Gravity is often considered a pseudo-force that is associated with the geometric curvature of spacetime. The electromagnetic force is considered a gauge force transferred by virtual photon messenger particles. Gauge theories are field theories that have the property of gauge invariance. These two mechanisms appear to be completely different.
However, this is a discussion question, and I will attempt to prove these two forces are closely related. The referenced preprint below presents a model of the universe based entirely on waves. An electron and other fermions are modeled as rotating soliton waves that exist in the sonic medium of oscillating spacetime. This model predicts that the electron’s electrical charge and its gravitational curvature are both the result of an electron’s wave properties interacting with the medium of oscillating spacetime.
When these forces are viewed as wave effects, predictions are made that these two forces should merge at the wave limit. The maximum charge that a wave-based particle can produce is Planck charge (qp) and the maximum mass a wave-based particle can produce is Planck mass (mp). The prediction is that the electrostatic force between two Planck charges (Fqp) equals the gravitational force magnitude between two Planck masses (FGp). At arbitrary separation distance r, the force magnitude is Fqp= FGp = ħc/r2. This merging of these forces at the Planck limit can be turned into equations that show that the forces are also closely related even at the level of two electrons or between any other particles.
What do you think? Are these forces fundamentally different? Is gravity even a force?
Preprint Oscillating Spacetime: The Foundation of the Universe
No. Gravity, also, follows from a gauge symmetry, the group is that of diffeomorphisms. And the fundamental difference between the group of diffeomorphisms and the groups that describe the other gauge interactions, is that the group of diffeomorphisms is noncompact, while the groups that describe tge electromagnetic, weak and strong interactions are compact. It is this difference that leads to the inevitability of spscetime singularities and is the reason why the description of the quantum theory that works for the other interactions inevitably can't work for gravity. It isn't known how to describe a quantum theory, whose classical limit is a gauge theory, with noncompact gauge group.
Stam Nicolis Thank you for the information about the difference between the two groups of gauge interactions (compact and non-compact).
What do you think about my main point that when the gravitational and electromagnetic forces are reduced to the level of fundamental particles, a previously unrecognized connection emerges between these forces? At the limit of maximum wave amplitude (Planck mass and Planck charge), these force magnitudes are both equal to ħc/r2. The equality at this limit means that even at the level of two electrons, there is a mathematical connection between the electron's gravitational and electrostatic forces. Several variations of this mathematical connection are described in the referenced article.
John A. Macken Your ``main point'', unfortunately, is incorrect. The reason is that classical gravity, simply, doesn't make sense, when quantum effects become relevant.
Stam Nicolis You say, "classical gravity, simply, doesn't make sense, when quantum effects become relevant." I think you must be referring to the fact that gravity is insignificant compared to the other three forces on the quantum mechanical scale. However, a single electron produces gravity. The electrostatic force between two electrons (Fqe) is 4.2x1042 times larger than the gravitational force between two electrons (FGe). This number is so large, gravity appears insignificant, but it can be expressed mathematically. The conventional way of calculating this is using electron's mass (me) and charge e is:
Fqe/FGe = e2/Gme24πεo = 4.2×1042
However, my calculation using the electron's wave properties (Planck length Lp, Compton radius rc and fine structure constant α) is:
Fqe/FGe = α(rc/Lp)2 = 4.2×1042
The wave properties generate the same answer using the underlying physics of gravity and electrostatic charge. This is new! However, you will not be able to understand this if you do not look at the paper. This paper has received over 1,000 reads on ResearchGate in less than 2 months. It has been reviewed by a journal and is currently undergoing minor revisions before publication.
Preprint Oscillating Spacetime: The Foundation of the Universe
No, I'm not referring to whether it's ``insignificant''; I'm saying that classical gravity doesn't make sense when quantum effects are relevant. The mathemaical expressions are wrong (for electromagneism, there are known quantum corrections) and meaningless (for gravity, where the corrections that are required aren't known) when quantum effects become relevant.
This question is intriguing, but my belief is that inertia is impossible without gravitational interaction.
Only in our limited view these interactions are distinct. Physics did not find yet a unification at interaction level. Nevertheless we all know quite well, at least at quasi-local level, that they are unified by conservation laws.. basically Energy can only be a sufficient unifying principle...
It seems to be generally accepted that the medium is non-linear, i.e. it has a smallest oscillating period and it will reflect a (very tiny: ~8∙10⁻³⁴) part of any EM-wave's energy per wave's period. Especially the existence of reflection shows that there is a natural base for the gravitational effect based on EM.
Obviously, we cannot fit this easily into quantum thinking so far...
Andreas Schwarz Stefano Quattrini
This question arose from an insight into my effort to develop a wave-based model of an electron. I discovered that the wave-based electron model I developed also produced an electron's gravity and electrostatic forces. I was able to see a connection between these forces that is not obtainable from the macroscopic "top-down" approach used by Einstein and others. The details are in the technical paper attached below. However, I can give an example that illustrates the importance of looking at gravity from the point of view of fundamental particles.
The wave-based model of fundamental particles implies that single particles have theoretical limits. For example, Planck charge is the theoretical maximum charge and Planck mass is the theoretical maximum mass/energy. The wave-based model predicted that the electrostatic force between two hypothetical particles with Planck charge would equal the gravitational force between two particles with Planck mass. At separation distance r, both forces equal to ħc/r2. This is explained and proven correct in the paper below. There are also more cases where the gravitational and electrostatic forces are closely related at the level of fundamental particles. This connection should not exist if the electrostatic force is conveyed by the exchange of virtual photons and gravity is spacetime curvature.
Preprint Oscillating Spacetime: The Foundation of the Universe