Einstein's 7 Erroneous Proofs of E=mc2

The book Einstein's Mistakes by Hans Ohanian gives a chronology of Einstein's many scientific mistakes including 7 erroneous proofs presented by Einstein of the crown jewel of his theory of relativity in the form of $E=mc^2$ stating proportionality between energy $E$ and mass $m$ with $c$ the speed of light. The need of a 7th proof indicates that proofs 1-6 are all incorrect and so it is not far-fetched to expect that also Einstein's 7th proof is incorrect.

To give perspective, let us recall the proof from Many-Minds Relativity chapter 14-15 of a related connection, this time between mass and momentum $P$ of the form $P=mc$. We recall that this relation can be seen as a consequence of a new Many-Minds form of Newton's 2nd Law stating the following connection between a velocity $v(t)$ and acceleration $\frac{dv}{dt}$ of a body of mass $m$ acted upon by a force $F=F(t)$ depending on time $t$:

• $\frac{m}{1+v}\frac{dv}{dt}=F$,   

This form of Newton's 2nd Law results from measuring velocity of a moving object through Doppler shift $\frac{1}{1+v}$ of received signals from the object with the speed of light normalised to 1. It states that objects in approach/recession with respect to an observer, appear to be subject to an increase/decrease of mass connecting to acceleration. Here $v$ is negative in approach and positive in recession and with $v > -1$ in approach, but unlimited in recession allowing far away galaxies to recede faster than the speed of light as observed in large redshift.

Using that for  $\vert v\vert$ much smaller than 1, $\frac{1}{1+v}\approx 1-v$, Newton's 2nd Law takes the form

• $F\approx m\dot v -mv\dot v\approx (m+P)\dot v$ 

with $P=-mv$ momentum. This relation has the form of a classical Newton's 2nd Law with the mass $m$ augmented by $P$, which trades to a connection between momentum $P$ and mass $m$ of 

the stated form $P=mc$ without normalisation to $c=1$. 

We have thus given a proof of the relation $P=mc$, as an alternative the relation $E=mc^2$, which Einstein could not prove and maybe nobody else can.

PS1 In Einstein's special relativity also the recession speed is limited by the speed of light.  This is not what is observed, since galaxies outside the Hubble sphere at a distance of 4300 megaparsecs are by their redshift observed to recede faster than the speed of light. The apparent contradiction with Einstein's special theory of relativity is handled in the usual way: The special theory is correct but it does not apply to receding galaxies, for which instead the general theory of relativity must be used and the general theory is so complicated that contradictions is beyond human

PS2 The suspicion that $E=mc^2$ is just a matter of definition, which is true by defining mass in terms of force and acceleration through Newton’s 2nd Law (thus in terms of energy), and not a physical fact, which could be true or not, is growing stronger and stronger. Einstein is the master of ambiguity between definition and fact, with the constancy of the speed of light as a key example, which by physicists mislead by Einstein is viewed to be both a definition and a physical fact.

Demystifying the New SI Base Units.

In the previous post we observed that Planck's constant $h$ appears as a conversion factor connecting light of frequency $\nu$ with attributed energy $h\nu$ (in eV or Joule) through the photoelectric effect with the release of an electron from a surface exposed to light (of sufficient high frequency). The inner mechanics of the atoms delivering the electrons upon excitation by exposure to light does not enter into the discussion and so Planck's constant can be given a meaning in macroscopic physics, thus without quantum mechanics, as a trade between light and electron energy and then further to mechanical energy. Its role in quantum mechanics then appears as an after construction.

Let us now turn to Boltzmann's constant $k$ to see its connection to Planck's constant and macroscopic physics. Boltzmann's constant appears in Planck's universal law of blackbody radiation law of the form

• $E(\nu ,T) = W(a)\, kT\nu^2$,
• $W(a) = \frac{a}{\exp(a )-1}$ with $a = \frac{h\nu}{kT}$,

where $E(\nu ,T)$ is the (suitably normalised) intensity of radiation of frequency $\nu$ from a blackbody of temperature $T$ and $W(a)$ is a cut-off factor with $W(a)=1 $ for small $a$ and
$W(a)$ small for medium to large $a$, expressing Wien's displacement law stating cut-off of high frequencies. We see that Planck’s constant only appears in the cut-off factor.

