NOTE: The members of the EDITORIAL BOARD are aware that many readers may not have studied physics or astronomy. They might be under the false impression that an article like the one that follows is going to be incomprehensible.
Nothing could be farther from the truth. Yes, those who have studied Maxwell’s Equations and Einstein’s theories will find his essay a kind of cakewalk. No doubt, eggheads will have issues with some assertions. Submit objections in comments — your head does not have to look like an egg.
WE, THE EDITORS wish to reassure readers — especially those who have yet to study math and science — that they have intelligence and imagination enuf to understand Billy Lee’s basic arguments.
We know Billy Lee. We work with him every day. He talks and tweets a lot but what does he really know?
Billy Lee likes to share notions with folks who can read. He claims it does no harm. For those who get “high” on science, Billy Lee included videos to make rabbit-hole hopping fun. Don’t be afraid to watch some.
THE EDITORIAL BOARD
UPDATE BY THE EDITORIAL BOARD: May 15, 2019; Victor T. Toth, the Hungarian software developer, author, and Quora guru of quantum physics wrote, “a photon has no rest mass, but it carries plenty of energy, and it has momentum. Its stress-energy-momentum tensor is certainly not zero. So it can be a source of gravity, it has inertia, and it responds to gravity. […] relativity theory predicts … twice the deflection angle for a photon in a gravitational field than the deflection of a Newtonian particle.”
Almost a century of experiments plus hundreds of upvotes on Quora by physicists seem to validate Victor’s argument.
The photon is known to be the only massless, free-moving particle in the Standard Model of physics. Other massless particles are the gluon, the graviton, and of course the Higgs, discovered in 2012 at CERN. Europeans plan to build a Higgs factory to learn more about them. Gluons mediate the strong force. They don’t propagate through empty space. No one has yet observed even a single graviton. Higgs give fermions like quarks their mass.
Photons have an electric and magnetic structure. They are electromagnetic pulses of energy that emerge from atoms when electrons drop from a higher energy state to a lower one. When electrons shed energy, a pulse of electromagnetic radiation is emitted — a photon of light.
Photons of light can be emitted from atoms at different frequencies — colors when wavelengths fall within the narrow range that humans see. These frequencies depend on the energy of electrons, which exist in many differently configured shells (or orbitals) within both atoms and molecules.
Wavelengths of light felt but not seen are called infrared; other invisible frequencies fall into broad categories such as radio waves, microwaves, x-rays, gamma rays and so on — all require instruments to detect.
Electromagnetic radiation is the medium through which humans observe and interact with everything knowable in the universe. Humans live inside an electromagnetic bubble that they are struggling to understand.
One thing most physicists understand is that a disturbing 95% of the energy and mass of the universe comes from a source no one can see. Physicists observe the effects of invisible (dark) matter and invisible (dark) energy by measuring the unusual dynamics of galaxies and by cataloging the physical organization and expansion of the universe itself.
These measurements make no sense unless folks assume that a lot of gravitationally interacting stuff is out there which no one has yet observationally confirmed. The missing mass is not debris or dark stars. The most exaggerated conjectures about how much mass and energy is scattered among the stars won’t come anywhere near enough to explain forces that make galaxies behave strangely.
Dark matter and energy don’t seem to be electromagnetic. Dark matter, if it exists, interacts with the mass of two-trillion galaxies and seems to refract their emitted light. Humans are blind to all of it.
Scientists postulate matter they call WIMPS, MACHOS, axions, and erebons. Each has a few properties necessary to make the universe work as observed, but none have all the required properties except perhaps erebons, if Roger Penrose’s Conformal Cyclic Cosmology (CCC) is someday verified.
Other candidates for dark matter? — why not sterile neutrinos, GIMPs, and SIMPs?
Space-saturating foam of micro-sized black holes is another idea some have proposed. The problem is that theorists believe tiny black holes might be too stable to radiate electromagnetic waves or gravity waves.
Micro-holes lie in a sort of crevice of invisibility — unobservable by LIGO and LISA style gravity-wave sensors, yet too massive for current and future particle-colliders like CERN to create.
Because micro-holes don’t radiate light at any frequency, light telescopes will never find them. No imagined interaction of micro-holes is able to generate gravity-waves with enough disruptive power in spacetime to be detected. The nature of physics seems to suggest that no technology can be developed to confirm or deny the black-hole foam idea.
