I remember discussing before about this question and your theory about it. I have a theory, which might be a satisfactory explanation for this question, Please see: Article Real/Virtual Exchange of Quantum Particles as a Basis for th...
In short, this theory assumes an infinitesimal but finite mass for photons of all energies. The real photons propagte through the exchange of positions with the virtual photons of the quantum vacuum. As the equation in the article for the exchange rate shows, this rate is extremely high (almost infinite) for photons because of their extremely small mass; such that the photons can propagate as a spherical wave front in all directions. The virtual particles have their inherent velocity, so the photons can maintain almost the same velocity for long distance, losing only some energy that is necessary to provide the mass equivalence of the virtual photons in each such exchange.
This theory is in contrast to the "path integral" formalism of Feynman that require the mathematical trick of "renormalization" to eliminate the infinities! Other quantum particles like electrons have more substantial mass in the denominator of the exchange rate equation; which means that the exchange rate is very low and the energy requirement for each exchange with a counter virtual electron is very high. The high mass quantum particle therefore can move only relatively short distance in one direction as a divergent cone giving a short wave front. The mass and the velocity of the massive quantum particles determine their range and the size of the wave-front. This theory also explain the wave/particle duality of quantum particles.
“Why does the Universe contain two types of particles, those that can travel at the speed of light, and those that can't?”
In Universe – more correct in Matter in Universe, indeed there are two main types of particles,
[which move in the 3D space of the 4D absolute sub-spacetime with metrics (cτ, X,Y,Z), of the absolute Matter’s [5]4D Euclidian spacetime with metrics (cτ, X,Y,Z,ct); where “cτ” is the “coordinate time” dimension/coordinate/axis, X,Y,Z are 3 spatial dimensions/coordinates/axes, “ct” is the “true time” dimension/coordinate/axis]
with the speed of light, c, and other then have 3D spatial speeds lesser then c.
At that every particle, body, galaxy…. moves in the 4D sub-spacetime only with 4D speed of light having 4D momentums P=mc [“bold” is 4D vector] and energies E=Pc=mc2; and with the speed of light in the true time, ct.
Every particle [body…..] is some close-loop algorithm, which constantly runs, and so every particle is some 4D gyroscope with “intrinsic” angular momentum be equal to 1ћ, which is always oriented relatively the 4D motion direction.
All coordinates/axes are orthogonal.
Thus particles are of two main types: “T-particles” that are created by momentums that were directed along ct-axis; so if they are at absolute rest in the 3D space, they move only along this axis with speed of light. If after a spatial impact a T-particle moves also in the space, then, since 4D speed is only c, its speed in the coordinate time decreases in the Lorentz factor – as that Pythagoras prescribed, when the spatial speed is always lesser then c.
Besides, because of the 4D gyroscope’s angular momentum cannot be as a vector in the 4D sub-spacetime, its “intrinsic” angular momentum cannot be observed “completely”, and so the fundamental T-particles are fermions with observable angular momentums/spins be equal ½ћ.
The other type, “S-particles”, are created by spatially directed momentums, so they always move in the space with the speed of light and don’t move in the coordinate time – just in the time that clocks show; and have “intrinsic” momentums be equal to ћ, e.g. – S-particles “photons”.
Though every particle have some inertial and gravitational masses, only T-particles have “rest masses”, i.e. when they move in the coordinate time only.
All particles that are composed from fermions have rest masses, though can be bosons.
And, besides, a note to your other RG question
“In Special Relativity can massive neutrinos travel at the speed of Light?”
All neutrinos are fermions and so all are T-articles, have rest masses, when Pythagoras prohibits for them to move in 3D space with the speed of light. Though, since their masses are extremely small, even in keV-th energies they move with large Lorentz-factors and so practically with speed of light.
More see https://www.researchgate.net/publication/273777630_The_Informational_Conception_and_Basic_Physics DOI 10.5281/zenodo.16494.
Knowing full well that the neutrino had been shown experimentally to travel at the speed of light, to higher and higher precision, limited only by experimental error, the Nobel Prize Committee awarded the 2015 Nobel Prize for the experimental verification of Neutrino Oscillation showing and emphasizing the fact that neutrinos have mass, in defiance of Einstein's E = mc^2. That lightspeed neutrinos had to be massive was known, theoretically, to have to be true since 1967 when it was realized that neutrino oscillation would solve the Solar Neutrino problem, but required neutrinos to be massive in order to occur. The 2015 Nobel Prize posed a challenge to the physics community to explain how lightspeed neutrinos could participate in neutrino oscillation in defiance of Einstein's E = mc^2.
In order to conform with the Einstein dictate, and having no other known recourse, physicists chose the course of denying that neutrinos travel at the speed of light, saying instead that they travel very, very, close to the speed of light but not at the speed of light, hiding behind ever present experimental error, which will always be there. And that is the position held to this day. I once had a Nobel Laureate hang up on me in a discussion on neutrino oscillation when I told him that massive neutrinos can travel at the speed of light because they do not have to obey Einstein's E = mc^2. How can anyone learn anything if they don't listen to you because of poisoned outlooks? In fact, Einstein's E = mc^2 does not apply to any particle that travels at the speed of light. I have proven this fact in a newly published paper on Photodynamics which you can easily find and download from the Open Access Journal of Physical Mathematics, 2018, Vol 9. The paper was denied publication for 4 years by the editors of a variety of journals, without being subjected to peer review, because of its obviously erroneous results. But the truth is coming out, cannot be denied, and will prevail.
