational waves in the LIGO experiment where an event in the form of a blip on a computer screen is claimed to be the recording of a gravitational wave created by the merger of two black holes, which is subject to increasing questioning.

PS3 The Postulates of SR speaks about the velocity/speed of light but says nothing about the nature of light e.g. as electromagnetic wave according to Maxwell's equations.  This is not helpful to the discussion because it opens to free speculation.

PS4 Of course I am not the first to say that the derivation of the Lorentz transformation is unphysical. It is made very clear in the talk by Thim Hartwig.

PS5 Recall Nikola Tesla (NYT 1935):

• Einstein’s theory of relativity is a mass of error and deceptive ideas violently opposed to the teachings of great men of science of the past and even to common sense... a magnificent mathematical garb which fascinates, dazzles and makes people blind to the underlying errors. The theory is like a beggar clothed in purple whom ignorant people take for a king… its exponents are brilliant men, but they are meta-physicists rather than scientists. Not a single one of the relativity propositions has been proved.

PS6 SR based on the postulates of (i) relativity and (ii) constancy of the speed of light, can be identified with the Lorentz transformation connecting coordinates in two inertial systems, which appears to express space contraction and time dilation.  Only (ii) contains an element of physics, and so the question comes up if space contraction and time dilation are real physical effects or only illusion without reality. Lorentz said illusion and Einstein reality. To Lorentz space contraction and time dilation are forms of illusion similar to that of seeing the apparent size an object decreasing with distance, which to Einstein would mean an actual shrinking like that of the head shrinking practiced by certain tribes. 

Einstein's Unphysical? Derivation of the Lorentz Transformation

Einstein's special theory of relativity SR boils down to the Lorentz transformation connecting the space-time coordinates $(x,t)$ and $(x^\prime ,t^\prime )$ in two (1d space) inertial systems with parallel space-axes moving with constant velocity $v$ with respect to each other:

• $x^\prime =\gamma (x - vt)$, $t^\prime =\gamma (t - vx)$,
• $x =\gamma (x^\prime + vt^\prime )$, $t =\gamma (t^\prime + vx^\prime )$,

where $\gamma = \frac{1}{\sqrt{1-v^2}}$ assuming the speed of light is 1 and $\vert v\vert \lt 1$. See that the origin $x^\prime =0$ of the $x^\prime$-axis follows the trajectory $x=vt$ in the $(x,t)$-system, and vice versa.

Let us now analyse Einstein's derivation of the Lorentz transformation. Recall that Lorentz, who presented his transformation before Einstein picked it up, did not view the two coordinate systems, the unprimed and the primed systems, to have the same physical significance. If the unprimed coordinate system had a physical meaning, the primed did not according to Lorentz concern real physics of space and time, only some form of fictitious or apparent ”local” space and time. It was Einstein who took the brave step to give both systems the same physical significance as an expression of full symmetry between the systems or complete relativity with no system more physical than another,  and so Einstein gave birth to SR as a fundamental pillar of modern physics.

Einstein's special ability was to derive far-reaching conclusions about concrete physics from some general assumption concerning mathematical form. Einstein thus formulated the following Postulates of SR:

• Laws of physics take the same form in all inertial systems. (Relativity)
• The speed of light (normalised to 1) is the same in all inertial systems. (Constant Light Speed)

We see that the Postulate of Relativity is an assumption about mathematical form and not about any concrete physics. Despite the very limited physics input in the form of Constant Speed of Light, Einstein was able to uncover deep truths about the very nature of space and time, including space contraction and time dilation,  as most surprising consequences of the simplest possible form of motion as translation with constant velocity. Amazing, but was it too good to be true? Let's see.

Note the important difference between the view of Lorentz (see PS below), as the inventor of the Lorentz transformation, with the primed coordinates expressing apparent physics with space contraction and time dilation as fiction, and the view of Einstein with the primed coordinates as real physics with space contraction and time dilation as real physics.

The difference is expressed  in the twin paradox with different rates of ageing only apparent according to Lorentz but most real according to Einstein. The question is then: Lorentz or Einstein?  

