Photons have zero mass so we know them to produce zero gravity, no?

Photons have zero rest mass, but energy itself has a gravitational effect too. It's even theoretically possible to create a black hole entirely out of light https://en.m.wikipedia.org/wiki/Kugelblitz_(astrophysics)

As I understand it (not a physicist), according to GR the Einstein field equations equate the curvature of spacetime to the stress-energy tensor, of which mass is just one component. Photons, having energy, should produce a gravitational field.

We can actually measure the mass of photons.

If you shine light on an object, the light pushes on the object and the object is accelerated. If the object absorbs the light, there's a certain amount of pressure, and if the object reflects the light, there's even more pressure.

This has practical applications. Optical tweezers are made of light's force acting on small objects. "Optical tweezers are used in biology and medicine (for example to grab and hold a single bacterium or cell like a sperm cell, blood cell or DNA), nanoengineering and nanochemistry (to study and build materials from single molecules), quantum optics and quantum optomechanics (to study the interaction of single particles with light)" (Wikipedia).

Conservation of momentum means the light has mass by definition, and this photon mass can be measured by multiplying the mass and acceleration of the object.

Not only does this mean photons have gravity in the theory of GR, because all mass/energy does, it means they attract each other in a vacuum. In theory, you can make photons orbit each other due to their gravity.

Radiation pressure is due to momentum, not mass. I have no idea where you got that idea, since the same sort of sources that teach you about these concepts are very emphatic about photons being massless.

Here is one of the 3-5 interesting facts I remember from my modern physics class: Two photons going the same direction have no mass, but two photons in different directions do have mass. Unfortunately I don't remember the math well enough to explain it. Maybe this means your right about being able to put photons in orbit around each other.

> Two photons going the same direction have no mass, but two photons in different directions do have mass.

This is not limited to photons, although the first part, "no mass" is due to the rest mass of photons being zero.

Two objects of any kind whatsoever have more mass going in different directions than going in the same direction.

> Radiation pressure is due to momentum, not mass. I have no idea where you got that idea, since the same sort of sources that teach you about these concepts are very emphatic about photons being massless.

You are right, I was sloppy with language, and accept my downvote honourably :-)

I was talking about what is sometimes called relativistic mass or effective mass (which are considered obsolete terminology), in order to address the GP (brabel)'s belief that photons having zero mass will have zero gravity.

> since the same sort of sources that teach you about these concepts are very emphatic about photons being massless

It depends how old you are; I learned these concepts in the 80s :-)

From https://physics.stackexchange.com/a/133380:

> There's no controversy about whether mass increases or not, there's controversy about what you call mass.

Something that may help readers:

From https://www.desy.de/user/projects/Physics/Relativity/SR/ligh...:

> Does light have mass? The short answer is "no", but it is a qualified "no"

> Part of this discussion is only concerned with semantics. It might be thought that it would be better to regard the mass of the photons to be their (nonzero) relativistic mass, as opposed to their (zero) invariant mass. We could then consistently talk about the light having mass independently of whether or not it is contained. If relativistic mass is used for all objects, then mass is conserved and the mass of an object is the sum of the masses of its parts. However, modern usage defines mass as the invariant mass of an object mainly because the invariant mass is more useful when doing any kind of calculation. In this case mass is not conserved and the mass of an object is not the sum of the masses of its parts. Thus, the mass of a box of light is more than the mass of the box and the sum of the masses of the photons (the latter being zero). Relativistic mass is equivalent to energy, which is why relativistic mass is not a commonly used term nowadays.

Energy gravitates. Photons have energy, therefore photons gravitate. Photons only have zero /rest mass/, not zero total mass.

Photos by definition don't have a rest mass because they are never at rest. They must always travel at the speed of light, which means they don't experience time, so rest does not even make sense for a photon.

That makes sense in English, however "rest mess" is also a technical and mathematical term, and in that terminology it has the value zero for photons.

There is the theoretical Schwarzschild Kugelblitz [1]

[1] https://en.wikipedia.org/wiki/Kugelblitz_(astrophysics)