The Trauma of Paradoxes of Modern Physics

• How wonderful that we have met with a paradox. Now we have some hope of making progress. (Niels Bohr)

Science appears to be filled with paradoxes, which it itself is a paradox, because true science should be free of paradox. For a true scientist a scientific paradox is thus something unbearable, which requires immediate action, because one paradox is enough to kill a whole theory.

There are logical paradoxes as contradiction between words and there are physical paradoxes as contradictions between theory and observation.

One logical paradox is enough to kill a mathematical theory. Thus Russell's paradox killed set theory as the foundation of mathematics in the early 20th century.

Zeno's paradox (still unresolved) of the arrow which is moving although it is not moving at every instant, triggered the development of Calculus, but with a delay of 2000 years!

One physical paradox is enough to kill a physical theory as a mathematical theory about phenomena of physics, all according to the famous physicist Feynman:

• It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong.

If theory does not at all fit with reality, then something is fundamentally wrong with the theory, not the other way around.

A paradox may be thus devastating to existing theory, while leading to new better theory by focussing on weak points.

Yet, the list of physical paradoxes has remained through the development of modern physics and in fact have multiplied since modern physics is loaded with many more paradoxes than classical rational physics, as if modern physics is irrational. Thus the pillars of modern physics in the form of relativity theory and quantum mechanics are both filled with paradoxes, which have remained unresolved for 100 years. This has formed the deep trauma of modern physics with no escape from ever more paradoxes.

Niels Bohr was a master of handling the many paradoxes of quantum mechanics lifting sophistry to a new level with his "complementarity principle" addressing the wave-particle contradiction with murky statements like:

• The opposite of a correct statement is a false statement. But the opposite of a profound truth may well be another profound truth.

While classical physicists had to come to grips with paradoxes, in one way or the other, modern physicists appear to welcome paradoxes as a sign of deep magical physics as opposed to shallow understandable classical physics.

The first defence line for a classical physicist is to simply deny the existence of a paradox formulated by some renegades. The next is to accept that there is indeed a paradox and then come up with an ad hoc explanation for the contradiction between theory and reality, showing that the contradiction is in fact only apparent, but not really real. If the ad hoc explanation is refuted, a new ad hoc explanation is presented and so on.

For a modern physicist, a paradox thus poses no real problem, but of course it is some kind of nuisance and so occasionally may get some attention. Like the Twin Paradox of special relativity discussed in earlier posts, unresolved since 100 years.

The prime paradox of fluid mechanics is d'Alembert's paradox comparing the prediction of zero resistance to motion through a fluid from potential flow solutions to Euler's equations of slightly viscous flow like air and water, with the observation of heavy resistance increasing quadratically with velocity.

The paradox was formulated by d'Alembert in 1755 but nobody was able to come up with a resolution until the young German fluid mechanician Ludwig Prandtl in 1904 came up with the ad hoc solution to discriminate the zero drag potential solution of Euler's equations because potential flow does not satisfy a no-slip boundary condition coming with a thin boundary layer. With the potential solution thus eliminated form the discussion, the paradox simply disappeared. But the act of discrimination of solutions of the Euler equations of course was not so glorious. Discrimination of prefect exact solutions on formal grounds carries the same weakness as discrimination of good citizens on purely formal grounds.

In 2008 we gave a different resolution of d'Alembert's paradox than Prandtl's, based on the fact that potential solutions of the Euler equations are unstable and thus turn into turbulent solutions with substantial pressure drag. This was not discrimination on formal grounds, but on real grounds; an unstable solution does not persist over time. This opened to a revolution in computational fluid dynamics freed from a perceived necessity to computationally resolve unresolvable thin boundary layers.

You find on this web site, if you are interested and make a search, resolutions of the following paradoxes:

• D'Alembert's paradox and other paradoxes of fluid mechanics.
• The Reversibility paradox of classical and quantum mechanics (Loschmidt's paradox) 
• Paradoxes of special relativity including the Twin paradox.
• Paradoxes of wave-particle and collapse of the wave function of quantum mechanics.

Yes, it is wonderful to discover a paradox and even more wonderful to resolve it!