Perhaps the same dilemma faces dark matter detection. We know it exists, but physics says we can never find it. It will always lie just outside our reach doing its work in an invisible universe no one will ever see.
Worse, not one of the proposed forms of “dark” matter has ever been observed or identified. It is likely that no experiment currently scheduled will detect dark matter, which many physicists believe is “out there” and makes maybe four parts out of five of all the matter in the universe.
It’s an incredible paradox for conscious humans to live in a universe where they are blind to almost every important thing that is happening within and around them.
Humanoids are like fish which spend their lives swimming in streams buried deep inside caves. Spelunkers like me know that certain species of cave fish have no eyes. They lack all ability to see their world — as do we, it seems. As intelligent as people are, they don’t yet build sensors capable of confirming their notions about what the universe might actually be at large scales or small.
Oh well… someday maybe new discoveries will make our predicament evaporate away. The universe will reveal itself to humans, as we knew it would. Our dream to fully understand reality will come true.
Some day.
Scientists have sensible mathematics to show that if electromagnetic particles are massless, they must travel at an upper limit, called “c“. Over decades, folks decided that this constant is the speed of a photon in a vacuum; they decided that photons have no internal rest mass and travel in vacuum at a speed limit — the speed of light.
The truth might be more mysterious. No one knows what the upper limit of “c” is, because no one knows with certainty that space is truly empty or that massless particles exist.
When physicists say that certain particles are massless, they sometimes mean that they don’t interact with the Higgs Field, which is known to give mass to fermions, like quarks. They don’t mean they don’t have energy, specifically kinetic energy, which is a form of inertial mass, right? They also aren’t saying photons don’t interact gravitationally. They do, in a special way described by the geodesics of spacetime in Einstein’s General Relativity.
More on this idea later.
British physicist Brian Cox wrote in his book Why Does E = mc2 ? that the question about whether photons have rest mass is not yet settled.
It’s true that more than a few reasonable people seem to believe that photons traveling freely in the vacuum of space are massless. If they truly are then the permittivity constant “ε” in Maxwell’s equation can be established for electro-magnetic particles (like photons).
The formula below is used to calculate the speed of a massless electromagnetic particle; it is thought to be a maximum speed.
For now, ignore the μ term. It is the permeability (resistance) of vacuum to infusion by a magnetic field, which is determined by experiment. It is sometimes called the magnetic constant.
Epsilon (ε} is the permittivity (resistance) of vacuum to an electric field. It is sometimes called the electric constant.
”c” is the so-called ”universal speed limit.” It is called the lightspeed constant.
These three numbers — μ, ε, and c — help to define the maximum velocity of an electromagnetic wave, which most people believe is the archetypal photon (of light). They assume that the photon packet travels at the maximum allowable speed in a vacuum.
A problem with this view is that no one has proved that space is free; or that space has no weight; or that photons have no rest mass; or that undiscovered particles formed from forces other than electricity and magnetism don’t exist. A few scientists have said that there might be no such things as free space or massless photons. It is also possible that space presents less resistance to other phenomenon yet to be discovered.
The idea that ”dark” matter and energy must exist to make the universe behave the way it does is compelling to many physicists. If true, it is possible — though light travels nearly 300 million meters-per-second — it is not traveling at the maximum speed of a generic, massless particle. The electric constant (ε) might need to be adjusted.
A decrease in the permittivity (resistance) of space (ε) — made obvious by inclusion of vast number of photons in the cosmic microwave background — drives ”ε” to be smaller and ”c” to be larger, right?
New particles, dark and as yet undiscovered, might do the same. The consequences could be significant.
Determining the upper speed of a massless particle requires a form of circular reasoning that is currently based on the measurement of the velocity of photons in a vacuum, which is called the speed of light.
The measured velocity of light in a vacuum is now an established constant of nature with a fixed value that doesn’t change regardless of the frame of reference. Modern labs have measured both the frequencies and wavelengths of various colors of light; multiplying the two numbers together always yields the same result — the speed of light.
Knowing the speed of light permits physicists to establish a value for ε by working backwards in the wave equation to solve for the electric permittivity of space. The value of “ε” falls easily from Maxwell’s Equations to a precision of 12 places.
It can’t be any other way. But is it the right way?
Here’s the problem: Physicists have measured mass in photons during experiments at the linear accelerator lab at Stanford University, SLAC.
