Einstein vs Lorentz, Planck and Bohr: Tragedy

Modern physics as relativity theory + quantum mechanics was born out of two misconceptions formed in the mind of the young Einstein as patent clerk in Bern in 1905 with little scientific training, but strong ambition to contribute to the emerging modern physics of  

1. Blackbody radiation.
2. Photoelectricity. 
3. Apparent absence of a unique aether carrying electromagnetic waves.  

In 1900 Planck had derived Planck's Law of blackbody radiation based on a smallest quantum of energy $h\nu$ connected to radiation/light of frequency $\nu$ with $h=6.55\times 10^{-34}$ Jouleseconds named Planck's constant. Planck did not assign any physical meaning to the smallest quantum $h\nu$ and viewed it simply as a "mathematical trick" used to derive Planck 's Law. 

In one of Einstein's 5 articles from the "miraculous year" 1905, Einstein assigns the quantum $h\nu$ a physical meaning as the energy of a "photon" as a "light particle" in a heuristic explanation of 2. Einstein thus did what Planck had said does not make any sense. In 1926 the mysterious quantum $h\nu$ appeared in Schrödinger's equation for the Hydrogen atom as the basic mathematical model of quantum mechanics.

In another 1905 article Einstein assigned the Lorentz transformation a physical meaning, which Lorentz had said would not make any sense, and so formed his Special Theory of Relativity SR.

Einstein thus contributed to the formation of modern physics in 1905 by attributing physical meanings to both Planck's quantum $h\nu$ and the Lorentz transformation, in direct contradiction to both Planck and Lorentz.  

As time went on and the authority of Planck and Lorentz faded, Einstein's ideas about physicality of photons and the Lorentz transformation slowly gained support, but when they became the standard of the new Quantum Mechanics of Bohr-Born-Heisenberg-Dirac in the 1930s, then Einstein said: Stop, QM is no longer real physics!  Only Schrödinger said the same thing, but both were efficiently cancelled by Bohr. 

Einstein thus started out and ended as a tragic figure. First he genuinely misunderstood Planck and

Lorentz about physical reality and so contributed the development of a new form of physics, which he on good grounds criticised for lacking physicality. The irony was that physicists listened when he was wrong but not when he was right.   

Einstein in Alice Wonderland

This a follow up of the previous post.

The mathematician Lewis Carroll anticipated Einstein's Special Theory of Relativity SR (1905) in his famous Alice's Adventures in Wonderland (1865) filled with "space contraction" and "time dilation" as core themes of the book. Very amusing and mind boggling! Einstein must have read the book in his youth, although he did not read much, since the connections cannot be accidental. 

In a further discussion with chatGPT representing mainstream professional physicists view, the following is made clear:

• A matter-only world is a Newton world to be Galilean invariant. 
• Adding light changes this matter-only world to be instead Lorentz invariant, even if there is no interaction between light and matter.
• Adding light to a matter-only world "reveals the true spacetime structure" to be Lorentzian and not Galilean as only an approximation of Lorentzian. 

This is really a very Grand Plan for the world and it is important to see what the basis is. We thus recall the form of a Galilean transformation and a Lorentz transformation between two space-time coordinates $(x,t)$ and $(x^\prime ,t^\prime )$ in two inertial systems moving with speed $v$ with respect to each other, assuming  speed of light = 1:

• Galilean: $x^\prime = x-vt$ and $t^\prime =t$.
• Lorentz: $x^\prime = \gamma (x-vt)$ and $t^\prime =\gamma (t-vx)$ with $\gamma =\frac{1}{\sqrt{1-v^2}}$.

We see two very simple linear transformations so simple that even Alice would understand the mathematics. We see the "time dilation" aspect of Lorentz in the dependence in the primed time coordinate $t^\prime =\gamma (t-vx)$ on the space coordinate $x$. In short, a Lorentz transformation mixes space and time, which a Galilean does not. 

The idea carried by modern physics is now that a Lorentz transformation reveals the "true nature of spacetime," which thus is not that of a Galilean transformation. 

But is this credible? How can a simple linear transformation reveal the true nature of a spacetime without physics? 

A Galilean transformation expresses that measurement of velocity depends on chosen coordinate system in a specific simple way, while Nature does not use any coordinate system at all. Physicists are thus free to chose coordinate system as they like and Nature will not protest.

Lorentz clearly stated that a Lorentz transformation has no physical meaning. But a Galilean transformation can be given direct physical meaning in the form of meter sticks moving with constant velocity keeping their length and clocks unaffected by such motion. 

But this kind of argumentation is dismissed by a modern physicist because it questions Wonderland Science. The Lorentz transformation in all its simplicity is claimed to reveal the "true nature of spacetime" and there is nothing more to say. Discussion closed. Forget what Lorentz said!

SR was from the beginning met with neglect or skepticism and in the motivation for the 1921 Nobel Prize in Physics to Einstein the Nobel Committee explicitly expressed that the Prize was given to Einstein despite his SR physics never done before or after. In the 1920s quantum mechanics took over with a Galilean invariant Schrödinger equation (1925) followed by a Lorentz invariant Dirac equation (1928), which took over the scene when Schrödinger left the field quickly thereafter. Dirac's equation gave SR respectability, while Einstein was removed from the scene by Bohr. 

