The electric charges, color charges and spin of elementary particles are obviously related to the ordering of the parameter spaces that are coupled to the (floating) platforms on which these elementary particles reside. The platforms float with respect to a background parameter space and the differences between the platform parameter spaces and the platform parameter spaces are essential in the determination of the properties of the elementary particles. These difference play a significant role in the multidimensional integration process. Parameter spaces  that have a different ordering must be encapsulated before integration takes place and the results must be added in an adapted way. If the encapsulation is using a cubic format where the axes of the cube are aligned to the axes of the applied coordinate system, then the short list of charges that appears in the SM becomes quickly apparent. For spin the application of a polar coordinate system on top of a selected Cartesian coordinate system offers the opportunity to distinguish between half integer spin and integer spin.

http://vixra.org/abs/1512.0225

Dear Viswanathan,

It is very interesting question. Hoping the following text will provide some contribution to the discussion on this important topic.

Every electron has a magnetic moment and spin quantum number  s= 1/2, with magnetic components  ms = +1/2 and ms = -1/2. In the presence of an external magnetic field with strength  B0, the electron's magnetic moment aligns itself either parallel (ms = -1/2) or antiparallel (ms = +1/2 ) to the field, each alignment having a specific energy due to the Zeeman effect:

 E=msgeuBB0 

where:  ge is the electron's so-called g-factor ge =2.0023} for the free electron,

uB is the Bohr magneton.

Therefore, the separation between the lower and the upper state is  Delta E= geuBB0 for unpaired free electrons. This equation implies that the splitting of the energy levels is directly proportional to the magnetic field's strength. An unpaired electron can move between the two energy levels by either absorbing or emitting a photon of energy  hn such that the resonance condition, hn = Delta E  is obeyed. This leads to the fundamental equation of EPR spectroscopy hn = geuBB0. In practice, EPR samples consist of collections of many paramagnetic species, and not single isolated paramagnetic centers. If the population of radicals is in thermodynamic equilibrium, its statistical distribution is described by the Maxwell–Boltzmann equation.

Applications of this property

1-EPR/ESR spectroscopy is used in various branches of science, such as biology, chemistry and physics, for the detection and identification of free radicals and paramagnetic centers such as F-centers. EPR is a sensitive, specific method for studying both radicals formed in chemical reactions and the reactions themselves. For example, when ice (solid H2O) is decomposed by exposure to high-energy radiation, radicals such as H, OH, and HO2 are produced. Such radicals can be identified and studied by EPR. Organic and inorganic radicals can be detected in electrochemical systems and in materials exposed to UV light. In many cases, the reactions to make the radicals and the subsequent reactions of the radicals are of interest, while in other cases EPR is used to provide information on a radical's geometry and the orbital of the unpaired electron.

2-Miniaturisation of military radar technologies allowed the development of miniature microwave electronics as a spin-off by the California Institute of Technology. Since 2007 these sensors have been employed in miniaturized electron spin resonance spectrometers called Micro-ESR.

3-Applications include real-time monitoring of free radical containing asphaltenes in (crude) oils, biomedical R&D to measure oxidative stress, evaluation of the shelf life of food products.[citation needed]

4-Medical and biological applications of EPR also exist. Although radicals are very reactive, and so do not normally occur in high concentrations in biology, special reagents have been developed to spin-label molecules of interest. These reagents are particularly useful in biological systems. Specially-designed nonreactive radical molecules can attach to specific sites in a biological cell, and EPR spectra can then give information on the environment of these so-called spin labels or spin probes. Spin-labeled fatty acids have been extensively used to study dynamic organisation of lipids in biological membranes, lipid-protein interactions[6] and temperature of transition of gel to liquid crystalline phases.

References & links

Odom, B.; Hanneke, D.; D'Urso, B.; and Gabrielse, G. (2006). "New Measurement of the Electron Magnetic Moment Using a One-Electron Quantum Cyclotron". Physical Review Letters 97 (3): 030801

Arthur Schweiger; Gunnar Jeschke (2001). Principles of Pulse Electron Paramagnetic Resonance. Oxford University Press. ISBN 978-0-19-850634-8.

Yashroy, R. C. (1990). "Magnetic resonance studies of dynamic organisation of lipids in chloroplast membranes". Journal of Biosciences 15 (4): 281. 

Yashroy, R. C. (1991). "Protein heat denaturation and study of membrane lipid-protein interactions by spin label ESR". Journal of Biochemical and Biophysical Methods 22 (1): 55–9.

Yashroy, R. C. (1990). "Determination of membrane lipid phase transition temperature from 13C-NMR intensities". Journal of Biochemical and Biophysical Methods 20 (4): 353–6.

https://en.wikipedia.org/wiki/Electron_paramagnetic_resonance

http://hyperphysics.phy-astr.gsu.edu/hbase/molecule/esr.html

http://iiith.vlab.co.in/?sub=19&brch=206&sim=583&cnt=1

Rafik

The obvious answer is: Since in QM the electron itself is not like a ball (see double slit experiment) why should a particular property of it (spin) be understandable as the behavior of a ball?

The normal answer to 'why has the electron a spin' is to tell the heroic story about Dirac's way to find a relativistic hyperbolic version of the Schrödinger equation. What he found (the Dirac equation, of course) asked for a wave function the values of which were made of 4 complex numbers. Analysing the motion of this four-component wave in an (un-quantized) electro-magnetic field showed that Dirac's electron had an 'internal angular momentum' and and a magnetic moment. Every textbook which covers the Dirac equation has the details. So, the most simple equation that can be conceived for a quantum particle that fulfils  basic requirements imposed by relativity and relativistic causality is the Dirac equation and this enforces spin and magnetic moment (quantitatively! - I omit the numbers here).

Unfortunately, the Dirac equation - considered as describing a single electron by a four-component wave function also implies that the kinetic energy of the particle can have negative values of any size. This is normally handled by embedding the electron into a  quantum field theory in which the electrons of negative kinetic energy shine up as positrons of positive kinetic energy. This framework of quantum field is wide enough that the internal angular momentum is no longer restricted to the value which it has for the electron. The W-Boson for instance has twice that value. So the exceptional role of the case spin 1/2 (to generalize from the electron) disappears.

Since your question expresses the desire to identify 'something real' in the quantum behavior of electrons let me try to provide a perspective which helped me in that same desire.

During most of the nineteenth century it was clear that none of the attempts to explain the  observed constancy of solar and stellar radiation worked. All known energy resources were by far too small. Nevertheless astronomers made the observations for which they had the means and worked out the explanations for which they knew the underlying laws. When in the twenties century the 'chemistry of atomic nuclei' offered an understanding of the internal energy resources of stars this insight was easy to integrate into the huge body of knowledge about stars which was   built in the decades before.

It may well be that with respect to quantum mechanics we are still missing insight into the next lower (more fundamental) level of 'inner working' of Nature, and that on this level our human mental categories of objects that really exist and processes that really happen fit much better than they fit with the level of quantum mechanics we are working with today.

Rafik gave you a rather extensive summary about what is known on the electron spin, particularly the fact that it relates to the magnetic aspect of electrons.

You might be interested also in an experiment carried out in 2014 with two electrons placed in parallel spin alignment that experimentally confirms  that the magnetic interaction between electrons obeys the inverse cube interaction law, contrary to the electric Coulomb force which obeys the inverse square interaction law between the charges of the same particles. It goes without saying that in anti-parallel alignment, both electrons would attract according to this inverse cube law when close enough together. This is what explains covalent bounding between atoms, and also the fact that electronic layers are filled when 2 electrons bound in anti-parallel alignment.

The first link leads to the Nature article that describes the experiment.

He mentioned also the Bohr magneton. The second link leads to a paper that describes the Bohr magneton and also gives its relation to the magnetic field of the electron.

http://www.nature.com/articles/nature13403.epdf?referrer_access_token=yoC6RXrPyxwvQviChYrG0tRgN0jAjWel9jnR3ZoTv0PdPJ4geER1fKVR1YXH8GThqECstdb6e48mZm0qQo2OMX_XYURkzBSUZCrxM8VipvnG8FofxB39P4lc-1UIKEO1

http://www.gsjournal.net/Science-Journals/Essays/View/2257

@ Viswanathan,

For a long time, I was haunted by the same question as you are now. I found it hard to understand and accept spin as an "inherent" property of elementary particles as most books throw up. I found a satisfying answer of this question in Stephen Hawking's book, A brief history of time, chapter 5. The idea of spin in quantum physics is as follows. I will just quote from his book to answer your question.

"One way of thinking of spin is to imagine the particles as little tops spinning about an axis. However, this can be misleading, because quantum mechanics tells us that the particles do not have any well-defined axis. What the spin of a particle really tells us is what the particle looks like from different directions. A particle of spin 0 is like a dot: it looks the same from every direction. On the other hand, a particle of spin 1 is like an arrow: it looks different from different directions. Only if one turns it round a complete revolution (360 degrees) does the particle look the same. A particle of spin 2 is like a double-headed arrow. It looks the same if one turns it round half a revolution (180 degrees). Similarly, higher spin particles look the same if one turns them through smaller fractions of a complete revolution. All this seems fairly straightforward, but the remark-able fact is that there are particles that do not look the same if one turns them through just one revolution: you have to turn them through two complete revolutions! Such particles are said to have spin 1⁄2."

