Post-Modern Physics without Relativistic Mass

The change from classical physics to modern physics has long been viewed to be marked by Einstein's Theory of Special Relativity SR published in 1905 coming with a fundamental revision of Newtonian mechanics introducing the new concept of relativistic mass increasing with velocity, as opposed to Newtonian invariance of mass under motion, and the mass-energy equivalence of the most famous equation in physics $E=mc^2$. 

When I discuss these topics with chatGPT I am informed that the idea of relativistic mass has been put aside as no longer relevant, in a return to the idea of classical physics that mass is invariant and so does not change under motion. That is certainly as step forward to more clarity since the concept of relativistic mass under motion coming with a concept of rest mass of bodies at rest, was $a source of endless confusion. 

What then about mass-energy equivalence $E=mc^2$? Has it also been abandoned? Here chatGPT is ambiguous:

• All forms of energy $E$ as potential, kinetic, electric, chemical and nuclear energy in principle can be traded with $m=\frac{E}{c^2}$  for some mass $m$. 
• As concerns potential, kinetic, electrical and chemical energy $E$ the corresponding mass $m$ is so small because $c^2$ is so large, that the trading does not make sense because sufficiently small coins are not available. 
• But for nuclear energy the trading is viewed to make sense because $E$ is so large that $m=\frac{E}{c^2}$ is not zero. 
• Accordingly, the nuclear fusion reaction in the Sun is viewed to result in a loss of mass about 4 million tons per second. The loss is estimated to be less than 0.1 percent after 10 billion years of burning mass. 

It appears the chatGPT still clings to $E=mc^2$ although the conviction is shaking: Mass-energy trading does in particular not make sense for chemical reactions, only possibly for nuclear reaction where an idea of loss of mass or mass defect still hangs on. 

We then ask chatGPT if there is a fundamental difference between chemical reactions supported by spatial re-configuration of electrons, and nuclear reactions supported by spatial re-configuration of nucleons? 

The answer is that the only fundamental difference is the nature of the forces involved, Coulomb force or strong force, and not $E=mc^2$. 

Quantum models of chemical reactions do not involve $E=mc^2$, because it has no role to play. Likewise, quantum models of nuclear reactions do not involve $E=mc^2$, since it has no role to play. 

So what remains is to give $E=mc^2$ a role by insisting that any $E$ computed by a quantum model without $E=mc^2$, in principle can formally be traded with some mass $m=\frac{E}{c^2}$ of unspecified nature. But this trade has no physical meaning and so is only a formality which can be viewed as the only remaining homage to Einstein, when now his relativistic mass has been put into the dust bin of meaningless physical concepts including phlogistons. 

It may be time to now let it be joined by $E=mc^2$. This would open to a clarification of the concept of energy as basically connected to work as force times displacement, then appearing in the form of kinetic energy, mechanical energy, friction energy, potential energy, electrical energy and chemical/nuclear energy connecting to inertial force, friction force, elastic force, gravitational force and Coulomb force.

This would essentially mean to give up SR and returns to rational physics. If you still want to speculate about space ships traveling at half the speed of light, you could then instead turn to Many-Minds Relativity connecting the views of observers traveling at very high speeds with inspiration from Ebenezer Cunningham seeking to make sense of SR in the 1910s.

Phlogiston Theory of Nuclear Physics

The phlogiston theory was a scientific hypothesis developed in the late 17th century stating that a combustible body contains a substance in the form of phlogistons, which during combustion is released into the air under loss of mass of the body. The theory was debunked by noting instead a gain of mass (in the form of oxygen taken from the air). 

Modern physics describes combustion in terms of chemical reactions where energy is released by rearranging electrons in space into lower total energy, not substantially as loss of mass or mass defect. 

Modern physics explains energy release in nuclear reactions in terms of mass defect with the products having smaller mass than reactants, as if mass is turned into energy according to $E=mc^2$.  

According to the (debunked) phlogiston theory, energy released in chemical reactions comes from "burning of phlogistons".  

According to modern physics, energy released in nuclear reactions comes from "burning of mass" with mass defect according to $E=mc^2$. Is this also a form of phlogiston theory not yet debunked? 

To seek an answer, recall that nuclear reactions can be described in terms of spatial rearrangement of nucleons, in the same way that chemical reactions can be described in terms of rearrangement of electrons.

Does this description capture all the energy released or only some of it, the remaining then coming from "burning of mass"? But why only some of the energy, and not all? 

