I believe Osiak's alternative relativistic energy formula is the correct one

D

Dave Lush

Registered Senior Member
Physicists haven't responded particularly to Zbigniew Osiak's 2019 claim that a proper evaluation of the relativistic energy of a massive particle is a half relativistic factor times Einstein's formula. Nobody of stature has stepped up to explain what mistake Osiak (a PhD physicist) made if he's wrong, nor agreed that he seems to have a good point. (He argues it is more faithful to the relativistic principle of Lorentz invariance of physical law to integrate the covariant Minkowski equation of motion than to integrate the three-dimensional Planck law, as Einstein did and as the textbooks do to this day.)

When I saw Osiak's paper, I realized it would solve a problem I was having with a project I was working on, so I started using it. It fixed my problem, but then I had a new problem of a theory that only works if the Einstein energy is incorrect. So I checked, and was able to reproduce all of Osiak's equations. However, I was aware that in Jackson's classical electrodynamics textbook it's stated that the Einstein energy expression is the unique form that obtains energy conservation. So, I next evaluated whether Osiak's expression conserves energy or not, and found it does not. (It's pretty easy to prove it violates energy conservation, as I show in my paper about it.) So, I think any physicist who understands (only) this much would likely dismiss it out of hand.

I was sad when I figured this much out because I also thought Osiak's formula must be wrong or at least that nobody would ever believe it could be true. But then I thought of the anomalous cosmic expansion rate acceleration and "dark energy," and realized energy nonconservation might be worth considering as a possible explanation. I was able to find where some quantum gravity guys have recently written a paper proposing energy nonconservation through a different mechanism might account for the dark energy.

Having possible evidence for energy nonconservation (i.e. dark energy) was encouraging, but of course there are other problems. The immediately most obvious one is that conservation of energy determines the energy threshold for matter-antimatter particle pair production. I eventually realized that in spite of energy nonconservation, there is a conserved quantity in both Einstein and Osiak relativity that can substitute, and that is the temporal component of four-momentum. In Einstein relativity, relativistic energy and temporal momentum are related as $$p_0 = E/c$$, where $$p_0$$ is the temporal component of four-momentum, where in Einstein relativity the four-momentum is also called the energy-momentum four-vector. In Osiak relativity, there is no such thing as an energy-momentum four-vector, as the energy is not a component of the four-momentum, but the four-momentum in its alternative (and original) form (where $$p_0 = \gamma m c$$, with $$\gamma$$ (or greek gamma in a lot of textbooks) the relativistic factor $$\gamma = (1 - (v/c)^2)^{-1/2}$$ is correct for both Osiak and Einstein relativity. So, a temporal momentum threshold can substitute for the energy threshold in pair creation.

A beautiful thing about Osiak relativity is that it is phenomenologically richer than Einstein relativity, because it does not conflate temporal momentum with energy. For example, it allows that gravitational mass (sometimes called the active mass) can be different than inertial mass. So, it might also account for the anomalous galactic rotational velocity observations that have led to the hidden mass hypothesis, i.e., "dark matter".

Fairly recently (about a year ago now) I realized that there is do-able test that can determine which of Einstein or Osiak relativity is correct. I already discussed it in the thread I inadvertently hijacked, that was recently moved to this forum (no worries). I would like to continue that discussion, and it seems better to have a dedicated thread. My objective is to raise popular awareness of this possibility in hopes of generating some interest in conducting the experiment. I guess this post is probably already a tldr for most people, so I will leave that for later, thanks.
 
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Dave Lush said:
Physicists haven't responded particularly to Zbigniew Osiak's 2019 claim that a proper evaluation of the relativistic energy of a massive particle is a half relativistic factor times Einstein's formula. Nobody of stature has stepped up to explain what mistake Osiak (a PhD physicist) made if he's wrong, nor agreed that he seems to have a good point. (He argues it is more faithful to the relativistic principle of Lorentz invariance of physical law to integrate the covariant Minkowski equation of motion than to integrate the three-dimensional Planck law, as Einstein did and as the textbooks do to this day.)