Today SR is kept like a toy model with amusing properties, but is no longer subject to scientific study. But the idea of spacetime with time mixed into space is alive in Einstein's General Theory of Relativity GR also believed to reveal the "true nature of space time" now as "curved spacetime". But no Nobel Prize to GR either. Maybe the true nature of space and time is not revealed in a coordinate transformation…

  

Modern Physics as Strange Physics as Crisis Physics

Modern physics is in a state of crisis, and we conclude from Leibniz' Principle of Sufficient Reason that the crisis must have some background. Modern physics can be described as being strange as compared to classical physics being rational with the shift taking place in the beginning of the 20th century.  

Strangeness was first introduced into modern physics by Einstein in 1905 in his Special Theory of Relativity SR presenting strange effects of time dilation, space contraction and relativistic mass leaving classical physicists aghast from solid experience of Newton's and Maxwell's physics.

Einstein based SR on the following Postulates

• Physical laws take the same form in all inertial coordinate systems.
• The speed of light is the same in all inertial coordinate systems. 

From these two Postulates Einstein derived the Lorentz transformation between space-time coordinates $(x,t)$ and $(x^\prime , t^\prime )$ of two inertial coordinate systems moving with respect to each other. Einstein then derived the strange effects of time dilation, space contraction and relativistic form of Newton's Law with relativistic mass.

To derive the Lorentz transformation (already derived by Lorentz without giving it any physical meaning) Einstein's started considering the following "thought experiment":

• Two light pulses are emitted by two light sources flashing at coordinate $(0,0)$ of two moving inertial systems in which the resulting light pulses are described by $x=t$ and $x^\prime =t^\prime $ in each system.  (TE) 

In this experiment Einstein thought of a "flash" to be an event described by the coordinates $(0,0)$ without any real physics attached to the event. The idea of "event" without physics uniquely described by a space-time coordinate like $(0,0)$ was new as subject of the "thought experiment".

Having formulated TE in his thought, Einstein then argued:

1. The two light pulses are the same light pulse since the "flash event" = $(0,0)$ is the same in both systems.
2. Since the light pulses are the same light pulse, only viewed in two different inertial systems, there must be a relation between the coordinates, which shows to be the Lorentz transformation.     

The key is here 1. Is it correct to conclude that the pulses are the same because the light sources happen to coincide in space when they flash? If they happened to flash at different points nobody would expect them to be the same.

Of course not, if you replace "thought experiment" by physical experiment. A physical flash has duration in space and time in a coordinate system attached to the flashing device. If two flashing devices moving with respects to each other happen to both flash when they meet, it does not mean that they give the same flash and so cannot be connected by a Lorentz transformation.

Einstein's conclusion that the light signals are the same light signal described in two different coordinate systems, is thus without physical meaning. It is then not strange at all that Einstein can derive strange new effects which are "thought effects" and not "physical effects".

A correct conclusion of Einstein's experiment as real experiment can be inspected as Many-Minds Relativity which is not strange at all.

The strangeness of modern physics as root to its crisis was thus introduced by Einstein in SR as a thought experiment without real physics only strange physics. Of course all sorts of "strange thoughts" should be viewed with suspicion in particular in science. A reasonable thought is not strange. Physics must reasonable to exist. The step from black magic to science was taken using reason as guiding principle. There is no reason to go back to strange magic fostered by strange thoughts.

But the strangeness of SR was soon overpowered by General Relativity and Quantum Mechanics into strange physics "nobody understands" according to famous leading modern physicist Richard Feynman.

 

The Role of the Lorentz Transformation in Modern Physics

The trade mark of modern physics as relativistic physics is the Lorentz Transformation LT connecting observations in two Euclidean coordinate systems moving with constant velocity $v$ with respect to each other (inertial systems), to be compared with the Galilean transformation of classical Newtonian physics, with difference scaling with $\vert v\vert ^2$, assuming normalisation of the speed of light to 1. 

In most cases $\vert v\vert <<1$ and then the relativistic effects are very very small, yet they serve as prime evidence of major advancement brought by modern physics in the sense that the effects are of an entirely new kind including time dilation and space contraction resulting from the fact that LT mixes space and time, which is not seen in classical physics. 

The relativistic effects of modern physics are thus presented as being very very small, except possibly in very very extreme cases like "colliding black holes", yet very very important by opening to a whole new world of strange relativistic effects all based on LT.

Recent posts have pointed to the following facts: 

1. LT was introduced by Lorentz to accommodate observations indicating that the speed of light is the same in all inertial Euclidean coordinate systems.
2. The meter length  scale in each Euclidean coordinate system is according to the 2019 SI Standard  to be determined in terms of travel time of light with the speed of light specified to be exactly 299792458 meter/second, with second defined by standard caesium clock.  

We understand that with the 2019 SI Standard the speed of light is the same in all Euclidean coordinate systems by definition/standard: The length scale in each Euclidean coordinate system is determined so that the speed of light is exactly 299792458 meter/second.

This means that the original mission of LT has been taken over by the 2019 SI Standard, and the real question is now to what extent observations in different inertial systems can be made to agree. There is full agreement on the speed of light by definition/standard but not on velocities and distances in general. This is the objective of Many-Minds Relativity.

Summary: LT has no longer any role to play under the 2019 SI Standard. The speed of light is the same in all inertial systems by definition/standard. There are no effects of time dilation since a caesium clock cannot be affected by inertial motion. Physics without LT may open to a unified theory viewed to be impossible with LT.

 

Non-Physical Lorentz Transformation

This is a follow up of the previous post with another aspect of the non-physicality of the Lorentz transformation. 

