Dear Frederick,

The plane wave source generates two plane waves propagating in opposite directions, for example one at angle phi and one at phi+180 degrees. This is why there is a negative v/c cos(phi) that cancels with the positive one.

Emmanouil Markoulakis , Thanks. It doesn't actually answer the specific question asked, and until that is settled we can't start talking about the physical interpretation.

Halim Boutayeb , Yes. The cosine is negative in the third quadrant. But we are talking about energy here. The total energy arising from the sum of the two rays should add, and not subtract. Energy is not a vector quantity. It seems as though Einstein has deliberately chosen two equal and opposite rays of light, especially so that he could cancel them. But you can't do that in an energy equation. And it seems as though he wished to do this so that he could carry out the rest of the analysis in the traditional transverse LT format, that seems to have dominated in textbook relativity.

Einstein’s claim of priority in the formulation of E = mc^2 is invalid. His derivation of this equation is based on dodgy mathematics and the deliberate mixing-up, to say the least (for subjective and wishful convenience) of relativistic and non-relativistic (v

Abdul Malek , What you have just said is very similar to my own end conclusion, but you have gone ahead of the game. As you say, Einstein's derivation is riddled with errors, such as you have mentioned, but I have spotted one big error in particular that trumps them all. Einstein would never have been able to use the first equation in this article, unless energy, L, had already assumed L = mc2 in the first place. And the correct derivation, as such, is based on radiation pressure, restricted to EM radiation, and probably does appear in earlier literature. Certainly the ground work is present in Maxwell's papers.

But exposing this big tautology isn't the immediate purpose of the question at hand.

I just want to know if anybody else has spotted the very obvious subtraction error in the third equation.

Frederick David Tombe : There is even an article on "General Derivation of Mass-Energy Relation without Electrodynamics or Einstein’s Postulates"!

https://www.scirp.org/pdf/JMP_2015081111000698.pdf

The wrong theories of Gravity and Cosmology (as ruling ideas), from Isaac Newton to Albert Einstein and till now; are being promoted, imposed and guided by the invisible hands of the established order led by Anglo-American imperialism; in the service of their ideology and theology. They are now so desperate that at the present time they are doing so even in spite of Einstein’ own views and by “Bending ‘facts’ to theories”. The copy of a comment from another forum:

Abdul Malek added an answer

23 hours ago

André Michaud > “Bending facts to theories is a constant danger”

Hi André, it seems an irony that Korzybski wrote this profound an unusual statement in 1921. But I think this was prompted by a real event in 1919; in the “proof” of GR by the British representative of (global) official science, namely Arthur Eddington, which has led to “a constant danger”that modern theoretical physics and cosmology is facing till to day! That “proof” involved “Bending facts to theories”, which even prompted Stephen Hawking to say, “results they wanted to get” (A Brief History of Time). Arthur Eddington himself doubled down on this practice, when he confidently asserted (Ref. Steven Weinberg: "Dream of a Final Theory"), “Experimental data are valid only when supported by a good theory”. Eddington tried to kill two birds with just one stone: the crisis in theoretical physics that the recognition of the “Evil Quanta” brought forth and the crisis of capitalism in Europe that brought World War I.

The same crisis continuing to World War II and even to the present are inspiring additional “proofs” (creating facts) for Einstein’s theories of relativity. But now, in spite of and in opposition to Einstein’s own views; and meriting Nobel Awards!

1. On the “Field” concept of objective reality:

Einstein in an August 10, letter to his friend Besso (1954): “I consider it quite possible that physics cannot be based on the field concept, i.e., continuous structure. In that case, nothing remains of my entire castle in the air, gravitation theory included, (and of) the rest of modern physics”A. Pais, Subtle is the Lord …” The Science and the Life of Albert Einstein”, Oxford University Press, (1982) 467,

2. On “Black Hole”:

"The essential result of this investigation is a clear understanding as to why the "Schwarzschild singularities" do not exist in physical reality. Although the theory given here treats only clusters whose particles move along circular paths it does not seem to be subject to reasonable doubt that more general cases will have analogous results. The "Schwarzschild singularity" does not appear for the reason that matter cannot be concentrated arbitrarily. And this is due to the fact that otherwise the constituting particles would reach the velocity of light.

This investigation arose out of discussions the author conducted with Professor H. P. Robertson and with Drs. V. Bargmann and P. Bergmann on the mathematical and physical significance of the Schwarzschild singularity. The problem quite naturally leads to the question, answered by this paper in the negative, as to whether physical models are capable of exhibiting such a singularity.", A. Einstein, The Annals of Mathematics, Second Series, Vol. 40, No. 4 (Oct., 1939), pp. 922-936

https://pdfs.semanticscholar.org/8dd0/dfafef0c53c428fdc3b58f8099aafcf7d089.pdf

3. On the Quantum Phenomena:

“Many physicists maintain - and there are weighty arguments in their favour – that in the face of these facts (quantum mechanical), not merely the differential law, but the law of causation itself - hitherto the ultimate basic postulate of all natural science – has collapsed”. A. Einstein, “Essays in Science”, p. 38-39 (1934)

4. On Gravitational Wave:

Einstein dismissed the idea of gravitational wave until his death:

“Together with a young collaborator, I arrived at the interesting result that gravitational waves do not exist, though they had been assumed a certainty to the first approximation,” he wrote in a letter to his friend Max Born. Einstein submitted his change of heart in a paper to the Physical Review Letters titled “Do gravitational waves exist?”

https://www.discovermagazine.com/the-sciences/even-einstein-doubted-his-own-gravitational-waves

Arthur Eddington who brought an obscure Einstein to world fame, and considered himself to be the second person (other than Einstein), who understood General Relativity (GR); dismissed the idea of gravitational wave in the following way: They are not objective, and (like absolute velocity) are not detectable by any conceivable experiment. They are merely sinuosities in the co-ordinate-system, and the only speed of propagation relevant to them is “the speed of thought”.

