An idea I’ve been toying with as an amateur physicist is to take the equal signs to mean “is” instead of “in proportion to”.
For example, take the famous equation:
E = mc^2
The common interpretation is that mass can be created from energy with the proportionality constant of c^2. That constant can be set to “1” using natural units. This just leaves:
E = m
But GR also have a similar equation basically saying that curvature = mass.
Soo… by my interpretation:
Mass, energy and spacetime curvature are the same thing! They’re not “proportional” to each other and one doesn’t “generate” the other like an electric field by an electron. Instead, everything is literally made up entirely of space time curvature. That’s what matter and energy are.
This is why all forms of matter have masses — the only other option is empty space with a flat curvature, but that’s just the absence of matter. If everything else is curvature, then they must cause long-range distortions — which we call gravity.
You can't just set c = 1 as a pure number and conclude that E = m, the units won't match.
Natural units are very useful when doing math, but they don't reduce constants down to plain numbers, they still retain their units. Once you factor this in the rest of your argument falls apart.
That's a valid criticism, but the point is that you can have two types of curvature that you assign different "units" to when measured, but they're still both curvature.
As a hand-wavey example, one could claim that energy in the form of bosons is just a "wiggle"[1] of the spacetime fabric, and that matter in the form of fermions are topological defects or knots.
That way they're different enough that you'd want to use different units to represent them, but at their core, they're both distortions in spacetime that must inherently cause a distortion in spacetime at a distance (GR).
It also explains how they're inter-convertible. E.g.: energetic gamma rays can be converted into electron-positron pairs. If they're both "made of distortions" then it's like a very strong wave creating a pair of vortices spinning in opposite directions. You can't count the waves (it's smooth and continuous), but you can count the vortices.
[1]
For the wiggle, imagine taking a huge sheet of cloth laid out flat over a smooth surface. If you tried to put a wave into the middle, the edges of the cloth would be pulled in. Contrast this with the typical view of fields as "vectors on top of a base (flat) spacetime", much like a mathematical function graph.
This doesn't appear to fit with other quantities like say, electric charge, or lepton number, or whatever. Like, there's more to matter than "how much is there here".
On the contrary, I got the idea from Kaluza Klein theory, which unifies general relativity and electrodynamics by converting the electric charge into spacetime curvature.
Roughly, my concept is conserved quantities are topological defects, which is why they seem to have a neat “algebra” and integral quantities.[1] Conversely, mass comes in fixed but non-integer quantities because the total curvature of some complicated knot doesn’t have a simple algebraic expression.
[1] Makimg the fractions disappear is easy. Just multiply by the denominator. E.g.: we say the electron has a charge of -1 because we discovered it before the quarks historically. If the quarks were discovered first, we would assign it a charge of +3.
For example, take the famous equation:
The common interpretation is that mass can be created from energy with the proportionality constant of c^2. That constant can be set to “1” using natural units. This just leaves: But GR also have a similar equation basically saying that curvature = mass.Soo… by my interpretation:
Mass, energy and spacetime curvature are the same thing! They’re not “proportional” to each other and one doesn’t “generate” the other like an electric field by an electron. Instead, everything is literally made up entirely of space time curvature. That’s what matter and energy are.
This is why all forms of matter have masses — the only other option is empty space with a flat curvature, but that’s just the absence of matter. If everything else is curvature, then they must cause long-range distortions — which we call gravity.