Hope that clarifies!

@Vis

This is a graphic of the half spin electron completing two turns to get to the same place, notice the electron is spinning on two axes.

https://www.youtube.com/watch?v=OfDjtabAuGw

As any good text book will explain, one cannot model electron's spin as arising out of a charged ball of radius e^2/mc^2 rotating about an axis passing through its centre. Given the measured spin angular momentum to be  h/4 pi, a simple calculation will show that  the surface speed of the charged sphere will have to exceed the speed of light. The electron spin is purely quantum, with no classical analogue. Another way to see it is that in the classical limit h --> 0, spin angular momentum also --> 0 implying that there is no non-vanishing classical limit. 

@Christian - I meant the standard Newtonian classical physics.

 classical physics 

The electron can be construed as living in a space of its own, which maps two-to-one onto the space of ordinary rotations.  It takes two full rotations in ordinary space, which continuously drag along the electron's space, to return the electron's state to where it began.  Maybe the electron can be represented as an object living in this so-called covering space, but such that its quantum states are somehow restricted to spin 1/2.  I am unaware of any detailed physical models/theories that ascribe "objecthood"  of this kind to particles with nonintegral intrinsic spin.  If such an object existed, it seems that it could undergo "rotational" excitations to quantum states with spin 3/2, 5/2, etc., and possibly also states of integral spin.  Since no such excited states are observed, the theory of particles with intrinsic spin normally restricts itself to a matrix formulation which includes just one value of intrinsic spin, rather than an analog of, say, a rotating rigid body in ordinary space, which does have such excited states.

Angular momentum is in general treated as a vector quantity. However,  the angular momentum is planar quantity and it is better defined as a bivector rather than a vector. In Dirac theory, electron has internal motion in the form of zitterbewegung. The cause of such motion is due to the presence of random fluctuating zero-point field through out space. Random oscillations of the particle in zeropoint field may be considered as rotations in a complex plane. A stochastic average of all such random rotations represent circular motion in complex vector space. Such internal circular motion is the main cause of deviations in the path of the particle. The internal angular momentum of this circular motion is defined as the spin angular momentum. Thus the spin of a charged particle like electron is a bivector representing a plane in local space. in this view, the spin is defined as zero-point angular momentum.

For further details see DOI 10.1007/s10701-014-9784-2 and doi:10.3390/math3010016

    The most curious and difficult to compare between classical and quantum behaviour, is the statistics that they follow. If the spin is integer we have bosons that they try to share always in the same quantum state, while if it is half integer then the Pauli's exclusion principle arises they cannot be in the same state if their four quantum numbers are equal. This is fantastic! Nothing as that happens in classical physics,

    Their Dirac spinors which joints relativity with quantum mechanics for giving a quantum field theory, the simple Zeeman splitting energy or Glebsh-Gordon coefficients for their addition, tell us that we speak about the most difficult magnitude to understand from a classical analogy. Clearly the name spin is a historical misunderstood.

1. This is a definition of electron spin, nuclear spin. It is independent property.

2. See many textbook about Einstein-de-Haase experiments of electron spin findings, e.g.http://demonstrations.wolfram.com/EinsteinDeHaasEffect/

Spin can also be explained by electromagnetism since it refers to mutual magnetic poles alignment between 2 electrons or any two electromagnetic particles.

More on this and the Einstein-de Haas experiment here:

http://ijerd.com/paper/vol6-issue12/B06120711.pdf

Did you ever consider that spin can be related to the ordering of a polar coordinate system? The polar angle runs over two pi radians. The azimuth runs over pi radians. You can start increasing the polar angle or you can start increasing the azimuth.

It is relatively easy to relate electric charges and color charges to the Cartesian coordinate systems that are used to order the parameter spaces on the platforms on which elementary particles reside. These platforms float with respect to a background parameter space that features its own Cartesian coordinate ordering.

Dear Viswanathan E.

Did you hear about quantum NMR gyroscopes? See in any encyclopedia. The spacecraft will rotate but the electron or nuclear spin placed in the spacecraft will not rotate at all!

If there is a spin p then a magnetic moment (magnetic field) M have to be! Vector p is collinear to vector M. So just as magnetic arrow the spin will rotate ONLY around the Earth magnetic field :). Is it amazing, isn`t? Theoretichian says about this that spin variable does not depend on space variables (coordinates).

Its incredibly simple:

If you allow the tiny (10E-18 cm) charge to revolve at the speed of light in an orbit with a Compton wavelength circumference, you can calculate the current by counting the number of times the charge passes a nearby observer.  Then, multiply the current by the area, and you have the electron's Bohr magneton, identically, all in three easy equations.  The mass-energy will be contained in the interior of the electron, not the charge itself.

See Eqs. 1-1 - 1-3 at website, www.tachyonmodel.com.

A possible, but not yet proven, angular momentum model is given in Eqs. 1-6 - 1-8, again, in 3 easy equations.

It is a semi-classical model, and wave mechanics is not needed unless you have the electron interact with another electron or a nucleus.  Then,  its back to the Schrodinger or Dirac equations.

    Dear Ernst,

    And also to the spin concept, which is the issue of this question.

Daniel:

The questions included “The spin of the electron in QM is not like a ball spinning in classical mechanics. Why?” , “How can we understand that the electron has spin?”, “Or is the spinning real?” 

To cover all these questions coherently, lets simply break it down to very brief QM descriptions of spin and physical descriptions of spin. Let’s start with QM.  

QM only deals with the state of the electron, spin up or spin down along some coordinate axis, insofar as the Pauli matrices are concerned.  That was worked out by Pauli outside of the Schrodinger equation in 1927.  

The Dirac equation (published 1928) provided the known expressions for the electron’s magnetic moment vector (the Bohr magneton) and its angular momentum vector ( h_bar/2 ), but to date, does not provide a  physical mechanism for the magnetic moment or the angular momentum. 

The Schrodinger equation (published 1926), itself, did not originally allow for spin angular momentum. The Schrodinger directly provides integer values of angular momentum as well as quantized radial solutions, but just not angular momentum ½, directly.  Further, it does not provide a physical model.  That is just the nature of the beast. 

Next, let’s discuss the physical spin model issues: 

But first, note this:  The last of these formulations, the Dirac equation was published in 1928.  In 2018, 2 years from now, it will be 90 years since it was published. Obviously, these models have been thoroughly researched by now, and there are many excellent books published that cover all of them in detail.

However, In all that time, there has been no well known model that describes the physical nature of electron spin.  

If anyone knows of one, please let all of us know! 

However, let’s take a look at one that is incredibly obvious and natural.  

As was stated in a previous post, the actual spin is a physical mechanism wherein the tiny charge (10E-18 cm) revolves at the speed of light in an orbit with a Compton wavelength circumference  ( 2.426E-10 cm ).  The mass is contained in the electron’s internal field, not the charge.  Hence, the charge is not precluded from being moving at the speed of light. This provides the Bohr magneton, identically, and a good guess at the mechanism that causes the angular momentum to be h_bar/2,  The same mechanism also provides the origin of the electron’s de Broglie waves. 

( Note that the size of the electron, as given above, is some 137.036 ( the inverse fine structure constant ) times larger than the classical electron radius, lest anyone get hung up on that. ) 

The physical origins are all discussed in Section 1 of the web page, www.tachyonmodel.com.  Eqs. 1-1 – 1-8 provide the basic origins of the magnetic moment, the mass energy, and the angular momentum models. Eqs. 1-9 – 1-11 provide the origin of the electron’s de Broglie waves. 

The latter part of Section 1 includes some brief commentary on the Pauli matrices and the Dirac equation. 

The critical physical part, above, is all done with very simple algebra, and is not at all complicated.

@Ernst

What is your answer to the obvious question: Why the electron looks point-like in high energy electron-electron scattering?

Ernst,

To my opinion you are exchanging descriptions with explanations. Using Pauli matrices is just another way of describing the phenomenon. It is no explanation. It becomes an explanation when these matrices represent different forms of symmetry that the descriptor can use to describe the target. Then you are still left with the task to explain why these different symmetries are possible. For example you must explain why these different symmetries can occur in parallel  within the same model.

The same trick can be applied for electric charges and color charges. Next you must deliberate about the fields of these charges.

http://vixra.org/abs/1607.0146

    Dear Ernst,

    Let's go back to the old problem of the electromagnetic mass if you have an electric charge distributed in a sphere with the finite dimensions that you say, could you calculate the energy necessary to maintain it joint? Could you see what is the amount of mass?

   Going to QED, do you know the accurateness reached in the spin of the electron (the main experimental result of QED, from my humble point of view)? Do you think that it would be interesting one model as the one that you say giving the actual knowledge that we have?

Gents:

Based on the comments, It appears no one tried the derivations or looked at the web page that were outline in my previous posts.  Furthermore, we are being picky about what was addressed and not addressed.

But to repeat: First of all, there are two issues here, and only two, and these cover all aspects of the questions.

First, there are the macroscopic, quantum mechanical descriptions of the electron's behavior that are used at the atomic level, and these have been around for almost 90 years.

Then, there is the physical origin of the spin at the particle level that was discussed.