To seek an answer let us recall Einstein's derivation of the Lorentz transformation:

1. Consider two (1d) inertial systems $(x,t)$ and $(x^\prime ,t^\prime )$ with the $x^\prime$-axis sliding on top of the $x$-axis with velocity $v$ with its origin $x^\prime =0$ at position $x=vt$ at time $t$ thus establishing a connection between the systems.

2. Consider a light signal $L$ emitted from a stationary source at $x=0$ on the $x$-axis at $t=0$ viewing the emission to be an event with coordinates $(0,0)$ in the $(x,t)$-system. Conclude that $L$ follows the trajectory $x=t$ in the $(x,t)$-system, because the speed of light is assumed to be equal to 1 in the $(x,t)$ system.

3. Consider similarly another light signal $L^\prime$ emitted from a stationary source at $x^\prime =0$ on the $x^\prime$-axis at $t^\prime =0$ viewing the emission to be an event with coordinates $(0,0)$ in the $(x^\prime ,t^\prime )$-system. Conclude that $L^\prime$ follows the trajectory $x^\prime=t^\prime$ in the $(x^\prime ,t^\prime )$-system, because the speed of light is assumed to be equal to 1 in the $(x^\prime ,t^\prime )$ system. So far we have two light signals $L$ and $L^\prime$ in two systems moving with respect to each other.

4. Now take the step to identify $L$ with $L^\prime$ on the ground that their emission event coordinates $(0,0)$ agree, and conclude that $(x,t)$ and $(x^\prime ,t^\prime )$ describe the trajectories of one and the same light signal, so that $x=t$ if and only if $x^\prime =t^\prime$.

5. Make the Ansatz $x^\prime =\gamma (x-vt)$ with $\gamma$ a positive constant recalling that $x^\prime =0$ follows the trajectory $x=vt$. Conclude by identifying $x=t$ with $x^\prime = t^\prime$ according to 4. that $t^\prime =\gamma (t-vx)$ and $\gamma = \frac{1}{\sqrt{1-v^2}}$, which gives the Lorentz transformation. Recall that new strange effects in the form of space contraction and time dilation are consequences of the Lorentz transformation.

Let us now take a closer look at Einstein's argument.

The crucial step is the identification in step 4. Before identification there are two independent light signals, one emitted in the unprimed system and another emitted in the primed system from stationary sources at the origins, two light signals without any connection. But after the identification the primed signal can be viewed according to 1. to have  presence in the unprimed system as a signal emitted by a source at $(x,t)=(0,0)$ moving with velocity $v$. There are thus in total four light signals, two in each system with one emitted from a stationary source and the other from a moving source, all identified to be one and the same light signal.  The key question is now if from physical point of view it is correct to identify:

• (i) two signals in the two systems on the ground that their emission events have the same coordinates? 
• (ii) two signals in the unprimed system, one from a stationary source and the other from a moving source, and vice versa for the primed system?  

Concerning (i), one may ask from where the need arises to introduce two systems and then seek a connection between the two? For the description of propagation of light signals, it is enough to consider just one spatial coordinate system with the source fixed at the origin. But this was not enough for Einstein, who wanted to uncover deep secrets of space and time by comparing descriptions in different systems of what Einstein considered to be one and the same light signal.

Concerning (ii) we ask if a stationary source emits the same light signal as a moving source? The answer is no, since the frequency changes according to the Doppler effect, so the signals cannot be the same. Moreover, since a light signal is extended in space, the initialisation of the primed signal as viewed in the unprimed system is different from that of the unprimed signal, because the Lorentz transformation mixes space into time so that initialisation at $t=0$ and $t^\prime =0$ do not have the same spatial form.

We conclude that the two signals in the unprimed/primed system cannot be identified if frequency and initial wave form counts, and without this identification the two signals in the two systems cannot be made either and so the connection by the Lorentz transformation cannot be made.