A.S. Eddington, F.R.S., The Proceedings of the Royal Society of London, Series A, Containing Papers of a Mathematical and Physical Character. The Propagation of Gravitational Waves. (Received October 11, 1922), page 268

Einstein should have cited Wien's 1900 paper:

https://en.wikisource.org/wiki/Translation:On_the_Possibility_of_an_Electromagnetic_Foundation_of_Mechanics

- Wien shows that the mass-energy relationship is a result of Maxwell's electrodynamics.

- Wien responded in 1900 to a question Einstein asked 5 years later.

- Wien obtained a Taylor series where he identified the classical kinetic energy for low velocity. This is exactly the same methodology used by Einstein, without reference to Wien.

There is no any new concept is Einstein's addendum 1905 paper. It is only more confusing compared to Wien's work.

Also, I am presently working on the following problem. There are different methods to define the energy of a wave. I have found at least 4 methods:

1. W=int(|E|^2) dt

For a moving plane wave source (as studied by Einstein) one need to take into account the load of the source

2. W=hf

3. Energy is function of amplitude only

4. Energy of a mechanical wave

For the 4 cases above we can write W' as function of W. It is not clear for me yet which one should be used.

For a Newtonian particle of light we can write for example Wk'=1/2 m (c+v )^2 =Wk(1+v/c)^2

Also, it is not clear for me yet why Wien's objective to use electrodynamics to explain Mechanics should be correct. The speed of propagation of a wave does not depend on the speed of motion of the source, contrary to a ballistic (Newtonian) model for light.

Finally, Wien suggested the electromagnetic origin of mechanics as an hypothesis. He proposed two models: Maxwell's electrodynamics and Weber's electromagnetics. When he used Weber's theory, the mass does not increase but the force is function of the velocity of the moving particle.

Halim Boutayeb , Thanks. That was an interesting paper by Wien, but I didn't see where Wien derived E = mc2.

What about the question in the thread title? Does Einstein make a subtraction error at the third equation by treating energy vectorially, along with the fact that cosine is negative in the third quadrant?

In my opinion, ordinary dynamics specially astrodynamics and including electrodynamics has to be reworked out, starting from the dialectical approach of Kepler and Leibniz (with Hegel’s contribution), against Newton's one-sided approach; and a new energy-momentum relation has to be formulated; the way this humble me have attempted to derive a new gravitational potential given by: Ep = m(a/r^3 – GM/r -Cr^2) Article KEPLER -NEWTON -LEIBNIZ -HEGEL Portentous and Conflicting Le...

Newton’s Law of Universal gravitational attraction and the potential GM/r, is at the root of the crisis in modern cosmology and all the Fairy Tales of Big Bang creation, Dark/Black Cosmic Monsters etc. This new potential eliminates the need of all these Fairy Tales of modern cosmology. Gravity like all other processes and things in this infinite, eternal and ever-changing universe is a contradiction of two opposites - attraction and repulsion. Galileo’s Free Fall and Inverse Square Law is valid, but only on and near the surface of a cosmic body like the Earth and within certain limit; but beyond this, things are very different. Newton through induction wrongly transported the ordinary dynamics and laws of motion beyond Earth to the universe in general, where dialectical “Absolute Dynamics” prevails, including vis viva (the centrifugal force) of Leibniz.

The “Absolute Dynamics” arises from the assertion by dialectical epistemology that motion is the mode of existence of matter. There can be no matter without motion and no motion without matter. The epistemology prevalent in modern official physics has no understanding of motion and also of matter. These are mysteries and given by a First Impulse from God like in Big Bang. For Einstein, for example, “Since the theory of general relativity (GR) implies the representation of physical reality by a continuous field, the concept of particles and material points cannot play a fundamental part and neither can the concept of motion. The particle can only appear as a limited region in space in which the field strength or energy density is particularly high”. Einstein, A. On the General Theory of Relativity, in David Levy (Ed.).The Scientific American Book of the Cosmos, N.Y., 2000, pp. 13.

This difference of epistemology is very obvious on the question of space and time as discussed in my following article (the dialectical view automatically leads to QED): Article The Philosophy of Space-Time: Whence Cometh "Matter" and "Motion"?

Like the dialectical perspective of gravity, the equations of classical dynamics and electrodynamics needs to be reworked. Unlike astrodynamics, classical dynamics and electrodynamics were developed through social historical practice and hence have a great deal of validity; but still are only approximate, because these do not take into account vis viva and Absolute Dynamics; which are dormant but still has some impact on ordinary mechanics; like the recently identified “hidden momentum” in electrodynamics. Einstein brought additional confusion in ordinary and electrodynamics with his axiomatic theories of relativity, which have no validity for objective reality. These confusions have to cleared up and a new energy-momentum equation like the new gravitational potential needs to be worked out before theoretical physics and cosmology can climb out of the deadly potential well it is now in with the official epistemology of natural science!