But to start with Ulrich’s question about the why the electron is point like at high energies:  First of all, its mass energy is only 0.5 MeV.  When an electron collides with another electron with energies of many GeV, especially at almost 1 TeV, its structure is totally demolished, leaving only the charge, although it is to be pointed out it is still intact (sort of) at 4.076 GeV.  

If you want to see more about the 4.076 GeV, BTW, take a look at the meson model in Section 2 of the web page www.tachyonmodel.com, where the meson energies are are given with an accuracy of typically less than 5%..  (Yep! My web page with no apologies.)  I think you might just be surprised!  All the meson information you see there is derived in (again) 3 easy equations, Eqs. 2-2 – 2-4. 

But please, take a look at the web page before commenting.

As to Daniel’s comments about the sphere, anyone should feel free to try to model that one!  I suppose it could be done, but that one could get to be just a wee bit complex, to say the least. 

Instead, the charge revolves in a simple, flat, planar orbit with a Compton wavelength size and a speed of light velocity, and the model is very simple.  That is described in Section 1 of the above web page. I think it is safe to say that nature uses the simplest solutions, and it is hard to see how anything could be simpler that this planar model, especially in light of the known size of the tiny charge.

In both of my previous posts, a simple algorithm to derive the Bohr magnetron from the simple physics was provided.  The physical origin of the Bohr magneton is so simple it can be carried out in three easy algebraic steps. 

Did anyone try the derivation?  I think you would find it to be most interesting!

But if you don’t want to do the derivation / model, you can make it easier by looking Equations 1-1 - 1-8 of the web page which should take only a minute or two.  Then, feel free to attack the model, but only after you have taken a look at it so you will understand it. And then, have at it!  Take your best shot at shooting it down, if you wish!  It is fair game, so have at it, if you wish.

In fact, your collective comments might help me clarify it or fix anything that is incorrect.

But as to the QED part of Daniel’s question, that is a fair question.   And a fair answer to that is a question, which is as follows:  The accuracy of the error is known to about 1 ppb, which is quite remarkable.  But, how can you get excited about finding the error of a parameter when you have no idea as to what the origin of this parameter itself is?

Suppose, for Instance, you have $70k to spend on a Corvette.  You go to the dealer and he tells you $70k will buy an unpainted Corvette. But he can give you a paint job for $70k!  But it’s not just any paint job, it is a super duper precision paint job that you can fold up and put in a plastic bag, or put on a wooden mock of the Corvette!  Wow!  Do you buy the unpainted Corvette, or the paint job?

QED provides the paint job. 

The algorithm discussed in the previous posts and on the web page is the unpainted Corvette. It's not pretty, but it provides effective and easy transportation to a knowledge base.

Which do you want?  (Actually, you can have both.)

Take a look at the algorithm and do the derivation, or take a look at the web page, and then, and only then, comment. You cannot discuss an algorithm you have not tried to derive or did not look at the derivation that is already provided. 

As to Hans’ comments, to repeat what was said above, the problem was broken down into two parts, and only two parts. There are no other viable approaches. 

First, there is the QM part which is almost 90 years old and well established. This includes Pauli, Schrodinger, Dirac, and even symmetries, color, strangeness, QED, or anything else about QM you care to bring up.  There are many books written on the subject.

However, QM alone does not provide an explanation for the physical origin of the spin/magnetic moment/angular momentum at the detailed particle level.  In only provides, at best, the expression for the Bohr magneton and the angular momentum.

Then, there is the physical model of the electron, which is a totally different animal

I repeat:  QM alone does not tell you how the tiny, 10E-18 cm charge physically produces that big, huge, magnetic moment or that big, huge angular momentum.

The methodology described above does.

Take a look at the algorithm described on the previous posts and try the derivation, or take a look at the web page, again, www.tachyonmodel.com , where the work is already done for you in a few of basic equations.

Then, and only then should you reply so that you understand this particular physical mechanism of spin. Then, as I said, and only then, feel free to try to shoot it down!

PS:

The other part of Daniel's question involved the mass-energy of the photon.  It is a single equation in the previously mentioned web page.  It is trivial.

Ernst,

May be the title of my reference,did not invite you to read the document, But that document is a serious trial to provide a solid mathematical test model for both the elementary particles AND the universe that embeds them. This test model does not yet touch the hadrons because the binding mechanisms of quarks appear to be rather complicated. I will look at your website.

I am continuously updating the document. I use my website as a scratchpad and vixra.org as an e-print archive.

http://www.e-physics.eu/ThouShaltConstructInAModularWay.docx

Hans:

What document is that?  I didn't know anything about any document. I was responding to your post.

Outside of that, I only referenced my own website, www.tachyonmodel.com.

Do you mean the website you just put up, www.e-physics.eu,etc? Also, I just now noticed it on the bottom of your post.  Looks interesting.  May I read it?

   Dear Ernst,

   I am very sorry to say that your work is non sense, most of it, you mixture basic equations without taking account of their basic meaning. For instance your equation 1.6 is contradictory because you equals one part of the moment at rest with other always at moving. That is wrong! But most of the formulae are in the same form. It is a pity that you pass all the work of writing these things without thinking in their meaning. I tell you these things try to be sincere and saving your work and time.

Ernst,

I scanned your website and saw that we both are investigating the foundations of physical reality, but do that in different ways that could complement each other.

For matured documents I use the vixra.org e-print archive because it is free accessible for both authors and readers and in addition offers a very effective revision service. In this way interested readers can follow the evolution of my ideas.

The archive only accepts pdf formatted documents. On my website I offer the latest version of my papers both as pdf and as docx documents. I do not request copyright and I stimulate the readers to use the ideas and the corresponding formulas.

Most of the papers are the result of a personal research project that I started in 2009. The main results of that project are collected in an e-book in which all applied items that cannot be easily found in literature are added in the appendix, That e-book is called "The Hilbert Book Test Model".

http://vixra.org/author/j_a_j_van_leunen

http://vixra.org/abs/1603.0021

http://www.e-physics.eu/TheHilbertBookTestModel.docx

Ernst,

I had a look at your site.

Quote:" In this model, the electron’s charge revolves in a Compton wavelength orbit at the exact speed of light."

Interestingly, in the 3-spaces model, the circular Compton wavelength orbit is precisely the orbit that the two charges of a 1.022+ MeV photon must reach at the speed of light to actually separate and move separately as an electron and a positron in normal space. In this model, the speed of light is the decoupling velocity of the pair in electrostatic space.

I don't know if you are interested in exploring a possible deterministic mechanics of decoupling that makes use of the speed of light on a decoupling orbit corresponding to the Compton wavelength that you use, but if so, you will find such a mechanics in the first paper below, published in 2013 in an engineering journal.

The space geometry that allows this mechanics is completely described and justified in the second paper below, which describes the photon before decoupling with supporting math, that was peer-reviewed, found to be Maxwell equations compliant and published very recently.

http://ijerd.com/paper/vol6-issue10/F06103649.pdf

http://www.omicsonline.com/open-access/on-de-broglies-doubleparticle-photon-hypothesis-2090-0902-1000153.php?aid=70373

Daniel:

Thank you for your comments.  Obviously I need to clarify a few things.

However, your comments about Eq. 1-6 are general and somewhat vague.  Could you be more specific?

However, first, start with Eqs. 1-1 - 1-3, the derivation of the magnetic moment of the electron.  What is your issue with that?

Also, I should point out that this model is not something out of a textbook where dozens of people have been working on it for 90 years.  It is a relatively new methodology and while it needs a good deal of work, it is a starting point. 

Andre’:

I read your paper briefly.  I like its approach because it is down and dirty in the physics as opposed to a high level “abstraction” like the Dirac or Schrodinger equations.

But further, it is along the lines of where I myself would like to get to at some point. 

Currently, however, I am looking at the Dirac equation to determine if anything can be gleaned from it that will relate it to my current model.  I.e., how on earth can an abstract relativistic equation like that generate the correct expressions for the Pauli matrices, the Bohr magneton and the angular momentum?  (It is easy to work through the mechanics of the algebra, but conceptually, how is it that by coincidence you generate these physical parameters?  It is bizarre indeed!!   )

Similar comments could also be made about the Schrodinger equation, but that one is more related to describing the electron’s behavior in atomic structures as opposed to the Dirac equation which, ultimately, is more related to the electron itself down at the particle level.

Also, I am trying to show that the electron’s internal electromagnetic energy, as generated by the revolving charge, is a planar field within the orbital circumference.

However, down the road, it would be interesting to see how this revolving charge couples to photons and vice versa, and then move onto pair production from there.

I was not aware that photon/photon collisions alone could generate positron-electron pairs.  That wasn’t around when I was in school back in the 1960s, and, I must admit I haven’t followed that particular field since then. 

That, then, raises the question as to what creates that tiny little 1E-18 cm lump of a charge?  It is one thing to generate a photon, which is assumedly an oscillating EM field, but another thing to generate a charge, and when that charge is generated, what causes it then to revolve in a circle?   Also, what is the nature of the charge itself, now that it has been created?

With all of these delicious problems to be solved, I’m never sure whether God is trying to torture physicists, or is throwing raw meat to the dogs and is enjoying watching them go into a feeding frenzy!