Lorentz invariance is a holy feature of modern physics coming to expression for a wave equation:

• $\frac{\partial u}{\partial t}-\frac{\partial u}{\partial x}=0$                 (W)

with solution $u(x,t)$ depending on a 1d Euclidean coordinate $x$ and time coordinate $t$. As shown in this post, the function $u^\prime (x^\prime ,t^\prime )=u(x,t)$ expressed in the Lorentz transformed coordinates $(x^\prime ,t^\prime)$ stated in the previous post, satisfies the wave equation

$\frac{\partial u^\prime}{\partial t^\prime}-\frac{\partial u^\prime}{\partial x^\prime}=0$  (W'),

which is viewed to express Lorentz invariance: The function $u(x,t)$ satisfying the wave equation (W), in transformed coordinates $u^\prime (x^\prime ,t^\prime )$ satisfies the wave equation (W') which reads exactly the same way as (W). 

The current wisdom is thus to say that the wave equation being invariant under Lorentz transformation, expresses a physical law which takes the same form in different coordinate systems connected by the Lorentz transformation. Invariance!

After having noted that the wave equation is Lorentz invariant, Einstein bravely proclaimed that all (true) laws of physics are Lorentz invariant, which immediately forced him to throw out Newtonian mechanics since Newton's 2n Law is not Lorentz invariant, and proceed to form a new relativistic mechanics unfortunately creating lots of trouble for modern physicists.

To someone with a bit of schooling in mathematics the wave equation (W) needs a qualification into an initial value problem with $t>0$, and $u(x,0)$ as an initial value as a function with spatial extension for all $x$, thus as co-existence in space for $t=0$. 

Now comes the catch: The initial value is not Lorentz invariant, since $t=0$ and $t^\prime =0$ do not say the same. In fact, $u(x,0)=u^\prime (\gamma x, \gamma vx)$, which is not an initial value for $u^\prime (x^\prime ,0)$. 

Co-existence as extended existence in space at a specific time is fundamental. Without co-existence the world collapses into point-like isolated events in space without cohesion and meaning.  

In other words, not even the wave equation (W) is Lorentz invariant, and so the whole idea of modern physics to consider laws of physics which are Lorentz invariant, collapses. This should be a relief for all students of physics for which exams in relativistic mechanics appear as road-block.

Why SR/Lorentz Transformation is Non-Physical

Recent posts have pointed to the fact that Einstein's Special Theory of Relativity SR is empty of physics and thus says nothing about the physical world, and so serves no scientific purpose. 

How can this be understood? We have put forward the argument that the basic postulate P of SR (with P stating that the speed of light is the same for all inertial observers moving with constant velocity with respect to each other), with the 2019 SI meter Standard is no longer a statement about physics but instead a prescription/standard/definition to follow by every observer to measure distance in lightseconds so that by definition the speed of light is the same for all observers, namely exactly 299792458 meter/second.

The basic postulate of SR is thus not a statement about physics, but a dictate to measure distance so that the speed of light is the same for every observer. 

The real question is then how well the 2019 SI Standard will work, that is to what extent different observers will agree on physics beyond the speed of light. SR has no information to offer, while Many-Minds Relativity has. 

Let us here understand the non-physical aspect of SR by inspecting the Lorentz transformation LT which Einstein in his 1905 article introducing SR derived from the basic postulate P.  

LT connects two 1d Euclidean space-time coordinates $(x,t)$ and $(x^\prime ,t^\prime )$ by the non-singular linear transformation

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

where $v$ with $\vert v\vert <1 $ is a given constant and $\gamma =\frac{1}{\sqrt{1-v^2}}$. 

We see that $x=vt$ in transformed coordinates reads $x^\prime =0$, which states the the origin $x^\prime =0$ in the $(x^\prime ,t^\prime )$-system moves along the trajectory $x=vt$ in the $(x,t)$-system.

We see that $x=t$ if $x^\prime =t^\prime$ and vice versa. So far LT is simply a coordinate transformation without physics. 

Physics is introduced by assuming that a light signal emitted at $(0,0)$ in the $(x,t)$-system follows the trajectory $x=t$ for $t>0$, thus with speed $\frac{dx}{dt}=1$. 

Likewise a light signal emitted at $(0,0)$ in the $(x^\prime ,t^\prime )$-system follows the trajectory $x^\prime =t^\prime $ for $t^\prime >0$, again with speed 1. 

In Einstein's SR these two light signals are viewed to be the same physical light signal, since they are both initiated from $(0,0)$. Einstein thus views the same physics being expressed in two different coordinate systems connected by the Lorentz transformation, which establishes a connection between the two systems coming with strange physical effects of time dilation and space contraction.

But a closer inspection shows that the two light signals are not the same, because emission of a light signal at $t=0$ in the $(x,t)$-system requires extension in $x$ of the emitting source to be physical. Similarly, emission of a  light signal at $t^\prime =0$ in the $(x^\prime ,t^\prime )$-system requires extension in $x^\prime$ of the emitting source to be physical. 

The catch is now that the emitting sources extended in $x$ at $t=0$ and extended in $x^\prime$ at $t^\prime =0$, are not same, and hence neither are the emitted light signals. It means that the two systems are not connected by a common light signal and so the Lorentz transformation is non-physical and so SR is non-physical and so serves no purpose in physics. Connecting to the previous post, co-existence is not the same and so the physics is different in the two systems.

Einstein is misled to believe the light signals to be the same because a distinction between $(x,0)=(0,0)$ and $(x^\prime ,0)=(0,0)$ cannot be made. 