When I saw Osiak's paper, I realized it would solve a problem I was having with a project I was working on, so I started using it. It fixed my problem, but then I had a new problem of a theory that only works if the Einstein energy is incorrect. So I checked, and was able to reproduce all of Osiak's equations. However, I was aware that in Jackson's classical electrodynamics textbook it's stated that the Einstein energy expression is the unique form that obtains energy conservation. So, I next evaluated whether Osiak's expression conserves energy or not, and found it does not. (It's pretty easy to prove it violates energy conservation, as I show in my paper about it.) So, I think any physicist who understands (only) this much would likely dismiss it out of hand.

I was sad when I figured this much out because I also thought Osiak's formula must be wrong or at least that nobody would ever believe it could be true. But then I thought of the anomalous cosmic expansion rate acceleration and "dark energy," and realized energy nonconservation might be worth considering as a possible explanation. I was able to find where some quantum gravity guys have recently written a paper proposing energy nonconservation through a different mechanism might account for the dark energy.

Having possible evidence for energy nonconservation (i.e. dark energy) was encouraging, but of course there are other problems. The immediately most obvious one is that conservation of energy determines the energy threshold for matter-antimatter particle pair production. I eventually realized that in spite of energy nonconservation, there is a conserved quantity in both Einstein and Osiak relativity that can substitute, and that is the temporal component of four-momentum. In Einstein relativity, relativistic energy and temporal momentum are related as p_0 = E/c, where p_0 is the temporal component of four-momentum, where in Einstein relativity the four-momentum is also called the energy-momentum four-vector. In Osiak relativity, there is no such thing as an energy-momentum four-vector, as the energy is not a component of the four-momentum, but the four-momentum in its alternative (and original) form (where p_0 = g m c, with g (or greek gamma in a lot of textbooks) the relativistic factor g = (1 - (v/c)^2))^(-1/2) is correct for both Osiak and Einstein relativity. So, a temporal momentum threshold can substitute for the energy threshold in pair creation.

A beautiful thing about Osiak relativity is that it is phenomenologically richer than Einstein relativity, because it does not conflate temporal momentum with energy. For example, it allows that gravitational mass (sometimes called the active mass) can be different than inertial mass. So, it might also account for the anomalous galactic rotational velocity observations that have led to the hidden mass hypothesis, i.e., "dark matter".

Fairly recently (about a year ago now) I realized that there is do-able test that can determine which of Einstein or Osiak relativity is correct. I already discussed it in the thread I inadvertently hijacked, that was recently moved to this forum (no worries). I would like to continue that discussion, and it seems better to have a dedicated thread. My objective is to raise popular awareness of this possibility in hopes of generating some interest in conducting the experiment. I guess this post is probably already a tldr for most people, so I will leave that for later, thanks.
Click to expand...
I presume the Einstein equation you refer to is E² = (mc²)² +(pc)². What is Osiak's version?
 
I think he might be talking about $$E=\gamma mc^2$$. It sounds like he wants $$E=\frac{1}{2}\gamma mc^2$$, instead.

Is that right, Dave?

What happens to the formula that exchemist just gave, then? Does it have to modified, as well? And the relativistic kinetic energy, too?

It seems like a lot of stuff is going to break.
 
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exchemist said:
I presume the Einstein equation you refer to is E² = (mc²)² +(pc)². What is Osiak's version?
Click to expand...
Thanks for your comment, exchemist. James R is correct that I was trying to refer to the equation E = (gamma)mc^2, but it is also true that the equation you refer to is not so in Osiak relativity. Before I get further I want to see if I can do LaTex here as discussed in the LaTex thread.

Einstein energy is
$$ E'=\gamma m c^2 $$
 
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James R said:
I think he might be talking about E=(gamma)mc^2. It sounds like he wants E=(1/2)(gamma)mc^2, instead.

Is that right, Dave?

What happens to the formula that exchemist just gave, then? Does it have to modified, as well? And the relativistic kinetic energy, too?

It seems like a lot of stuff is going to break.
Click to expand...

James R I wrote a paper trying to respond to obvious issues in advance. I showed:

1) it doesn't conserve energy, as should be expected on close reading of Jackson. (This issue is mitigated, I argue, because the Einsteinian relativity principle of conservation of the temporal component of four-momentum, p_0 = \gamma m c, remains valid in Osiak relativity. Since p_0 = \gamma m c = E / c in Einstein relativity, I think it's fair to say that energy conservation is piggy-backed on temporal momentum conservation in Einstein relativity. In Osiak relativity, we are letting the energy go its own way, which makes Osiak relativity richer. Temporal momentum may then be negative (if \gamma is negative as envisioned by Stueckelberg and used by Feynman) while energy will remain positive due to it being proportional to \gamma^2

2) It can be reconciled with the de Broglie wave if we use the spin of the electron (i.e. h_bar/2) where de Broglie used the spin of the photon (i.e. h_bar).