In short, the 2015 Nobel Prize challenge was needed and has achieved results. We should put the errors of the past to bed, and use the insights of Photodynamics to work for us in making important new findings which are now in our grasp.
Please carefully read my paper in JPM, leave the past behind, spread the good news, and join me in this effort.
“…Knowing full well that the neutrino had been shown experimentally to travel at the speed of light,…..”, etc.
Again – see the SS post above: any/every particle, if we don’t consider quantum effects and some exotic materials, moves in the 4D sub-spacetime of Matter’s absolute [5]4D Euclidian spacetime only with 4D speed of light.
The T-particles, which at the absolute rest in 3D space, move so only along the “coordinate time” axis with the speed of light. If such particle is impacted by a spatially directed momentum, it moves in the space also, and, because of the absolute value of the 4D speed cannot be changed, its speed in the space is always lesser then the speed of light. Neutrinos are T-particles [because of are fundamental fermions, again see the SS post above] , and so always move in the space with speeds that are lesser than the speed of light.
Indeed, in 2011 OPERA collaboration in CERN “discovered” that neutrinos move with the speed that is a bit larger than the speed of light, and in a few month more than hundred of papers, including in prestige journals, were published, where the theoreticians “grounded/explained” how that happens. However in some time the collaboration found corresponding damage in a cable connector…
RJM> "In fact, Einstein's E = mc^2 does not apply to any particle that travels at the speed of light"
This is what Einstein and the relativists say! For them light is not a particle, but a wave in a medium and its velocity is the highest attainable only for bodies that has no mass like light photons; which are not particles but wavelets of the massless medium that carries only the energy of a disturbance in the medium; hence no massive particles are involved. Any particle with mass can never attain this velocity. This is the reason why they deny the fact that neutrinos can travel at the speed of light, and even at superluminal velocity as shown by the OPERA experiments. You seem to accept this wrong and axiomatic truth and then try to make a correction of it, to give it a better formulation! You are following classical physics, Robert! This must be totally rejected and not patched-up to make it look better!
The fact is that the photon of any energy is a particle with some finite mass no matter how small! There can be no matter without mass content and motion, according to dialectics. Quantum electrodynamics (QED) and the uncertainty principle provides incontrovertible proof of this fact. It is not only the celebrated photoelectric effect, but there are many other cases where discrete particle nature of quantum entities including photons is essential. We see tracks of these particles, including gamma ray photons from the cosmic rays, in the Cloud Chamber pictures; the collimated (beam) emission of EM radiations of all kinds (including microwave) from the active galactic nuclei (AGNs) that travel millions of light years in cosmic space!
Please note: I will have no further comments to make. Regards, Abdul
Whether you like it or not, there is still a classical region of physics which exists and must be properly addressed before jumping to quantum physics to use its approaches which are not needed at this stage and confuse the issue further. My question exists in the classical domain, addresses an important issue that has been misunderstood, unresolved, and avoided by all means because it is too hard to resolve. Its proper understanding leads to the resolution of several outstanding problems, unresolvable by other means, one of which is the neutrino oscillation problem which resides in the classical domain of relativity and a proper understanding of such. There is no need to address faster than light and other esoteric results of neutrino velocity measurement experiments which turn out to be experimental artifacts under closer examination, when good repeatable measurements of neutrino speed always give the speed of light to experimental error and acquire more precision as the experiments improve with time. In addition, nobody has observed slow neutrinos moving about, like slow electrons.
There is no need to go to all this trouble to avoid the issue when you can read and understand my solution that Einstein's E = mc^2 does not apply to any particle that travels at the speed of light. This is a simple and understandable solution, needing no fancy physics and only College entry level algebra and calculus to understand. Please read my paper on Photodynamics discussed for some time, and recently published in the Open Access, Peer Reviewed Journal of Physical Mathematics 2018 Vol 9. After reading the relevant section of this 8 page paper please let me know if you agree with me that it is invalid to use Einstein's E = mc^2 on any particle that travels at the speed of light for the reasons I have stated, and that therefore lightspeed neutrinos can travel at the speed of light. I request all readers of my posts on this question to please answer this question first, then give reasons why, and hopefully as short and as clear as possible.
As far as lightspeed particles having mass is concerned even relativists up to this day say that photons, for example, have mass, making a distinction between rest mass and relativistic mass. The present physics community understanding is that lightspeed particles can have no rest mass, only relativistic mass. I have stated and shown repeatedly why this is wrong. and have derived the correct classical equations, Photodynamics, in relativity that apply to lightspeed particles. I have shown that all particles have mass, and can be properly understood if the correct equations are used, Einstein's for particles that can't attain the speed of light, and mine for particles that can and have to. The reason I asked the above question is to get you to consider mathematically and physically, why these two sets of equations are needed to determine the dynamics of all particles. I am not asking that the Einstein equations be abandoned for all particles, just the ones that travel at the speed of light. Atom smashers are good reasons to retain the Einstein equations and employ them properly to particle that can't attain the speed of light.