In superconductors, photon mass has been measured to be as high as 1.2 eV.
Photon mass has been observed in wave guides and in plasmas.
Fact is, photons have inertial mass, which is a measure of their energy as calculated from their wavelengths or frequencies. In relativity theory, energy and mass are measured in the same units, electron-volts, because in the theory, mass and energy are equivalent.
Cosmologist, Raphael Bousso, believes that empty space has weight, which is a measure of the cosmological constant, which is a measure of dark energy.
Space seems to be saturated like a sponge with something that gives it energy or force or weight if you will. The weight of empty space determines the size of the universe and some of its fundamental laws. Universes beyond our own with different weights of space can be larger or smaller and obey different rules.
Most physicists agree that photons become massive when they travel through transparent materials like glass, where they slow down by as much as 40%.
The problem is that these observations conflict with both the Heisenberg and the Schrodinger view of quantum mechanics, which is the most tested and confirmed model physicists have. Modern ideas seem to work best when photon mass is placed on the energy side of the mass-energy column. Otherwise, the presence of internal mass suggests that photons can be restrained to a defined size, which drives their momentums to infinity.
The truth is that it is not possible to prove that photons are massless. The stress-energy-momentum tensor in Einstein’s equation of General Relativity implies that photons can be both the source and the object of gravity. I’m referring to this tensor as “mass” and leaving it there for others to dispute. A rabbit hole for courageous readers to explore is the concept of pseudotensor, which this essay will avoid.
It is also not true that a photon can never be at rest either. Lab techs do unusual things with photons during experiments with lasers and superconductors — including slowing photons down and even stopping some (with supercooled helium-4). Right?
Another problem is the electromagnetic nature of light. The electric part of a light-wave carries enough energy to move an electron up and down. The magnetic part carries the same energy but its motion creates a force that pushes electrons outward in the same direction as the light. It’s why light-sails work in space. Oscillating magnetic fields push light forward. Otherwise, light might stand in one place and simply jiggle. But is light-speed the best magnetic fields can do?
Electromagnetism could be irrelevant in the search for an upper speed limit “c“, because “c” might prove to be the result of an unknown set of particles with properties outside the current boundaries of the Standard Model.
Massless particles, — undiscovered ones anyway — might not be electromagnetic. Humans might be biologically unfit to detect them; unable to measure their properties.
For those who might be rolling their eyes, remember that physicists claim that 95% of the mass and energy required to make the universe behave the way it does is missing. They call the missing stuff “dark” because they can’t find it. Excuse me should anyone catch me rolling my eyes.
Some theorists have speculated that “dark photons” might exist to help fill in the gaps. The popular TV show How the Universe Works actually repeated the idea in an episode of its latest series. The writers were probably referring to axions, which some physicists propose are similar to photons except that they have mass and are slower moving.
Photons are bosons. They are force carriers for electrons, correct?
Maybe folks should try to accept the notion that nothing in physics prevents bosons like photons from having mass or from taking on mass when they whiz over and through atoms and molecules (in glass and water, for example) where some physicists conjecture, they stimulate the release of polaritons in their wake. Jiggling electrons that lack the energy to jump states emit polaritons, which seem to add enough equivalent mass to photons to slow them down. Think of polaritons as light-matter wavelets.
Massive, gravitationally interacting photons are not required to be “dark.” If photons are the dark matter, axions are unnecessary to solve certain problems both in cosmology and the Standard Model. No experiment will find them.
I mentioned that three other particles are presumed to be massless: the gluon, the graviton, and the Higgs boson.
To review, the gluon is not easily observed except in particle colliders where it lives briefly before decaying into other particles; it is confined among the protons and neutrons in the nuclei of atoms. The graviton, on the other hand, has never been observed. The Higgs boson was discovered in 2012. CERN plans to build a Higgs factory someday to explore its properties.
The only particle available to physicists right now that enables them to establish the permittivity of space and compute the velocity of massless particles is the photon.
That’s it.
If the photon has internal mass, i.e., rest mass, everything changes.
Let’s hop into a rabbit hole for a moment and go back a step: What if massless, non-electromagnetic particles mediate entanglement, for example? Wherever paired electrons are found, entanglement rules, right?
Everyone knows that entanglement violates laws of logic and physics. No one can make sense of it.