With these arguments we are led to question the idea of "energy from burning of mass" as the prevailing idea. We are led to suspect that the mass defects trivially computed from list values of masses of reactants and products have been assigned values so as to allow mass defects to account for observed energy release as a form of self full-filling prophecy to impress the average mind along the Einstein model of the previous post.  

More Orwellian 1984 Physics

This is a follow up of the previous post identifying a practice in both modern western society and modern western physics to erode language of meaning by equating things which are different as a form of equality politics, used to keep the ruling class on top. 

In modern physics this practice was introduced by Einstein in his famous $E=mc^2$ equating energy $E$ with mass $m$ through the speed of light $c$ squared, over the heads of the people: 

• It follows from the Special Theory of Relativity that mass and energy are both (but different)  manifestations of the same thing, a somewhat unfamiliar conception for the average mind.   

 

In the 2019 update of the SI Standard of units in physics, this is incorporated by simply defining the unit of mass in terms of energy according to $m=\frac{E}{c^2}$ by a specific procedure using a Kibble balance as the official picture. 

Inspecting a Kibble balance we discover that it measures mechanical energy $mgv$ by equating it to  electrical energy $VI$, which is measured in the balance and so gives a measure of mechanical mass $m$ with given values of gravitational constant $g$ and velocity $v$. We thus understand that a Kibble balance measures mechanical mass as the classical form of gravitational/inertial mass, and there is here no role for $m=\frac{E}{c^2}$ in contradiction to the official picture. 

Even an average mind can now understand that equating mechanical energy connected to mechanical mass $m$ to some other unspecified form of energy $E$ somehow connected to $m$ through $E=mc^2$, means eroding the concept of both energy and mass of meaning. 

The physics community were long skeptical to Einstein's unspecified form of energy according to $E=mc^2$, but the temptation to fool the average mind has now taken over in a desperate effort to secure funding to fundamental physics. 

In classical physics there are ultimately only two forms of energy: mechanical energy and electrical energy connected to gravitational force and Coulomb force. There is no need of inventing some new unspecified form of energy as $E=mc^2$.  

But what about photon energy $hf$? Well, light can transmit energy between oscillating charges carrying electrical energy, but light cannot store energy, because it has no mass. This is seen in electrical grids which need rotating mechanical masses like turbines to stabilise the grid over variations in input and output.  

Summary: The relation $E=mc^2$ appears as an add on which serves no purpose to define the unit of mass and how to measure mass. It remains to understand its role to compute energy release in nuclear reactions from measured mass defects, which will be the topic in a next post.     

The Black Hole Of Modern Physics

Newtonian and Einsteinian Mechanics

The Universe is formed from micro-scale electromagnetics and macro-scale gravitation. The essence of modern physics, as compared to classical (Newtonian) physics, is (i) the theory of quantum mechanics for micro-scale electromagnetics/light without gravitation, and (ii) Einstein's theory (special+general) of relativity for gravitation without electromagnetics/light.  

These two theories are hailed as the greatest triumphs of human intellect all times, way beyond Newton's mechanics, but there is a caveat: Quantum mechanics is viewed to be incompatible/inconsistent with general relativity. There is no convincing theory of modern physics including both electromagnetics/light and gravitation as the building blocks of the Universe, despite the more than 100 years which have passed since (i) and (ii) were introduced. 

There is thus bitter poison in the cup of glory when modern physicists are celebrating their achievements. If (i) and (ii) are incompatible/inconsistent/contradictory, then either (i) or (ii) must be wrong. Both cannot be true. The acknowledgement by leading physicists that this is so, is then viewed to be an act of scientific heroism rather than incompetence.   

It is also admitted that there is no incompatibility/inconsistency between quantum mechanics and  (iii) Newton's gravitation, only with Einstein's gravitation (ii). It is also admitted that Newton's mechanics captures almost everything on a macroscopic scale. 

What is then the difference between (ii) and (iii), that is between Einstein's equation and Newton's equations for a mechanical system subject to gravitation? 

The quick answer is: not much! It is like putting a moustache on da Vinci's Mona Lisa, which Dali did with a simple pen stroke (+added his own eyes). Mona Lisa is a true masterpiece made by a true master, while Dali's version is a simple distortion albeit done by a genius of some sort. But an art curator may tell you that Dali's version offers a whole new view on the World, da Vinci has been surpassed.

It is the same with (ii) and (iii): Einstein's equation reduces to Newton's equation in a system without space-time curvature like the flat Universe we apparently happen to have around us. Einstein's equation is is supposed to describe some ultimate extreme case like a black hole, which however is so extreme that observation is impossible, like a true real lady with moustache never to be seen. 