Dear Frederick,

Yes you are right, I am presently reviewing all possible methods for the energy of a moving plane wave source, including Einstein's method. His energy change like frequency, following his relativistic Doppler formula. He must have forgotten an absolute value function, but I didn't complete my analysis yet.

Wien derive E=4/3 mc^2 (please see after his equation 7}, but the coefficient 4/3 is not relevant in the problem. His paper is exactly the same work than Einstein's addendum paper but with more information.

Halim Boutayeb , OK, so the purpose of that particular sleight of hand on Einstein's part was to convert the longitudinal version of the Lorentz transformation into the transverse version, which is the one used in the case of the energy-momentum four-vector.

Let's give Einstein the benefit of the doubt that he didn't know that it's only possible to do a Lorentz transformation on energy, providing that the rest energy already takes the form, L = mc2, in the first place. What Einstein has done is, he has used a binomial approximation of the transverse Lorentz transformation in order to connect L with the ½v2 factor. Then on the other side of the equation, he has employed classical kinetic energy in order to equate the change of L with the change in mc2.

But, contrary to what he claims, he has not isolated L = mc2 from electromagnetic radiation, because any change in mass that occurred when the radiation was emitted had nothing to do with the Lorentz transformation. The mass that was lost due to radiation, went straight into the radiation, and this is fully accounted for when we derive E = mc2 from radiation pressure. Maxwell was already nearly there. See, section VI here,

Article The Double Helix Theory of the Magnetic Field

There is still no theoretical evidence that E = mc2 has any applicability outside of the particular context of EM waves, or the medium for the propagation of EM waves.

“…There is still no theoretical evidence that E = mc2 has any applicability outside of the particular context of EM waves, or the medium for the propagation of EM waves.…..”

- that isn’t correct. All main kinematical [first of all Lorentz transformations] and dynamical, including the E = mc2 equation, equations of the fast bodies mechanics are completely rigorously scientifically derived outside of any, including particular context of EM waves, context in the Shevchenko-Tokarevsky’s informational physical model , more see

https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics, sections 2.4 Lorentz transformations and 2.5 Dynamics, equations (1a) – (4c).

To derive all equations, including Lorentz transformations, besides E = mc2, it is enough to know the Pythagoras theorem; to obtain the equation for energy it is necessary to solve rather simple integral – see Eq.(3)

Cheers

Sergey Shevchenko , From where does the speed of light enter the analysis if EM radiation is not involved in the context?

Dear Frederick,

To find a response to this question we should study what the inventor wrote.

The inventor is Wien.

Wien's objective was to use Maxwell's equations as a basis of classical mechanics.

I see at least one problem with such approach. Maxwell's theory is for sources, scatterers and observers of electromagnetic fields in a medium (aether). It is not clear for me how the mechanical kinetic energy of any body should be function of the aether. Moreover, without aether (Einstein's theory) such correspondence make no sense.

“…Sergey Shevchenko , From where does the speed of light enter the analysis if EM radiation is not involved in the context?…..”

- that is explained in the linked in the SS post above paper; if quite briefly – everything in Matter is/are some specific disturbances in the Matter ultimate base – the (at least) [4+4+1]4D dense lattice of primary elementary logical structures – (at least) [4+4+1]4D binary reversible fundamental logical elements [FLE].

The disturbances [including any/ every particles] always constantly move/propagate so in the lattice in (utmost universal “kinematical”) 4D space [and in parallel in the time ct-dimension] with metrics (cτ,X,Y,Z) with 4D velocities that have identical absolute values be equal to the standard speed of light, c, [bold means 4D vector], what is determined by the main parameters of FLE, i.e. “FLE size” , and “FLE binary flip time interval”, which are [Planck length and Planck time] lP and tP, c=lP/tP. That’s all.

More see, say, SS post, page 1, August 15 in https://www.researchgate.net/post/NO12_Should_an_Object_at_rest_have_Rest_Momentum/1

- here only note that photons, which compose classical ED EM waves, are quite banal just particles, which are created at impacts on some Electric Force mediators’ FLEs [what is fundamental Nature Electric force, and this Force mediators, see the Shevchenko-Tokarevsky’s 2007 Planck scale initial model of Gravity and Electric Forces in

https://www.researchgate.net/publication/365437307_The_informational_model_-_Gravity_and_Electric_Forces] of some momentums that are directed along some 3DXYZ space lines, and so photons move in the 3D space with the speed of light. Having rest mass particles are created by 4D momentums’ components that are directed along the cτ-axis, and, if are at rest, such particles move only along this axis, and only with the speed of light.

Cheers

Frederick David Tombe > "As you say, Einstein's derivation is riddled with errors, such as you have mentioned, but I have spotted one big error in particular that trumps them all."

Do you see (or agree) the mother of all errors in Einstein's theories of relativity, including his derivation of E = mc^2 !? This occurred in Einstein's derivation of LTs and "spacetime" (the fundamental basis of all of Einstein's subsequent works) as discussed in my article on Lorentz Transforms: INSPIRE>HEP: https://inspirehep.net/literature/2158754)

The following is a copy of a section of my article:

[All kinds of mathematical jugglery are being used to derive LT. One such attempt by Einstein [4] himself in the Appendix of his book, “Relativity, The Special and General Theory" is shown below: The following is a copy of the initial steps of Einstein’s derivation of Lorentz Transformation: “Simple Derivation of the Lorentz Transformation FOR the relative orientation of the co-ordinate systems indicated in Fig. 2 (Fig. 1 above, AM), the x-axes of both systems permanently coincide. In the present case we can divide the problem into parts by considering first only events which are localised on the x-axis. Any such event is represented with respect to the co-ordinate system K by the abscissa x and the time t, and with respect to the system k' by the abscissa x' and the time t', when x and t are given. A light-signal, which is proceeding along the positive axis of x, is transmitted according to the equation x = ct

or

x - ct = 0 .............(1)

