Is it true that, according to Einstein, gravity is not a force, so the graviton should not exist?

No, no, and no.

First of all, if you asked Einstein, he would probably have told you not to think such nonsense. I don’t think that at any point in his life, he actually seriously thought that gravity was not a force. For starters, if you grabbed a brick and felt its weight in your hands, you would know that you are feeling a force, and Einstein, ultimately, was a physicist’s physicist, one who would never deny things we can directly observe, or subject it to clever wordplay.

Of course, arguably, if I take the geometric interpretation of the theory of gravitation seriously, I find that gravity truly is a pseudoforce, like the centrifugal force: it arises because we are measuring it in a noninertial (i.e., accelerating) reference frame. That does not make it any less a force, mind you, it’s just a way of explaining that force.

Could other theories be subject to such a geometric interpretation? Certainly. In fact, it is routinely done. But gravity has a special property: it is universal. Which means that the same geometry applies to all objects in a gravitational field. This is not the case for electromagnetism; negatively charged electrons “sense” the electromagnetic field very differently from positively charged (and heavier) protons or electrically neutral neutrons. So these particles all experience different geometries.

In any case, the existence of a geometric interpretation does not mean that the theory cannot be quantized or that it does not have excitation quanta. From a quantum field theory perspective, gravity (represented by the metric tensor of spacetime in the geometric interpretation) is just a spin-2 tensor field that couples universally and minimally to all fields, including itself. Like other fields, this field can, in principle, be Fourier-transformed, its Fourier coefficients promoted to operators, leading to quantized field excitations, aka. gravitons.

In practice, this approach fails because unlike other theories, like electromagnetism, gravity leads to infinities that are “unrenormalizable”, cannot be tamed using standard mathematical tools. So we don’t know how to quantize gravity. But it is pretty clear that if we ever find a quantum theory of gravity, in the perturbative limit of weak fields, low energies, its excitations will manifest themselves in the form of gravitons.

By: Viktor T. Toth (Physicist )

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