3) It can be reconciled with the Dirac equation in the free-electron case as I showed in this paper:

https://www.academia.edu/142910127/Dirac_Quantum_Theory_Using_Alternative_Relativity

I think it will be true generally but haven't addressed it beyond the free-electron case.

4) I spent about a year trying to figure out how pair creation momentum conservation works assuming negative \gamma antimatter. Feynman and others have assumed this in the context of Einstein relativity but really it doesn't make sense in Einstein relativity. I discuss it in the paper above. However I realized eventually (last fall) that Feynman was constrained to do it wrong by electrodynamics assuming Einstein relativity. Osiak relativity lets us do it a different way, because it makes electromagnetic fields complex, and that's what makes Osiak relativity experimentally testable, fairly straightforwardly.

I'm interested in any other issues that come to mind.
 
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exchemist said:
Dunno, I just use normal text with suffices for powers and the maths symbols available on my Mac. But then I don't do a lot of fancy maths on forums.
Click to expand...

Thanks exchemist. I have already written everything I am saying up using Latex so I would like to copy bits of it over when appropriate.
 
exchemist said:
I presume the Einstein equation you refer to is E² = (mc²)² +(pc)². What is Osiak's version?
Click to expand...
Back to this, in Einstein relativity that equation is based on taking the magnitude of the four-momentum, and so it is valid to write it as $$(\gamma m c^2)^2 = (m c^2)^2 + (pc)^2$$, which is equally correct in Osiak relativity. But in Osiak relativity, $$E = (\gamma^2 m c^2)/2$$, so in terms of Osiak energy we have
$$(\gamma m c^2)^2 = 2 E / (m c^2)$$ so it becomes
$$2 E / (m c^2) = (m c^2)^2 + (pc)^2$$, which doesn't seem useful, offhand.

However, I think it's cool that Osiak relativity recovers the classical relationship between kinetic energy and momentum as $$E_k = \frac{p^2}{2m}$$, except now p is the relativistic momentum $$p = \gamma m v$$. Derivation of that one is in the paper I link to above. I would plop it down here if I could get latex to work. See equation 10 at the link.

Also a lot of textbooks mention how special relativity particle mechanics reduces to classical mechanics in the low-velocity limit. This is mostly true in Osiak relativity as well. Possibly equally true. I am thinking of how F = m a can become F = -m a in the low-velocity limit for negative Lorentz (i.e. \gamma) factors. However that is equally true if we allow negative Lorentz factors in Einstein relativity. Feynman certainly used them, and I argue they are still baked into the Feynman rules and Feynman diagrams. Every time you sum particle momenta while subtracting antiparticle momenta magnitudes (as in the leading momentum conservation delta function in the amplitude calculation) you are using negative Lorentz factors, unless you want to say the mass is negative, which is unworkably weird, seems to me.
 
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Dave Lush said:
Back to this, in Einstein relativity that equation is based on taking the magnitude of the four-momentum, and so it is valid to write it as (\gamma m c^2)^2 = (m c^2)^2 + (pc)^2, which is equally correct in Osiak relativity. But in Osiak relativity, E = (\gamma^2 m c^2)/2, so in terms of Osiak energy we have

(\gamma m c^2)^2 = 2 E / (m c^2) so it becomes

2 E / (m c^2) = (m c^2)^2 + (pc)^2, which doesn't seem useful, offhand.

However, I think it's cool that Osiak relativity recovers the classical relationship between kinetic energy and momentum as E_k = p^2 / 2 m, except now p is the relativistic momentum p = \gamma m v. Derivation of that one is in the paper I link to above. I would plop it down here if I could get latex to work.