What if massless non-electromagnetic particles entangle the electromagnetic particles of the subatomic world? If they travel a thousand or ten-thousand times the speed of light, they will present an illusion over short planetary scales that entanglement is instantaneous. No instrument or lab will detect the difference.
What are the consequences if massless non-electromagnetic particles travel at a billion times the speed of light? Maxwell’s equations won’t apply to particles like these.
Because it seems that speeds of subatomic particles like photons are able to increase as their masses approach zero, it is possible that “c” could be orders of magnitude faster than the speed of a photon — that is, the speed of light — if it turns out that photons harbor tiny but significant rest masses.
I’m not advocating this notion. Let’s crawl out of the rabbit hole. I’m suggesting only that such a state of affairs is possible, because the assumption that photons at rest are massless — that internal mass of photons is always zero — though reasonable and desirable to justify models, is not yet settled according to some physicists.
And there is, of course, the phenomenon of entanglement which no one can explain.
Here’s speculation that should blow the mind of any thinking person: Could photons, if shown to have internal mass, be the stuff that make the galaxies move in the non-intuitive ways they do?
Yes, some physicists argue that the upper limit on the internal (rest mass) of a photon must be less than 10-52 kilograms, which is about 5.6E-17 eV for folks who think that way. (Multiply mass by the speed of light twice to make the conversion and divide by 1.60218E-19 Joules per eV.)
5.6E-17 eV doesn’t seem like much mass at all until folks realize that the minimum number of photons in the universe might be as high as 1090. This number is ten billion times the number of atoms in the universe. It means that the internal mass contribution from photons alone could easily exceed 1038 kilograms if the upper limit proposed by some is used to perform the calculation.
Do the math, anyone who doesn’t believe it.
Guess what?
Prepare for a letdown.
Based on the conjectured eVs, the mass of all material in the visible universe is in the neighborhood of 1053 kilograms. The video below will help the reader understand how this value and others are calculated. The mass of the visible universe turns out to be 1,000 trillion times more than the conjectured internal mass of all photons.
Think about it.
Is it enough mass to account for the galaxy anomalies seen by astrophysicists? To any reasonable mind the answer is obviously, no. But this conclusion is not the end of the story.
Those who study astronomy know that the outer stars in galaxies seem to move at roughly the same speed as the inner. Yet the galaxies aren’t flying apart.
By way of contrast, the planets in solar systems like ours travel slower the farther away they orbit from their sun. If Neptune orbited as fast as Earth, it would fly away into deep space.
A recalibration to account for the internal mass of photons of light (which seems to always be discounted) does not at first blush offer the gravitational heft that astrophysicists require to make everything on galactic scales fall into place.
The cosmic background radiation — which is nothing more than photons that decoupled close to the beginning of time — saturates the universe like vinegar in a sponge, right? It is distributed evenly across all space for as far as human-built instruments can see.
The CMB makes an annoying hum in radio telescopes no matter their focus or where they point. Photons with tiny internal masses or no mass at all will have no influence on the understanding by astrophysicists of how the universe behaves.
Neutrinos, which seem to oscillate between three (or perhaps four) as yet undetermined massive states, might at times take on values below the actual mass-value of photons — if photons turn out to be more massive than most believe. The laws of physics require that neutrinos less massive than massive photons, should they exist, must travel superluminally (faster than light). Agreed?
Several “discredited” observations have reported faster-than-light neutrinos, including the unexpected outcome of the infamous OPERA experiment, which inspectors eventually blamed on a loose fiber-optic cable that was ever-so-slightly longer than it should have been.
OK. It seems reasonable. Who can argue?
Scientists who believe that superluminal neutrinos actually exist don’t speak up, perhaps out of fear for their careers. They probably couldn’t get their opinions published anyway, right?
Crackpot ideas that later prove valid is how science sometimes works. It’s how science has become the mess that it is — a chaos of observations that can’t make sense out of 95% of what is going on all around; a plethora of experimental results that don’t quite match the work of theorists.
The super-brilliant people who paint the mathematical structures of ultimate reality rely on physicists to smear their masterworks with the muds of perturbation, renormalization, and a half dozen other incomprehensible substrates to get the few phenomenon folks think they understand to look right and make sense. Theory and experiment don’t seem to match-up as well as some folks think they should more times than not.