Dirac tried to split the second order partial differential equation into two first order partial differential equations. That is why he applied his Dirac matrices. These Dirac matrices represent bi-quaternions. One of the first order partial differential equations describes the behavior of electrons. The other describes the behavior of positrons.

In quaternionic differential calculus exist two second order partial differential equations. One of them uses an equivalent of d'Alembert's operator. This equation cannot be split into two first order partial differential equations. It offers waves as part of its solutions.

The other second order partial differential equation can indeed be split into two quaternionic first order partial differential equations. This equation does not offer waves as part of its solutions.

http://vixra.org/abs/1505.0149

Ernst,

Really searching minds are a rare commodity. Your way is the way to go.

The photon/photon collision experiment resulting in massive electron-positron pairs creation is recent (1997) and is not much discussed about in the community because it not considered a major breakthrough, which I think it is: massless electromagnetic photons giving birth to mass (which is contrary to current Higgs driven theories). Probably why you have not heard about it.

As for charges, we still have nothing definitive about them. However, the 3-spaces model, which is entirely electromagnetism based,  let glimpse that charges may fundamentally be neutral and that their sign might well be a property (vectorial?) acquired as the pairs separate.

Anyhow, if in the course of your exploration you wish to see how your findings relate to the 3-spaces model, all aspects of the model have been published in a series of papers in 2013, with the 3 most important recently peer-reviwed and published also.

If you wish to discuss physics issues at the "down and dirty" level, as you say, I'll be around.

For your eventual reference if interested, the index into the complete model is here:

Article The 3-Spaces Model - Electromagnetic mechanics

The electron and other particles of nonintegral intrinsic spin can be thought of living on an internal space that is  a double cover of the space of rotations, such that it takes two full rotations of an electron in ordinary space to restore it to its initial state.  It is mathematically possible to create a theory of objects living on this internal space and having excited states of other spins, noninteger and integer.  There is no physical evidence of such a spectrum of states for the electron, however---spin 1/2 seems to be all there is.  Therefore, theories of the electron are confined to the single irreducible representation of the covering space (groupwise SU(2)) corresponding to spin 1/2.  Therefore, the spinning ball model in the space of SU(2) is  apparently unphysical and is not used.

Hans/Gerhard:

Since you have both raised the dread “quaternion” word, all I can say is that I personally am putting off even thinking about that one for the time being.

I had some dealings with them a few years back when writing test algorithms for an inertial guidance module that was attached to kiteboards and snowboards.  The idea was to record the 3D trajectory of these little fun things so the athletes could get bragging rights about their performance, and quaternions were used to avoid gimbal lock.  ( The motion of these things is far more violent that a fighter jets. )

But, where are the gimbals on an electron with its two states?  If we wish to be superstitious and say that the pretty magic of Dirac likely carries over into quaternion space as it does with the other parameters, then one might suspect that quaternions must mean something with respect to this physical spinning charge electron model.   

Being realistic however, because an electron can only be spin up or spin down, it is likely meaningless in that it has no spectrum of values, as Gerhard states.  Even so, the model would not be complete without a look at it, but again, with respect to the physical spinning charge model.

Insofar as Hans’ comment about the two solutions, wave and non-wave, it is to be noted that this model has no internal waves, sort of.  It would likely have an internally propagated impulse that moves toward the center, which might be considered some sort of pseudo wave.  However, that needs an analysis.

But it does have the Compton wavelets that propagate outward externally.

Hence, the no-wave solution might represent the interior of the electron’s disk and the wave solution might represent the external Compton wavelet field, maybe, possibly, perhaps.

This is, of course, all wild (but fun) conjecture, but sometimes that is where the next idea comes from.

     Dear Ernst,

    Sorry for my delay in the answer. Equation 1.6 assumes the equality between two approaches of the 4-linear moment

            E=pc                (1)

            E=mc2             (2)

And that is not possible, because in (1) is assumed that m=0, while in (2) that p=0. But this is just a trivial example.

Dear Daniel

Not so sure about this.

Since p=mv, then if m=0 then p also =0

But if v=c then (1) seems ok

    Dear André,

    I don't know what is the reason to have a photon being a fermion, if we exclude the interest of de Broglie for exploring such possibility. For me there are problems that you don't enter in them as:

   1. Two fermions follow the Pauli's exclusion principle, which would split the electromagnetic waves. This is far of what I know in Optics or in Electromagnetism.

   2. Such splitting would give singlets and triplets. The triplets exhibit magnetism which would be also would interact in a very different form with magnets or other devices. 

Dear Daniel

I don't think photons are fermions. Quite the contrary I can't see how they could be anything but bosons, since they can be polarized.

De Broglie never considered that photons could be anything but bosons.To my knowledge, it was him in fact who solved the riddle by proposing that fermions such as electrons should be defined as having half spin so that localized photons could be defined as having spin 1, thus resolving the polarization issue for localized photons.

     Dear André,

     That was my contribution trying to understand it. If you have a photon with spin 1 and you divide it in two photons, what is the spin of these new photons?

What is the origin of spin?

Why does it influence the applicability of the Pauli principle/

What has spin to do with permutation of two objects that have similar properties?

What proves that bosons are elementary particles?

Or better what proves that an object is elementary?

Dear Daniel,

To my knowledge, no experiment ever revealed that a photon could be split in two more photons. I don't even think this is physically possible.

What has been extensively confirmed in experiments since first discovery in the 1930's is an electromagnetic photon, with spin 1 of course, and energy exceeding 1.022 MeV splitting under very special conditions into two massive particles, 1 electron with spin one half plus one positron with spin one half also.

    Dear André,

    I understood that the photon was splitting in two photons. Sorry, now everything is clear if it creates a pair e-+ e+. That is well known and no problems at all, but this idea was given by Dirac and I didn't know the contribution of de Broglie. Notice that this is pure relativistic effect combined with quantum mechanics.

Dear Daniel

Understandable.

When Dirac hypothesized the possibility, much less was known then about the elementary particles level. From what was known at the time, such an hypothesis made sense, pending experimental confirmation.

But in this case, experimental confirmation never came, and even theoretically, from what is now understood based on confirmed experiments, to my knowledge, it doesn't seem to be possible.

    Dear André,

    I am lost, what is the paper that de Broglie study this possibility that say?

Dear Daniel

Not sure what you are referring to by "…what is the paper that de Broglie study this possibility that say?"

You didn't say what.

Regarding Louis de Broglie, note that practically all he wrote, and he wrote quite a bit, was never translated to English, so it is difficult to refer you to a specific paper. I myself had to read about his theory in many of the books he wrote (in French).

However, what I can contribute about his work on electromagnetic photons can be found in the peer-reviewed paper that was just published about his hypothesis on the double particle photon. I translate some quotes from him that summarize his hypothesis, and give reference to the sources, which are still available in French.

http://www.omicsonline.com/open-access/on-de-broglies-doubleparticle-photon-hypothesis-2090-0902-1000153.php?aid=70373

Daniel:

Thanks for the pointing out the issue Eq. 6-1.  That was one of those elephants in the room I had overlooked.  Not the first time!

Nothing like having other people look at your work to find issues such as these.  This one needs a little clarification, that one along with a few other things I have noticed.

André,

"To my knowledge, no experiment ever revealed that a photon could be split in two more photons. I don't even think this is physically possible."

X-ray quanta are detected by scintillator crystals that break down the energy of the photon into parts that can be absorbed and re-emitted by the crystal's atoms. In this way an X-ray image intensifier uses the full energy of the impinging gamma quanta in order to produce a bunch of electrons in the photocathode that is optically coupled to the crystal. This quantum multiplier effect reduces the quantum noise at the output of the image intensifier. 

A photon is quite probably constituted from solutions of the differential equation that describes the behavior of our living space and is certainly not an EM wave.

Dear Hans,

I always understood that individual incoming photons were first absorbed by electrons in atoms of the crystal and that their energy was then re-emitted as many photons of lesser energy as the electrons de-excited.

Isn't it the case?

André,

An atom can only absorb photons that fit in its atomic spectrum. The rest energy is either absorbed by lower levels or it is converted in kinetic energy of the atom. In the seventies and the eighties I was taking part in the development of X-ray image intensifiers and I calculated through the absorption processes of the scintillation crystals. In the first years the industry used zinc cadmium sulfate crystals. Later they used cesium iodide crystals. My calculations corresponded with measurements of the detective quantum efficiency (DQE) of the X-ray image intensifiers.

As far as I know the LHC uses scintillation crystals as well as calorimeters for detecting photons

My biggest problem is that most physicists have a false idea of what photons are. In my opinion photons are not waves. Waves cannot do what photons do. Also their carrier field (the field in which they are transported) is not the EM field. Instead photons are strings of equidistant one-dimensional shape keeping fronts. They not only keep their shape, they also keep they amplitude. Each front carries a bit of energy. Locally all photons are generated with the same length. The strings follow the deformation of our living space, which acts as their carrying field.

If some process cuts the string into pieces, then that process must redistribute the fronts, such that the resulting photons again show the same length. This can only occur when absorption and subsequent emission is involved. That is what atoms do.

   Dear Ernst,

   You are welcome and I hope that criticism only can help and stimulate to go deeper in your interesting idea of presenting physics in more simple mathematical formalisms.