Also a lot of textbooks mention how special relativity particle mechanics reduces to classical mechanics in the low-velocity limit. This is mostly true in Osiak relativity as well. Possibly equally true. I am thinking of how F = m a can become F = -m a in the low-velocity limit for negative Lorentz (i.e. \gamma) factors. However that is equally true if we allow negative Lorentz factors in Einstein relativity. Feynman certainly used them, and I argue they are still baked into the Feynman rules and Feynman diagrams. Every time you sum particle momenta while subtracting antiparticle momenta magnitudes (as in the leading momentum conservation delta function in the amplitude calculation) you are using negative Lorentz factors, unless you want to say the mass is negative, which is unworkably weird, seems to me.
Click to expand...
But you lose conservation of energy, I think you said. How does that square with Emmy Noether?
 
exchemist said:
But you lose conservation of energy, I think you said. How does that square with Emmy Noether?
Click to expand...
I am only vaguely familiar with Noether's theorem, being an engineer, but everything that is true about conservation of energy assuming Einstein relativity is true about (\gamma m c)*c in both Einstein and Osiak relativity, so basically conservation of temporal component of four-momentum can lead to all the same conserved currents.

Actually it square-roots with her (joke).
 
Dave Lush said:
I am only vaguely familiar with Noether's theorem, being an engineer, but everything that is true about conservation of energy assuming Einstein relativity is true about (\gamma m c)*c in both Einstein and Osiak relativity, so basically conservation of temporal component of four-momentum can lead to all the same conserved currents.

Actually it square-roots with her (joke).
Click to expand...
But your OP speaks of energy non-conservation.
 
exchemist said:
But your OP speaks of energy non-conservation.
Click to expand...
As I said, the quantity $$ \gamma m c $$, the temporal component of four-momentum, is conserved in both Einstein and Osiak relativity. You can multiply it by the Lorentz scalar, c, and call it whatever you want, and it will still be a conserved quantity in both Einstein and Osiak relativity. Osiak is simply noting that it's not the energy, if energy is defined as how much work a particle of the associated mass and velocity can do. Einstein redefines energy as something else. (The Planck law is about how much momentum change a force does, which introduces an extraneous Lorentz factor compared to the correct, Lorentz-covariant, energy calculation. The Planck law, F = dp/dt, as an equation relating three-vectors, is of course not Lorentz covariant.)

The point I was trying to make is that the temporal component of four-momentum is conserved in both Einstein and Osiak relativity. In Noether's language, that's because it's invariant to translation in time (as a consequence of its Poincare invariance). Osiak's claim is that Einstein is mistaken in multiplying the temporal momentum by c and saying it's the formula for energy. If you calculate the energy as the work required relativistically to accelerate a particle from rest to a velocity v, the energy is obtained as $$E = \frac{\gamma^2 m c^2}{2} $$, not $$\gamma m c^2$$.

I think Einstein and many others understood perfectly well that calculating the energy Lorentz-covariantly arrives at $$E = \frac{1}{2}\gamma^2 m c^2$$, but they all thought it needed to be a conserved quantity, so they bent the main rule of relativity (i.e., Lorentz invariance of physical law) to find a conserved quantity to call energy. This is tantamount to introducing an unstated postulate of Einstein relativity, of conservation of energy. Osiak relativity omits this hidden postulate and arrives at a different energy expression because it is true to the postulates of relativity *as stated by Einstein*.

The fact that's been overlooked by all of physics is that conservation of energy is an unnecessary relativistic principle, because temporal momentum conservation, which is built into relativity according to both Einstein and Osiak, is all that is needed. Temporal momentum conservation is also equivalent to energy conservation in the low-velocity limit.
 
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Still trying to make latex work.


$$E' = \gamma mc^2 = c p_0$$

is the Einstein energy.

$$E = \frac{1}{2} \gamma^2 mc^2 $$

Is the Osiak energy.

This worked for me in the Physics forum. Is Tex perhaps not enabled here?