A minor recalibration based on the acceptance of photons as quantum objects with tiny, almost unmeasurable masses will not change ideas about the nature of the universe and what is possible, because the upper-bound on photon masses might be undervalued — perhaps by a factor of billions.
Theorists like Nima Arkani-Hamed work on abstract geometries called amplituhedrons to salvage notions of massless particles while simplifying calculations of scattering probabilities in quantum mechanics. It seems to me like hopeless adventures doomed to fail. But in fairness so did Columbus’s exploration for new worlds.
To be a serious candidate for dark matter, a typical microwave photon should have an average mass of nearly .05 eV (electron volts), which is about 9 x 10-38 kilograms. If multiplied by the number of photons ( 1090 ), the photon masses add almost miraculously to become 85% of the theoretical mass of the universe.
(1E90)*(9E-38) = 9E52. (9E52) / .85 = 1E53 kg.
It’s the same number conjectured by dark-matter advocates.
To qualify for dark matter means that a typical or average photon must have close to one ten-millionth of the mass of an electron.
Only then does everything fall into place like it should.
Pull out the calculator, anyone who doesn’t believe it.
Einstein, in his famous 1905 paper on special relativity, showed that mass is equivalent to the energy of an object divided twice by a constant, which is “c” squared, right?
Later, he added a second term to the internal energy of a particle which is its inertial energy, pc2 . Simplified, this term equals hf for a massless photon. The total energy of any object is the square root of the sum of its internal energy and its inertial energy.
If Einstein is taken at his word, then the inertial mass of a photon is a function of its characteristic frequency — i.e. the inertial mass of a photon is equal to
where “h” is the Planck constant and “c” is the speed of light. The internal mass, should any exist, can be discounted.
An argument can be made from Einstein’s equations that the mass of a photon might be 
times larger. A factor of 1.414… won’t change the argument. It strengthens the point but is, in the end, not important enough to include in an article that is already overly long. Curious readers can review the reasoning in my essay General & Special Relativity.
If the average photon has an inertial mass of .05 eV, it requires that — all else being equal — the combined photon energy in a non-expanding universe would lie in the range of infrared light, a frequency in this case of 12E12 Hz, which is sometimes referred to as far-infrared.
(Set equivalent-mass equal to .05 eV (8.9E-38 kilograms) and solve for frequency.) The frequency approaches the lower energy microwave part of the light spectrum.
Note: For perspective, one eV is the energy (or mass equivalent) of a near-infrared photon of frequency 242E12 Hz, which approaches from below the higher-energy visible-light part of the light spectrum.
The mass equivalence of the inertial energy of 1E90 infrared photons is sufficient to hold the universe together to prevent runaway expansion caused by repulsion due to the gravity constant Λ in Einstein’s equation for General Relativity.
Do the math.
I know what some people might be thinking: Didn’t the 29 May 1919 solar eclipse, which enabled observers to confirm Einstein’s theory of General Relativity, demonstrate that photons lack internal mass? Didn’t Eddington’s experiment prove wrong Newton’s idea that photons, which he called corpuscles, were massive objects?
Maybe. Maybe not. Maybe internal mass isn’t necessary. There is enough energy in the inertial term of Einstein’s equation to yield the required mass.
Unlike massive particles where internal energy far outweighs inertial energy, for photons, inertial energy is dominant. Even if science admits to a small amount of internal mass in photons, it is their inertial energy that dominates.
I found a good mathematical argument for light mass on Quora by Kyle Lochlann, an academic in relativity theory. Here is the link:
Be sure to read comments to his answer — especially those who find math incomprehensible, which might be nearly everyone who reads my blog.
After all, Newton’s theory of gravity predicted that the light from stars would deflect near the Sun at only half what Eddington’s experiment clearly showed. Eddington’s eclipse proved Einstein’s theory — the geodesics of spacetime bend in the presence of massive objects like stars.
Many concluded that photons followed the geodesics of spacetime, because photons lacked mass equivalence of any kind. Newton erred about pretty much everything involving gravity and light, some said.
But their conclusion can’t be right, can it? Doesn’t their conclusion ignore what the math of Einstein’s formulas actually says?
Won’t it make more sense to say that the geodesics of spacetime constrain and overwhelm whatever internal and inertial mass photons might possess? Doesn’t it make more sense to convert the frequency-related inertial energy of photons to mass to better explain their behavior near objects like the Sun?
