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this post was submitted on 05 Nov 2023
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If there's anyone who can, please let me know if the similarities between these two formulas imply a relationship between gravity and electrical attraction or hint at a unified theory, or if it's just a coincidence or a consequence of something else.
Electromagnetism and gravity are both mediated by massless bosons; photons and gravitons respectively. This is why both forces follow the inverse square law.
I don't think there's any evidence for gravitons yet, and gravity hasn't been quantized. I'd say it's this similarity that's the best argument of quantum gravity, not the other way around.
Fair. The masslessness of the bosons that should mediate gravity, along with them being spin-2, can however be deduced from the properties of gravitational waves.
We know that gravity is a wave that travels at the speed of light, this has been experimentally measured many times. If it is also quantized (a very reasonable ~~symptom~~ hypothesis since everything else that we've ever seen is) then by definition there are particles that carry gravity.
If gravity is continuous then we would end up with something like the ultraviolet catastrophe but for gravity.
Hmm, I hadn't considered an "ultragravity catastrophe". I wonder if this could accout for dark energy or the supposed inflatons? Probably not, the catastrophe suggests infinite energy, not just lots of energy, eh?
The ultraviolet catastrophe was averted due to the discreet nature of electrons though, and I don't recall gravity behaving as a blackbody radiator anyway. Would this come into effect at horizons?
Sorry, I think I came off as too confident in my previous comment. I'm quite sure about my first paragraph but the rest is just speculation from an amateur.
If I would risk speculating even further though, there's some similarity in the sense that infinities indicate a problem. In the ultraviolet catastrophe the infinity arises from the energy of arbitrarily short EM wavelengths. With gravity it arises in the density of black holes. It seems unreasonable that it would actually be infinite, and it's possible that quantization of gravity plays a part in preventing that from happening.