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I began wondering about this when working through this question: is there anything analogous to spacetime or matter? Both spacetime (note: most of what I know of about the concept of spacetime comes from special and general Relativity) and mass are fundamental things in this universe. That is, our most fundamental physical laws contains measurements of position, time, and mass; they cannot be derived from anything. We know that space and time are inherently linked thanks to special and general relativity, but I can't think of anything else like spacetime. Is there even any other quantity that can be separated into dimensions?

Mass is similar in that we can't really get to a lower level of how much of something there is (volume is mostly empty space, not stuff, so it can vary when the amount of stuff remains constant). The thing that sets it apart from spacetime, though, is that space and time make up a coordinate system, in which everything is measured with respect to a defined origin (zero). Mass, however, is an absolute scale, so it seems to me that it is something fundamentally different.

Is there anything else like spacetime? Or mass? When thinking of fundamental quantities, I went to the base SI units. Besides position, mass, and time, they measure current (simplified to electric charge/time, and we've already discussed time, so let's just say electric charge here), thermodynamic temperature, luminous intensity, and number of moles (which is related to mass by a factor that's unique to each element, so we'll leave that as well and just use mass as the only measure for the amount of a substance).

So, electric charge, thermodynamic temperature, and luminous intensity seem to be the only logical choices for analogues. These are all manifested forms of energy (the quantifiable ability to cause change), and they are all absolute in scale. How does energy fit into all of this? (My instinct is to say it resembles mass, but then what is the "matter" of energy?)

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Hausdorf
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You seem to be interested in the concept of dualities. Dualities are incredibly informative in Physics in that every time we've come across one, it's led to unification of the two dual entities. You've already stated the most common one of spacetime. This was of course unified by relativity. You mentioned the Mass-Energy duality. This arises right from relativity as well. SR founds that the speed of light is a universal constant: a feature taken to be intrinsic of the universe. It also found the relation between mass and energy, the Mass-Energy Equivalence, which we all know to be $ E=mc^2 $.

Another example is that of Electricity and Magnetism. We had thought they were two different phenomena, but it turns out per the work of Maxwell, that they are really two sides of the same field, related by Maxwell's Equations. One of which is:

$$ \nabla \times E = -\frac{\partial B}{\partial t}$$

Where $E$ is the Electric Field and $B$ is the Magnetic Field.

Those are just a few off the top a my head. You can find a list of the prevalent ones here.

Doryan Miller
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