Evidence exists that light-mass is a thing and that it matters. Einstein included a mass-equivalence term for light in his tensors for general relativity. Frank Wilczek, MIT Nobel laureate, is famous for insisting that the mass of anything at all is its energy content. The energy of light is in its frequency, its momentum, which is a measure of its mass.
It’s true that light does not seem to interact with the Higgs field. Nevertheless, the energy of light seems to interact gravitationally with ordinary matter. The interaction is not measurable when photon numbers are small. When photon numbers are huge, perhaps it is.
A single photon in the presence of the Sun has no chance. When 10E90 photons saturate a space that is almost entirely devoid of matter, photons can shape a universe — especially when their number is 10 billion times the number of atoms.
It seems possible, at least to me.
According to data gathered by the NASA WMAP satellite, ordinary matter in the observable universe amounts to a little more than 1/4 of a neutron per cubic meter of space. It amounts to 253.33E6 electron-volts of mass. Everything else WMAP observed was “cold dark matter” and “dark energy”.
How many .05 eV photons does it take to flood a cubic meter of space with enough mass-equivalence to reduce the mass-energy of 1/4 of a neutron to 15% of the total? How many photons are required to sum to 85% of the energy WMAP attributed to “cold dark matter”? It turns out that the number is 34 billion photons per cubic meter.
The question is: how many photons are there?
The observable universe has an estimated volume in the neighborhood of 1E80 cubic meters, right? Yes, it might be as much as 4 times that number.
The lower-bound number of photons in the observable universe is 1E90. It might be ten times more.
It turns out that the number photons per cubic meter in the universe must be somewhere close to 25 billion. 25 is pretty darn close to 34. Since all the numbers are estimates with large margins of error, it’s possible that everything will fall into place as it should if and when the statistics of the universe are ever known with precision.
Could photons of light might be the “cold” dark matter everyone is searching for?
A single neutron has no chance when it is bathed in 136 billion .05 eV photons, which surround and envelop it on all sides from every direction. It makes a kind of quantum scale Custer’s Last Stand for random neutrons, right?
When scientists look at the universe today, they see an accelerating expansion. They see in the cosmic background radiation photons that have slipped from infrared into longer, less energetic microwave wavelengths which no longer have enough mass-equivalence to hold the universe together.
As light stretches into longer and longer wavelengths through interaction mechanisms such as Compton scattering and other processes (like the push of “dark energy” or the less popular gravitational tug of parallel universes), light frequencies and energies diminish.
Eventually, when the total of all light falls below an average frequency of 12E12, the equivalent mass of the 1E90 primordial photons loses its grip; it becomes unable to hold the universe together.
Near the beginning of time when photons were orders-of-magnitude higher in frequency than now, their stronger gravitationally-equivalent-masses pulled together the structures astronomers study today, like stars and galaxies.
But now scientists seem to be witnessing a runaway expansion of the universe. Light has stretched and dimmed into the microwave and radio-wave frequencies where its mass-equivalence is unable to hold together the universe as it once was.
Because we can’t detect it, isn’t it possible that dark energy and dark matter don’t exist? That is to say, the idea that dark matter and energy are necessary to account for observations is no more than a conjecture made necessary by a misbehaving universe of unusual galaxies. But direct observational evidence for dark matter and energy is the part of the conjecture that is missing. No one has ever seen any.
What astronomers are observing instead is faraway galaxies that existed billions of years ago when the mass-equivalent energy of photons was greater than it is now.
The intact universe of galaxies seen in the night sky today, which is photographed with high-resolution space-borne telescopes, is not up to date in any sense at all, except that it is the view of an ancient past that goes back almost to the beginning of time depending on how deep into space anyone looks.
Everyone who cares about astronomy knows it’s true.
To qualify as a candidate for dark matter means that a photon must have close to one ten-millionth of the mass of an electron. It seems like a reasonable ratio, right?
In the Standard Model, only neutrinos are less massive than electrons. No one knows what the mass of each of the three “flavors” of neutrinos is, but when added they are less than 0.12 eV — about 2.4 times the equivalent-mass of infrared photons and about one four-millionth of the mass of electrons. It seems possible to me that the mass of at least one of the flavors of neutrinos will be less than the conjectured equivalent-mass of an infrared photon packet.
Neutrons and protons are, by contrast, 2,000 times “heavier” than electrons.
I am asking working physicists to reexamine estimates that claim the mass of a photon can be no more than trillions of times less than the mass of an electron.