To be more precise, what are the observations showing that Newton's equations have to be replaced by Einstein's? A prime example is still Einstein's correction of size 45 to the 531 arcseconds/century prediction of the very slow precession of the perihelion of Mercury's elliptic orbit around the Sun, made by solving Newton's equation including all the planets in the Solar system. Einstein thus made a small correction of about 10% to an already very small effect computed by carefully solving Newton's equations, like putting a moustache on Mona Lisa and then claiming a complete revolution of world view. Or more accurately, after modifying Mona Lisa in a way which is not observable.

Einstein computed his "correction" by hand on the back of an envelope in several attempts during the 1910s until finally getting the desired result known beforehand, while solving Newton's equations for the Solar system from scratch by hand calculation is a formidable task, of course today feasible by computer. 

Einstein thus did not solve his equation to predict the precession, because he could not and this is still the case today even with biggest possible computer. 

What is truly remarkable, is that solving Newton's equations for the Solar system within the precision offered by the uncertain values of the gravitational constant, masses/positions of planets and the Sun, gives a prediction over a century in accordance with observation. In other words, da Vinci's Mona Lisa is as perfect it can be. There is no real need to modify neither Newton's equations nor Mona Lisa!

In any case, modern physicists claim that Newton's equations have to be replaced by Einstein's equations  even if solutions differ so little that it is beyond measurement. Einstein expressed his hesitance to take this step in "Newton, forgive me". In fact, modern physicist only took this step in 1950's after 50 years of brooding. 

The question remains: Why has modern physicists driven themselves into an impossible situation with two main theories which are inconsistent/incompatible, if there is not really any good strong scientific reason to do so?  If Newton is ok also today? Why has Einstein been chosen to be the icon of modern physics, thus reducing Newton? Which were the leading physicists in the creation of this myth?  

The crisis of modern physics witnessed by leading modern physicists may be seen as the inevitable result of a contradiction originally created by a young patent clerk desperately searching for scientific recognition, and succeeding! 

The aspect of small correction beyond observation is also present in Einstein's $E=mc^2$ with the mass defect in chemical/nuclear reactions too small to measure, a formula known by everybody as a fetish of modern physics without real meaning. Einstein's physics thus concerns corrections to known physics, so very small that experimental verification invariably rises more questions than answers.

Recall that according to $E=mc^2$ fully turning 1 grain of sand (as 0.000001 of 1 kg) into energy would suffice to heat an ordinary home in Sweden one year. One grain of sand! This would be 1 billion times more efficient then burning carbon, and 100-1000 times more efficient than what can be reached in a nuclear reaction. In other words, only a very small fraction of mass is really "equivalent" to energy, and so $E=mc^2$ has little if any meaning, yet is the beacon of modern physics visible to everybody.  

Recall that the mass $m$ viewed to effectively be transformed into energy $E$ in a nuclear reaction, is computed from $m=\frac{E}{c^2}$ and then shows to be 100-1000 smaller than the total mass involved. The "equivalence" of mass and energy thus appears as a formality from assuming $E=mc^2$, which has driven modern physics into a dead-end of contradiction. If anything: mass is not "equivalent" to energy. $E=mc^2$ cannot be used to predict the energy release in a chemical/nuclear reaction, because the small fraction effectively released is hidden. 

Recall the previous post on the new 2019 SI specification of unit of mass (kg), which is explicitly based on $E=mc^2$ thus making this relation into a definition including also a specification of the speed of light $c$ to be exactly 299792458 m/s in a specification the unit of length m.

The cornerstones of Einstein's contribution to science, $E=mc^2$ and the constancy of $c$, thus appear as definitions or SI agreements, which are to be viewed to be true independent of any physical reality and as such are empty of physics in the same way that the specification that there are 100 centimeters on a meter does not say anything about reality.  

Mathematicians make a clear distinction between between definition or agreement, which cannot be false, and theorem, which can be false or true. This is expressed in mathematical text by clearly announcing Definition: and Theorem:.  

Modern physicist make no distinction between between definition or agreement, which cannot be false, and physical law, which can be false or true. $E=mc^2$ and constancy of $c$ are thus introduced as definitions/agreements and then turned into physical laws, which cannot be false. This opens a black hole to modern physics.

Or is it ok to use $E=mc^2$ in the form $m=\frac{E}{c^2}$ to define mass in terms of energy $E$ and $c^2$ as an agreement among physicists (to be accepted by also the people). Does it hurt to make a possibly arbitrary agreement about something and then adjust other things accordingly. Of course we can agree that there are 50 centimetres on a meter and adjust measure accordingly. It could be a bit awkward but would cause a collapse of physics. In this spirit we could view $E=mc^2$ as a formality, which does not have any real consequence, just an empty gesture to salute Einstein. But by Occam's Razor such an empty gesture could as well be dispensed with.  Insisting would just add to the mystery of modern physics.