Paradoxes of Fluid Mechanics

The book Hydrodynamics A study in logic, fact and similitude (1950) by Garrett Birkhoff gives a long list of paradoxes of fluid mechanics including the following concerning incompressible flow:

1. D'Alembert's paradox (zero drag of (potential) inviscid flow). 
2. Reversibility paradox (reversion of flow direction does not reverse flow).
3. Fatness paradox of Kutta-Joukowsky theory (lift decreases with thickness of wing).
4. Magnus effect (lift of backspin tennis ball opposite to that of table tennis ball).
5. Eiffel paradox ("drag crisis" as sudden drop of drag). 
6. Dubaut paradox (smaller drag of stationary pole in streaming fluid than pole moving through stationary fluid).  

Birkhoff describes the role of paradoxes:

• These paradoxes have been the subject of many witticisms. Thus, it has recently been said  that in the nineteenth century, " fluid dynamicists were divided into hydraulic engineers who observed what could not be ex­plained, and mathematicians who explained things that could not be observed." (It is my impression that many survivors of both species are still with us.)—Again, Sydney Goldstein has observed that one can read all of Lamb without realizing that water is wet!  
• I think we should welcome the discovery of hydrodynamical paradoxes—recognizing frankly the inadequacy of existing mathematics (and logic) to analyze the complex wonders of Nature. Experience shows that man's imagination is far more limited than Nature's resources: as Pascal wrote, "l'imagination se lassera plutot de concevoir que la nature de fournir.

Solving paradoxes thus may open roads to progress. The mother of all paradoxes of incompressible flow is d'Alembert's paradox. Prandtl was crowned Father of Modern Fluid Mechanics because he saved the face of fluid mechanics confronted by the paradox, by coming to rescue in a short 1904 article selling the idea that drag somehow is an effect of a boundary layer caused by an imagined necessity of a no-slip boundary condition forcing a fluid to "stick" to a solid wall. However, Prandtl's boundary layer theory came with a serious side effect as the impossibility to computational resolve thin boundary which has paralysed Computational Fluid Dynamics CFD throughout the 20th century.

  

The paralysis was lifted only in 2008 with a new resolution of d'Alembert's paradox (check video) showing that inviscid flow modeled by the Euler equations can be described as potential flow modified by 3d rotational slip separation into turbulent flow, which can be resolved computationally by Direct Finite Element Simulation DFS. This is described in Computational Turbulent Incompressible Flow with subsequent elaborations, resolving all the paradoxes listed by Birkhoff, and more as shown in the previous post with references including revealing The Secret of Flight (check video).

Towards Resolution of Gray's Paradox

Gray's paradox concerns the contradiction between standard fluid mechanics predictions of the resistance to motion (drag) of a dolphin and the observed speed of a dolphin. Gray estimated that the required muscle power would be seven times bigger than that available. A real paradox!

The search to resolve the paradox has tried different routes: One is to claim that the muscle power of dolphin in fact is much bigger (seven times) than what can be envisioned. Another is to claim that the skin of a dolphin has a magical composition somehow decreasing drag by a factor of seven.

None of the attempts has been successful.

Let us see if the new approach to computational fluid dynamics presented in Computational Turbulent Incompressible Flow and The Secret of Flight, offers a resolution.

We term the new approach DFS Direct Finite Element Simulation (of turbulent flow) based on computing turbulent solutions to the Euler equations for incompressible flow with slip/small skin friction boundary conditions. We have found that DFS predicts the drag of a wing, full airplane and car in close correspondence with observation, with slip as zero skin friction.

Our conclusion is that skin friction gives a minor contribution to total drag as pressure drag plus skin friction in many applications of aero- and hydromechanics, including the locomotion of a dolphin.

This is against the common view of the fluid dynamics community that skin friction is 50-90% of total drag. DFS thus gives design fundamentally new conditions to work from.

DFS in particular seems to offer a resolution of Gray's paradox, by showing that the drag of a dolphin is severely overestimated by conventional techniques as being based on a formula for flat plate drag.

The resolution is a spin-off of the resolution of D'Alembert's paradox (check video) as the mother of the paradoxes of fluid mechanics, a resolution which is intimately connected to DFS.

