# Why is Dark Matter not simply explained by QED?

My understanding is that Dark Matter needs to exist to explain the mass of the universe -- that is, all the observable matter in galaxies are not sufficient to explain the gravitational behavior -- and hence there must be additional matter which is not observable, which is what is called Dark Matter.

After re-reading QED, im at a loss as to why Dark Matter is simply not explained through Quantum Dynamics -- for example, a simple loop like

gives rise to electrons that has mass and anything with mass will exert a gravitational force, and since gravity travels in waves the gravitational force will continue to exist somewhere in space even after the mass of the electron has ceased to exist in the loop.

So, now as a observer at a particular junction of time and space, I will not be able to see any matter because it doesn't exist at that time (or space) only the effect, the gravity caused by the matter, is there

.. but that sounds to me exactly like the description of Dark Matter, and we just need to have the loops happening sufficiently frequent to account for all the missing matter.

So to sum up, why is dark matter not explained through QED?

• It's simply a matter of accounting. All of the mass due to QFT corrections is already accounted for in the baryonic mass. It doesn't matter how you slice it and dice it in the math of the field theory. At the end of the day an electron has 511keV of rest mass, protons and neutrons have approx. 1GeV each and that's it. – CuriousOne Jun 2 '16 at 3:57

In QED these loop diagrams are renormalizations of the photon mass term. However, the photon mass is zero, as enforced by the gauge symmetry. So the contributions of all such loop diagrams to all orders must add up to zero. As a result these diagrams would not produce a mass that can contribute to dark matter.

Moreover, the electrons that exist in these loops are severely off-shell. They are virtual particles. So their invariant mass would not be the electron mass.

These diagrams do not depict any actual physical process. The photon (in vacuum) does not physically separate into electron and positron and these do not curve their path to annihilate again into the original photon. Decay of photon (in vacuum) into electron-positron pair would violate conservation laws.

Such diagrams are only a mathematical tool: they represent terms in a perturbation series (see for example this post). The internal lines of electron and positron should definitely not be interpreted as particles moving along the sketched trajectory, because they cannot be associated with any meaningful particle states. They just represent interaction between photon and fermion field.

Even if such process would be happening, it would not affect the gravitational field. The source of gravity is the stress-energy tensor, so even light can curve space-time. Decay of particles does not change the amount of energy and momentum in the given region (due to conservation), so the gravity is unaffected.

"Another explanation for how space acquires energy comes from the quantum theory of matter. In this theory, "empty space" is actually full of temporary ("virtual") particles that continually form and then disappear. But when physicists tried to calculate how much energy this would give empty space, the answer came out wrong - wrong by a lot. The number came out $10^{120}$ times too big. That's a 1 with 120 zeros after it. It's hard to get an answer that bad. So the mystery continues."

• The question was about dark matter. The copied answer is about dark energy. – Brandon Enright Nov 16 '16 at 6:03
• Internal lines are refering to dark energy, since the 'particles' are virtual. Its true that the OP used the word matter, but hes process is not related to matter. So in this sense the answer is good. – lalala Sep 12 '17 at 7:53
• No. This answer is not good. Dark energy and dark matter are name for different phenomena and offering an explanation for one to a question about the other is simply wrong. – dmckee Sep 13 '17 at 19:31

## protected by Qmechanic♦Sep 14 '17 at 8:38

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