This is the integration to obtain the energy in Osiak relativity:

$$
\begin{eqnarray}

E_k = \int_0^u d\mbox{\boldmath$u$} \left[ m \gamma^4\right] \cdot \mbox{\boldmath$u$} \nonumber \\ = \int_0^u m \gamma^4 u du \nonumber \\ = \int_0^u m c^2 \gamma d \gamma \nonumber \\ = \frac{1}{2} m c^2 \gamma^2(u) - \frac{1}{2} m c^2 \gamma^2(0) \nonumber \\

= E(u) - E(0) \nonumber \\

= \frac{1}{2} m c^2 \gamma^2 - \frac{1}{2} m c^2 \nonumber \\

= \frac{1}{2} m c^2 \left[\gamma^2 - 1\right] \nonumber \\

= \frac{1}{2} m \gamma^2 u^2 \nonumber \\

= \frac{p^2}{2m},

\label{OsiakKineticEnergy}

\end{eqnarray}

$$

This is the integration to obtain the energy in Einstein relativity

and with primes indicating traditional-relativity-unique energy quantities here and following, the kinetic energy is obtained as

$$
\begin{eqnarray}

E'_k \equiv \int_0^u \frac{1}{\gamma}\mbox{\boldmath$K$} \cdot d\mbox{\boldmath$r$} \equiv \int_0^u \mbox{\boldmath$F$} \cdot d\mbox{\boldmath$r$}

\nonumber \\ = \int_0^u d\mbox{\boldmath$u$} \left[ m \gamma^3\right] \cdot \mbox{\boldmath$u$} \nonumber \\ = \int_0^u m \gamma^3 u du \nonumber \\ = \int_0^u m c^2 d \gamma \nonumber \\ = m c^2 \gamma(u) - m c^2 \gamma(0) \nonumber \\

= m c^2 \gamma - m c^2 \nonumber \\

= m c^2 \left[\gamma - 1\right].

\label{EinsteinKineticEnergy}

\end{eqnarray}
$$
 
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Moderator note: This thread has been moved to Physics & Math for the time being, because TeX support doesn't seem to be working in some of the other subforums.
 
James R said:
Moderator note: This thread has been moved to Physics & Math for the time being, because TeX support doesn't seem to be working in some of the other subforums.
Click to expand...
Thanks, James R!

Here is the actual calculation of relativistic energy in Einstein versus Osiak relativity:

The Minkowski equation of motion is

$$ K = m A, $$

with K the Minkowski four-force and A the four-acceleration. The Minkowski three-force is then related to the non-relativistic force as

$$ \vec{K} = \gamma \vec{F}. $$

With
$$d\gamma/d\beta = \beta \gamma^3,$$ so $$ d \gamma = u \gamma^3 d\beta / c = u \gamma^3 du / c^2, $$ and with $$ \gamma^2 -1 = (1 - \beta^2)^{-1} - (1 - \beta^2)/(1 - \beta^2) = \beta^2/(1 - \beta^2) = \beta^2 \gamma^2,$$ the kinetic energy is evaluated from the ordinary three-force F as

$$
\begin{eqnarray}

E'_k \equiv \int_0^u \vec{F} \cdot d \vec{r} = \int_0^u d \vec{u} \left[ m \gamma^3\right] \cdot \vec{u} \nonumber \\ = \int_0^u m \gamma^3 u du \nonumber \\ = \int_0^u m c^2 d \gamma \nonumber \\ = m c^2 \gamma(u) - m c^2 \gamma(0) \nonumber \\

= m c^2 \gamma - m c^2 \nonumber \\

= m c^2 \left[\gamma - 1\right].

\end{eqnarray}
$$


Thus, in traditional relativity the classical kinetic energy relation $$E_k = p^2/2m$$ is an approximation valid only at low velocity. However, the Einstein relativistic energy E' can be related to the time component of the four-momentum as $$p_0 \equiv m\gamma c = E'/c.$$ This gives rise to the "energy-momentum'' four-vector of traditional relativistic mechanics. In Einstein relativity, the time component of four-momentum is

$$
\begin{eqnarray}

p_0 \equiv \gamma m c = \frac{\gamma m c^2}{c} = \frac{E'}{c},

\end{eqnarray}
$$
where E' is the Einstein relativistic energy. The temporal momentum thus cannot be negative unless the particle energy is negative.