I agree with you that experimentally, neutrinos do not travel faster than the speed of light. That "discovery" has been disproved. Also, the fact that neutrinos have been measured to travel at the speed of light within experimental error with ever better precision as the experiments are improved in time, and that no slow neutrinos have ever been seen indicates that they travel at the speed of light (see my response to Abdul above).
Using standard relativity, that the physics community uses, that means to me that massive neutrinos undergo neutrino oscillation in violation of Einstein's E = mc^2 because neutrino oscillation requires neutrinos to have mass, a fact known since 1987. Do you agree with me that massive neutrinos travel at the speed of light in violation of Einstein's E = mc^2?
That is the simplest way that I can pose that question without introducing new concepts.
Looking forward to your reply and continued discussions on this matter.
“…massive neutrinos undergo neutrino oscillation in violation of Einstein's E = mc^2 because neutrino oscillation requires neutrinos to have mass, a fact known since 1987. Do you agree with me that massive neutrinos travel at the speed of light in violation of Einstein's E = mc^2?….”
Again, neutrinos have rest masses always, including at possible “oscillations”, and, again, since they are T-particles, i.e. are created by the directed along the “coordinate time” [cτ] axis momentums, they, because of all axes in the 4D sub-spacetime of Matter’s absolute [5]4D Euclidian spacetime, are orthogonal, when they move in the space after some impact wich is directed in the 3D space momentums, the momentum along the coordinate time axis remains be the same as was at the creation.
Correspondingly they always have non-zero cτ –axis component in their 4D velocities; and so, because of all/every particles, including neutrinos, move in the 4D sub-spacetime only with 4D speeds of light, their speed in the 3D space, by the Pythagoras theorem, is always lesser then c.
In the supernova 1987 event indeed seems the neutrino flash reached Earth earlier than the light flash, however that was quite natural – for the light to go out from the bang remnants it was necessary come time; when, since for neutrinos the remnants were practically transparent, neutrinos left the bang region practically at the bang; when, again, the neutrinos’ rest masses are very small, and so even having energy a few Kev a neutrino moves practicaly with the speed of light.
Again, if you indeed want to understand what is correct– in contrast to the SR – mechanics, see the SS posts and papers that are linked in the posts; about real SR problems see SS posts in, for example, https://www.researchgate.net/post/Is_there_a_solid_counter-argument_against_Dingles_old_objection_to_Relativity_Theory#view=5cd2f2873d48b75a601d3058
I appreciate discussing physics with you very much, and don't want to give the impression of being negative to your input. I have read your paper above and considered the ideas behind it. At this time, I am trying to focus the attention of the reader on a very simple question, which has a very clear and important answer with extensive implications. The purpose of all my questions on these posts has been directed to this objective, and I try mightily to stick to the point because of vanishing available time. But I appreciate the direction you are investigating in your paper. I don't see that it is necessary to resolve the present issue, whose solution is susceptible to and would have more widespread acceptance through use of a simpler and more traditional approach familiar to everyone.
Let me just say again that there is nothing inherently wrong with special relativity . Unfortunately, its understanding and meaning has been corrupted by a 100 year old error which has been incorporated into its understanding and application, has never been discovered until now, and continues to cause numerous problems in physics, one of which is the neutrino oscillation problem highlighted by the 2015 Nobel Prize in physics. My objective is to have the readers understand what this error is, how easy it is to get rid of it, how its elimination resolves a number of stubborn problems, and how its elimination preserves special relativity without need of modification until one begins to consider its application to quantized dimensions. But we must first all agree to get rid of the insidious 100 year old error that has crept in and refuses to be dislodged (because it is attached to Einstein's name?) Will you help me?
The error of course is the one I identified and have been discussing all along in my posts and in my paper on Photodynamics, which has finally been published in the peer reviewed, open access Journal of Physical Mathematics, 2018 Vol 9. (See my project: Theoretical Physics). It is a very simple error, needing only entry level college algebra and calculus to identify and eliminate (unless one wants to close his eyes for other reasons). With its elimination, it is clear that the Einstein equations do not apply to any particle that travels at the speed of light, but is still absolutely necessary to explain the motion of atomic particles. The discovery of the laws of Photodynamics in the paper then restore special relativity to the un-corrupted version it was meant to be, capable of explaining correctly the dynamics of all particles, those of type 1 which can and must travel at the speed of light, and those of type 2 which cannot.
With this clarification of purpose, I will ask you and all readers to focus on one question, and to answer it with a yes or no, giving a reason for your choice if you want to:
Does the elimination of the identified error in the present understanding of the theory of relativity allow lightspeed neutrinos to participate in neutrino oscillation, and resolve the neutrino oscillation problem identified in the 2015 Nobel Prize?