Einstein's big mistake to give meaning to events labeled by $(x,t)$-coordinates as something without extension in space happening at the point $x$ at time $t$, thus with events being non-physical, because physical events have extension in space. 

We have now seen two arguments showing that SR is non-physical or void of physics:

1. Non-physicality of basic postulate P with 2019 SI Standard made into a prescription/definition. 
2. Non-physicality of LT as describing events without extension in space. 

   

Non-Physics of Lorentz Transformation

This post directly connects to the previous post Physics Illusion: Lorentz Transformation to which we refer for clarifying figures. 

The basic postulate of Einstein's Special theory of Relativity SR is the Lorentz transformation connecting the coordinates $(x,t)$ and $(x^\prime ,t^\prime )$ by 

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

where $v$ with $\vert v\vert \lt 1$ is a given constant and $\gamma =\frac{1}{\sqrt{1-v^2}}$. This is a very simple linear transformation, which by the chain rule satisfies

• $\frac{\partial}{\partial x}=\gamma (\frac{\partial}{\partial x^\prime}-v\frac{1}{\partial t^\prime})$
• $\frac{\partial}{\partial t}= \gamma (\frac{\partial}{\partial t^\prime}-v\frac{\partial}{\partial x^\prime})$

which leaves a wave equation invariant in the sense that if the function $u(x,t)$ satisfies 

• $\frac{\partial u}{\partial t}-\frac{\partial u}{\partial x}=0$,         (1)

then the function $u^\prime (x^\prime ,t^\prime )=u(x,t)$ satisfies an equation of the same form:

• $\frac{\partial u^\prime}{\partial t^\prime}-\frac{\partial u^\prime}{\partial x^\prime}=0$.  (2)

This is very simple mathematics, of the same complexity as 1+1 = 2. Here $(x,t)$ may be viewed to represent Euclidean space-time coordinates with (1) expressing propagation of a wave with unit speed, while according to Lorentz $(x^\prime ,t^\prime )$ does not represent any physical reality.    

This is were Einstein stepped in with SR declaring:    

1. (L) connects the coordinates $(x,t)$ and $(x^\prime ,t^\prime )$ in two Euclidean coordinate  systems moving with respect to each other, both with the same physical meaning.
2. True physical laws must take same form in coordinate systems connected by Lorentz transformation (be Lorentz invariant)  = Principle of Relativity. 

Einstein then accepted the wave equation as a true physical law, but not Newton's 2nd Law because it is not Lorentz invariant, and so modified Newton's mechanics into a new form of relativistic mechanics with all sorts of strange effects including space contraction and time dilation by the coupling of space with time in (L).

In 2 Einstein decides over physics. In 1 Einstein contradicts Lorentz and so we ask who was right? 

An answer is given by recalling from the previous post the concept of coexistence or simultaneity, as the presence in space of a spatially extended body B represented by a range of coordinates $x$ like $0<x<1$ for which the time coordinate is the same e.g. $t=0$. If we plug in $t=0$ into (L) we get

•  $x^\prime =\gamma x$, $t^\prime =-\gamma vx$ or $x^\prime = -\frac{1}{v}t^\prime$ 

which represents a trajectory in the $(x^\prime ,t^\prime )$-system without coexistence. This is contradictory and so shows that SR is non-physics.

The bottom line is that SR does not make sense for extended bodies. But a Universe without extended bodies with coexistence is not a real Universe, only a fantasy. The consequences for modern physics based on SR are far-reaching.

Or is it possible to save SR by insisting that the Universe consists of bodies without spatial extension somehow interacting under Lorentz invariance? We are thne led to ask how different such point-like bodies may interact? So we image two point-like objects with space coordinates $x_1$ and $x_2$ in the $(x,t)$ system, and we ask about the corresponding time coordinates $t_1$ and $t_2$? With $t_1=t_2$ the interaction is instant as an expression of coexistence,  while if $t_1>t_2$ or $t_2>t_1$ there is delay excluding true interaction. We are thus led to expect that true interaction between bodies requires coexistence and so would not satisfy Lorentz invariance. 

The case for SR is weak.  

More on the non-physics of (L): Three Major Inconsistencies of the Lorentz Transformation.

      

Local Coexistence: Leibniz vs Einstein

Local coexistence.

A basic idea of modern physics is that the conceptions of space and time of classical physics formed by Leibniz/Newton have to be replaced by a concept of curved space-time of Einstein's theory of relativity. Einstein struggled through his entire scientific life to give meaning to this new concept, but today very few modern physicists claim to have a proper understanding of what Einstein wanted to tell humanity, while it is commonly agreed that Einstein was right and so that Leibniz/Newton was wrong.   

But the physics of Leibniz/Newton is the classical physics of the scientific revolution reaching full power with Maxwell's equations at the end of the 19th century thus capturing all of macroscopic mechanics and electromagnetics in differential equations in terms of functions $f(x,t)$ of classical Euclidean space coordinates $x$ and time $t$. It was a formidable success, which met the young patent clerk Einstein preparing for a scientific career at the turn to the 20th century with the demanding question: How to impress the World?

At the patent office Einstein tested his abilities on some main open problems of classical physics including black body radiation, photo-electricity and the (non-)existence of an ether as medium for the propagation of electromagnetic waves. Einstein's efforts resulted in 5 articles on these topics in 1905 named Annus Mirabilis. 

