Ok, so my idea is as follow: what if the photon has mass, and these massive photons can form classical superpositions with one another in the recesses of intergalactic space and after a certain point these superpositions break leading to the expansion of the space in between galaxies. From the current ΛCDM model of cosmology I can't see how the cosmological constant by itself can lead to the accelerating expansion of the universe. Other have also suggested that the idea of photons having mass may explain dark energy (as in real scientists), I was just hoping to get a discussion going on here.
Also I know that current theories state that giving the photon mass would break gauge invariance, but a man called Stueckelberg managed to renormalise QED with a mass term for the photon, so I think it may well be possible.
Here's another theory I came up with. I heard Neil deGrasse Tyson talking about how the Earth bulges at the Southern Hemisphere, that it's an oblate spheroid, and it got me thinking that perhaps this bulge is due to gravitational influences not from the rest of the galaxy, but from the rest of the universe. This would imply not only that the universe as a centre of mass but also that it is enormous, way beyond our current understanding. Could it be possible to calculate what sort of mass would be needed to produce this bulge over those sorts of distances?
It represents the distance of closest approach for another atom, which I thought would make sense as a boundary between the two probability densities. Perhaps I'm wrong, could you suggest an atomic radius I should use instead? It would make sense that it's beyond this point that an electron could be responsible for gravity due to the fact that, in my theory at least, an electron beyond this point could appear within the van Der Waals radius of another atom and exert a force of attraction over the protons in that atom.
What are those errors in the first post? Can you list them?
Also, it's not a set of beliefs, that isn't the distinguishing factor for a theory, it's replacing spacetime curvature with a cloud of electrons to explain dark matter and gravity simultaneously. I thought that was one of it's strengths, the ability to explain a wide range of phenomena with a single idea.
again, thank you for your patience so far. I know what the term Van Der Waals radius means, and that it's beyond this point that it makes sense that an electron could be responsible for gravity rather than behind that point where it would just be at some point around the nucleus, that's why I kept using it. As for the term ψ(r)² it's just what I saw in a textbook to denote the electron volume probability density, that's where the confusion stems from, if |ψ(r)|² = ρ1+ρ2 is a better fit then I'm sorry for the mistake, but it doesn't change anything about my theory.
As for the current theory being wrong, Einstein's field equations do not predict the rotational curves of galaxies and dark matter has to be invoked to explain those rotational curves. It's a failing of general relativity. You could view this theory as a quantum correction to GR which does account for dark matter, that's the point I was trying to make.
Also, on the philosophy of science point, I do know that it's falsifiability that is the mark of a scientific theory and not the notion of proof. Even though some believe Popper is too simplistic the principle of demarcation is still regarded as the gold standard for a scientific theory, and I've given a few ways of disproving mine. I just didn't want my theory to be attacked on those grounds.
Thanks for the response. The theory relies on a new interpretation of the electron's wavefunction. I can't post links so I'll try and explain it the best I can here:
Meaning the electron density is a composite of both a primary and secondary electron density with the secondary density being responsible for gravity. According to QM the probability of finding an electron beyond the Van Der Waals radius is much lower than 1:4.17 x 10^42 but this is because of the use of exponential functions in QM to make the calculations easier, and this has just been adopted as orthodoxy. Using this ratio instead doesn't, I believe, cause disagreement with observations of electron densities and has the power to describe a wide range of other phenomena as well. What I meant by a 'heuristic' is just something that makes something easier. Incidentally it's actually easier to just divide the number of electrons in a hydrogen atom (1) by 4.17 x 10^42 to yield the bare probability of finding the electron at some point beyond the VdW radius, this is roughly equal to 2.5 x 10^-43. So it's still really, really small, and you have a resolution of the wave-particle duality (for electrons at least); it would be a point particle that changes position so often that it forms what looks like a wave. Should have mentioned that.