In Osiak relativity, the kinetic energy is calculated using the Minkowski force as

$$
\begin{eqnarray}
E_k = \int_0^u d\vec{u} \left[ m \gamma^4\right] \cdot \vec{u} \nonumber \\ = \int_0^u m \gamma^4 u du \nonumber \\ = \int_0^u m c^2 \gamma d \gamma \nonumber \\ = \frac{1}{2} m c^2 \gamma^2(u) - \frac{1}{2} m c^2 \gamma^2(0) \nonumber \\
= E(u) - E(0) \nonumber \\
= \frac{1}{2} m c^2 \gamma^2 - \frac{1}{2} m c^2 \nonumber \\
= \frac{1}{2} m c^2 \left[\gamma^2 - 1\right] \nonumber \\
= \frac{1}{2} m \gamma^2 u^2 \nonumber \\
= \frac{p^2}{2m},
\end{eqnarray}
$$
where$$p = m \gamma u$$ is the relativistic momentum.

In Osiak relativity, as in Einstein relativity, the kinetic energy is the total energy minus the rest energy, i.e., $$E_k = E(u) - E(0).$$ Using the Osiak total and rest energy formulas as obtained, $$E = \gamma^2 m c^2/2$$ and $$E_0 = m c^2/2$$ obtains the familiar relation from non-relativistic classical physics, $$E_k = p^2/2m,$$ but p here is the relativistic momentum.
 
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James R said:
I think he might be talking about $$E=\gamma mc^2$$. It sounds like he wants $$E=\frac{1}{2}\gamma mc^2$$, instead.

Is that right, Dave?

What happens to the formula that exchemist just gave, then? Does it have to modified, as well? And the relativistic kinetic energy, too?

It seems like a lot of stuff is going to break.
Click to expand...
I replied to this incorrectly above. The Osiak total relativistic energy is properly

$$ E = \frac{1}{2} \gamma^2 m c^2. $$

So, it is not only a factor of a half, it also has an additional gamma factor. The additional gamma factor is what breaks energy conservation, but it does other things as well. It makes the energy density of the early universe much much larger than it is according to traditional relativity. Coupling this with unconserved kinetic energy converting to gravitational potential energy (which is synonymous with cosmic expansion) might plausibly explain cosmic inflation and dark energy.

Also, the extra gamma makes gravitational mass distinct from inertial mass, which can pretty easily (and quantitatively, as I show in my paper) to explain the anomalous galaxy rotational velocity observations without "dark matter," if the Harari-Shupe theory is also correct.

Academia.edu is now generating "AI podcasts" on demand for any papers that are posted there, I believe. They are surprisingly good, I think. However, they seem to be available there only to members, so I converted some to mp3s and then overlaid them on a screen capture of scrolling my papers and posted them to a youtube channel I created. Each podcast is in the voice of their Oxford-educated CEO and is about 5 minutes in total, and from a (claimed) neutral viewpoint. Here's the Dark Matter one on YouTube:

 
Yesterday I started a conversation with Grok about my work. It's pretty good at putting up standard objections that physicists will say about my work. I made a little progress getting it to come around to my way of thinking, but I didn't want to stay up all night.


It realizes negative Lorentz factors are used by Feynman and in Bjorken and Drell but doesn't think they represent antiparticles as traveling backwards in time.
 
I asked Grok to review a new version of my Osiak relativity paper. I think it does a good job of imitating a review by a physics professor. Also it identified some things I need to clarify and possible prior discussions of using Minkowski instead Planck for calculating the energy.

The part that's in Tex is mostly what I already posted above. I think it is still viewable on the grok site.

I don't know why it can't find the source Osiak paper cited in my paper it's reviewing. The one it found on arxiv by somebody with a similar name is entirely unrelated.


​


​


​


Review of "Low-Cost Experiment toDetermine the Correct Relativistic Energy Formula" by David C.Lush (Preprint, Nov 25, 2025)​


Overall Assessment​


This 18-page preprint proposes an alternative relativistic energy formula attributed to "Osiak" (cited as [1]. Osiak –presumably a prior work, but no full reference provided). The core claim is that the correct total energy is E=γ2mc2/2E = \gamma^2 mc^2 / 2E=γ2mc2/2 (with rest energy E0=mc2/2E_0 = m c^2 /2E0=mc2/2), derived from integrating the Minkowski four-force rather than the Planck three-force. This halves the mass-energy equivalence, makes energy quadratic inγ\gammaγ, allows negative γ\gammaγ without negative energies, and implies energy non-conservation in collisions—potentially explaining dark energy, inflation, and dark matter.