In one of the papers Einstein picked up an observation by Lorentz that wave equations take the same mathematical form under a simple linear transformation of coordinates mixing space and time, named Lorentz transformation. Lorentz cautioned that coordinates transformed from physical coordinates were absolutely not to be viewed as physical coordinates. But here young Einstein found a thread to follow, by opposing Lorentz and claiming that all coordinates subject to Lorentz transformation have a physical meaning. So was Einstein's special theory of relativity formed as the physics of Lorentz transformations, which showed a very new form of physics with space contraction and time dilation unheard of by Leibniz/Newton and classical physics. But this did not impress the physics community at all, which made Einstein double down by extending his special theory to a General Theory of Relativity GR during 10 years of hard struggle to make sense of his curved space-time. Again the physics community was not impressed and GR was not hailed as a trade mark of modern physics until Einstein had passed away and no longer could be asked to clarify his ideas, and so the physics community was free to exploit Einstein's $E=mc^2$ and nuclear power to attract funding to Big Physics, which succeeded very well until lack of results resulted in a backlash as the crisis of modern physics of today...

The mantra of modern physics is that the classical concepts of space and time by Leibniz/Newton have to be replaced by Einstein's space-time coming to expression in the Lorentz transformation mixing space and time into strange new physics. The mantra was based on a perception that Newton's physics required absolute space and time, which was hard to rationalise. 

But Leibniz viewed both space and time to be relational (and so relative) and thus not absolute in Newton's sense: 

• space is order of coexistence
• time is order of succession/change    

which can pull the rug under the necessity to give up classical concepts. It is natural to qualify Leibniz view to 

• space is measure of local coexistence
• time is measure of change of local coexistence.    

The central concept is local coexistence or simultaneity as something appearing with nearby space coordinates at the same time, like an extended body existing at a specified time. The novelty as compared with Newton's absolute space as global space is the aspect of locality. 

This aspect is expressed in explicit time stepping of the heat equation $\dot T(x,t) = \Delta T(x,t)=0$ with $T(x,t)$ temperature depending on a (1d for simplicity) Euclidean space coordinate $x$ and a time coordinate $t$, which takes the form

• $T(x, t+dt) = T(x,t)+0.5(T(x+dx,t)-2T(x,t) + T(x-dx,t))$

where $dx$ is a small space step and $dt=0.5dx^2$ a time step. We see that $T(x,t+dt)$ at new time $t+dt$ is updated from $T(y,t)$ at previous time $t$ and $y=x$ and nearby $y=x\pm dx$ expressing local coexistence (with effectively finite speed of propagation). This connects to the previous post on Newton's law of gravitation and Universe Model.

The Lorentz transformation connects space-time events without extension in space and so has no room for local coexistence/simultaneity. But without local coexistence/simultaneity the World falls apart and so must a physical theory based on the Lorentz transformation. 

Locality of space and time comes to expression by the clock of the local village church telling the villagers when to quit work and go home to eat, or a local Sunset. Global coordination is not needed to make physics without human intervention to go around. Explicit time stepping under local coexistence/simultaneity is enough. 

It is important to make a distinction between man-made physics and natural physics without human intervention. Man-made physics like the GPS system uses global time shared by satellites realised by man-made synchronisation, while natural physics only requires local time as local coexistence. 

Sum up: With a Leibnizian concept of space as local coexistence and time as change of local coexistence there is no compelling reason to replace classical concepts (which make sense) by Einstein's concept of curved space-time (which does not make sense). Leibniz thus offers a theory of relativity without the confusing aspects Einstein's theories.   

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. 

Modern Physics in Free Fall Crisis

Modern physicists in joint free fall under quantum supergravity.

There are many witnesses of a modern physics in serious crisis. The process started at the turn to 20th century modernity with Einstein's special theory of relativity and Planck's derivation of the law of blackbody radiation based on statistics of energy quanta opening to quantum mechanics.

Evidence of the crisis can be seen in the 2019 Special Breakthrough Prize in Fundamental Physics to a 1970 speculation about supergravity, which has resisted 50 years of experimental verification, see also Where are we now?. The Breakthrough website motivates the Prize to supergravity as follows:

• In the four decades since its development, supergravity has had a powerful influence on theoretical physics. It showed that supersymmetry was capable of accounting for all the phenomena we see in the real world, including gravity. It represented a completion of the current understanding of particle physics – a rigorous mathematical answer to the question, “What theories of nature are compatible with the principles of both quantum mechanics and special relativity?” And it provided a foundation for the attempt – still ongoing – to build a full theory of quantum gravity that describes space and time at a fundamental level.

We see that the 2019 Breakthrough Prize concerns precisely the question discussed in this sequence of posts: How to reconcile the principles of quantum mechanics and special relativity? But the 1970 answer in the form of supersymmetry appears to have few proponents today outside the Prize committee as a (failed) "attempt". It is not impossible that the 2020 Fundamental Physics Prize will go to the discovery that special relativity is not fundamental physics, and thus that there is no contradiction with quantum mechanics.   

The shift to modernity was a break-off from classical physics as science of "what is" (ontology) into a modern physics as science of "what we can say" (epistemology) as expressed by Niels Bohr, in which a material world going around even without any (human) observer was replaced by a mist of statistics of (human) observation.

In the new view of modern physics causality/determinism was given up, under much agony because that had been the basic principle of physics since Aristotle, while the monumentality of the sacrifice added to its thrill.  But a sacrifice carries a cost and the cost is now showing up in the form of a modern physics in free fall without any thinkable connection to experiments as string theory in 11 dimensions and multiversa statistics of all possibilities.

What is then the effect of a physics in free fall? Is it helpful to humanity? What was the basic reason that forced Einstein and Bohr followed by generations of modern physicists, to give up causality and rationality?