Since the same light-signal has to be transmitted relative to k' with the velocity c,the propagation relative to the system k' will be represented by the analogous formula x’ - ct’ = 0 .........(2)

Those space-time points (events) which satisfy (1) must also satisfy (2). Obviously this will be the case when the relation

(x’ - ct’ ) = ƛ (x - ct) ...... (3) is fulfilled in general, where ƛ indicates a constant; for, according to (3), the disappearance of (x – ct) involves the disappearance of (x' – ct').

If we apply quite similar considerations to light rays which are being transmitted along the negative x-axis, we obtain the condition

(x’ + ct’ ) = μ (x + ct) ...... (4)]"

Now, before we proceed further with this derivation of Einstein, there is no physically meaningful reason why he would introduce ƛ and μ constants in equations (3) and (4). But even if there is a rational, do they make any sense at all? If we substitute (1) and (2) into (3) we get ƛ = 0/0.

Similarly, from (4) we get μ = 0/0.

This much for a great mathematician and physicist like Einstein. So, mathematical fallacy is one of the mysteries Einstein used in his “Simple Derivation of the Lorentz Transformation”, which then became the fundamental basis of his theories of relativity!

Abdul Malek , I always got the impression that Einstein's derivations didn't exactly lead up to his end results. While the end results always seemed to be correct, mathematically, there often seemed to be no clear reason as to how he got there.

On top of that, in his 1905 paper, he indulges in a messy derivation of the return-path longitudinal Doppler effect for a ray of light, but having turned logic on its head by deeming the speed of light to be a constant, he ends up presenting the correct equations for the optical Doppler effect, but with an absurd physical interpretation. He presents these Doppler effect equations as inertial transformations, in a context involving time dilation.

I think there was someone else involved behind the scenes with respect to Einstein's writings. It seems to have been a project involving mixing truth with lies, in order to sow confusion.

Halim Boutayeb , Wien has introduced the speed of light into the proceedings through Maxwell's equations. But I got completely lost with Wien's ellipsoid. I couldn't work out what that was all about. But I do know that Maxwell's equation for radiation pressure provides a direct route through to E = mc2, without any unwanted coefficients.

Can you please show me your derivation.

I will try to understand more in details Wien's work, which is based on Heaviside and Searl.

I have found that the equation after the sentence "The ellipsoid with the same axes, has the energy in a state of rest" has been derived by Searl [1]. Using this equation and the previous equation (also derived by Searl), Wien write W'=kW. W' is the energy for the moving charged ellipsoid and W the energy for the charge at rest.

Wien obain k=gamma x (v/c(1+1/2 (v/c)^2)/(arcsin(v/c)))

In Einstein's paper, k=gamma. Einstein considers a simpler problem compared to Wien: a moving plane wave source.

I am presently working in a similar problem using a moving plane wave source and a numerical technique to resolve Maxwell's equations. The preliminary results do not agree with Einstein.

[1] On the Steady Motion of an Electrified Ellipsoid, G F C Searle 1896 Proc. Phys. Soc. London

Halim Boutayeb , The radiation pressure derivation is in section VI here,

Article The Double Helix Theory of the Magnetic Field

It's very easy.

In this paper fromm Abraham (1909), I think that another method is shown for the derivation of the mass-energy formula from Maxwell's equations:

https://en.wikisource.org/wiki/Translation:On_the_Electrodynamics_of_Moving_Bodies_(Abraham)

please see equations (40) and (53)

This is called " the relation between the energy current and momentum density"

Halim Boutayeb , Thanks. The notation is difficult, so before I look at it closer, can you please clarify, if by the term energy current, he is referring to the Poynting vector S = vxH?

Remember, the important thing is, that E = mc2 never exists outside of the context of either radiation pressure, or the medium for the propagation of EM waves.

Halim Boutayeb , Meanwhile, since you are interested in non-relativistic derivations of E = mc2, in this link here, the late Dr. Carl A. Zapffe has presented a few such alternatives. One of them is the radiation pressure argument which I have already mentioned. See pages 40-47 in the link (pages 6-13 in the pdf numbering system),

https://www.gsjournal.net/Science-Journals/Research%20Papers-Relativity%20Theory/Download/865

I agree that there is a subtraction error in the addendum to Einsteian's 1905 paper, but don’t understand how the energy of electromagnetic radiation, radiating from a body, can be derived from the energy content in a mass. The electromagnetic radiation from a body is only dependent on body’s temperature, not the mass. If no energy is supplied, the body's temperature decrease. Einstein's equation E=mc^2 is not physically correct. First 1938 was the fission process discovered by Lise Meitner and Otto Hahn, where energy production can be related to mass loss. There is no mathematical or experimental relationship from this process that would confirm E=mc^2. I believe that Einstein's theory can only be seen as a hypothesis until this can stand up to a serious examination of mathematics and physical processes.

Frederick David Tombe. In your paper you have obtained the equation E=mc^2. Why can two calculations, one with subtraction errors and one with correct mathematics, give the same result? You write "But just because equation (14) relates numerical values, it certainly doesn’tmean that mass and energy are equivalent, as is nowadays wrongly claimed tobe the meaning of this famous equation. (PDF) The Double Helix Theory of the Magnetic Field. Available from: https://www.researchgate.net/publication/295010637_The_Double_Helix_Theory_of_the_Magnetic_Field [accessed Sep 07 2023].".