Experimental observation of $E(\nu ,T)$ makes it possible to determine $W(a)$ and thus $kT$ in terms of $h\nu$, from which Boltzmann's constant $k$ can be determined with respect to a chosen scale for temperatur $T$, or the other way around as in the new SI units by specifying by definition 

• $k=1.380650\times 10^{-23}\, J/K$,  

thus setting a new standard for Kelvin $K$ as measure of temperature. The connection between the energy measures $h\nu$ and $kT$ then shows to be

• $h\nu_{max} \approx 2.8214391\times kT$,

where $\nu = \nu_{max}$ gives maximum of the spectrum $E(\nu ,T)$.

Again, this can be done without having to invoke quantum mechanics in its standard form with $h$ as a "smallest quantum of action" as exposed in detail on Computational Blackbody Radiation, which presents a derivation of Planck's law using deterministic continuum physics instead of as usual statistics of discrete quanta. In particular, the new derivation captures the universality of blackbody radiation beyond specific inner atomic mechanics.

The universality of Planck's law is expressed by the fact that an ideal blackbody can take the form of a set of oscillators without very specific inner structure. In particular different blackbodies with different inner structure can share the same temperature scale.

To sum up, both Planck's constant and Boltzmann's constant are specified by definition in the new SI units, from which the new units kilogram and Kelvin can be determined by macroscopic experiments without resort to quantum mechanics in its standard form.



Hopefully this helps to demystify both Planck's and Boltzmann's constant, and the new SI units.
 

New Perspective on New Unit of Mass in terms of Planck's Constant

In the 2019 redefinition of the SI base units the kilogram as unit of mass is defined in terms of Planck's constant

• $h$ set by definition to exactly $6.62607015×10^{−34}$ Joule-second ($J\cdot s$), 

where

• $Joule = Newton\times m = M\times\frac{m}{s^2}\times m=M\frac{m^2}{s^2}=Mc^2$

with $m$ meter, $s$ second, $M$ mass in kilogram and $c$ the speed of light.

This defines kilogram in terms of Planck's constant $h$, second $s$ and speed of light $c$ with meter $m$ defined in terms of $c$. The relation $E=Mc^2$, viewed as a profound discovery attributed to Einstein's relativity theory, then appears simply as a definition (of mass).

The connection to quantum mechanics comes by attributing a certain energy $h\nu$ to light of frequency $\nu$ through the law of the photoelectric effect

• $h\nu = eV_0 + \phi = eV_0 + h\nu_0$, 

where $eV_0$ in electronVolts is the energy of a released electron with charge $e$ and $V_0$ a stopping potential in Volt, and $h\nu_0$ is the work to release an electron with $\nu_0$ a threshold frequency. This relation determines $h\approx 4.1357\times 10^{-15}$ in $eV\cdot s$, which fits with the new definition of $h$ in terms of $J\cdot s$ with the conversion $eV= 1.602176634×10^{−19} J$.

The photoelectric effect connects the macroscopic phenomena of light of different frequencies and stopping potential to the microscopic phenomenon of electron charge. In this connection there is nothing that says light of frequency $\nu$ is to be viewed as a stream of discrete photon particles of energy $h\nu$ and that Planck's constant $h$ has the physical meaning of a discrete smallest quantum of action.  Instead Planck's constant has the role of connecting light energy to electron potential energy ultimately to mechanical energy.

For a new continuum physics approach to blackbody radiation and the photoelectric effect with discrete quantum replaced by a threshold condition (as in the photoelectric effect), see Computational BlackBody Radiation.

The new definition of kilogram gives perspective on the very small size of Planck's constant $\sim 6.6\times 10^{-34}\, J\cdot s$ misleading to an idea of an absurdly small Planck length $\sim 1.6\times 10^{-35}\, m$ believed to have a physical meaning, in string theory in particular.  On the other hand, the length scale of atoms (and X-ray light of frequency about $3\times 10^{18}$) is about $10^{-10}\, m$ and that of a proton $10^{-15}\, m$, with the Planck scale 20 orders of magnitude smaller, way beyond any thinkable experimental exploration and thus meaning. Planck time  $\sim 5.3\times 10^{-44}\, s$ is even more absurd. No wonder that modern physics playing with Planck length and time is in a state of deep crisis, with the scientific madness come to full expression in the  Chronology of the Universe starting with the Planck Epoch before $10^{-43}\, s$ after Big Bang.

In Schrödingers equation $h$ multiplies the time derivative of the wave function, which means that
the atomic energy (potential + "kinetic" energy) of an eigenfunction of frequency $\nu$ is equal to $h\nu$, which comes to expression in the photoelectric effect.  Schrödinger's equation is a continuum model without any smallest quantum of action, only discrete eigenvalues representing different energies.

