Thoughts please? Theory of Everything think tanking

[Jack Egerton]

Hi all

! Please read this before reading the attached document ! The mathematical formulations in the attached are logical and rigorous. The physical applications of these mathematical formulations are solely exemplifications of the mathematical formulations and how they can be applied in seeking the Theory of Everything. Please discuss and advise how the Egertonian quanta and Egertonian relative relation could have been and could be applied to physical law description.

Disclaimer: The work provided here is by myself, the author and Originator of said work, but is not affiliated with my institution, Imperial College London. This is a work in progress and would require the above stated improvements before publication in a peer reviewed journal.

Thank you very much in advance for you help with this!

Best wishes

Jack S. Egerton

 

 

egertonian-quanta-tetration.pdf

Edited April 11, 2018 by Jack Egerton

[Mordred]

You have your work cut out for you to adapt titration to the other unification groups to start development on a TOE. Particularly since the majority of the work is done in normalized units. To your credit though, there is a decent amount of mathematics in your paper which I am still sorting through. Equation 8 will not represent total energy as you used the wrong equation for total energy as the basis equation.

[latex]e=mc^2[/latex] is not the total energy but is the invariant energy only of a particle.

Edited April 11, 2018 by Mordred

[Jack Egerton]

Thank you Mordred,

I have also written it with E^2 = (cp)^2 + (m0c^2)^2, but when m=gamma.m0 and m0 can be sum of all rest masses, then it seems general to me, to write it how I did.

Have I missed something?

[Mordred]

I must be blind because I don't see it in your document

[Jack Egerton]

N.b. the Lorentz factor, gamma = 1/sqrt(1-v^2/c^2) maps one inertial frame of reference to another via their relative velocity, again, if I am not mistaken. It has been a few years since I studied this last.

I commented it out. I mean that I had written it that way and decided that it seemed superfluous.

I had a section that had that form of the energy-momentum relation, and also the Hamiltonian formulation of Schrodinger's equation, but that reached the cutting room floor as well.

My main aim was to concisely convey each novel way that the Egertonian quanta and relative relation may be applied and then see where it could be taken from there.

[Mordred]

Well then equation 8 isn't dealing with total energy of a particle for that section of said particle is it? Particularly since line 68 specified total energy

Edited April 11, 2018 by Mordred

[Jack Egerton]

The rest energy is E0=m0c^2, the total energy, that includes its motion is E=gamma.m0c^2 = mc^2, in my mind, and also how I have described above. Again, I have not fully thought this through yet, but that seems correct to me.

I would even suppose that Lorentz may have got his gamma factor from E^2 = (cp)^2 + (m0c^2)^2 by subbing in that p=mv, but I have not read his formulation, only been taught it.

[Mordred]

No total energy is given by the energy momentum relation which reduces to E-pc for photons

https://en.wikipedia.org/wiki/Energy–momentum_relation

photons are invariant under relativity there is no frame of reference for  a photon so gamma cannot be applied in that case.

[Jack Egerton]

I fully agree. But, I also state twice that E=mc^2 is equivalent to that relation, via the gamma factor, etc, that I have stated. The substitution of gamma into one equation yields the other and vice versa, if I am not mistaken algebraically.

Regarding photons, my workings yield photon energy with no constraint on its mass. I used the de Broglie relation for matter waves, or particles with wavelike nature, or waves with particle like nature, I would suggest.

 

SEE HERE: I am unable to post a reply, Mordred, so I will reply here instead. I think massless particles are moving at velocity, c, or that limit may be approached asymptotically for particles with finite mass. If the are not changing direction or velocity, they are inertial, maybe. Consequently, from your below comment, I would personally rephrase 'gamma is not applicable in those cases' to 'gamma is not conventionally applied in those cases'. It seems it can be.

IN REPLY TO studiot: I upvoted things I agreed with; I downvoted things I disagreed with. I am just in the process of uploading an updated version of the article which clarifies the point in contention.

 

 

 

! ALL ! please see here an updated version of the article where line 78 now reads: 'mq is the mass quantum of, in general, multiple masses in motion,' Thank you Mordred for pointing me in that direction. Hence why I have upvoted those points.

 

 

 

egertonian-quanta-tetration.pdf

Edited April 11, 2018 by Jack Egerton
Cannot now comment or reply below.

[Mordred]

The problem is that any massless particle does not have an inertial frame of reference so gamma is not applicable in those cases. All massless particles are invariant to all observers under relativity. The e=mc^2 relation is primarily the invariant or rest mass in older literature and does not account for particle momentum.

 

Edited April 11, 2018 by Mordred

[studiot]

I hope there is no sort of vendetta going on here against a well respected member who puts in a lot of effort to help others.

Or perhaps I just don't like the colour red.

 

[Mordred]

Thanks Studiot for the accolade. One other detail to note for the SR regime you will want to use the Klien Gordon equation as opposed to the Schrodinger equation. Here is a half decent article on Klien Gordon and how it leads to  Dirac and the Pauli matrixes

http://hitoshi.berkeley.edu/221B-S02/Dirac.pdf

edit sidenote to OP I see you reached your new account first day limit, so I will hold off till tomorrow on further comments etc

Edited April 11, 2018 by Mordred

[Jack Egerton]

Yes, I did run out of first day comments in my quota.

