Why are real photons so much less efficient in carrying momentum than virtual photons? When two like magnetic poles are brought together, there's a repulsive force felt that's inversely proportional to their separation. In the standard model, the answer to "What is transmitting this repulsive force through empty space between the two magnets?" is described as virtual photons.
If I want to measure 15 newtons of force between two north poles of adjacent magnets, I can position my magnets accordingly and measure the force directly.  I'll never see photons involved because of their virtual nature, but the force they're delivering is very real, and easy to measure.
If I want to produce the same amount of force on my magnet by directly bombarding it with real photons, however, it would take an enormous amount of energy.
It seems strange to think that the same particles responsible for producing a force strong enough to keep two massive objects apart, are barely capable of moving a light sail in microgravity.
Why are real photons so much less efficient in carrying momentum than virtual photons?
I have to believe virtual particles are the topic for a sizeable portion of questions on SE; if this is a duplicate please feel free to close, but from my review I haven't seen this addressed directly.
 A: Within the usual handwavy accounts of virtual particles, the answer is "simple": Virtual particles aren't required to obey on-shell mass-energy relations (in this case $E=pc$), so there can be virtual particles with large momenta but very small energies.
However and as usual, I would advise not to think in terms of virtual particles at all - they are artifacts of drawing perturbation theory as Feynman diagrams and you cannot even say non-perturbatively what they are supposed to be. The reason "virtual photons" act so differently from actual photons is that the term "virtual photon" doesn't describe a quantum state that would resemble a free, real photon at all, it describes a certain computation in an interacting quantum field theory. There isn't really any reason except for the name to expect this to have anything to do with the behaviour of actual photons.
See this answer of mine for a lengthier discussion on why it is misleading to think of "virtual particles" as particles or as actual intermediate states at all.
A: The electric fields of charges of the same sign behave like elastic bodies (where there is a body, there cannot be a second one). If two charges of the same name are approached, they recede in the free state, as elastic bodies do.
Opposite charges, however, attract each other and it is observable that they emit EM radiation. In order to loosen a connection again - i.e. to remove an electron from the atom, photons are sufficient (as sole and at the same time necessary condition) to restore the fields around the opposite charges and to consider the particles isolated from each other again.
To get a capacitor with separated charges, you have to separate the electrons from the rest atom. This can be done by a solar cell. Photons hit electrons, these absorb the photons, are accelerated, penetrate an isolation layer and must take the way back over a consumer. So for example our capacitor.
A magnet, on the other hand, is only a mediator. If you move a magnet near an electrical conductor, the magnet is not consumed. Its magnetic field causes a Lorentz force, i.e. the displacement of charges. Thereby, the movement of the magnet is opposed by a resistance, but its magnetic field remains unchanged.
What enables us to turn the concept of virtual photons into a science of interaction between fields is the modeling of the structure of these fields.  Because why fields with the same sign behave like elastic bodies, there is currently no model-like idea for it.
Virtual photons are an embarrassment, which will dissolve as soon as the scientific interest in the investigation of the inner structure of fields leads to new model conceptions.