A reformulation of quantum mechanics in the form of a Schrödinger equation as a continuum model in real 3d space plus time without statistics, can be inspected at Real Quantum Mechanics.

To get an idea of the absurdly small Planck length scale $1.6\times 10^{-34}\, m$, one may compare with the estimated size of the observable Universe which is about $10^{27}\, m$ or $10^{33}\, \mu m$ with $\mu m$ mikrometer.



In short, Planck's constant $h$ converts light energy to mechanical energy through electron potential energy, and as such does not ask for a meaning as a "smallest quantum of action" in a mist of "quantisation" into absurdly small "quanta".

The new kilogram standard is specified to high precision using a Kibble balance, where gravitational force is balanced by an electromagnetic force (between two coils), which depends on Planck's constant. Mass is then derived by measuring the local gravitational constant.  

Does Sabine Hossenfelder Exist?

Sabine Hossenfelder on BackReaction claims herself to be a modern physicist expressing truths about the state of modern physics:

• I do not know what it means for something to be “real” or “true.” You will have to consult a philosopher on that.
• If you want to claim that the Higgs-boson does not exist, you have to demonstrate that the theory which contains the mathematical structure called “Higgs-boson” does not fit the data. Whether or not Higgs-bosons ever arrive in a detector is totally irrelevant.
• Here is a homework assignment: Do you think that I exist? And what do you even mean by that?
• From November on, I will be unemployed, at least that is what it presently looks like: If you don't exist, can you be employed?

If this is the truth, no wonder that modern physics is in a state of crisis.

But Sabine's criticism of modern physics appears well founded and thus admirable. At the price of making employment difficult, which is even more admirable.  But she is not alone saying that modern  physics in a state of stalemate crisis without progress, as evidenced in the new book
The Universe Speaks in Numbers by Graham Farmelo summing up:

• ...the slow rate of progress of the string framework may presage a more sedate pace in fundamental physics that may persist for centuries to come.

Of course the pessimism of deep crisis can be turned around into its opposite, as expressed by the leading star of modern physics Arkani-Hamed: 

• There has never been a better, more exciting time to be a theoretical physicist.

Concerning the crisis of modern physics it is commonly accepted that one reason is that the two basic building blocks, relativity theory and quantum mechanics, are contradictory/incompatile . If you dig a little deeper you will find that the underlying reason is that both theories are unphysical as exposed in detail as Many-Minds Relativity and Real Quantum Mechanics and also here.

Two theories which are physical cannot be contradictory, because physics which exists cannot be contradictory. But unphysical theories may well be contradictory, as ghosts can have contradictory qualities.

The Special Theory of Relativity of Einstein is unphysical because the Lorentz transformation is not a transformation between physical coordinates, as strongly underlined by its inventor Lorentz, but misunderstood by the patent clerk Einstein believing that the transformed time is real and thus that time is relative. Quantum Mechanics is unphysical because its interpretation is statistical which makes it non-physical, because physics is not an insurance company. Here Einstein was right understanding that God does not play dice.

Concerning the crisis of modern physics, listen to

• Alexander Unzicker 
• Bill Gaede (with Quora comments)
• Hartwig Thim on Einstein's relativity

It is comforting to see that I am not alone in my criticism of relativity theory and quantum mechanics.

It is impossible to discuss these things with main stream physicists, since their common wisdom is that neither relativity theory nor quantum mechanics can be understood as rational science.

An example of the confusion is the hype about quantum computing with the sound criticism by Dyakonov in The Case Against Quantum Computing of course being dismissed by main stream physicist Lubos.

The confusion is exposed in an exhibition combining arts and science about quantum mechanics at Center for Contemporary Culture in Barcelona commented on at BackReaction. Here is an artistic expression of the quantum leap of an electron which infuriated Schrödinger:

In this context you are invited to a previous post on the true meaning of Planck's constant $h$ shows The text book view is that $h$ is a fundamental quantum of action connecting the energy
$E=h\nu$ to a particle/photon of light of frequency $\nu$ according the Planck-Einstein relation with light viewed as a stream of discrete particles/photons.

But it is not at all necessary to view light this way to understand the true meaning of Planck's constant, which is revealed through the way it is measured, that is through the photoelectric effect which simply connects light frequency to the energy unit of electronVolt.

