# For a wavelength of the size of the universe, do virtual and real photons differ?

Some theories of quantum gravity assume that very low temperatures of 10^-30 K arise - roughly corresponding to the temperature of a black hole with the size of the universe.

Such a low temperature would yield photons whose wavelength is roughly the size of the universe. Is it possible to distinguish, for such "huge" (i.e., large-wavelength) photons, real from virtual photons?

A related question: can such "huge", i.e., cosmic-wavelength photons be real (i.e. on-shell) at all? Or are such huge photons always virtual (i.e. off-shell)? One could argue that for such cosmic-wavelength photons, the uncertainty relation does not allow to achieve on-shell state.

• All photons are the same size. Each photons energy depends on it's frequency. As the photon propagates at the speed of light it also oscillates at a certain frequency. The distance the photon travels during one oscillation is called the wavelength. Feb 4, 2020 at 19:09
• Above, "huge" was meant to describe the wavelength. The size of photons themselves is a tricky subject that is best avoided - and in any case plays no role here. Feb 7, 2020 at 4:27

Such a low temperature would yield photons whose wavelength is roughly the size of the universe. Is it possible to distinguish, for such huge photons, real from virtual photons?

Lets clear up the terms.

Take a real photon. What does the wave length represent? It comes from taking the $$E=hν$$ and assuming the frequency to be the frequency of the imaginary number $$Ψ$$ wavefunction whose $$Ψ^*Ψ$$ , is equal to the probability to find a photon at an (x,y,z) as the photon footprints seen in this single photon at a time experiment, see image..

So for a real photon such a large wavelength means that the probability to find it at an (x,y,z) is very very small. I cannot imagine the experiment and how long it should wait to get a single hit ( it will of course depend on the flux etc).

What is a virtual photon?

A virtual photon is not measurable as it is the exchange of photon number quantum numbers under an integral, it is off mass shell and only the integration over virtual photons indicates their existence.

Thus there is no meaning in comparing virtual photons of very large wavelength, they may always exist under an integral, and a real photon of energy $$E=hν$$ . Virtual ones are mathematical constructs , while real ones carry energy and momentum in a four vector, and have invariant mass zero.

The real photons are not huge, as I explained above, they are always point particles . It is just that their energy is so small that the probability of finding one is practically zero.

• Of course photons are point particles. Sorry, I disagree that the two cases cannot be compared: The universe could be either full of virtual photons or full of real photons. The global effects are measurably different: the equation of state is different in the two cases. The question here is (1) Is there also a way to locally distinguish the two cases? (2) Are real photons of this huge size possible at all? Can such huge photons be on shell? Feb 4, 2020 at 17:58
• virtual photons do not have an independent existence. They need at least two real four vector incoming particles and real four vector out going particles ( energy momentum four vectors) and they are infinite because they are mathematical functions in a continuum between limits of integration) Feb 4, 2020 at 18:02
• You can't just pick out a single energy for virtual particles either, once you write down an interaction, the integral comes along with it as anna v mentions, this integral is performed (over all frequencies available to these photons) and there is no more virtual particle to talk about. Feb 4, 2020 at 18:09
• Two magnets repel with a tangible force without real photons. Feb 4, 2020 at 18:20
• @safesphere Sure, they exchange virtual photons, but again they are between two real magnets. One can write numerous Feynman diagrams full of virtual photons between the two magnet molecules and atoms. Feb 4, 2020 at 18:40