We may compare with Newton's 2nd Law $F=am$ with $F$ force, $a$ acceleration and $m$ inertial mass, which is the analog of the corresponding relation for gravitational force, gravitational acceleration and gravitational mass as primordial with thus force defined as gravitational force. Here $F=am$ gets real physical meaning by the fact that inertial mass = gravitational mass. In other words, the gravitation potential is primordial making bodies move according to gravitational forces thus prescribing motion to other (ultimately electromagnetic) forces. In this sense $F=am$ is a physical law and not only an agreement.    

E=mc2 as Fetish vs Atomic Bombs

In addition to the experimental tests of $E=mc^2$ of the previous post, let us consider a bit more the difficulties of such tests. On microscopic scale the required accuracy is hard to reach in a convincing way. This includes both nuclear and chemical reactions measuring mass before and after reaction. It is possible to restrict the science to just consider the binding energy as it is, as a form of energy, without connecting it to any mass defect which is difficult to assess.  

In any case, on macroscopic scale the accuracy requirement may be less of a problem and so we may envision the following tests:

1. Stretch an elastic spring to give it energy to do work. According to $E=mc^2$ its mass should increase. Compare with an unstretched otherwise identical string using a balance scale and record the difference. 
2. Similarly, use a balance scale with two weights in balance to record if heating changes the balance.    

Would we be able to measure an increase of mass from stretching or heating both increasing energy? That would certainly be most surprising and the measurement accuracy would again not be sufficient to validate anything like that. So such experiments would probably be inconclusive and not serve to validate $E=mc^2$.

Neither does it seem possible to get a validation on cosmic scales, since if increasing the speed of a planetary object would increase its mass, it would not change its reaction to a gravitational potential since all objects independent of mass react the same way.

We conclude that it seems exceedingly difficult to verify the truth of $E=mc^2$ on any scale. What about the possibility of disproving it?  First, one would ask for theoetical support and then we enter muddy waters including Einstein's argument from 1905 and so theory is not sufficient. To disprove it experimentally is also hard since it requires even better accuracy than verification. 

The net result is that $E=mc^2$ is hard to verify/disprove since it is such a small effect. It is like verifying/disproving the existence of ghosts, which is impossible. Does this mean that we can anyway assume that $E=mc^2$ or that ghosts exist, since it does not change anything? Occam's Razor then tells us that it is better to forget all about it, since it does not seem to serve any purpose. Or maybe it does:

The magic formula $E=mc^2$ then appears as a fetish carried by physicists used to boost their importance by connecting the formula to the undeniable power of nuclear energy and weapons. Is this the true role of $E=mc^2$? Is this the reason that still after 118 years there is no real verification, only countless suggestions that there is. A fetish does not need any verification only an agreement that it brings magic power.

A final reflection: $E=mc^2$ connects mass, which is gravitational mass, with $c$ as the speed of light as a stream of "photons" without mass. This certainly seems contradictory. But the argument goes like this: The momentum of a photon is given $p=\frac{E}{c}$ where $E$ is its energy, and momentum is formally given by $p=mc$ with $m$ the mass of the photon and $c$ its velocity. So we derive $E=pc=mc^2$. Voila!

The only trouble is that the photon is massless with $m=0$, so the argument has no meaning, which is an indication that also $E=mc^2$ is without real meaning: To rely on photons without mass traveling with the speed of light to conclude something for bodies with mass traveling at much smaller speeds, seems to be completely off-the-wall. But it is modern physics at its best. 

Experimental Test of E=mc2?

Let us seek experimental test for the cornerstone of modern physics Einstein's $E=mc^2$. We find on MIT News 2005: E=mc2 passes tough MIT test (as a celebration to Einstein's Annu Mirabilis 1905):

• MIT physicists report the most precise direct test yet of Einstein's most famous equation, E=mc2. And, yes, Einstein still rules. 
• The team found that the formula predicting that energy and mass are equivalent is correct to an incredible accuracy of better than one part in a million. That's 55 times more precise than the best previous test. Team member prof. Pritchard says:
• "In spite of widespread acceptance of this equation as gospel, we should remember that it is a theory. It can be trusted only to the extent that it is tested with experiments....If this equation were found to be even slightly incorrect, the impact would be enormous -- given the degree to which [it] is woven into the theoretical fabric of modern physics and everyday applications such as global positioning systems."
• (We meet here the common claim by physicists that GPS relies on relativity theory ($E=mc^2$), which is not the reason GPS works). 
• The mass loss was obtained at MIT by measuring the difference between the mass of the nucleus before the emission of a gamma ray and after. 
• Pritchard informs: "Determining the mass difference requires the individual masses to be measured with the incredible accuracy of one part in 100 billion -- equivalent to measuring the distance from Boston to Los Angeles to within the width of a human hair! This doesn't mean it has been proven to be completely correct. Future physicists will undoubtedly subject it to even more precise tests because more accurate checks imply that our theory of the world is in fact more and more complete."

