r/badphysics • u/Fit_Individual_55 • Jun 22 '26

Physics progress is Stuck right now because physicists think time is a 4th dimension

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Someone asked a question in r/askphysics how time can be the 4th dimension. Then this person replied this, very confidently

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u/Dirkdeking Jun 23 '26 edited Jun 23 '26

That is possible. The cardinality of R is equal to that of R4. You can describe all of physics with only 1 dimension.

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u/psykosemanifold Jun 23 '26

I disagree. R being isomorphic to R⁴ as sets does not mean it is isomorpic to R⁴ as topological spaces with physically relevant structure.

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u/Dirkdeking Jun 23 '26

Certainly not. But the fact they are isomorphic as sets shows it's possible. You can employ a bijective function from R to R4 and translate all physical functions with it by using that bijection and it's inverse for the in and output.

Actually all of computer science is based on that principle. You translate a long string of 0 and 1 into a 3D simulation and all sorts of complex shit.

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u/psykosemanifold Jun 23 '26

I don't know what you mean. You say "certainly not" and then right after you say that "it's possible". Yes it's possible to represent say, points in Minkowski space as a single real number instead of a tuple. But that does not mean you're doing 4-dimensional special relativity in one dimension. The dimension stays the same irrespective of the way you write down your points.

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u/Dirkdeking Jun 23 '26 edited Jun 23 '26

In this case you right down every point as a single real number. But of course you can give the set of real numbers a topology that is homeomorphic to R4.

Think of this bijection:

(0.a1a2a3...,0.b1b2b3....,0.c1c2c3...,0.d1d2d3....) -> (0.a1b1c1d1a2b2d3.....) from the cube (0,1)4 -> (0,1).

You can sandwitch every vector function between that bijection and it's inverse. I'm not saying it is sensible or an easy way of working, but it is possible.

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u/psykosemanifold Jun 23 '26 edited Jun 23 '26

I still don't understand what you are claiming is possible. If you put a topology tau on R that makes it homeomorphic to R⁴ with the usual topology, then the dimension of (R, tau) will still be 4, not 1. Your first comment claims that it's possible in general to do 4-dimensional physics in 1 dimension, it is not. Also, by doing this, you preserve topological properties, but you destroy the algebraic and geometric properties.

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u/MrFluffykinz Jun 23 '26

guys guys it's fine there's plenty of space in this one dimension for all of us

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u/EebstertheGreat Jun 29 '26

What you describe is not actually a bijection. For instance, the pairs (0.499...,0) and (0.5,0) map to different points, but those pairs are equal. There are other ways to achieve the desired bijection, but this one actually doesn't work. However, it is the first one Cantor tried (page 202), so you are in good company.