Why do we think the graviton is not the photon?

Question

Why couldn't the photon be the graviton? How sure are we that the photon could not fill the role of gravitons?

Answer 1

Briefly, because the photon is a spin 1 boson and the graviton is spin 2 boson, so they can not be the same particle. If the photon was the particle responsible for gravitation, then the classical limit of the theory would not be general relativity or anything like it. And yet we have a great deal of evidence that GR works in practice, extremely well, as a classical theory of gravity.

Answer 2

The photon does not have the properties required of a graviton, but the question in the form given by @my2cts does have an answer

How could gravity and electromagnetism be the same thing?

When I was still at school I was introduced to special relativity in a public lecture by Hermann Bondi at York university. Bondi made use of the $k$-calculus, as used in his book Relativity and Common Sense, and placed great emphasis on the fact that Minkowski geometry is determined by the process of photon exchange, described explicitly in the radar method, but which is also implicit in quantum electrodynamics, and is the process underlying electromagnetism, and with it the physical structure of everything we observe in our immediate environment (including the structure of rulers).

At the end of the lecture questions were taken and someone asked "What would be the implication if the reflection of light in radar were not instantaneous?". Bondi replied "Ah, that is the start of general relativity". At the time, I took it seriously, but I have never found a trace of this idea in the literature. I have been forced to conclude that Bondi was just giving an off-the-cuff answer. Nonetheless I still thought it was correct. Later, when I had studied quantum electrodynamics and learned that instantaneous reflection is actually not possible (it would require a 4-node vertex, and failure to exclude it from the integrations is the source of divergence problems in qed) I managed to complete the argument to show that gravity is actually a perturbation to geometry required by a rigorous treatment of quantum electrodynamics. I have given a treatment Mathematical Implications of Relationism and in my books (see profile).