Einstein was led to special relativity in an effort to handle the lack of physicality of a vacuum or "aether" as a medium for propagation of electromagnetic waves/light. It appeared in experiments like that by Michelson-Morley as if there was not just one single "aether", but many different as if each source/receiver system in motion would "drag" its own aether along. Einstein however could not handle the diversity of many aethers (put forward by e.g. Ebenezer Cunningham) and so took the radical step of declaring that there is no aether at all, in particular not many aethers causing confusing. In modern psycho-physiological terms it could be described as a syndrome of not being able to handle the many sometimes conflicting perspectives of life.

In any case the "no-aether" idea led Einstein into the his special relativity where all observers are compelled to share the same mathematical formulas under a banner of Lorentz invariance, however  without being able to agree on anything else of importance such as simultaneity, time and space. The scientific world met Einstein's special relativity with a yawn as epistemology without physics, which made Einstein turn to his general theory of relativity, which as a consequence of efforts to reconcile England and Germany after World War I in the hands of Eddington, took off in the media and then was turned into a pillar of modern physics.

The trouble was that this pillar was incompatible with the other pillar of modern physics, namely quantum mechanics founded on Schrödinger's equation, which resisted to Lorentz invariance. Modern physics has carried this incompatibility for 100 years as a basic trauma on which much of the present crisis can be blamed, with supergravity as failed attempt to reconcile quantum mechanics with gravitation. The rest of the blame can go to the use of statistics as a collapse of causality/determinism, which was forced from the multi-dimensional form of Schrödinger's equation.

Modern physicists bear witness of the crisis, but I have met little interest in possible ways to take off instead of falling down, by questioning Lorentz invariance and the necessity of a statistical approach to the physics of an atom. But the crisis goes on and maybe some day, discussion will be possible.

The similarity with a climate science dominated by one gospel of alarm is obvious. More precisely, the corruption of climate science today is made possible by the fact that modern physicists have retreated from the world.

The last sequence of posts give arguments that Lorentz invariance has no role to play in physics.
In Real Quantum Mechanics a variant of Schrödinger's equation free of statistics as a system in 3 space dimensions, is presented.

Comments from physicists are welcome. Is any form of discussion possible? Or is the crisis permanent?

PS In many respects modern physics appears as a game of poker, where the physicist player all the time can raise the bet and avoid being called by the public/tax payer. This is what Einstein did, when confronted with questioning of the special theory of relativity, by turning to general relativity, which when questioned was further raised to cosmology. Or when Schrödinger's equations for atoms was confronted with Lorentz invariance and the bet was lifted to Dirac's equation, not for atoms but only for one free electron, and then further to quantum field theory with a universe of infinities, which was handled by "renormalisation" and so on to string theory in 11 dimensions, which cannot be called because it is very far beyond both experimental conformation and refutation.

The Seduction and Spell of the Lorentz Transformation

Modern physics is based on the idea of Lorentz invariance as the basic postulate of Einstein's special theory of relativity:

• Laws of physics are invariant under the Lorentz transformation between different inertial systems, that is, laws of physics are Lorentz invariant.  

Recall that the Lorentz transformation connecting two inertial space-time coordinate systems $(x,t)$ and $(x^\prime ,t^\prime )$ for two observers moving with velocity $v$ with respect to each other, reads:

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

where $\gamma = \frac{1}{\sqrt{1-v^2}}$ assuming the speed of light is 1 and $\vert v\vert \lt 1$. We see that the space coordinate $x$ and time coordinate $t$ appear in symmetric form with a an apparent similarity between space and time, which Lorentz viewed to be a formality without physics, but Einstein took as a basis of modern physics with space mixed into time.

Which laws of physics are then formally Lorentz invariant? By the chain law, we have

• $\frac{\partial}{\partial x}=\gamma (\frac{\partial}{\partial x^\prime}-v\frac{\partial}{\partial t^\prime})$,
• $\frac{\partial}{\partial t}=\gamma (\frac{\partial}{\partial t^\prime}-v\frac{\partial}{\partial x^\prime})$,

and so 

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

We see that the second order wave equation

• $\frac{\partial^2u}{\partial t^2} - \frac{\partial^2u}{\partial x^2}=0$, 

is Lorentz formally invariant, in the sense of reading exactly the same in the $(x^\prime ,t^\prime )$ system.  On the other hand, for the first order wave equation:

• $\frac{\partial u}{\partial t} - \frac{\partial u}{\partial x}=0$,

the multiplicative factor $\gamma (1+v)$ appears, and so only a form of restricted formal Lorentz invariance is in place.

The second order wave equation describes waves in an elastic string with clear material spatial presence or coexistence, as well as plane electromagnetic waves in a vacuum without material spatial presence.  

The idea of Einstein (picked up from Lorentz) was that since the wave equation takes the same form in all inertial systems connected by the Lorentz transformation (more or less), all inertial systems are equally valid (with in particular the same speed of wave propagation/light), which Einstein declared to be the essence of the new physics of the special theory of relativity. This was the seduction of Lorentz invariance which promised to solve the mystery on an "aether" medium for the propagation of electromagnetic waves in vacuum without material presence.   

For both wave equations we see the space coordinate $x$ and time coordinate $t$ appearing in symmetric form, which opens up to some invariance with respect to the Lorentz transformation with similar symmetry.