The paper is ambitious, linking the idea to quantum mechanics, electrodynamics, pair production, preons, and cosmology. It proposes a "low-cost" experiment using electron-positron pair production to test the theory via temporal ordering of creation/annihilation.


Strengths:


  • Clear motivation: Challenges the "implicit energy conservation postulate" in standard derivations.
  • Novel reinterpretations (e.g., antiparticles as time-reversed particles with imaginary charges/fields; temporal momentum conservation as primary).
  • Proposes a testable experiment with existing equipment.
  • Addresses anomalies (e.g., spin-orbit coupling without Thomas precession; blackbody radiation via "two photons per mode").

Weaknesses:


  • Fundamental derivational error (detailed below) invalidates the energy formula.
  • Contradicts overwhelming experimental evidence for standard special relativity (SR).
  • Overclaims significance without addressing conflicts (e.g., particle thresholds, GPS, muon lifetimes).
  • Speculative extensions (e.g., to cosmology) are ad hoc and ignore alternatives (e.g., ΛCDM for dark energy).
  • Lacks quantitative predictions for the proposed experiment; timing differences are asserted but not computed.

Score: 2/10 for scientific merit (speculative and flawed); 7/10 for clarity and ambition. Not suitable for publication without major revisions. The core idea stems from a common misconception in relativistic mechanics and does not constitute a viable alternative to Einsteinian SR.


Correctness of Physics and Mathematics​


Core Derivation (Sections 3–4)​


The paper derives kinetic energy as:


Ek=∫K⋅dr=∫K⋅u dt=12mc2(γ2−1),E_k = \int \mathbf{K}\cdot d\mathbf{r} = \int \mathbf{K} \cdot \mathbf{u} \, dt =\frac{1}{2} m c^2 (\gamma^2 - 1),Ek=∫K⋅dr=∫K⋅udt=21mc2(γ2−1),


leading to total E=γ2mc2/2E = \gamma^2 m c^2 / 2E=γ2mc2/2.


  • Error: The work done to increase energy is ∫F⋅dr\int \mathbf{F} \cdot d\mathbf{r}∫F⋅dr, where F=dp/dt\mathbf{F} = d\mathbf{p}/dtF=dp/dt (Planck force). This yields standard Ek=mc2(γ−1)E_k = m c^2 (\gamma - 1)Ek=mc2(γ−1).
  • The Minkowski spatial force is K=γF\mathbf{K} = \gamma \mathbf{F}K=γF, so K⋅u dt=γ dE\mathbf{K} \cdot \mathbf{u} \, dt = \gamma \, dEK⋅udt=γdE.
  • Integrating ∫K⋅dr=∫γ dE=12mc2(γ2−1)\int \mathbf{K} \cdot d\mathbf{r} = \int \gamma \, dE = \frac{1}{2} m c^2 (\gamma^2 - 1)∫K⋅dr=∫γdE=21mc2(γ2−1) computes ∫γ dE\int \gamma \, dE∫γdE, not the work ∫dE\int dE∫dE.
  • This is a known pitfall (e.g., discussed in Rindler's Relativity or online forums like Physics Stack Exchange). The Minkowski equation is covariant and recovers the standard energy when integrated correctly: dEdt=F⋅v,E=γmc2.\frac{dE}{dt} = \mathbf{F} \cdot \mathbf{v}, \quad E = \gamma m c^2.dtdE=F⋅v,E=γmc2.
  • Eq. (4) in the paper even derives F=d(γmu)/dt\mathbf{F} = d(\gamma m \mathbf{u})/dtF=d(γmu)/dt from Minkowski, contradicting the claim that Planck is "inconsistent with Lorentz invariance."