The claim can be found at the back of articles in science journals as well as in blogs across the internet. For me, the idea seems ridiculous on its face. The energy-equivalent mass of photons varies with frequency, but only the lowest energy radio wave photons can hope to approach the low equivalent-mass estimated in the latest publications.
Scientists might want to revisit the mass of a photon and the methodology of its measurement. The stakes are high, and science doesn’t have many options. Hope — like the energy of ancient photons — is fading.
Science would be served best if scientists started from scratch to reexamine every assumption and lab procedure. The search for dark matter has become an expensive and compulsive quest that seems futile, at least to me. Several costly experiments have reached disappointing dead ends, which are reviewed in the “VICE on HBO” video located near the start of this essay.
What if photons of light really are the dark matter, which is hiding in plain sight waiting to be discovered by anyone who dares to look at the problem with fresh eyes?
What if the delay between the observations of the CMB (cosmic microwave background) and the structure of the universe is a natural disconnect in time and space that misleads folks to believe that mass must be “out there”, when it has in fact long since dissipated?
From another perhaps opposite perspective, what if photons are instead stimulating emissions from virtual particles as they travel at fantastic speeds through the vastness of space? What if these emissions add mass to photons sufficient to bring them to the “dark matter” threshold, as they do in materials like glass?
Such a state of affairs would imply that not all photons travel the same speed in the so-called vacuum of “empty” space. It is a heretical idea, for sure — a can of worms, perhaps to some, but hey! — you can catch a lot of fish with a can of worms.
A photon is a packet of electromagnetic oscillations built-up from many frequencies. Superposition of these frequencies adds to give a photon its characteristic frequency from which its equivalent mass can be calculated. Right?
Use imagination to think of the many ways a higher “speed limit” that is mandated by the existence of massive photons might work to stimulate the interest of a space-traveling civilization to explore the universe, which ordinary folks begin to understand is more accessible, more reachable than anyone thought possible.
Consider the number of inexplicable phenomena that would make sense if particles thought to have zero internal mass don’t really exist, and photons, gluons, gravitons, and Higgs bosons aren’t the only ones.
Recalibration might save a lot of time and effort in the search for the putative missing energy and mass of the universe.
Should “dark” particles exist whose internal mass is less than that of photons, they will likely move at superluminal speeds that make them difficult to track. To influence stars, their number would have to dwarf photons. Such an idea strains credulity.
A counterproposal by Roger Penrose speculates that dark matter particles might have the mass of the eye of a flea; he calls them “erebons.” These particles are electromagnetically invisible, but their huge masses relative to other particles in the Standard Model make them gravitationally compelling.
Erebons decay; evidence for their decay should be showing up in data collected by LIGO detectors.
So far persuasive evidence for erebons has not been found.
For scientists and explorers, the access-barrier to a universe shaped and configured by massive photons will most certainly shrink — perhaps thousands to millions of times.
The stars and galaxies that people believed were unreachable might finally fall within our grasp.
Or — perhaps less optimistically and more cynically — the mass-equivalent energy of 1E90 photons might by now be so severely degraded that nothing can save a universe that has already come undone and flown away into an abyss that humans will never see.
The radiation-evidence from a catastrophe of disintegrating galaxies that has already occurred won’t reach Earth-bound viewers for perhaps billions of years.
Should humans survive, our progeny — many millions or billions of years from now — may “see” in the vastness of space a cold and diminished radio-wave radiation that hums in a soul-less vacuum devoid of galaxies and visible light. Microwave light will by then be nothing more than a higher-pitched, prehistoric memory.
Roger Penrose says that the fluid dynamics of an exhausted universe devoid of matter will become indistinguishable from the singularity that gave its start. A new universe will ignite from the massless, radiation-ashes of the old.
The idea is called Conformal Cyclic Cosmology — or CCC.
Human-nature forces us to want to know more; most folks want to search for and find the answers to the questions that will determine the fate of all life on Earth and in the vast stretches of spacetime that remain beyond our reach.
Is the universe within our grasp, or has it already disintegrated?
We search for truth to set ourselves free.
Billy Lee
. Energy and massless particles like photons of light are equivalent based on their frequencies; Einstein included this feature in his less familiar but expanded equation 
. These equivalencies are clues that might enable someone to properly explain how the universe works on large scales and small. 