But the formal symmetry in space and time in the wave equations does not say that space and time have the same nature and can be mixed into each other. In the wave equations there is a clear distinction between space and time which is expressed in the initial condition complementing the wave equation in a mathematical description of a wave $u(x,t)$, which takes the form  

• $u(x,0)=u_0(x)$ for all $x$, 

for the first order equation (with also an initial condition for $\frac{\partial u}{\partial t}$ in the second order case), where $t=0$ is an initial time and $u_0(x)$ an initial wave form with extension in space. With the initial condition a clear distinction between space and time is made. This is physics which is very obvious for the elastic string but also relevant for electromagnetic waves. The initial wave form shows spatial coexistence at different points $x$ for some common initial time $t=0$. 

And now comes the catch showing that the Lorentz transformation is not compatible with physics, even if the wave equation is formally (more or less) Lorentz invariant: The initial condition is not invariant under Lorentz transformation, because $(x,0)$ translates into

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

which does not have the form of an initial condition for $t^\prime =0$. The physics of coexistence expressed in the $(x,t)$-coordinates through the initial condition for $t=0$ does not carry over to physics of coexistence of an initial condition for $t^\prime =0$. This means that the physics expressed in the different inertial systems is different. The whole idea of relativity of expressing the same physics in different inertial systems thus collapses.

The formal symmetry of the space and time coordinates in the two forms of the wave equation misled a confused Einstein to believe that space and time could be mixed, because Einstein did not properly understand the physical meaning of the mathematics of the wave equations. The sad fact is that generations of physicists have followed in the footsteps of Einstein with a mantra of Lorentz invariance as a necessary requirement of a law of physics.

A traveling wave is a solution $u(x,t)$ of either of the above wave equations of the form 

• $u(x,t)=f(x+t)$, 

where $f(\cdot )$ is a function of one variable. For example $f(y)=\sin(y)$ with 

• $u(x,t)=\sin(x+t)$. 

The initial condition for $t=0$ would then have the form $u_0(x)=\sin (x)$ as a wave in space, while an observer sitting at $x=0$ would experience a wave in time of the form $\sin(t)$, but the observer would have no reason to mix the wave in space with the wave in time just because the mathematics looks the same. To do that as Einstein did, shows that the mathematics is misunderstood.

The second order (but not the first order) equation also has standing wave solution of the form

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

with seemingly stationary spatial character in $(x,t)$-coordinates, but visibly not so in $(x^\prime ,t^\prime )$ coordinates. A standing wave solution is not Lorentz invariant. A standing wave for the observer using $(x,t)$-coordinates is not a standing wave for the observer using $(x^\prime ,t^\prime )$, of course not since the observers are moving with respect to each other.

In general the equations of mathematical physics do not show the symmetry of space and time of wave equations and thus do not show any Lorentz invariance at all. The physics is the same for all observers but its mathematical description varies between moving observers, as soon as the physics has some spatial presence, which is the nature of physics.  Only Maxwell's equations for vacuum can show formal Lorentz invariance, but not in the presence of charges and not with respect to initial conditions. The equations of physics are not Lorentz invariant. Not Maxwell with charges, not Schrödinger, not MHD, not Navier, not Navier-Stokes, not anything.

The net result is that the notion of Lorentz invariance has only a purely formal mathematical meaning and carries no real physics. If the spell of Lorentz invariance can be broken, then many possibilities  to progress seem to open up. But this is not something physicist like to hear. They will cling to Lorentz invariance no matter the cost and lack of reason. It is a spell.

Getting out of the spell means understanding that Leibniz distinction between space and time is valid also for modern physics:

• space = order of coexistence.
• time = order of succession.

But the spell has such strong grip on the minds of modern physicist that not even a basic discussion is possible.

Einsteins "Scientific Method": Magic Physics from Definition

Einstein "scientific method", which brought him immense fame as the greatest physicist of all times, consists of:

• Start from a definition, convention or stipulation/law without physical content, and then draw far-reaching consequences about the physics of the world.

It is not hard to understand that such a "method" cannot work: You cannot draw meaningful conclusions about the world simply from a definition empty of physics content. You cannot develop a meaningful scientific theory from a definition that there are 100 centimeters on a meter. 

Einstein cleverly covered up by naming his definitions or conventions or stipulations/laws, "principles":

1. Equivalence Principle: Gravitational mass is equal to inertial mass.
2. Relativity Principle: Observations in inertial coordinate systems moving with constant velocity with respect to each other, are to be connected by the Lorentz transformation.
3. Covariance Principle: Physical laws are to have the same form independent of the choice of coordinate system.

Here 1. is an empty definition, because there is only one mass, and that is inertial mass, which measures acceleration vs force and gravitational force is a force. Gravitational mass is equal to inertial mass by definition. Attempts to "prove/verify" this experimentally, which are constantly being made with ever increasing precision and always with the same result of equality, are as meaningful as experiments attempting to verify that there are 100 centimeters on a meter, which could very well be the next grand challenge for LHC, in the spirit of Einstein.

2.  stipulates that different physical phenomena are to be viewed to be the same. This is because the Lorentz transformation is not invariant with respect to initial conditions, and thus Einstein stipulates that  two waves satisfying the same form of wave equation, but having different initial conditions, shall be viewed to be the same. No wonder that with this play with identities, all sort of strange effects of time dilation and space contraction can be drawn out of  a magicians hat.

It is clear that physical laws in general take different forms in different coordinate systems, and thus 3. is an absurd stipulation. Alternatively, it is trivial and just says that a physical law will have to transform when expressed in different coordinates so that the law has the same physical content. So 3. is either absurd or trivial, in both cases devoid of physics.