Ok, detection of the mass loss required a measurement accuracy of one part in a billion (0.000000001) since the measurement was made on a single nucleus emitting a gamma ray. To measure mass defect it would seem to be better to involve a more easily measurable bulk of mass. To measure the mass/weight of a pile of sand, it would be senseless to measure the mass/weight of each grain of sand and then add up. It would be more sensible to seek to measure the mass defect in some nuclear reaction since it would require less precision, like the mass defect in an atomic bomb explosion...

In any case Pritchard admits that this does not suffice to be sure that $E=mc^2$ is exactly correct. And this is needed, because if $E=mc^2$ is not exactly correct, then the floor of modern physics collapses. If $E=mc^2$ is only approximately correct, then an abyss of questions opens: What is then missing? In my case, how much can I rely on $E=mc^2$? Which mass cannot be converted to energy and vice versa?  The suspicion from previous posts comes back again: Is $E=mc^2$ just and agreement, and as such always exactly correct, like the statement that there are 100 centimetres on a meter, for which experimental verification would be met with laugh.

A detailed inspection of many tests supporting the suspicion is given in Mass-energy equivalence not experimentally verified with punch line 

• It was not a verification of E = mc2, but just another experiment to deduce the mass of the neutron. To date, we have not measured the true mass of the neutron to any degree of accuracy; we only have a deduced estimate of the neutron mass based on the mass-energy equivalence of E = mc2.

We understand that the mass defect of the neutron, used as a proof of the correctness of $E=mc^2$, in fact is computed from $E=mc^2$ because the true mass of the neutron cannot be measured with enough accuracy. And so the mass defect is an agreement and not verified physical fact.  

What is Equality in Physics?

In modern western society the concepts of equity or equality plays an important role. Equality can refer to equality of possibilities or equality of outcomes in a democratic system or equality of everybody in an Orwellian sense in a communistic society. Equity can refer to equality over different gender/sex and can connect to an idea of equality woman = man and man = woman.

We also find extreme forms of equality in 1984: War is Peace, Slavery is Freedom....

We understand that equality can express both a truth and serve as a disguise or cover-up of a truth. 

We also remind of the difference of the statement A=A expressing identity and B=A typically expressing that B inherits certain aspects of A (but not all). Often these aspects are not specified completely and the statement thus sometimes is open to confusion.  

The previous post discussed two different expressions of equality in physics: 

1. inertial mass = gravitational mass.
2. mass = energy, energy = mass 

Here 1. represents a truth resulting from viewing inertial mass to be an expression of (derived from) gravitational mass and thus the same. 

2. is Einstein's E=mc2, which is viewed to be the corner stone of modern physics. Since in physics energy is power to do work, it says that a body falling in a gravitational field doing work, such as the falling water in a Hydropower Plant, will loose energy (gravitational potential energy) and thus should loose mass according to 2. So there will be less water coming out than coming in to the plant, in contradiction to the physical principle of conservation of mass. A physicist would argue that the difference is too small to be noticed, but surely it is there, in principle. 

In any case a suspicious mind may wonder if that there is something fishy with the statement that energy = mass = energy (E=mc2). Ok, so more precisely Einstein does not say that mass and energy are equal, only that they are equivalent without specifying in what sense. But even so, as shown in the above example, a forced equivalence of mass and energy seems to lead into a strange contradiction.

It connects to Orwell's War = Peace which as identity is absurd, but as equivalence certainly has been used to justify a war by claiming that the aim is peace, that is Peace = War.  

We learn that equalities of the form B = A with B not identical equal to A, can (purposefully) be ambigious and need further specification to be meaningful. Seeking a specification of the meaning of energy = mass (E=mc2) may well lead to the conclusion that the equality does not make much sense. 

A contemporary physicist of course will claim that both chemical and nuclear exothermic reactions releasing energy suffers from a corresponding loss of mass according to E=mc2, which at least in the case of nuclear reactions is measurable and then shows to always exactly match E=mc2, nota bene if only properly measured. Any measurement not complying with a dogma of E=mc2 then must be corrected.