Einstein gave a heuristic explanation of the photoelectric effect from an idea of light as a stream of particles. By the common Aristotle logical fallacy of confirming the assumption by observing the consequence, this has convinced modern physicists that light indeed consists of a stream of particles, which however is against all scientific rationale and a basic reason for the crisis of modern (particle) physics. Schrödinger understood that there are no particles. See posts on the photoelectric effect showing that it does not require Einstein's particle heuristics to be understood; wave mechanics serves much better!     

Why Does a Modern Physicist Buy the CO2 Global Warming Hysteria?

Sabine Hossenfelder on BackReaction claims herself to be a physicist, yet it seems as if she without
thinking buys the CO2 Global Warming Hysteria:

• Climate Change: There are no simple solutions.
• The Earth is warming. Human carbon-dioxide emissions are one of the major culprits. We have known this for a long time. But in the past two decades, evidence for global warming has become more noticeable on local levels, as with seasonal shifts, extreme weather events, declines in biodiversity and, depending on where you live, droughts. And it will get worse.

She does not acknowledge that there are many knowledgeable physicists who do not buy this story, because it has no support in known laws of physics, including Dyson, Happer, Singer and many more. 

So how can it be that she jumps on the climate alarmist wagon? I have asked her, but she does want not to communicate with me, so I have to guess: Is it because of a monumental confusion concerning quantum mechanics, which makes it impossible for a modern physicist to grasp even basic physics of the climate system of the Earth, and what does that then say about modern physics?

PS To get perspective listen to Hearing of the House Committee on Natural Resources May 22.

Yes, Quantum Mechanics Is Wrong

Sabine Hossenfelder on BackReaction has become a truth-teller about the state of modern physics, and now she tells the truth about quantum mechanics: It is wrong:

• Yes, I am sorry. But I have a message for you from the depth of abstract math: We know that quantum mechanics is wrong. 

The same idea has been expressed by almost every notable physicist, including Roger Penrose:

• Physics Is Wrong, From String Theory to Quantum Mechanics.

This is a funny situation, unprecedented in the history of science, and it has been like that for now

more than 100 years. 

A restart is obviously needed and my contribution is Real Quantum Mechanics. Take a look! And think! See also recent posts.

But Sabine Hossenfelder is a physicist and thus must seek to rescue the hopeless situation in one way or the other:

• And whatever your misgivings are about quantum mechanics, there is no denying that it is useful.

So quantum mechanics is wrong, but it is nevertheless useful? That does not make sense. A theory which is wrong cannot be truly useful, because from something which is wrong cannot come something which is right. Only if the theory is right in some sense, can it be useful. But no physicist has any clue to what is right about quantum mechanics, only what is wrong!

Sabine Hossenfelder resorts to the common trick of referring to yet a more incomprehensible theory in the form of Quantum Field Theory, when basic Quantum Theory is questioned. This was used by
Einstein when he increased the bet to general relativity when his special theory of relativity was questioned on most rational grounds. This 

Quantum Mechanics Still a Complete Mystery 2

Tim Maudlin introduces his new book Philosophy of Physics: Quantum Theory with the following credo:

• A physical theory should clearly and forthrightly address two fundamental questions: what there is, and what it does. 
• The answer to the first question is provided by the ontology of the theory, and the answer to the second by its dynamics. 
• The ontology should have a sharp mathematical description, and the dynamics should be implemented by precise equations describing how the ontology will, or might, evolve.
• The Copenhagen Interpretation, in contrast, does not. There is little agreement about just what this approach to quantum theory postulates to actually exist or how the dynamics can be unam- biguously formulated. Nowadays, the term is often used as short-hand for a general instrumentalism that treats the mathematical apparatus of the theory as merely a predictive device, uncommitted to any ontology or dynamics at all.
•  Sometimes, accepting the Copenhagen Interpretation is understood as the decision simply to use the quantum recipe without further question: Shut up and calculate. Such an attitude rejects the aspiration to provide a physical theory, as defined above, at all. 
• Hence it is not even in the running for a description of the physical world and what it does. More specific criticisms could be raised against this legacy of Bohr, but our time is better spent presenting what is clear than decrying what is obscure.

The Copenhagen Interpretation is the text book interpretation of quantum mechanics, which Maudlin thus refutes as meaningless. I agree totally. 

What does then Maudlin offer in the book instead of the Copenhagen Interpretation? Very little: pilot wave theory and many worlds theory, both failed attempts to give meaning to Schrödinger's wave function. The book thus gives yet another account of the mystery of quantum mechanics 100 years after its creation. 