   Dear André,

   The result of antimatter creation is the main result of Dirac and if you prove that was de Broglie that would be a great surprise for many people (including me).

Dirac was looking for a way to split the second order partial differential equation into two first order partial differential equations and by accident he found two equations of which one related to the electron and the other related to the positron.

His equations are in fact bi-quaternionic equations, because the equation he started with was using d'Alembert's operator.

In fact two quaternionic second order partial differential equations exist of which one is an equivalent of d'Alembert's equation. The other can be split into two quaternionic first order partial differential equations. These equations use proper time rather than coordinate time.

Dear Daniel

My turn to be lost.

I never even mentioned antimatter creation, much less that de Broglie had anything to do with this.

I just don't know what you are talking about.

Dear Hans,

I fully agree with you that photons are not waves.

In fact my paper on the de Broglie hypothesis explains how such a localized photon needs to be internally structured to be conform to Maxwell's equations, by showing how inductive and capacitive properties can be logically assigned to localized photons, which allows electromagnetic photons to be described with clearly structured LC and fields equations.

Comment of one of the reviewers: " The represention of permanently localized photon of de Broglie's hypothesis in a manner totally conform to Maxwell's equations is explained well. The work done can be accepted for publication."

What you are talking about with crystal absorption of a photon and subsequent re-emission of lesser energy photons, that I associate to Raman and Compton scattering, is not what I was really talking about when I wrote that "no experiment ever revealed that a photon could be split in two more photons".

In context, I was talking of splitting in the same manner that e+ e- pairs are created from a 1.022+ MeV photon passing close to a massive particle. This was what Daniel and I were discussing. At least, this what I understood he meant.

I understand that in e+ e- pairs production, the photon does not actually collide with the massive particle that destabilizes it since no energy is lost to the massive particle during such encounters, since it was shown that the energy captive of the masses of the 2 newly created out-going particles plus their translational energy was equal to the total energy of the incoming photon.

It apparently only comes close enough to be destabilized. To my knowledge, there is no experiment on record showing that a photon of less than 1.022 MeV ever decoupled into two separate photons during such encounters. This was what I was referring to.

Pair production is probably due to the capability to construct a quaternion from two complex numbers and pair annihilation relates to the reverse process. This is elucidated in the latest version of "Thou Shalt Construct in a Modular Way". Photons proceed in complex subspaces of a quaternionic encapsulating Hilbert space.

http://vixra.org/abs/1607.0146

Gents:

On the question of the photon being a wave or not being a wave:

It would seem to me that it has to be a wave.  For example, consider an electron being accelerated towards a proton and not stopping until it gets to the first Bohr Radius, at which point it suddenly ( more or less ) stops. As it accelerates toward the proton, it will emit an electromagnetic pulse.  When it stops, that pulse will relax and initiate an oscillating electromagnetic field.  That will be the Lyman 912 Angstrom line.

This, of course, is getting down and dirty in the basic physics as opposed to using quantum field theory.  However, Clerk Maxwell’s stuff will be used, but that falls into the category down and dirty basic physics, unless you choose to use his quaternion approach which I, myself, have not looked at, as yet.  Hans might have some fun with that one!

Also, I point out that when a photon hits a diffraction grating, it is diffracted at an angle that is easily calculated by simple classical methods based on it having an electromagnetic wavelength, again, down and dirty with waves.  I believe most of us have seen this in our undergraduate labs. I, especially, had my nose rubbed in this because my optics professor was a spectroscopy freak.  Hence, that is another reason to consider it to be an electromagnetic wave.

I had intended to work the Dirac issue, along with the angular momentum issue, but you gentlemen’s commentary is making photons sound more and more delicious.  I think I might have a few.

However, my initial approach will be based on Section 8 of my web page, especially Section 8.2. Note that the units I use are natural units for the electron.  The unit of length is a Compton, the unit of time is the rotation time of an electron, and the unit of velocity is Comptons/rotation.

Also, note the compression/decompression of the Compton wavelets of Figure 8-4.

Any time one gets into spectral and atomic issues, sooner or later the issue of the fine structure constant will come up.  Hence, for any fine structure constant freaks with a masochistic streak, I found that if you use the finite, reduced Compton wavelength for the electron radius, you get an entirely different view of a number of fine structure relationships from that usually covered in the standard text books. 

I though on several occasions I had found the origin of the fine structure constant, but nope, it was always back to square one!  It is enough to drive you crazy!  Hence, we are back to the question “Is God trying to torture physicists, or is he throwing raw meat to the dogs?”

If it is indeed raw meat, then it has a lot of bone and gristle and is also covered with tough hide and long hair.

That is covered in Section 8.3 of my web page, for anyone interested.

Also, I still owe Daniel an explanation for Eq. 6-1.  Hope to get to it in a few days.

Dear Ernst,

What has experimentally observed regarding electron  capture by a proton is the following.

The cause of the acceleration between two oppositely signed charged particles is the Coulomb force, that induces kinetic energy in the particles as a function of the inverse square of the diminishing distance between them, an energy that is vectorially directed towards the other particle.

When the electron is captured in electromagnetic equilibrium on the hydrogen mean least action orbital, a single photon of energy 13.6 eV is emitted, no doubt due to the inertia of this energy, which tends to continue on even if the electron is stopped, carrying away the unstopped translational kinetic energy that the electron accumulated during its acceleration phase.

This 13.6 eV single photon can have been emitted only at the moment of capture, because it is only at this distance that this complete amount of translational energy has been completely accumulated.

It seems to me that if evacuation of this energy was progressive as the electron closed in, then this would logically prevent the electron from gaining velocity, by having the induced translational energy that sustains its increasing velocity being evacuated before reaching the mean rest orbital.

The electron will remain captive in this state while being adiabatically induced unreleasable amount of 27.2 eV of kinetic energy by the same Coulomb force for as long as it will remain captive on the rest orbital.

Andre:

Your point is well taken, but still, an accelerated charge is known to emit radiation while it accelerates.

It gets weirder by the moment!

Also, take a look at my Figure 8-4.  Any opinions on that one?

Dear Ernst.

I know about this longstanding theory. but to my knowledge, this was never experimentally observed in the case of electron capture by a proton.

If it was, I never came across any formal paper describing a confirming experiment. If one exists, I will definitely reconsider if I can lay eyes on it.

I am very old school in this regard, I admit that I trust only formally confirmed experimental verification.

I will have a look at your Figure 8-4.

Dear Ernst.

I had a look at your Figure 8-4.

The enegry level is correct of course, but I find it very difficult to correlate your description of the process with my own understanding, because as I understand acceleration and motion, acceleration of charged particles can only be due to Coulomb force application. This force application progressively induces kinetic energy in the charged particles, and it is this kinetic energy, which is progressively increasing as a function of the inverse square of the decreasing distance as the particles close in to each other, translationally moving in the direction of the opposite sign particle involved that "carries", so to speak, the inert invariant rest mass of the particle.

So in my own understanding, any energy emission during motion of any part of this increasing amount of kinetic energy being induced, can only slow the particle down since it diminishes de facto the momentary amount of carrying kinetic energy that sustains the motion, and would prevent it from maintaining and/or increasing the particle's velocity.

My own understanding doesn't mean however that your model is not self-consistent. It may well be, but I just am unable to correlate it with my own understanding of kinetic energy behavior.

Do you address in your model the 27.2 eV amount of unreleasable kinetic energy which is permanently induced by the Coulomb force at the mean rest orbital of the hydrogen atom?

     Dear André,

     Sorry I have explained me so badly. What I wanted to say is that Dirac proposed the pair e- + e+ as one of the possible creations under high energy processes: electron plus positron. The positron is the corresponding antiparticle of the electron,i.e. it has the same mass and opposite charge. This is only a possible pair because every particle has its own antiparticle, thus matter has an equivalent symmetric antimatter word. One of the misteries is that we have only matter in our Universe and how the antimatter has disappeared or no being created.

     Dirac proposed the pair e- + e+ as one of the possible creations: electron plus positron. The positron is the corresponding antiparticle of the electron,i.e. it has the same mass and opposite charge. This is only a possible pair because every particle has its own antiparticle, thus matter has an equivalent symmetric antimatter word. One of the misteries is that we have only matter in our Universe and how the antimatter has disappeared or no being created.

     I hope that now I have explained enough well, sorry.

A greater mystery is the fact that the neutral photons help to create the correct electric charge and color charge of the created elementary particles.

Further, the photons arrive from opposite directions. How do these point-like objects meet?

      Dear Hans,

      When it is created a lepton–antilepton pair, only quantum electrodynamics (QED) is involved, but when a quark–antiquark pair is created, it involves both QED and perturbative quantum chromodynamics (QCD).

      This is not a mystery at all because it is in the base of Quantum Field Theory and whose starting is in the Dirac's equation as a quantum operator interpretation of the relativistic 4-linear momentum.

Dear Hans,

From your comment, I have the impression that you seem to be under the impression that 2 photons coming from 2 different directions are involved in creating a pair of electron positron and that each photon then converts to one of the created massive particles.

Correct me if I did not understand well.

Note that when pairs are created, a single photon of energy 1.022 MeV or more is involved, which has enough energy to make up the energy contained in the mass of both particles plus residual energy sufficient to cause the newly created particles to move away from each other with a velocity corresponding to this residual amount of kinetic energy.