Phyisc is full of ambiguities as concerns equality. A first check is always to see if the units on both sides of the equality sign are equal. Sometimes this is also used to derive an equality by "dimensional" analysis.

Energy Cannot Be Equivalent to Mass

Identifying Mass with Energy is the same as identifying Being with Doing. Not so Clever.

The most famous formula attributed to the most famous physicist all times is Einstein's Law

•  $E=mc^2$      (1)

apparently stating that energy $E$ is equal or "equivalent" to mass $m$ multiplied by the large coefficient $c^2$, where $c$ is the speed of light in vacuum.  

A modern physicist will inform you that (1) is a consequence of Einstein's Special Theory of Relativity SR, even if the details of such a derivation cannot be recalled. To counter further questions you will be informed that in fact (1) is just a special example of of a more "relativistically correct" Einstein Law of the form 

• $E^2=(pc)^2+(mc^2)^2$,     (2)

where $p$ is momentum, which is supposedly easier to prove even if details of proof cannot be recalled.  You will also be informed that both (1) and (2) have been confirmed by the same experiments. And do not forget that atom bombs build on (1) and so show the amazing "power" of this "equivalence".

First, let us seek to understand the meaning of (1). We recall that in the physics of thermodynamics 

• energy is capacity to do (mechanical) work 
• work = force x distance measured in Joule = Newtonmeter.   

Energy comes in forms of large scale ordered kinetic energy and potential energy and heat energy as small scale unordered kinetic energy. Here the kinetic and potential energies associated with a body are extrinsic or relational quantities i.e. depending on the environment of the body. The energy produced by the decent of the bob of a classical pendulum clock depends on bob weight and decent distance. 

The typical expression of kinetic energy of a body of mass $m$ and and speed $v$ is viewed to be $m\frac{v^2}{2}$ as the work required to bring the body from rest to speed $v$, with the rest state as the reference state. This energy/work can be regained letting the body impact with an environment at rest.

Likewise potential energy is created by lifting an object from some reference level, which can be regained by letting the body return to the reference level. Large scale ordered kinetic and potential energy can be transformed to heat energy as small scale unordered kinetic energy in turbulent dissipation, and the 2nd Law of Thermodynamics puts limits to recovery of large scale energy from heat energy, that is limits on production of work from heat energy. 

We conclude that thermodynamical energy is an extrinsic relational quantity which is measured in terms of what it can do depending on the environment. 

What then is the mass $m$ of a body? Is it an extrinsic or intrinsic quantity/quality? Well, mass is inertial mass which is equal to gravitational mass as resistance to motion induced by a force.  This is expressed in Newton's 2nd Law $m=\frac{F}{a}$, where $F$ is force and $a$ acceleration. This is an intrinsic quantity in terms what it is. All bodies independent of quantity of mass react the same way on gravitational force, that is,  carry an intrinsic property of reacting to inertial or gravitational force. We can think of the mass of a body as being equal to he sum of the masses of the pieces of atoms forming the body. All the atoms react the same way on inertial or gravitational force, and this explains why a body is not ripped apart by such forces. Mass is maybe the most intrinsic quality of all. 

Sum up: Energy is extrinsic (what it can do) while mass is intrinsic (what it is). Is it possible that an extrinsic quantity can be equivalent to an intrinsic quantity as expressed by $E=mc^2$? There seems to be no sufficient reason to insist that  "energy is equivalent to mass", so the answer can only be No. 

Let us now turn to (2) as an "improved version" of $E=mc^2$, keeping the first term, that is let us look at the Law, motivated by Many-Minds Relativity MR:

• $E=pc$,     (3)

where $p=mv$ is momentum $v$ velocity. This Law seems to make a bit more sense since $p$ is both intrinsic thorough $m$ and extrinsic through $v$, but the previous post shows that this only an illusion. There is no sufficient reason to insist that "energy is equivalent to momentum".

When confronted with the above arguments a modern physicist will say that "is is all wrong" without showing what is wrong. 

In any case, the bottomline may well be that the by many witnessed crisis of modern physics ultimately depends on (1) as a foundational relation that does not make sense. More detailed arguments in recent previous posts. 

Photons 

Physicists use (2) with $m=0$ to give momentum to the massless photon with energy $E=h\nu$ through the connection $p=\frac{h}{\lambda}=\frac{h\nu}{c}$ with thus $E=pc$. Magic!

Thermodynamics and Atom Physics 

$E=mc2$ is supposed to be a result of SR which does not describe thermodynamics nor atom physics. 