It is depressing that none of this can be understood by leading modern physicists. Nada. Even more depressing is that the discussion is closed since 100 years.

Physics Illusion 11: Lorentz Transformation as Holy Doctrine of Physics

A Galilean transformation gives the connection between the coordinates in one system at rest and another system translating with constant velocity with respect that at rest. Fundamental with a clear physical meaning and relevance.    

Lorentz transformation with $x^\prime$-axis in red pointing into the $(x,t)$ first quadrant making it unphysical since different parts of an object extended in space get different time coordinates and thus does not exist as an object. For this reason, Einstein only speaks about points in space-time as events which excludes interactions of objects extended in space. 


The coordinates in two space-time coordinate system $S$ and $S^\prime$ with coordinates $(x,t)$ and $(x^\prime ,t^\prime )$ moving with constant velocity $v$ with respect to each other is in classical (non-relativistic) mechanics connected by a Galilean transformation:

• $x^\prime  =x - vt$,
• $t^\prime  =t$,  

In relativistic mechanics according to Einstein's special theory, the connection is instead postulated to be that of a Lorentz transformation: 

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

where $\gamma = \frac{1}{\sqrt{1-v^2}}$ assuming the speed of light is 1 and $0 < v < 1$.

In the Galilean case the time rate in $S$ and $S^\prime$ are the same, but in the Lorentz case it differs with a factor $\gamma$, so that with $S$ motionless the time in $S^\prime$ would seem to run slower, and the other way around.

The Lorentz transformation is by physicists regarded to reveal deep truths about physics, as a result  of the fact that it leaves a wave equation in $(x,t)$ coordinates:

• $\frac{\partial^2u}{\partial t^2}- \frac{\partial^2u}{\partial x^2} = 0$

invariant under a Lorentz transformation, that is the wave equation looks precisely the same in $(x^\prime ,t^\prime )$ coordinates. 

On the other hand, a Galilean transformation brings in a second order correction term in the velocity $v$ of the form:

• $v^2 \frac{\partial^2u}{\partial x^2}$,

and therefore a Galilean transformation is not viewed to have the same dignity as the Lorentz transformation without such a correction. For human observations $v^2 < 10^{-10}$ (with the speed of light normalized to 1) the correction is miniscule and of no practical significance.

However, as strongly emphasized by Lorentz himself, the Lorentz transformation is not a transformation between physical coordinates. In particular the transformed time $t^\prime$ should not be viewed as real physical time.

This was not understood correctly by Einstein, who gave $t^\prime$, against the strong advice by Lorentz, a physical meaning and so the special theory of relativity was born based on the Lorentz transformation, which then (surprisingly against all odds) became a fundamental pillar of modern physics. Anything which is not Lorentz invariant is not modern physics!

And there we are today with the Lorentz transformation as a Holy Doctrine of Modern Physics of the same stature, and mysticism, as the Doctrine of the Holy Trinity of the Catholic Church. But a Lorentz transformation is just a very simple linear coordinate transformation and as such cannot reveal deep truths of physics, while the Holy Trinity may well represent a deep truth of religion.

Newtonian mechanics is Galilean invariant, but not Lorentz invariant, and so in Einstein's hands Newtonian mechanics had to be sacked, according to the Doctrine of Lorentz Transformation. Instead a wonderful magical world of space contraction and time dilation was born from the Doctrine, but of course inheriting the unphysical nature of the Lorentz transformation and thus only a world of illusions without the reality of Newtonian mechanics.  

Why Time Dilation (and Special Relativity Theory) Is Illusion

Is it possible that inertial motion under zero external forcing can change the rate of a mechanical or atomic clock? No! Because with zero external forcing there is nothing which can affect the inner working of a clock and thus the clock rate must be independent of inertial motion. It is inconceivable that clock rate can be affected by inertial motion.

An illusion of changed clock rate is created by the Doppler effect: The light from a receding body will be red-shifted and thus will give the illusion of a changed frequency or change of clock rate. But this is only an illusion like the illusion of the size of an object decreasing with distance.

What about special relativity then? The reading of the same event in space-time in two inertial systems $S$ and $S^\prime$ with coordinates $(x,t)$ and $(x^\prime ,t^\prime )$ moving with constant velocity $v$ with respect to each other, are here supposed to be connected by the Lorentz transformation (in one space dimension)

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

where $\gamma = \frac{1}{\sqrt{1-v^2}}$ assuming the speed of light is 1 and $0 < v < 1$. The time rate in $S$ and $S^\prime$ then differ with a factor $\gamma$, so that with $S$ motionless the time in $S^\prime$ would seem to run slower, and the other way around.

What to make out of this? Is the clock rate really affected by motion, or is it only an illusion? Lorentz gave the answer by pointing out that the transformed time $t^\prime$ is not physical time, but only illusionary time. It was Einstein who against the judgement of Lorentz claimed that the transformed time $t^\prime$ is physical time, and out came the special theory of relativity, which is no theory according e.g. Louis Essen as shown in the preceding post. An mere illusion is not a physical theory.

Real clock rate cannot change by inertial motion, only imaginary illusionary invented non-physical clock rate can change by inertial motion. This statement is believed to be wrong by 99% of living physicists. No wonder that modern physics is in a state of crisis.

Physicists have been complaining since the mid 1920s when quantum mechanics was born, that quantum mechanics is incompatible with relativity theory, without however doing anything about it.
But if two theories of physics are incompatible or contradictory, then one must go. Your choice?

See also Questioning Relativity 1-18.