What is the mass (m) in the electromagnetic radiation?

Jan Lagerström , As regards the first part of your question, once we realize that E = mc2 only ever applies in the context of electromagnetic radiation, or the medium in which EM waves propagate, then it becomes clear that Einstein's derivation, aside from the other many faults in it, is simply a tautology, because his energy equation only holds in the first place on the condition that E is already equal to mc2, in the context of EM radiation. That's part of how a nonsense derivation can appear to produce the correct result. The end result was already there in the main feeder package. Einstein's derivation of E = mc2 is just a series of conjuring tricks.

The focus should therefore be on the real derivation of E = mc2 through the radiation pressure argument.

That then leads to your next question, which is, "how can we have mass in wireless EM waves?".

Well, the radiation pressure derivation tends to suggest just that. In my own books, EM waves are in fact a fine-grained vortex flow of pure electric fluid aether, and aether, being the stuff from which everything is made, does have mass.

EM waves are not simply a propagated disturbance in an elastic medium. The waves are inter-laced with a flow of fluid electric current. See, "The Commonality between Light and Electric Current",

Article The Commonality between Light and Electric Current

Jan Lagerström > "There is no mathematical or experimental relationship from this process that would confirm E=mc^2. I believe that Einstein's theory can only be seen as a hypothesis until this can stand up to a serious examination of mathematics and physical processes."

Agree, completely! There must be some equivalence between mass and energy (both are elements of physical/material objective reality. Many people long before Einstein suggested (like him) this relation from deal/mathematical consideration:

http://www.mrelativity.net/Papers/8/Sharma4.htm

Einstein is given credit by official science, simply for ideological reason to big him up. Einstein evidently for sure, used dodgy and fuggy mathematics to arrive at this relation. Even so (if at all) E = mc^2 (indeed, as you say what is m here?) may only be applicable to "photon mass"; strangely denied by official physics and Einstein himself! If photons have mass, it would be a catastrophe for SR (remember the story of FTL neutrino, found by the OPERA researchers in Italy?). But then, Einstein used the following alphabetic expression m = m0 x gamma, which is nonsensical in numeric terms! You can see how many fudge factors, arbitrary parameters, baseless assumptions are used in modern theoretical physics; which are promoted as logically and mathematically perfect!

Mathematical idealism (Metaphysics for Hegel) introduced in theoretical physics by Newton and its imposition on natural science and humanity as a ruling idea for Capitalism; and subsequently reinforced by Einstein; is at the root of all these confusion and crisis in modern theoretical physics and cosmology:

INSPIRE>HEP: https://inspirehep.net/literature/2158754

Article KEPLER -NEWTON -LEIBNIZ -HEGEL Portentous and Conflicting Le...

A generally applicable and quantitative mass-energy equivalence relation can only be determined based on nuclear reactions and would probably involve an empirical factor or parameter, like the one suggested by Sharma, cited above.

On December 29th, 1934, Einstein was quoted in the Pittsburgh Post-Gazette, saying, “There is not the slightest indication (evidence) that nuclear energy will ever be obtainable.” Even after Lise Meitner and Otto Hahn claimed the discovery of the fission reaction in 1938, Einstein reportedly repeated his skepticism about nuclear energy!

Dear Frederick David Tombe Unfortunately, i must say, there is no single one dimension static equation ( from Newton to Einstein...) exist to describe three dimension of nature that it is changing constantly through temperature pressure and time. On the other hand, science practices artificial light (electromagnetic, flashlight ) not actual of natural sunlight that has massive different frequencies, short wavelength, and visible/invisible character, with different speed. simply Einstein E/m formula is not science for anyone to follow.

Article Title: Science is wrong on…Light & Photon

“…Remember, the important thing is, that E = mc2 never exists outside of the context of either radiation pressure, or the medium for the propagation of EM waves.……”

- as that is pointed already in the SS posts on page 2 that isn’t so. Every particle and system of particles always has energy that is determined by equation E = mc2, which, in turn, is determined by the energy that was spent ; and, in some cases lost at creation of particles systems, if a system .after creation is unstable and dissipates energy at the relaxation;

- and all that happens at creation of particles and systems at interactions where any fundamental Nature force acts, not only at Electric Force interactions.

An example – if particles “electron” and “proton” are created when some 4D momentum, P0, that has only non-zero cτ-component in the Matter’s 4D space with metrics (cτ,X,Y,Z), impacts on an FLE in the Matter ultimate base – the (at least) [4+4+1]4D dense lattice of primary elementary logical structures – (at least) [4+4+1]4D binary reversible fundamental logical elements [FLE]; after creation they have masses me=P0e/c and mp=P0p/c, and contain energies E0e/p=P0e/pc=m0e/pc2;

- if these [charged electrically] particles interact by Electric Force, they compose the system “H-atom”, at that photon with energy 13.6 eV is radiated, correspondingly H-mass – and masses mep, of course – are lesser on the 13.6 eV/c2value, i.e. on the electrical mass defect,

- and if some masses interact by fundamentally different from Electric one Gravity Force, again after dissipation of energy from the corresponding G-coupled system the system has energy and mass lesser than of sum of energies/masses when the bodies were free, on gravitational mass defect, which doesn’t differ in this sense from electrical mass defect; etc.