The whole problem comes from the multi-dimensionality of Schrödinger's equation asking for a statistical unphysical interpretation. How many new books will be written on the theme that physicists do not understand the quantum mechanics they preach?

But there is light in the tunnel: Real Quantum Mechanics.

Free Will and Quantum Mechanics

Sabine Hossenfelder on BackReaction believes that quantum mechanics says that humans do not have a free will:

• Physics deals with the most fundamental laws of nature, those from which everything else derives. These laws are, to our best current knowledge, differential equations. Given those equations and the configuration of a system at one particular time, you can calculate what happens at all other times. 
• That is for what the universe without quantum mechanics is concerned. Add quantum mechanics, and you introduce a random element into some events. Importantly, this randomness in quantum mechanics is irreducible. It is not due to lack of information. In quantum mechanics, some things that happen are just not determined, and nothing you or I or anyone can do will determine them.
• Taken together, this means that the part of your future which is not already determined is due to random chance. It therefore makes no sense to say that humans have free will.

This is an expression of the monumental confusion of modern physicists caused by the idea that atoms play games of roulette attributed to quantum mechanics as being based on Schrödinger's multidimensional wave equation, something which Einstein and Schrödinger never accepted.

I have followed a different line of thought viewing physics as forms of analog computation with finite precision, which can be simulated by digital computation with finite precision presented at The World as Computation including a new approach to quantum mechanics as Real Quantum Mechanics without games of roulette. 

In this world there is room for humans with free will, although you cannot control everything in your life, due to lack of precision. If you are not an addicted gambler this may be the world for you.

Determined or Random??

PS The idea that atoms play games of roulette has corrupted modern physics into incomprehensible voodoo-science. Macroscopics as complex systems of simple microscopics can express random behavior, but random microscopics destroys cause-effect and demands contradictory microscopics of microscopics. Contradictory science is voodoo-science, even if it is text book modern physics. 

Quantum Mechanics Still a Complete Mystery 1

Lee Smolins new book Einstein’s Unfinished Revolution (lecture here) repeats yet another time what every physicist already knows:

• I think I can safely say that nobody understands quantum mechanics. (R. Feynman)
• Quantum mechanics is magic. (Daniel Greenberger) 
• Everything we call real is made of things that cannot be regarded as real. (Niels Bohr) 
• Those who are not shocked when they first come across quantum theory cannot possibly have understood it. (Niels Bohr) 
• If you are not completely confused by quantum mechanics, you do not understand it. (John Wheeler)
• If [quantum theory] is correct, it signifies the end of physics as a science. (Albert Einstein) 
• I do not like [quantum mechanics], and I am sorry I ever had anything to do with it. (Erwin Schrödinger) 
• Quantum mechanics makes absolutely no sense. (Roger Penrose)

To come to grips with this monumental mess Lee Smolin takes on the role of bringing physics back  to realism and rationality:

• So I have no better answer than to face the blank notebook. 
• Start by writing down what you are confident we know for sure. 
• Ask yourself which of the fundamental principles of the present canon must survive the coming revolution. 
• That’s the first page. Then turn again to a blank page and start thinking.
• It is not just that to try to invent a whole new physics is risky for my career and damaging to my emotional stability. 
• I don’t even know how to begin.

This is not a promising start and the book offers little hope for progress. So there we are today 100 years after the birth of modern physics in the form of quantum mechanics (and relativity theory) which nobody can understand. No wonder that modern physics is in a deep crisis.

My input to a rational realistic quantum mechanics is Real Quantum Mechanics. Take a look and see if it opens a door...

Recall that the whole mystery of quantum mechanics arises from the standard text book formal generalisation of Schrödinger's equation for Hydrogen to atoms with N > 1 electrons resulting in a linear equation in 3N space dimensions, which has no interpretation as a model of any reality only as a form of  statistics in the mind of an observer.  Real Quantum Mechanics explores a different generalisation into a system of non-linear equations in 3 space dimensions which describes a possible reality.   

Greta Thunberg: Farlig Infantil Klimatpropaganda

Klimatalarmismen med Greta Thunberg som utvald portalfigur analyseras av av Klimatrealistene samt den franske filosofen Pascal Bruckner i en stor artikel i Le Figaro (som refereras här):

• Greta Thunberg ou la dangereuse propagande de l’infantilisme climatique

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