Basic postulates of thermodynamics say that mass and energy are conserved. This means that $E=mc^2$ in the sense of actual transformation of mass into energy cannot happen in thermodynamics. Unless you say that by definition energy and mass are equal and so $E=mc^2$ is a tautology without physical meaning. 

Can $E=mc^2$ or $E=pc$ have a meaning in atom physics, when SR and MR say nothing about atom physics?  Or is also here $E=mc^2$ a tautology without physical meaning? Probably. MR says that (3) is an illusion. Einstein was a master of double play mixing physical fact with definition/logical truth. SR is filled with this ambiguity: Is time dilation and length contraction real or illusion? Ask your physics professor!

 

Einstein's 1905 Kick-off of E=mc2: Definition?

Einstein kicks off modern physics in the last of the five articles from his Annus Mirabilis 1905 as a short note starting with the question:

• DOES THE INERTIA OF A BODY DEPEND UPON ITS ENERGY-CONTENT?

and ending with the answer:

• If a body gives off the energy L in the form of radiation, its mass diminishes by $\frac{L}{c^2}$. The fact that the energy withdrawn from the body becomes energy of radiation evidently makes no difference, so that we are led to the more general conclusion that
• The mass of a body is a measure of its energy-content; if the energy changes by L, the mass changes in the same sense by $\frac{L}{9}\times 10^{20}$, the energy being measured in ergs, and the mass in grammes.
• It is not impossible that with bodies whose energy-content is variable to a high degree (e.g. with radium salts) the theory may be successfully put to the test.
• If the theory corresponds to the facts, radiation conveys inertia between the emitting and absorbing bodies.

This is nothing but $E=mc^2$, which thus to Einstein was only a loose hypothesis in 1905 (If the theory corresponds to the facts), but became a truth after proclaimed experimental conformation to a very high precision, much welcomed by Einstein as you can hear above: 

• It followed from the special theory of relativity that mass and energy are both but different manifestations of the same thing -- a somewhat unfamiliar conception for the average mind. Furthermore, the equation E is equal to m c-squared, in which energy is put equal to mass, multiplied by the square of the velocity of light, showed that very small amounts of mass may be converted into a very large amount of energy and vice versa. The mass and energy were in fact equivalent, according to the formula mentioned above. This was demonstrated by Cockcroft and Walton in 1932, experimentally.

As a 100 year celebration of Einstein's $E=mc^2$ a team at MIT including David Pritchard presented an experimental conformation with improved accuracy of one part of a million, with the following caveats by Pritchard:

• In spite of widespread acceptance of this equation as gospel, we should remember that it is a theory. It can be trusted only to the extent that it is tested with experiments.
• Determining the mass difference requires the individual masses to be measured with the incredible accuracy of one part in 100 billion -- equivalent to measuring the distance from Boston to Los Angeles to within the width of a human hair!
• This doesn't mean it has been proven to be completely correct. Future physicists will undoubtedly subject it to even more precise tests because more accurate checks imply that our theory of the world is in fact more and more complete.

So we still cannot be sure. We should also be aware that if a physical law is confirmed to an extreme precision, then it may be that the law is not something created by Nature, but rather a logical necessity created by human minds as simply a definition. The equivalence of energy and mass may well be true by definition and so exactly true and then there is no wonder if experiments can confirm with extreme precision.

 

It is like experimental confirmation to a very high precision that there 100 centimeters on meter, which certainly can attract funding, although rather meaningless...

The equivalence of inertial and gravitational mass comes with the same ambiguity as definition or physical fact. Why should Nature play with two different notions of mass? Compare with Many-Minds Relativity.

Feynman prides himself of having predicted using his theory of QED, the anomalous magnetic dipole moment of the electron to a precision of better than a part in a billion. Again too precise to be credible as an agreement with real physical fact, rather than definition?

Experimental evidence

Here a neat little experiments which you can do with a pot of water and a kitchen scale: Heat the water allowing it to gain heat energy and check if its mass increases, and report back!

Another is to climb 10 stores and check if your mass has increased, or descend instead if you want loose weight:

Easy way loose body mass, if needed.

 

Is Mass Converted to Energy in Fusion/Fission of Atoms?

According the Einstein's $E=mc^2$ the energy released in fusion/fission of atoms corresponds to a decrease of mass. The atoms before fusion/fission have more mass than after, with the mass difference being transformed to energy. 

The process of fusion/fisson of atoms is thus considered to be different from chemical reactions generating energy from recombination of the electronic clouds of molecules/atoms/ions into new energy levels in exotermic reactions producing energy and in endothermic reactions consuming energy. Her the total mass of the molcules/atoms/ions involved does not change, only the total electronic energy level, up or down. 