So, keeping as much content in one comment, I will now attached a newer version, which has the previously removed content with the two-term energy-momentum equation and with the Schrodinger equation. I did not have much time to think about that section, but there seems to be something to it once it can be linked to the previous work. 

There is an extra graph and associated Egertonian zero-point relation, for clarity, that features the desired constant values on small scales and linear values on large scales of zero-point energy, for example. It also inherently has excluded energies.

There is still some confusion surrounding a few things such as the velocity quantum values.

Open discussion is welcomed.

Thanks
Jack

egertonian-quanta-tetration.pdf

Also, I did look at adding time dependence to the Schrodinger equation, but that seems not to affect the workflow much, at present.

Edited April 12, 2018 by Jack Egerton
Fixed typo in document

[StringJunky]

13 minutes ago, Jack Egerton said:

Yes, I did run out of first day comments in my quota.

I think that only happens on the first day. You should be ok now. 

[Mordred]

Looks better, I will study the second document in more detail later on.

[Mordred]

This work is actually fairly decently thought out. Though I'm still thinking about the advantages of using hyper operations in modern  physics applications when typically the majority of the math operations are done in Natural units. The advantage of Natural units being all the major units are given an equivalence of length.  I'm still thinking on this, but I do not wish to discourage your work as I would like to see it progress further as it has the potential in certain applications on improving computation times.

 Anyways still thinking on this as well as kicking ideas around in my head on where the application can be more readily useful.

Also I have to do some digging as this has familiarity in certain research papers I've read in the past. I can't shake the feeling that this technique is already used in various physics papers

Edited April 13, 2018 by Mordred

[Jack Egerton]

On a side note, to anyone else reading this thread, a little bit of history on what I have so far published. These are, first, a multiparameter spectral ultrasonic method, and, second, an efficient and accurate finite element method. There should be wide and general applicability here, so enjoy, https://asa.scitation.org/doi/abs/10.1121/1.4976689 https://asa.scitation.org/doi/abs/10.1121/1.5000492

I would love to share a general noise reduction, signal processing, paper also, but it is yet to be finally approved. The same can be said for an ultrasonic imaging paper or two.

Edited April 13, 2018 by Jack Egerton

[Jack Egerton]

Hi Mordred, I always like to be transparent in my review of literature. I searched Google scholar for hyperoperation, tetration, iterated exponentiation. I could not initially find any physics examples. The briefest of checks just now with 'hyperoperation physics' found some very involved set/group theory work with hyperoperations but I am honestly not at a level to know whether I am repeating anyone's work in those fields. My physics education is half applied and half theoretical, to Masters level. My 'major' or, in UK, final project, was on instabilities in nuclear fusion plasmas in tokamaks (very interesting read that! -- not even sure if I could legally share that work to you, it is not published, so likely). My Engineering Doctorate research is all ultrasonics based -- there we are. 

To reiterate: I cannot say whether anyone has done work like I have done on quantisation of physical laws using hyperoperative mathematics, because their level is beyond what I can comprehend at present.

Thank you for understanding.
Jack

egertonian-quanta-tetration.pdf

Edited April 13, 2018 by Jack Egerton
I have added to the Decleration of Originality based on the above comments in this reply.

[Jack Egerton]

I have extended the Declaration of Originality to include broader inspirations for this work. This seems all-encompassing, though I may think of more to add, in due course. However, the maximum file size upload is currently less than the PDF, so the broader inspirations will be quoted here: 

Further, under the label of `broader inspiration' comes any or all works on fractals including, most notably, Mandelbrot, or otherwise, anything associated with the year two thousand and sixteen film, Dr. Strange, for example, and any works by anyone associated with that film. As well as, for example, discussions I recall with any friends or colleagues on similar or such subjects, for example, Dr. Anthony Vaquero-Stainer, Mr. Christian Vaquero-Stainer, or Mr. Stephen Wall, and others. Also `broader inspirations' includes any popularisation of science, any dissemination of science, or any personal exposure to science by any persons or people known personally by myself or otherwise. Under `broader motivation' comes, utmost, family and friends, and less, anyone or anything.

Edited April 13, 2018 by Jack Egerton

[inSe]

On 4/12/2018 at 10:00 AM, Jack Egerton said:

There is an extra graph and associated Egertonian zero-point relation, for clarity, that features the desired constant values on small scales and linear values on large scales of zero-point energy, for example. It also inherently has excluded energies.

Would it be possible to apply a non-vanishing rule that makes 0 the asymptotic where the wavelength is black. Imagine a non-zero, zero-point virtual-particle pseudo-energy. It's highly dispersed like a normal amount of butter spread about a piece of toast the size of this galaxy. Even state a neutrino with a shorter wavelength is heavier than a neutrino with a longer wavelength? I believe this is all you need in order to do what you were trying to do. 

 

[Jack Egerton]

Thank you inSe: I will think more about your comments and questions. My initial response is that it seems, at first, not possible to have a tendency to zero of the linear asymptote in the current formulation. Wavelength tends to a length quantum, lambda_q, as I currently see it. Any localised particle with more energy -- shorter wavelength -- is heavier via relativistic relations and my formulations include such, this includes neutrinos. Thanks again, Jack.

[Jack Egerton]

inSe: If I do think more about this, it may be a while yet, so do not hold your breath for it