That skin friction drag predicted from flat plate experiments gives an overestimate of the drag of a streamlined body, like a dolphin, is supported by the article TURBULENT SKIN-FRICTION DRAG ON A SLENDER BODY OF REVOLUTION AND GRAY’S PARADOX, by Nesteruk and Cartwright (13th European Turbulence Conference (ETC13), Journal of Physics: Conference Series 318 (2011) 022042):

• The presented analysis shows that turbulent frictional drag on a slender rotationally symmetric body is much smaller than the flat-plate concept gives and the flow can remain laminar at larger Reynolds numbers. Both facts are valid for an unseparated flow pattern and enable us to revise the turbulent drag estimation of a dolphin, presented by Gray 74 years ago, and to resolve his paradox, since experimental data testify that dolphins can achieve flow without separation. The small values of turbulent skin-friction drag on slender bodies of revolution have additional interest for further experimental investigations and for applications of shapes without boundary-layer separation to diminish the total drag and noise of air- and hydrodynamic hulls.

We will now compute the drag of a dolphin by DFS and report the results shortly. Reducing prediction of skin friction from 70% to 10% may correspond to Gray's factor seven...

PS  From Passive and Active Flow Control by Swimming Fishes and Mammals by F.E. Fish and G.V. Lauder:

• Dolphins have the muscular capacity to swim at high speeds for short durations while maintaining a fully attached turbulent boundary layer. The turbulent flow conditions would delay separation of the boundary layer (Figure 1; Rohr et al. 1998). When the boundary layer separates from the skin surface and interacts with outer flow, this results in a broader wake and increased drag, so delaying separation is beneficial to the dolphin. Separation is more likely to occur with a laminar boundary flow, producing a greater drag penalty compared to turbulent boundary conditions. Thus, the turbulent boundary layer remains attached longer because it has more energy than the laminar boundary layer. The increased drag of a turbulent boundary layer is small compared to the increase in drag due to separation, which is more prone to occur with a laminar boundary layer.

This conforms with the theory and practice presented in Computational Turbulent Incompressible Flow showing in particular that flow with a slip boundary condition stays attached with small drag, while flow with a no-slip laminar boundary layer separates early with large drag. The observed small drag of a dolphin thus can be explained by the theory behind DFS, but not by any commonly accepted theory seeking the origin of drag in thin boundary layers following the legacy of Prandtl.       

What is the "Relic Radiation" of CMBR?

The 2019 Nobel Prize in Physics is awarded to the Big Bang theory supposedly supported by a the observation of "relic radiation" as a "remnant" from the bang:

• The cosmic microwave background (CMB, CMBR), in Big Bang cosmology, is electromagnetic radiation as a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all space.

But there are views contesting the "consensus" adopted by the Prize Committee, claiming that CMBR is nothing but (black body) radiation from "cosmic dust" at 2.7 K surrounding the Milky Way.

What to believe? Let me seek an answer in the analysis of blackbody radiation presented at Computational Black Body Radiation based on a model of radiative heat transfer as a resonance phenomenon between a material source and material receiver transmitted by (standing) electromagnetic waves connecting source and receiver. 

In this model there are waves connecting source and receiver, but no "ocean of photons" filling space as a "remnant" of a disappeared Big Bang source. Instead, the model is compatible with the presence of cosmic dust. 

What do you think? Is it possible that there is some form of "remnant radiation" filling all of space even though the source of the radiation disappeared 15 billion years ago? 

In any case, maybe this gives some incentive to review conceptions of black body radiation.

And what is even more unbelievable than relic radiation? Right, Big Bang. Utterly improbable and impossible. How is it possible that this has become the highest wisdom of the Nobel Committee in Physics? A Committee that never gave the Prize to relativity theory.

   

Nobel Prize to Cosmology with Dark Energy

Dark energy filling the announcement of the 2019 Nobel Prize in Physics.

The previous post on dark energy and exponential cosmic expansion anticipated the 2019 Nobel Prize in Physics announced today with motivation:

• for contributions to our understanding of the evolution of the universe and Earth’s place in the cosmos

including in particular the discovery that the dark energy apparently filling 68% of the Universe,
is not understood at all.

As a compensation, the previous post contributes the understanding that the exponential expansion being observed and then believed to require massive dark energy, in fact can largely be viewed to be an optical illusion from misinterpretation of red-shifts and if true reduces the need of massive dark energy.

Take a look and see if light enters your mind. There is a new Prize to collect 2020.

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.