The destabilizing factor is the presence of a massive particle that the photon grazes close enough to cause the photon to destabilize. Metaphorically speaking, like an asteroid that would come close enough to the Earth to become visible by being heated in part in the atmosphere, but that would miss the Earth.

See here on the photograph of experiment E632 at the FERMILAB 4,6 meters bubble chamber, the trace of a positron that no doubt hits head on an electron (at position A), converting to a single 1.022 MeV+ photon that a little further away reconverts to a pair (position B), at which point it probably came close ehough to a nucleus to be destabilized.

Dear Daniel

I am familiar with Dirac's acurate prediction about the possible creation of pairs of e+ e- massive particles. It was effectively confirmed in the early 1930's by a process first observed and confirmed by Blackett and Oc­chialini from analyzing recorded cosmic radiation scattering impact traces in a bubble cham­ber in the early 1930’s.

Such electron-positron pair production has been consistently experimentally confirmed since.

The reverse process of electron-positron pairs re-uniting to entirely convert back to various photon states has also been first observed and confirmed by Blackett and Occhialini, such as in the case of positronium decay.

So this is a hypothesis that was definitely confirmed.

I don't understand though why you thought that I assigned this hypothesis to de Broglie.

Regarding the antimatter issue.

Positrons being the anti-particles of electrons, they are viewed  as "antimatter" with respect to electrons, which are thus viewed as "normal" matter. There is besides a century old assumption that the universe is made almost entirely of "normal" matter (which also includes protons and neutrons), and endless speculation as to why so few "antimatter" is to be found, which is deemed to directly contradict the principle of symmetry.

This issue is completely resolved if we realize that protons and neutrons are not elementary particles like the electron, but "systems of particles" made up of charged and scatterable up and down quarks, which are only marginally more massive than electrons or positrons. These up and down quarks are charged in opposition just like the electron and positron, although with lesser charges, and are also elementary, meaning that they behave point-like.

These are the truely fundamental building blocks of matter in the universe: electron, positron, up quark and down quark.

When it is put in perspective that the charged inner components of protons and neutrons (the up and down quarks) are taken into account instead of the protons and neutrons themselves, it is found that there exists by structure in the universe exactly the same amount of normal matter and anti-matter, that is, the same number of negatively charged elementary particles and of positively charged elementary particles.

André,

I indeed had the impression that two photons are involved. If that is a false impression then I must reconsider my model. I had the impression that particle creation/annihilation can be explained with the fact that quaternions can be constructed from two complex numbers. Elementary particles are represented by swarms of quaternions and photons are represented by strings of equidistant complex numbers. The current status quo is represented by a vane that is a subspace of the quaternionic Hilbert space that scans over the eigenvalues of an Hermitian operator that is a part of a normal operator, which has quaternionic eigenvalues. The creation/annihilation process takes place in the vane.

Maybe now I must conclude that the two complex numbers are mixed into the same string. My impression was that the two photons represented the advanced and the retarded solutions of the homogeneous second order partial differential equation that describes the behavior of the field, which carries the photons as well as the elementary particles. Together the two photons have the required energy. Are you sure that your detector did not catch them both?

If two photons would result, then the number of swarm elements that together represent the elementary particle, will correspond to the number of elements that together represent the corresponding photon. The elements are hop landing points. This view means that the mass of the elementary particle is proportional to the number of swarm elements and the number of string elements is proportional to the energy of the photon. The event turns spherical solutions into one-dimensional solutions (or vice versa) 

I used wikipedia in order to get info about annihilation.

http://vixra.org/abs/1607.0146

https://en.wikipedia.org/wiki/Annihilation

Dear Hans,

I saw many other bubble chamber photographs in books and articles in the 1960's onwards, all leading to the conclusion that only a single photon of energy 1.022 MeV or more was involved. It was also the conclusion that textually accompanied the photographs. But that was long ago and the only photograph I could relocate to show you is the one from experiment E632.

Maybe you could be able to locate more

To my knowledge, no photon with less than 1.022 MeV energy was ever observed to produce an electron or a positron nor any other massive particle.

I see that you have en entirely mathematical model. Mathematics being a language, I have no doubt that if you also conclude that this is more conform to physical reality, it should be possible for you to unite your twin representations into a single string, as you say, that would represent a single photon that could then split into the two massive particles involved.

I observe though that your current approach could possibly be adapted to represent one positron plus one electron being made to interact to convert to various photon states, representing positronium decay. Or maybe you have already done this.

Daniel,

QED and QCD are both models and they are not even based on a comprehensible foundation. You can hardly use them as explanation. However, they appear to be good descriptions.

In my model I use a quaternionic Hilbert space and quaternionic differential calculus.

The model uses stochastic operators that generate the locations of elementary particles.

These operators describe the result of inhomogeneous spatial Poisson point processes. This is a category of processes. Maybe modified Thomas processes or something like that will form a proper description.

I never saw a physical theory that describes or explains these mechanisms. Without these dedicated mechanisms reality will not show coherent dynamics.

In my model I can use the swarm of locations that represent the elementary particle in order to construct a kind of path integral. This operation results in the generation of the a Lagrangian. Usually the path integral uses the Lagrangian as input.

http://vixra.org/abs/1603.0021

Dear Hans,

In my own model, which is geometry based and where photons are totally made of kinetic energy, the localized photon already possesses two separate charges (neutral) in conformity with de Broglies hypothesis on the double particle photon. See first paper below.

This is why in the 3-spaces model it is easy to explain how this sort of photon possessing sufficient energy (1.022 MeV or more) can easily split into two separate particles, that acquire their opposite electric signs as the two charges of the single photon actually part company to move separately as the two massive electron and positron. If interested, see second paper.

http://www.omicsonline.com/open-access/on-de-broglies-doubleparticle-photon-hypothesis-2090-0902-1000153.php?aid=70373

http://ijerd.com/paper/vol6-issue10/F06103649.pdf

     Dear André,

    I am not sure to understand you and perhaps I intrepete you, instead to understand you. Sorry.

    The title of the paper that you put is: "On De Broglie âs Double-particle Photon Hypothesis" and first I tought that you refered to two photons. No. After that you say that it was electron- positron. No, but I didin't understand why (although I doubt the authorship of the de Broglie). I extended this relation to the antimatter, as Dirac in fact did, predicting the antiproton. Notice that Dirac in fact was wrong because he didn't know that the proton was formed by three quarks uud, and he was assuming that the antiproton (charge=-1) needed simultaneously the change of the three quarks. By the way, the Standard Model, tell us that we have 6 leptons, 6 quarks and 4 boson of the interactions (photon,gluon,Z0, W+-).

    Please , could you explain what was the idea of "Double-particle Photon" was? Thank you!

An interesting discussion in response to this question.

On the question: I would describe the spin property (in QM also called quantum number) of an electron or other particle similar to the charge property: Both of them are existing in two opposite characteristics resp. in duality. The comparison with a "spinning ball" is misleading and only a weak mechanical (and mathematical) description. Particle spins add up like electrical charges with one exception.

@Daniel: Did Dirac predict really the anti-proton? I think he was predicting the positron as second solution of a quadratic equation.

Hans

    Dear Hans,

    Although Dirac worked clearly with the electron, I attach the first paper where he see that must appear a +e charge (in 1932 Anderson called them positrons) associated to the one of the electron - e, he interpreted this charge as the one of the proton. Hermann Weyl was who pointed out that the mass would be equal and therefore it couldn't be a proton.

     Nowadays, it was created an antiproton and also a positron for building an antihydrogen atom in the CERN in 1995 for first time. That is one atom formed by one positron and an antiproton. There are many forms to obtain antihydrogen and it is very close the antihelium which was not found in astrophysics although many attempts.

Dear Daniel

Maybe you did not read my paper on the de Broglie hypothesis.

It does explain de Broglie's theory in fine details and shows how it is possible to make it completely conform to Maxwell's equation, which brings a mechanical explanation to the reason why photons can travel only at c in vacuum in the 3-spaces model, and why they always tend to move in a straight line unless they are interacted with transversally.

I see that you belong to the University of Santiago de Compostela, so maybe you would find it easier to read this Spanish translation I made of the formally published paper. See below. I hope my translation is proper. Please let me know if you find language errors.

Due to the number of pages that were required to describe de Broglie's hypothesis and the solution, it is very difficult to summarize it in a few disconnected sentenses during such a discussion, although I have tried, which is probably what confused you about what I tried to explain.

If you read the paper and still have question, I will then be able to answer specific question about the contents of the paper here.

http://www.gsjournal.net/Science-Journals/Research%20Papers/View/5905

André,

Everybody here appears to have their own model. It is fruitless to discuss the validity of these models. I have mine and it obviously differs significantly from yours.

I used WikiPedia for the annihilation reference. That reference tells about two photons of 0.511 MeV. I have the idea that they are right.

Dear Daniel

With reference to the Standard Model and the 6 quarks that are mentioned.

Note that only the up and down quark are stable and they are the only elementary particles that can be detected via non-destructive scattering in side nucleons.

The other 4 quarks are unstable partons that were detected via destructive scattering and they quickly decay into either electrons or positrons or photons. They have never been detected inside protons or neutrons via non-destructive scattering.