Again - see the SS posts on page 2 – the equation E=mc2 is completely general and universal, and so is derived by completely general and universal way in the Shevchenko-Tokarevsky’s informational physical model, more see the SS posts on page 2 and links in the posts.

Note, nonetheless, that the above relates to some “static” cases, when particles/bodies contain energies/masses – and, at that, the coupling Forces fields fundamentally don’t contain energies and so masses, but at particles/bodies motion in 3D space till now we cannot exclude that the fields can contain some energy/mass, and elaboration of this problem can have essential, if fundamental, importance.

Cheers

Sergey Shevchenko , So why then is the speed of light involved in a brick?

“…Sergey Shevchenko , So why then is the speed of light involved in a brick?…”

Frederick David Tombe, again - see the SS posts above – everything in Matter, including light and bricks, is/are some specific disturbances in the Matter’s ultimate base – the (at least) [4+4+1]4D dense lattice of primary elementary logical structures – (at least) [4+4+1]4D binary reversible fundamental logical elements [FLE],

- which [lattice] is placed in the Matter’s fundamentally absolute, fundamentally continuous, fundamentally flat, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct),

- at that all/every disturbances always move at 4D velocities in the lattice – and so in the observed now [in mainstream physics as 4D spacetime] 4D space with metrics (cτ,X,Y,Z) - and so velocities have identical absolute values be equal to the standard speed of light, c [bold means 4D vector],

- what is determined only by the main FLE parameters - FLE “size” and “FLE binary flip time” which are equal to Planck length and Planck time, c=lP/tP. Photons move at 4D velocities (0,c), in this case c is 3D vector.

Recent SS post in https://www.researchgate.net/post/NO7_Is_there_a_minimum_value_of_m_in_the_mass-energy_equation_Emc2#view=64fbc3721b17d1bd0e0d4bac is relevant in this case.

Cheers

Frederick David Tombe ,

I confirm that Abraham 's derivation of E=mc^2 is equivalent to the radiation pressure method used by Carl A. Zapffe:

https://en.wikisource.org/wiki/Translation:On_the_Electrodynamics_of_Moving_Bodies_(Abraham)

Abraham shows that Cohn, Lorentz and Minkowski approaches give all this result, which is thus inherent to Maxwell's equations.

Abraham states that momentum (and thus radiation pressure) is absent from Hertz's theory of electromagnetism with moving bodies.

I think that you have shown that Hertz's theory can be correct if the total time derivation is considered. We can get the vxB term by using such method.

Halim Boutayeb , Maxwell's radiation pressure equation first appeared in his 1873 paper, but it is quite distinct from any of those other equations that we commonly know as "Maxwell's equations".

In fact, I can't see how Maxwell's equations themselves, as such, predict radiation pressure. So the issue of Hertz and total time derivatives doesn't really come into it.

What is important is to realize that the equation E = mc2 never applies unless EM radiation is involved.

Frederick David Tombe, "So why then is the speed of light involved in a brick?"

We know that in a proton-proton collision, gamma radiation (energy) is obtained when the mass of the particles disappears. A brick contains protons and neutrons which in turn contain quarks. How the quarks are built is not known today, but according to my hypothesis, “all matter around us is made of elementary particles, electrons and positrons, the constituent parts in the proposed quark model, the building blocks of matter”. (PDF) The building blocks of matter. Available from: https://www.researchgate.net/publication/331099892_The_building_blocks_of_matter [accessed Sep 10 2023], there is a relationship between energy and mass of the size order E=mc^2. See also my explanation of proton-proton collision. “Regarding to my proposed quark model, the 4 high energy electrons are the 2 electrons from each of the 2 protons down quark shell, and all other particles are positrons. All positrons will then be annihilated in the electron cluster and produce gamma ray.” (PDF) Proton-proton collisions. Available from: https://www.researchgate.net/publication/339338871_Proton-proton_collisions [accessed Sep 10 2023].

The positrons proposed in the quarks model have a form of "spin" that probably is close to c because the positrons electrical potential turns into kinetic energy.

I agree according to your equations, E=mc^2 never applies unless EM radiation is involved.

“…What is important is to realize that the equation E = mc2 never applies unless EM radiation is involved.……”

- again, the equation E = mc2 is fundamentally universal and is valid in every case, including, when no any EM radiation is involved, and even, say, if a particle is electrically neutral – neutrinos have “evident” mass, i.e. “rest” mass, and energy E = mc2;

- that is because of that every particle/system of particles after creation at/by transmission to some FLE some creating 4D momentum, P, always moves in the Matter’s extremely uniform FLE-lattice, and so in 4D space with metrics (cτ,X,Y,Z), only with 4D velocities that have identical absolute values be equal to c, since that is determined by the FLE main “kinematical” parameters – FLE “size” and “FLE binary flip time interval”

- and having, of course, 4D momentum P=mc, and energy E=Pc; where the mass “m” is measure of the absolutely fundamental phenomenon “Inertia”, which absolutely necessarily is actualized at every change of everything, including at creation of something absolutely always together with other absolutely fundamental phenomenon “Energy” portion;

- since any change of anything is logically prohibited, so inertia characterizes the logical resistance to changes, while energy/momentum are necessary to overcome this resistance.

More see the SS posts above and links in the posts.

Cheers

Jan Lagerström Sergey Shevchenko , Yes, but in the examples that you have given, the equation E = mc2 resides in the gamma rays.