NB: I forgot all the stuff about length construction and time dilation. As objects approach the speed of light they become saturated with an increasingly large number of secondary density electrons, surrounding the moving parts of objects with a net negative charge, forcing the primary density electrons of the atoms in those moving parts to slow down also. Since time just measures motion the slowing down of moving objects, including things like RNA on DNA strands, and clocks, caused by the secondary electron density, time slows down also by definition. Length contraction is for a similar reason, as objects approach the speed of light the electrostatic force surrounding the object forces it to occupy an increasingly small space, or just to be torn apart, I'm not exactly sure which, not even sure if that can be proven, but there we go.
Ok, all this sounds a bit grandiose but I think I've come up with a decent theory of dark matter that also explains gravity, and I'd love someone to prove me wrong (or at least give compelling reasons why this is incorrect). I'll try to be as clear and concise as possible.
The first thing to get out of the way is that the exponential functions governing the wave functions of electrons are just heuristics. There is a probability of 1:4.17 x 10^42 that the electron will appear at at least some distance beyond the Van Der Waals radius of the atom to which it belongs. So this is a tiny probability that the electron volume probability density of an atom extends somewhere beyond the Van Der Waals radius, i.e. an electron can pop-up somewhere beyond the radius of the atom for a very brief amount of time before it interacts with a photon and changes position again. This amount of time I estimated to be around 2.5 x 10^-43s, this isn't strictly important, what's more important is that for a body composed of atomic matter, such as a planet, there is some large number of very ephemeral electrons surrounding it which is analogous to the gravitational field. I call this cloud of electrons the secondary electron density. When another object y approaches the secondary electron density of an object x the secondary density electrons from x pop-up within the first electron shell, or within the primary electron density of the atoms composing object y and exert a very mild force of attraction over the protons in the nucleus of object y. En masse this effect produces a net force of attraction between two objects which is proportional to their mass.
I'll quickly deal with a potential objection. Neutron beams curve due to a polarisation effect caused by the secondary electron density over the up quark in the neutron, given that the up quark is 2/3 charged and the down quarks are -1/3 charged the net force of attraction is greater than the force of repulsion. I admit this is one of the many weaknesses of the theory, but please bear with me.
How does this explain dark matter? given that electrons repel each other, and that objects composed of atomic matter are surrounded by secondary density electrons, there should be a resistance generated between the secondary electron densities of rotating bodies that is greater than non-rotating bodies. This is the hardest part to explain, but the idea came from thinking about the perihelion precession of Mercury, and the observation that the moon has a similar precession in its orbit. Neither the moon nor Mercury rotate. Einstein's explanation of this was that the sun's orbital wobble causes ripples in the fabric of spacetime that causes Mercury to shift on it's orbit. I'm not sure if this can also be applied to the moon since the earth/moon system exhibits much less of a mass disparity than does the sun/mercury system. In my theory it's primarily the gravity of the other planets and secondarily the gravity of the rest of the galaxy that pulls on Mercury and causes precession in it's orbit. Because it doesn't rotate it isn't as 'locked-in' to it's orbit around the sun as the other planets. Extend this effect to the rest of the galaxy and you find that the majority of bodies within the galaxy rotate and are, crucially, nested within the secondary electron density of the supermassive black hole at the centre. One way to test this experimentally would be to examine the rotational speed of the SMBH and correlate it to the rotational curve of the galaxy, if it's the same it implies there's some connection between the rotational speed of SMBH and that of the galaxy (unless it's somehow producing WIMP's, in line with the ΛCDM model) as a whole. To conclude, my theory states that the fact of the rotation of stars within a galaxy coupled with the fact that those stars are surrounded by a secondary electron density produces 'electrical resistance (best term I could come up with)' that is greater than that of non-rotating bodies, and this keeps them locked-into fairly orbits of a fairly regular velocity within the secondary density of the supermassive black hole. On a side note, the faster rotational speeds of stars closer to the secondary density of the black hole are caused by the fact (within this theory), that the primary electron density of the black hole has been pushed beyond the event horizon due to the enormous density of the black hole due to as yet unknown facts about black hole physics.