Summary: Einstein's derivation of the Lorentz transformation between the coordinates in two inertial systems is based on an identification of two different signals, which can be questioned on physical grounds. Einstein's conclusion that the Lorentz transformation connects coordinates in two systems with the same real physical significance, thus can be questioned. For Lorentz the question does not have the same weight, since if only appearance is sought, the argument can be weaker. 

So what do you think: Is the identification anyway correct in some sense, if not concerning frequency and initial wave form, so that anyway the Lorentz transformation gives correct information about deep stunning secrets of real space and time, and not only appearances?

Or do you say that there is no reason to spend effort on a question like this, since all professional physicists know that the Lorentz transformation correctly describes real physics and thus does not require any justification a la Einstein or anyone?

If the view of Lorentz is the one that is correct, then much of modern physics qualifies as fiction.
In order for Einstein to be correct, a physically correct derivation of the Lorentz transformation is needed. Is there any?

PS1 Lorentz expressed his view on his transformation:

• ...a transformation of the time was necessary, so I introduced the conception of local time which is different for different frames of reference which are in motion relative to each other. But I never thought that this had anything to do with real time. This real time for me was still represented by the older classical notion of an absolute time, which is independent of any reference to special frames of coordinates. There existed for me only one true time. I considered my time transformation only as a heuristic working hypothesis, so the theory of relativity is really solely Einstein's work.

We read that Lorentz takes his hands off from Einstein's relativity theory based on misunderstanding Lorentz local time to be real time. Lorentz or Einstein?

PS2 From physical point of view with the $x^\prime$-axis gliding on top of the $x$-axis with constant velocity $v$, the only possible connection between the coordinates is that of a Galilean transformation:

• $x^\prime = x- vt$. 

It is unthinkable that there mere translation with constant velocity of  the $x^\prime$-axis on top of an $x$-axis, can change the scale of the $x^\prime$-axis vs that of the $x$-axis in any real sense. Unthinkable.

PS3 Recall that the Postulates of SR can as well serve as the postulates of Many-Minds Relativity MMR in which there is no need of the Lorentz transformation, and all the mysteries of SR resulting from Einstein's misinterpretation of the Lorentz transformation simply evaporate.

PS4 Recall that Einstein in his 1905 article introducing his special theory of relativity started by admitting that his Postulates appear to be contradictory:

• ...the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, 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.

It was not a good start..

PS5 The Constant Light Speed Postulate was in Einstein's 1905 article formulated as follows:

• The speed of light in empty space is always 1 independent of the state of motion of the emitting body.

Einstein viewed this postulate to be in apparent contradiction to the Postulate of Relativity.  Why? Because the  notion of "empty space" and the qualification "state of motion of the emitting body" appear to give "empty space" the role of a "stationary aether" to which a "state of motion" can be related, which would be in conflict with the Postulate of Relativity interpreted as stating non-existence of any preferred (inertial) system.

On the contrary, the Constant Light Speed Postulate can be viewed to be a consequence of the Relativity Postulate, and as such carrying no contradiction.

PS6 Einstein (but not Lorentz) got hooked up by the idea of a necessity to describe propagation of a light signal in different inertial systems moving with respect to each other. But why not be content with one description, a description where the source or the receiver/observer is stationary? This is the set-up in MMR, where each observer is stationary in his/her chosen inertial system, while the source may be moving. If there are more than one observer, then the question is to what extent different observers will agree, which is analysed in MMR. There is then no need to ask about a description from the point of view of a moving observer required to be in full harmony with that of a stationary observer, as the (unreachable) objective of SR. There is then no need to go into SR with all its contradictions, and modern physics can be liberated to focus on realities instead of shadows.

PS7 SR can be described as follows: 

• All inertial systems are equally valid and there is a common description (of light signals) mediated by the Lorentz transformation.

MMR can be described as follows:

• All inertial systems are equally valid and there is no common description. 

MMR naturally connects to an idea that "all is relative", but not so for the idea in SR of a common description (of a light signal). MMR is like a many-gods religion (polytheism) without common god in harmony with full relativity, while SR is like a common-god religion (monotheism) in contradiction to full relativity.