A molecule/atom/ion is here considered to be one or more positively charged kernels surrounded by negatively charged electrons held together by electromagnetic Coulomb forces with corresponding electronic energies.  

In the same way atom kernels are viewed to consist of collections of protons and neutrons held together by the strong force overriding electromagnetic repulsion between protons with corresponding nuclear energies. In fusion/fission atomic kernels recombine just like electrons clouds of molecules/atoms/ions into new energy levels with corresponding production/consumption of energy. Does here the total mass change?  

In modern physics it does because energy is viewed to be equivalent to mass according to Einstein's $E=mc^2$. 

In classical physics energy mass is inertial/gravitational mass and so is not expected to change under recombination of molecules/atoms/ions, because a sufficient reason in the spirit of Leibniz is lacking. Recombination of electron configurations into new electronic energy levels is enough. This is what is observed. Reorganising a truck load does not change its mass/weight, but possibly its potential energy by putting things on top of each other.  

Why expect anything different when reorganising collections of protons and neutrons with corresponding change of nuclear energy?  Is there any sufficient reason? If not, then what?

But what about experiments? Isn't it true that 0.1% mass is lost in fission energy? Maybe, but measurement of inertial/gravitational mass is very delicate. How do you measure the loss of mass in an atomic bomb explosion? 

The fission mass of Little Boy was about 1 kilo releasing about $64\times 10^{12}$ Joule, to be compared with the $10^{17}$ Joule of the SI standard based on Einstein's $E=mc^2$ discussed in the previous post, with thus a formal loss of mass of less than 0.1%. Was it measured?

We may compare with the discussion of phlogiston theory predicting a loss of mass in chemical reactions into phlogistons of energy, which showed to be wrong because mass showed to be conserved.   

 

Is E=mc2 without Meaning?

As noted in the previous post the new 2019 SI definition of kilo kg as unit of mass is based on Einstein's 

• $E=mc^2$      (E)

stating equivalence of energy $E$ and mass $m$ mediated by the speed of light $c$, which is viewed to be signum of the progress from classical physics to modern physics of relativity and quantum mechanics. 

Endless speculations have been devoted to give meaning to equivalence of energy and mass apparently expressed by (E). But is it really possible to give a meaning or is (E) meaningless? 

Let us consider some basic facts, starting with units. Energy is expressed in Joules with 1 Joule = 1 Newtonmeter as the work performed by force of 1 Newton over a distance of 1 meter. Energy is here viewed as a capacity to do work measured in units of work = force x distance or 

• Joule = Newtonmeter.      (1) 

Next, mass $m$ is classically viewed as a measure of resistance to motion or inertial mass expressed in Newton's 2nd Law

• $m = \frac{F}{a}$

where $F$ is force and $a$ acceleration. When $F$ is gravitational force $m$ is referred to as gravitational mass which is equal to inertial mass with unit 

• $\frac{Newton\times second^2}{meter}$.     (2) 

We see that the units in (1) and (2) are very different and requires the coefficient $c^2$ in $\frac{meter^2}{second^2}$ to harmonise. 

There is classically no relation between energy as capacity to do work and inertial/gravitational mass. 

What Einstein did with $E=mc^2$ was to make energy "equivalent" to mass thus breaking completely with classical physics where there is no relation between energy and mass. This break is viewed to be the main heroic accomplishment of modern physics from the hands of Einstein. Paradoxically, this was never awarded any Nobel Prize, evidently because the Nobel Committee could not understand the meaning of (E).

Einstein thus connected two entirely different aspects of physics, namely work and inertial/gravitational mass, which have no connection whatsoever. No surprise that this caused a monumental confusion which opened modern physics to also other forms of confusion. 

To give perspective on the absurdity of $E=mc^2$ recall from the previous post that transforming 1 kg (of e.g. sea water) per second into energy is "equivalent" to a power of $10^{17}$ Watts, to be compared with the power of 1 nuclear reactor of $10^{9} $ Watts, thus equivalent to the combined power of 100 million nuclear reactors! Can we conclude that (E) lacks meaning?

Recall that $E=mc^2$ is the main result of Einstein's special theory of relativity, which is critically analysed in Many-Minds Relativity.

Recall further that Einstein uses the concept of "rest mass" as the mass of a body at rest (in some coordinate system or with respect to other bodies), carrying the idea that the kinetic energy of a body in motion will add to the "relativistic mass" of the body as being bigger than the "rest mass". If you do not find this confusing, you need to study the question in more depth.  

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.