In Einstein's September addendum to the 1905 paper, the derivation hinges totally on EM radiation emerging from a body, causing it to lose mass. Einstein had no basis upon which to declare that E = mc2 lies in the vestibule of the lost mass, prior to its emission. It lies in the emitted radiation that is travelling at the speed of light.

I have gone through Einstein's derivation very carefully in section III of this article. Einstein's derivation is a tautology.

Article The Myths Surrounding Time Dilation and E = mc^2

Frederick David Tombe Sergey Shevchenko. You are both right.

Einstein's calculation is not done correctly, but a relationship between energy and mass exists. This relationship has not yet been demonstrated with an equation derived with correct mathematical calculations and physically correct boundary conditions.

“Einstein had no basis upon which to declare that E=mc^2 lies in the vestibule of the lost mass, prior to its emission. It lies in the emitted radiation that is travelling at the speed of light.” Agree completely.

Jan Lagerström , But if you believe that E = mc2 applies generally in the absence of EM radiation, can you provide an example?

Frederick David Tombe, I say that there is a relationship between energy and mass, not that it must be E=mc^2. For exempel, in fission and fusion processers.

Jan Lagerström , Yes, you are probably right, but we haven't got it quantified. All classical physics equations are based on the fact of mass being constant. It's possible that mass increases with speed, but this is not the so-called velocity dependent relativistic mass. The latter is simply standard rest mass multiplied by the asymptotic factor of the LT.

But it's possible that mass itself might actually increase with speed, or that it might convert into energy in the situations that you describe. But we just don't know the relationships.

Frederick David Tombe > "But it's possible that mass itself might actually increase with speed,"

Although Einstein once wrote the relation m = m0 x gamma for photons; which makes no sense if m0 = 0, Einstein later changed his mind and never approved relativistic mass:

Article Einstein Never Approved of Relativistic Mass

The hard-core relativists will swear by God that relativistic mass increase is impossible. Some of course, opportunistically claim that this increase in mass applies in the case of particle accelerators.

Velocity dependent mass was proposed by Max Planck in a sheepish and apologetic way in a publication. Please see:

https://en.m.wikisource.org/wiki/Translation:The_Principle_of_Relativity_and_the_Fundamental_Equations_of_Mechanics

My anti-relativist friend Wolfgang Engelhardt, supported Planck and insisted on velocity dependent mass until his death; and this in fact was a cause of some friction in the otherwise excellent friendship between us! For me as a dialectical materialist; abstract space and time and tangible (matter) "mass" of quantum particles are invariables under any circumstances; so LTs ans SR are decidedly false, please see:

INSPIRE>HEP: https://inspirehep.net/literature/2158754)

In the particle accelerators, the charged particles exponentially lose energy with increasing velocity to the virtual particles of the quantum vacuum; making some of them real particles: Please see:

Article The Philosophy of Space-Time: Whence Cometh "Matter" and "Motion"?

Frederick David Tombe ,

I searched for the inventor of the main idea. For example, for Lorentz transformation, I consider that Voigt is the inventor (this was also the late Wolfgang Engelhardt point of view).

I consider Wien the principal inventor of the application of E=mc^2 to everything. Maxwell used mechanics to develop electrodynamics. Wien proposed to use electrodynamics to predict equations of mechanics. This results in E=mc^2 which would apply for all bodies according to his suggested idea (the application of Maxwell's electrodynamics to mechanics).

However, for me, this cannot work. For example, the energy of a transverse wave is not the same than the kinetic energy of an object with mass m. Wien’s methodology (which Einstein copied) does not even work if we analyze the kinetic energy of an object and we change the reference frame:

W=1/2 m c^2

W’=1/2 m (c+v)^2=W(1+v/c)^2

W’-W does not give 1/2 m v^2.

This show, that even within classical mechanics, his methodology cannot be used.

On the other hand, Wien suggested this idea as a possibility, not something we should take for granted. He also analyzed the application of Weber electrodynamics to mechanics and found that, within this approach, the mass would not increase, and the formula E=mc^2 would not be present.

Conclusion: I agree with you that E=mc^2 applies only in the context of electromagnetic radiation in Maxwell's electrodynamics.

p.s. Wien got E=3/4 mc^2, but the factor 3/4 is not relevant. The methodology he used is exactly what Einstein did, except that Einstein considered a moving plane wave source and Wien considered a moving ellipsoid.

Halim Boutayeb , I tried very hard to understand Wien's argument, but I got lost with his ellipsoid. He seemed to be involving the speed of light with the bonding forces in matter. He was getting the electrostatic force, gravity, and the speed of light, all mixed up together inside an ellipsoid and I simply couldn't get his point.

Did you follow his argument?

The thread question is scientifically commented/clarified in the SS posts in the thread on pages 2- 4; more see the posts, if quite briefly:

- the equation, E = mc2, as that is rigorously shown in the Shevchenko-Tokarevsky’s informational physical model

https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics, is fundamentally universal and it is hold at any interaction between everything in Matter by any – Gravity, Weak, Electric, Strong, Forces;

- and so in the model the equation is rigorously scientifically derived without using of any, including particular, including of EM waves, context; more see the linked paper above, sections 2.4 “Lorentz transformations” and 2.5 “Dynamics”, equations (1a) – (4c).

Matter on its ultimate – Planck scale - level is rather simple logical system, and so to derive all equations, including kinematical Lorentz transformations, and main equations of fast bodies dynamics, besides E = mc2, it is enough to know the Pythagoras theorem; to obtain the equation for energy above it is necessary to solve rather simple integral – see Eq.(3) in the link.