The only elementary particles that I give attention to are the electron, the positron, the up quark and the down quark, because they are the only scatterable building material that can be detected in all atoms of the periodic table of elements via non-destructive scattering.

To my knowledge, only those atoms that we have experimental proof of existence are needed to build the whole universe. This is why I explored only this restricted set, because all fleetingly existing partons systematically decay into one or other of the stable set: electron, positron, proton, neutron, photons and neutrinos.

Dear Hans.

No problem.

I prefer however the formally published sources.

Hey Daniel (& anyone else):

First of all, thanx for pointing out the issue with Eq. 1-6..   It was an elephant in the room that I should have seen.  However, it turned out to be rather interesting.

Second, feel free to sharpen your spears!

My response is covered by Eqs. 1-9 – 1-12 in Section 1.6 of my web page, www.tachyonmodel.com, so have at it!

There is more in Sections 1.18 & 1.19. (Not Section 1.17 as was erroneously stated in the text.)

I had intended to put my response here in this blog, but that would have been a  little too grubby.

     Dear André,

     Thank you very much, although I'm afraid that the difficulties are not in the language. For instance, one interesting part in your paper is devoted to find the different masses of the photon, when it is assumed that the photon has always zero rest mass. Another is that the photon is a pure relativistic object which is very difficult to distinguish what "kinetic energy is". There are many others but, in any case, I would appreciate all the work made for trying to understand from simple concepts what a photon is.

      I have made a question about a quite similar issue:

     Are magnetic and electric fields made by different photons?

Quantum field theory tries to reduce the fields to particles (bosons) which interact with their sources (fermions) transferring energy and momentum, if we restrict to electrodynamics. In the case of the weak or strong nuclear interactions the gluons carry also color or flavour, that we can forget for the moment ,without entering in this question dtirectly, given its complexity.

Considering only electrodynamics then, we know that a magnetic field cannot give energy to a free electron, while the electric does. Could we understand this different physical behaviour using a Feynman diagrams or the concept of photon-electron interaction instead of the field? How could we understand the change of "magnetic photons" by "electric ones" using the Faraday or Ampere's law? 

   Are magnetic and electric fields made by different photons? - ResearchGate. Available from: https://www.researchgate.net/post/Are_magnetic_and_electric_fields_made_by_different_photons [accessed Aug 28, 2016].

    And still I have no idea of how is possible to understand it,

This does not touch the fact that the mainstream physical interpretation of what a photon is, contains nasty conflicts.

a) waves cannot proceed over millions/billions of light years and still keep their energy, which is coupled to their amplitude. Spherical waves very quickly diminish their amplitude with distance from the source. Planar waves offer geometrical problems. 

b) the field that carries the photons must extend rather flat over the billion light year range. The range extends over empty space. The EM field relies on the nearby existence of electric charges. Thus, another field must act as a carrier field.

c) photons must be constituted of solutions of partial differential equations that describe the behavior of the field that carries these photons.

d) at least locally the energy contained in a photon must be proportional to its frequency.

e) at least locally photons proceed with a maximum speed that is determined by the properties of its carrying field.

The equations that describe the vibration behavior of fields are homogeneous second order partial differential equations. At least two types of such equations exist.

f) as a result locally all photons have a fixed length

g) the frequency of the photon relates to the number of constituents that locally carry a standard bit of energy

This interpretation of the photon must influence the measuring process

The local conditions at the instant and/or the location of emission may differ.

The equations that describe the vibration behavior of fields are homogeneous second order partial differential equations. At least two types of them exist. One of them is based on d'Alembert's operator and can describe waves. The other can be split into two first order partial differential equations and cannot describe waves. Both equations can describe solutions that keep their shape when they proceed. The one-dimensional version of that solution also keeps its amplitude. These last types of solutions can travel huge distances without loosing their integrity. 

Dirac tried to split an equivalent of the inhomogeneous version of the second kind of equation and obtained his famous equations for the electron and the positron.  The Dirac equation is a bi-quaternionic version of the d'Alembert's equation..

You are welcome to criticize these statements, but if you cannot do that and still maintain the mainstream physical interpretation of photons, then I can no longer take you seriously. 

Dear Daniel.

In the physics community, many physicists assume that the photon has zero mass, while others "conclude" that it has an electromagnetic mass because it can be deflected by gravity, as witnessed by the fact that light has been proven to be deflected by the mass of the Sun. Some even refuse the idea that photons exist, and that there exists only waves. All opinions can be found in the community.

From the Sun deflection observations plus the Kaufman experiment and Marmet conclusions, I also conclude that the permanently localized photon has an electromagnetic mass that can be acted upon by gravity. I explain why in this paper.

I understand that it is difficult to understand what kinetic energy is. In fact, we do not know what it is. What can be established is that it really exists, because it can be accumulated by Coulomb acceleration of an electron, can be liberated as an electromagnetic photon when the electron is stopped in its motion when captured by an atom, can move for thousands of light years and be captured by another electron, giving back this kinetic energy to that electron, causing it to escape from the atom, or at least jump to an orbital further away from the nucleus if not enough kinetic energy has been transmitted to the electron.

Let's remember that "kinetic" only means "movement", so "kinetic energy" simply means "energy in motion".

So, even if we still do not know what kinetic energy is, we can nevertheless acknowledge its existence and observe its effects.

Regarding Maxwell's equations.

In Maxwell's theory, electric and magnetic fields are mathematical representation of what is observed about free moving energy.

In this theory, it is impossible that magnetic fields be dissociated from electric fields, because they induce each other in alternance in this theory, which I agree with. This is why free moving energy is named  "electro-magnetic energy" in Maxwell's theory.

Let's remember here that this is just a different name given to "energy in motion" or free moving "kinetic energy".

In Maxwell's theory, for any quantity of electromagnetic energy, when its electric field diminished in intensity, its magnetic field increases its intensity in proportion and when this magnetic field diminishes in intensity, then its electric field increases its intensity in proportion.

This is what allows defining the LC equation that you find in the paper as a solution to the double particle photon hypothesis of de Broglie, which makes it conform to Maxwell's equations.

The duration of one complete cycle is related to the frequency of electric-magnetic alternance of this amount of free moving energy in Maxwell's theory. From maximum electric intensity (zero magnetic intensity) to maximum magnetic intensity (zero electric intensity) and back to maximum electric intensity is 1 cycle.

The larger the amount of free moving energy, the faster the cycle will be accomplished.

So, if we remain conform with Maxwell's electromagnetism, it is impossible that magnetic fields and electric fields be made by different photons. Each individual photon has both fields by definition, if it is to remain conform to Maxwell's equations.

We have to always keep in mind that "fields" are only a convenient mathematical representation of the real behavior of the energy involved, that was conceived of by Gauss to help describe the real physically existing energy.

Just a note regarding representing electromagnetic oscillation with Feynman diagrams.

There is a basic incompatibility between a Feynman "static" representation and a Maxwell "electromagnetic oscillation" because a Feynman diagram represents a "static" state linked to a Lagrangian, while a Maxwell compliant electromagnetic oscillation is a "progressive" change from electric state to magnetic state and back.

This doesn't mean however that Feynman representations are not useful. They have their uses. Just not the correct representation for electromagnetic oscillation.

André,

Photons follow the deformation of their carrying field (which is our living space). They do not deform that field. Instead massive particles deform that field. You must not see our living space as a flat parameter space. However, it is possible to describe our living space as a dynamic function of a flat parameter space. 

I constructed a mathematical test model that represents many features of physical reality. In contrast to mainstream physics it applies a Euclidean space-progression model that uses proper time instead of the coordinate time that mainstream physics uses. As a consequence the model applies a quaternionic Hilbert space as a repository for dynamic geometric data. In fact the model precisely stores all historic, present and future data. A vane that represents the static status quo is a subspace that represents all present data that can be observed. The vane scans over the repository and the observers receive data from the past that arrive to them via fields. In addition they encounter new conditions when the vane scans over them. The fields are eigenspaces of the non-separable companion of the separable Hilbert space that can be considered to be embedded in its non-separable companion. 

Quaternions can be constructed from two complex numbers. This procedure can be used to split quaternionic subspaces into two complex subspaces.The reverse is also possible.  I use this possibility to explain the origin of the pair production and the pair annihilation processes.

In my model elementary particles are represented by coherent swarms of locations that represent a quaternionic hopping path. The swarm is represented by a closed quaternionic subspace of the quaternionic Hilbert space. Each hop landing is represented by a one-dimensional subspace. The model represents photons as strings of equidistant hops in a complex number based subspace. The complex numbers represent function values. Again each hop is represented by a one-dimensional subspace.

The hops correspond to solutions of the homogeneous second order partial differential equation of the field that carries the corresponding hopping objects. The hops of the elementary particles appear to correspond with spherical symmetric solutions that represent shape keeping fronts.The hops of photons appear to correspond with one-dimensional solutions that represent shape keeping fronts.

This view throws new light on what photons are and makes clear what the difference is between photons and massive elementary particles.

Dear Hans,

I do not completely understand your model. It may well be self-consistent.

I must say that my model is in fact simple Maxwell electromagnetism clarified in light of the de Broglie's hypothesis about the possible internal structure of localized photons, which leads to a clear mechanics of sufficiently energetic photons conversion to electron-positron pairs and more. This is all I have to offer.

