# Photons exerting force

Since gravity affects photons, and forces always work in pairs.

Does this mean that photons have a resultant force.? And would we be able to harness this resultant force to move objects using light?

Does this mean that photons have a resultant force.? And would we be able to harness this resultant force to move objects using light?

Photons are elementary particles in the standard model of particle physics . They have zero mass, energy=$$h*ν$$, and spin $$1$$.

They are described by a four vector of special relativity, i.e., they have energy and momentum, and the length of this four vector, the invariant mass, is zero.

The length of this 4-vector is the rest energy of the particle. The invariance is associated with the fact that the rest mass is the same in any inertial frame of reference.

As photons have mass zero, they have no rest system.

As they have momentum, when they interact according to the rules of particle interactions, they transfer a dp/dt, i.e. a force, to the particle they interact with.

Here is a video giving an explanation of radiation pressure .

• @BruceGreetham I read the question differently, not asking for an explanation of gravity which was given as an example, but the question "And would we be able to harness this resultant force to move objects using light?" – anna v Jan 8 '19 at 17:15
• @annav in the video (or anything to do with E=Mc2) why is it assumed the momentum (that accounts for the energy) comes from c or the linear motion of the photon? Maybe c plays a very small part but most of the energy comes from the speed of the photon’s oscillation. For example a 10lb mass moving 10 mph has a certain energy but if the 10lb mass was a five foot long dumbbell shape and spinning at million rpms, the energy would be much higher. – Bill Alsept Jan 8 '19 at 20:43
• @BillAlsept because the photon spins in the complex plane of its wavefunction, which is inaccessible to measurement except as Ψ*Ψ. The only variables measurable for a photon are energy and projection of spin on direction of motion.these oscillations have no impact on the real number world – anna v Jan 9 '19 at 4:33
• – anna v Jan 9 '19 at 4:43
• @annav I am suggesting photon’s have two energy components. A linear motion which is calculated in E=Mc2 and an oscillating or angular energy directly proportionate to frequency E=hv. The second being the major source of the photons energy. – Bill Alsept Jan 9 '19 at 4:59

Does this mean that photons have a resultant force?

Yes it does. If we send a light ray past a massive object and the path of the light ray is changed that means the momentum of the light is changed, and to conserve momentum the momentum of the massive object would also change. It would look like this:

This shows a star bending the light downwards, and the star will move upwards due to the reaction force. But:

And would we be able to harness this resultant force to move objects using light?

The momentum of light is tiny and for any mass heavy enough to significantly bend a light beam the deflection of the mass would be completely undetectable. So no, we can't use gravitational deflection of light to move objects.

For completeness we should note that you can use light to move objects and this is what optical tweezers do. This technique also exploits the momentum change of the light, but it is unrelated to gravitational deflection of light.