All derivations in mainstream physics, including the Einstein’s 1905 one, really have no grounds besides that fit to experimental data; in 1905 that were in this case only experiments with EM interactions, and now [after the derivation in the SS&VT model above] consideration of these derivations are of only a historical interest.

Nonetheless a really questionable discussion goes on in the thread, say, as

“…Sergey Shevchenko , Yes, but in the examples that you have given, the equation E = mc2 resides in the gamma rays…..”

- again, the equation in question is fundamentally universal, and in SS posts not only examples, where the equation E = mc2 resides in the gamma rays are given; say, see example with gravitational mass defect in SS post. And there can be arbitrary number of other examples, when, say, at unstable particles and nuclei decays and at high energy physics interactions besides gamma rays numerous particles of the now few hundreds particles zoo are created, etc.,

- and all that happens only in complete accordance with the equation above.

More see the SS posts above in the thread and links in the posts.

Cheers

Wien actually didn't make the calculation. As you know, Heaviside calculated the electric field of a moving charge, using Maxwell's equations. Searl, did the analyse for a moving electrified ellipsoid, he also calculated the electric field of the ellipsoid at rest. Searl calculated the total energy for both cases. Wien used Searl results and interpreted the difference between the energies as the mechanical kinetic energy of the moving ellipsoid. He interpreted the first term of the series that he got with 1/2 m v^2 (this is where the mass m comes into the picture). This is exactly the same methodology followed by Einstein, except that Einstein worked on a moving plane wave source. Einstein found in his approach that the energy changes like the frequency, ie it follows his Doppler effect formula. A plane wave source send two waves in opposite directions. For a moving plane wave source, the frequency of one wave will increase and the frequency of the second wave will decrease, ie the energy of one wave increase and the energy of the second wave decrease. By added both energies to get the total energy. He interpreted the difference between this energy and the energy of the waves of the plane wave source at rest as the kinetic energy of a body. He interpreted the first term of the series he got to be 1/2 m v^2. This is exactly the same methodology used by Wien.

For me, the problem of Wien's methodology (copied by Einstein) is the following: a transverse wave is defined by amplitude and frequency and depends on the characteristics of the medium (tension, elasticity). It is not the same thing than an object with a mass m and with a volume. I don't see how the aether intervene in the Newton's inertia of a body. For me, it should be an additional mechanical force not the origin of the principle of inertia.

Halim Boutayeb , Could you please clarify how Wien got the v2/c2 factor into it. Einstein used the Lorentz transformation for that purpose. How did Wien do it?

I am studying Searl paper. I didn't complete yet.

Halim Boutayeb , You see, Einstein didn't concern himself with the physical content of the emitted radiation pulses. He brought the (1/2)v2/c2 into the proceeding through a totally irrelevant transverse Lorentz transformation, and then matched it up with the classical kinetic energy.

But as regards Wien/Searle, did he do a Lorentz transformation? If not, how did he get the speed of light into the mix? I got completely lost when he introduced the ellipsoid.

The thread question is scieltifically answered in SS posts above in the thread, but after the last post on page 5 again some srange posts appeared, what creates some inconveniences for the readers who want to know real answer, but in this case that isn’t essential, the tread isn’t spammed heavily;

- and so note only here that to write really scientifically substantiated post it is necessary to spend some time, and for readers to understand some non-trivial post it is necessary to spend some time; besides every post shifts posts of other posters’ posts eventually from the visible page.

So the posters who write substantiated posts and know what is ethics as a rule write in a thread no more than 1 post/day,

- though yeah, posting of a trash in numbers of posts in a day is rather easy job.

“…I am studying Searl paper. I didn't complete yet. …..”

- yeah, before posting something it is well useful to read what is in a science about the something, and to think…

Cheers

Dear All,

Do you realize where modern physics would be without the great SS-T and JF wisdom, which pops up like a virtual particle out of nowhere and graces the physics (and now also the philosophy) threads of RG? This virtual wisdom contains all knowledge that one has to know and its light shines down to bless every poor learner of physics and philosophy!

So, after this wisdom makes its appearance, one must not hinder it from shinning its light and blessings, in any way. Further posting of your pitiable comments makes the great wisdom go out of sight of the visible page, hence prevents the lowly mortals to benefit from this wisdom, for eternity!

Sergey Shevchenko,

Everyone participating in this thread was able to see your posts and understand your 4D concept. You don't have to worry about not having your post in the last page.

Best regards

Relating to the thread question – see the SS post above.

Halim Boutayeb,

“…Everyone participating in this thread was able to see your posts and understand your 4D concept. You don't have to worry about not having your post in the last page..”

- SS posts – as all other posters’ posts on RG – are intended, of course, for any reader on RG, not only for participating ones; and SS posts are intended, first of all, for the readers who are educated enough to understand what is written in the posts. The last in some cases doesn’t relate to the participating ones; at that those ones, who have rather strange imaginations about what physics is, are too vivid posters.

In that somebody has some strange physical approach when addresses to some physical problem there is nothing too bad, and if such somebody writes in a thread no more a post/day, that is, though undesirable, however not too;

- and, besides – see the SS post above – even when a professional physicist writes a post, to do that so that the post would contain some really interesting and essentially substantiated information, it is necessary to spend some time, and for readers to understand such post it is necessary to spend some time, so really such posts can be written again mostly one post/day.

Best regards