     Dear André,

     It seems that we have entered in the "opinion physics" which is a form to waste time speaking about non defined things. Let me try to tell you, some clear concepts which are out of the opinion ( I hope) and which we teach following tested knowledge

    1. Photon is a pure relativistic object, whose rest mass is zero, this is independent of being curving in a gravitational field, because it follows the geodesic of the Riemann space-time instead Minkowski's one. Thus there is not an interaction of mass as in Newtonian gravity.

    2. In pure relativistic objects whose rest mass is zero, the kinetic energy hasn't sense because the photon always has the same velocity for every inertial observer, independently of its state of motion.

    3. Maxwell equations are far of being intrepreted in terms of photons, because even the magnetic or the electric fields are difficult to do, as I have told you.

Dear Daniel.

In my understanding, the localized photon cannot be a relativistic object, since its velocity is invariant.

Maxwell's theory has been around for 150 years, and is still the best theory to account for electromagnetic energy. Matter of opinion maybe, but an opinion that I share.

The 3-spaces model is strictly and uniquely based on Maxwell's theory. Matter of fact.

Maxwell's equations can be interpreted in terms of localized photons when de Broglie's hypothesis on the double particle photon is resolved, which requires expanding the space geometry. Matter of opinion maybe also, but matter of fact also since the outcome has been deemed Maxwell equations compliant by the editors and peer-reviewers.

Electric and magnetic fields are easy to deal with when understood strictly within the guidelines of Maxwell's theory.

The description is now peer-reviewed and published and will forever remain available for whoever wishes to dig sufficiently into Maxwell's theory to be able to understand at some point what this paper explains. The deed is done, the rest is now out of my control.

All theories are matter of opinion.

Matter of opinion again. I admit.

     Good luck, André!

No need for luck. The only need is for solutions based on established and proven theories.

The up coming generation will decide what is closest to physical reality.

Why wait for the next generation? Lets solve it in our generation!  The next generation can then look back at us and....

Dear Ernst.

This is not what history has shown can happen.

The reality was very clearly described by Planck more than 1 century ago:

"A new scientific truth doesn’t triumph by convincing it opponents and making them see the light, but rather because its opponents end up dying, and the following generation grows, becoming familiar with it."

Max Planck, 1900

I have no doubt that it is what is going to happen in each case of new solutions being proposed. The solution I propose is no exception.

The next generation will shed the same look at us that Planck shed on his prior generation.

However, let's go ahead and solve problems knowing these solutions will be likely be rejected by the current generation, but knowing that the next generation latch onto these solutions and will wonder what all the fuss was about.

I have long been very aware of Planck's comments.  Yep!  He was spot on, at times!

I agree.

But note that coherent solutions are not rejected outright by everybody in the community.

I found that mathematically oriented journals have a tendency to accept for publication solutions that are logically coherent with proven theories even if purely physics journals would outright reject them for not being kosher with currently popular interpretation of established theories.

As an example, regarding the de Broglie paper, this is one I was specifically invited to submit by the editors, apparently based on the appreciation they had made of other papers I had published previously in engineering journals.

However, only people having an understanding of the progressive induction of energy by the Coulomb force, and other progessive processes, are likely to connect with this development. I know there are plenty around.

General awareness however is something else that I most probably won't be around anymore to witness.

All elementary particles reside on a private platform and that platform owns a private parameter space. That parameter space can be ordered in different ways. For example it can be ordered in eight independent ways by a Cartesian coordinate system. By starting from that Cartesian coordinate system it can be ordered by a polar coordinate system. That ordering can start with the polar angle or it can start with the azimuth. The polar angle has a range of two pi radians and the azimuth has a range of pi radians. These angles can run up or down. The ordering occurs relative to a background platform, which uses its own ordering. The differences in ordering with respect to the background determine the influence on the properties of the elementary particles. These differences determine their electric charge, their color charge and their spin. You can yourself figure out what these values can be!

http://vixra.org/abs/1512.0225

http://vixra.org/abs/1507.0185

Hey, Daniel:

You said that my model was nonsense, apparently because you got hung up on Eq. 6-1. 

I agree that the section around Eq. 6.1 might have been poorly expressed, so I fixed the issue, and the fix turned out to be extremely interesting, to me at least. 

It turns out that there are three expressions for the energy here, but only for Compton wavelength entities.  I've never seen that one before, so your comment was most helpful.

However, when I then called your attention to the fix a day or so ago, you didn’t respond.

So I challenge you again:  Show me why it is nonsense now!

Specifically, my response is covered by Eqs. 1-9 – 1-12 in Section 1.6 of my web page, tachyonmodel.com, so have at it!

There is more further down in Sections 1.18 & 1.19. (Not Section 1.17 as was erroneously stated in the text.) 

Further, I claim there that parts of the model are rigorously correct. Show me why this is not the case!

I had intended to put my response here in this blog, but that would have been a little too long and grubby without a local equation editor, so it is only in the web page.

BTW:  Anyone else that wants to comment is most welcome.  In fact, the comments are most appreciated because they help me immensely in clarifying the presentation before I move on and become a photon freak.

Dear Ernst,

Following your equation 1-12, you conclude "Insofar as the algebra is concerned, this is logically correct, but only for a Compton wavelength entity".

If you have a look at the paper below that I had published in 2013, you will see following equation (15) identical to your 1-12, the following quote: "the energy of the electron (or positron) rest mass is the only energy level for which this direct equality is possible."

If you read and understand the paper you will see that it is not only algebraically correct, it is geometrically correct, when the space geometry is expanded to describe localized photons in a manner compatible with Maxwell's equations, which makes the relation being drawn from first principles.

In fact, this unique possibility is the reason why electrons and positrons are the only massive particles that can be created by destabilizing a single photon of energy 1.022 MeV or more.

Anyway, at least mathematically, our models concur on this issue.

http://ijerd.com/paper/vol6-issue10/F06103649.pdf

Andre':

Thanks for the comment.

I had read through your paper a while back, but not in utter detail, so that I had not noticed the similarity when I pulled these three equations together several days ago.  However, Eq. 15 is the same as mine, except for the explicit E(p), which is actually implicit in the equations.  In short, we seem to be skirting on the same issues, except that I haven’t explored photons as yet.  But you came to the same conclusion that this is true only for an electron, which is a Compton entity, but have done so based on photon models whereas mine was based on an electron model

Insofar as your section XII is concerned, it is also skirting on the fine structure constant relationships of my Section 8.3 when you bring up the Bohr radius' angular momentum.  I think you might find a few worthwhile tidbits there that relate the Bohr radius and angular momentum to the electron’s physical parameters and, hence, your photons.

However, the comment I was making there was with regard to all three expressions for energy being correct for the same entity.  In the case of your model, then that would be the electron and positron as individual entities, and also from my perspective, but perhaps also, for two entities together.  I definitely need to study your paper in more detail.

I intend to start looking at photon generation in the hydrogen atom shortly, but I have a lot of catching up to do before I can call myself a full fledged photon freak and actually contribute something here.  Outside of occasional antenna work, I haven't looked at Jimmy Maxwell's equations in any detail for a long time, like, my days as a graduate student in Panofsky-Philips' book and the first edition of Jackson's book.  In short, I am still a babe in the woods insofar as photons are concerned.  However, I intend to fix that shortly.

Inertia, as in your section XXL is still another one where we are skirting on each other’s territory, but again, we are using different approaches.

You had once mentioned the idea of collaboration.  That might be very worthwhile at some point, but for the moment I would be a drag on you because I am just getting started in that field.

Also, perhaps Hans might have some similarities, except he seems to be a quaternion freak. However, the interesting point there is that, as I recall reading, Maxwell’s equations were originally written as quaternions, so he might also cross paths at some point.

Actually, anyone with good ideas is welcome to chime in.

This, BTW, is an invitation, not a summons.

Hi Ernst,

The conclusion is that the relation of equation 15 (your 1-12) is that they refer to the threshold energy level that allows converting a 1.022 MeV massless electromagnetic photon into 2 massive 0.511 MeV/c^2 particles, which are a pair of electron/positron.

Note that the mathematical notion of quaternions and even vectors we not yet invented when Maxwell developed his theory from Gauss, Ampere and Faraday's work. He united their findings by generalizing the use of Gauss's electric and magnetic fields as if they induced each other in alternance for free moving electromagnetic energy. That's how he found the way to calculate the actual speed of light from other known parameters.

It appears I was misinformed about Maxwell, then.

However, Whitaker published some papers in the late 1800, early 1900 time frame using quaternions for electromagnetic waves, i.e., Maxwell's equations in quaternion notation. 

One person claimed that this quaternion model predicted longitudinal waves, but I didn't examine them that closely.  However, that, and discussions with a friend, gave me the idea of using a longitudinal impulse electric field for a neutrino model, regardless of the quaternion claim.  I published that one around 2000, as I recall.

That one is described on my web page.

Insofar as creating a pair of particles from photons is concerned, that is extremely intriguing.  For example, exactly how are positive and negative charges created, and why do charges attract and repel?   Again, I'm talking nitty-gritty physical details.

Can't wait to get far enough along with E&M details to tackle the creation issue along  with the photon generation issue