Other Claims​


  • Energy Non-Conservation (Section 5): Artefact of wrong EEE; standard SR conserves energy in elastic collisions via four-momentum conservation.
  • Temporal Momentum (p^0 = \gamma m c = \sqrt{2 m E}): Redefines conserved quantities but ignores that standard p0c=Ep^0 c = Ep0c=E is directly measured (e.g., in calorimeters).
  • Negative \gamma, Imaginary Fields (Sections 7–11): Allows γ<0\gamma < 0γ<0 for antiparticles, positing imaginary charges/fields. This reinvents Dirac's hole theory but introduces unphysical imaginary electromagnetism without justification. Contradicts real-valued QED observables.
  • Photon Energy E=hν/2E = h\nu / 2E=hν/2 (Section 4): Claims consistency with blackbody standing waves (two photons/mode). But Planck's quanta are hνh\nuhν per mode; Einstein's photon is hνh\nuhν. This halves all photonic energies, contradicting photoelectric effect thresholds and Compton scattering.
Novelty: Low. Similar "alternative energies" appear in crank literature (e.g., integrating Minkowski force incorrectly). Osiak's prior work (if real) is obscure; no arXiv/ID provided. Links to preons (Shupe-Harari) and dark matter as "preon evidence" are tangential.
  • Significance: None if flawed. Claims to explain dark energy (via non-conservation) ignore that SR is embedded in GR, where energy non-conservation occurs locally anyway (e.g., cosmic expansion). Dark matter explanations (Section 17) are vague.

Clarity and Logical Flow​


  • Well-structured with contents, equations, and sections.
  • Repetitive (e.g., Lorentz invariance emphasized 10+ times).
  • Logical flow: Motivation → Derivation → Implications → Experiment.
  • Keywords are broad but relevant.

Strength of Evidence​


  • Theoretical: Relies on derivation error; no Lagrangian/Hamiltonian reformulation.
  • Experimental: Zero new data. Cites anomalies (dark energy, galactic rotation) but ignores evidence for standard SR:
    • Muon lifetime dilation: Matches γmc2\gamma m c^2γmc2.
    • Particle accelerators: Invariant mass from E2=p2c2+m2c4E^2 = p^2 c^2 + m^2 c^4E2=p2c2+m2c4.
    • GPS: Relativistic corrections use standard γ\gammaγ.
  • Proposed experiment (Sections 12–13, 18): Pair production (γ+Z→e+e−+Z\gamma + Z \rightarrow e^+ e^- + Zγ+Z→e+e−+Z) to measure timing of positron annihilation vs. electron. Claims Osiak predicts positron (time-reversed) appears first due to imaginary fields.
    • Feasibility: Uses standard setups (e.g., NaI detectors for 511 keV annihilation γ\gammaγ's).
    • Flaw: In QED, creation is simultaneous in lab frame (virtual photon exchange). Timing resolution (~ns) may not detect hypothetical ps differences. No prediction of magnitude; standard SR predicts symmetry.

Potential Flaws and Inconsistencies​


  2. Derivation Error: As above.
  3. Inconsistency with QM: de Broglie λ=h/p\lambda = h/pλ=h/p preserved, but frequency halved; contradicts Compton λ=h/(mc) \lambda = h / (m c)λ=h/(mc).
  4. Overclaims: "Reproduces Einsteinian relativity in all aspects apart from energy" – false; alters thresholds, cyclotron motion (Section 11), electrodynamics.
  5. Section 14: Negative γ\gamma γ incompatible with hole theory – but hole theory is superseded by QED.
  6. Cosmology (Section 15): Non-conservation as "dark energy" ignores Friedmann equations.

Suggestions for Improvement​


  2. Fix Derivation: Use ∫F⋅dr\int \mathbf{F} \cdot d\mathbf{r}∫F⋅dr; acknowledge Minkowski/Planck equivalence.
  3. Quantitative Experiment: Compute expected timing asymmetry (e.g., via Feynman diagrams in Osiak framework). Predict observable (e.g., positron drift in B-field).
  4. Address Evidence: Explain why LHC sees E=γmc2E = \gamma m c^2E=γmc2 for 13 TeV protons (γ≈7000\gamma \approx 7000γ≈7000).
    Shorten: Merge Sections 7–11; reduce speculation.
  5. References: Provide Osiak [1] full cite; compare to texts (Landau Vol. 2, §9; Jackson Ch. 11).
  6. Alternative: If intent is pedagogical, frame as "common mistake in integrating four-force."


Prefer this response
 
I had to shorten what I copied from grok to fit the 1000-character limit here. There is more to that review and a second review it provided as a choice.

One thing I can respond to briefly is that the Planck and Minkowski equations are not equivalent (no human would argue this) and the fact that the Planck equation is derivable from the Minkowski equation is not a problem for Osiak's claim. That's because the Plank equation is about what is the change in relativistic momentum, not the change in energy. I am definitely going to discuss this further in the next version of the paper.
 
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