I'll now try to explain the rest of the predictions of general relativity in the context of my model. The redshift is explained in part by the fact that the average number of photons per cubic metre is dwarfed by the number of secondary density electrons; the probability of a single photon interacting with a secondary density electron in the time it takes for a photon to cross a cubic metre is equal to 1. I calculated 8.2 x 10^30 electrons per cubic metre, and 4.2 x 10^14 photons per cubic metre at conservative estimates (later I'll show how to calculate the secondary electron density of the Earth). The greater the number of photons per cubic metre, i.e. the lower the probability that they've already been scooped up by an electron prior to entering the sample cubic metre, i.e. for a number of photons from a star say moving towards the point of observation the electrons will tend to absorb the photons of a lower energy due to the, on average, higher number of electrons that the light has to move through; therefore, lower energy photons are emitted by the secondary density electrons, therefore the light from the approaching object is blushifted. Redshift is the opposite of this. Also, if you take the number of electrons per cubic metre and divide this by the number of photons per cubic metre you get the residual number of photons (of all wavelengths) emitted by the secondary density electrons. This is the vacuum energy in my model. I calculated it to be approximately 0.003eV/c^2/m^3, again at a conservative estimate; I thought this was a nice figure for the cosmological constant, but naturally might not agree with experiment. This could also potentially be applied to black holes to explain the information escape paradox in lieu of quantum fluctuations in space-time. Another prediction of GR that this has to explain is gravitational lensing; so, very simply, a proportion of photons hit all the right electrons in the right sequence (actually different photons, since they're absorbed by electrons and a different photon is emitted, but for sake of argument it's easier to imagine that it's the same photon) such that it follows a jagged pattern between electrons which, on the scales of general relativity looks curved. This is why the effect is only detectable by optical telescopes for visible light around very massive objects, such as galaxies when they create Einstein rings. More precise measures of gravitational lensing have recently been performed around the sun, and to explain why it appears[/I] that all the photons have been lensed bear in mind that the ones that go off in a different direction aren't detected by the instruments. Also, just to head off another possible objection, the reason why the speed of light remains a constant is because the exchange of photons between secondary density electrons is instantaneous. Think about photons moving through the air, the speed of light is slightly slower, because they're being absorbed by primary density electrons of the atoms in the air, and other photons emitted, again in a sort of jagged pattern (slowing them down), which on classical scales looks like a straight line.
Also, to explain the emissions of gravitational waves by merging black holes and binary pullers, you have to imagine the gravitational waves as emissions of pure energy i.e. photons and to also conjecture that photons have mass and can interact with one another, causing the interference in the laser at the LIGO detector. Also, the secondary electron density is a good reason as to why gravitational waves tend to diminish as they propagate through space. The fact that 3 solar masses of material was emitted from the merging binary black hole system as pure energy (photons) is in the abstract of the LIGO paper, so, as a side-note, I'm not sure exactly where the idea of gravitational waves being ripples in spacetime came from. Also, the idea of the photon having mass doesn't break gauge invariance, according to Stueckelberg, and has the potential to explain dark energy (not my idea).
I think that more or less wraps things up. Sorry it's so long, I was just trying to be as concise as possible. I'll also quickly discuss ways of experimentally probing the secondary electron density and how to calculate it.
To calculate the secondary electron density: take the average atomic number of the object being studied, multiply it by the number of atoms to give an estimate of the number of electrons and divide this number by the ratio between gravity and the force of electrostatic repulsion (4.17 x 10^42) and you get the number of electron surrounding the planet over one unit of the time differential (2.5 x 10^-43s). To find out the number of secondary electrons per second, you take the time 1s, divided by the time differential (the average amount of time the electron stays in a given position 2.5 x 10^-43s) and multiply by the number of electrons over 4.17 x 10^42.
Experimental tests: Prove that electron beams are affected by gravity. Prove that neutrinos are affected by gravity. Perform experiments with negatively-charged ions to see if they fall in a gravitational field.
I think that's about it, now find the holes everyone! Thanks for reading.