Are space and time really 2 separate things? Why can we describe the first 3 dimensions in terms of space, but then we switch to time when we move to the 4th?
That'd be spacetime, from Einstein's general relativity. I suppose different names for the dimensions are warranted, since we can move freely forwards and backwards in the space dimensions, but the same does not apply for time. I can't go backwards with that, or stop. It's all part of one thing, thoigh. Or at least solving gravity made Einstein realize space and time are connected.
Special relativity came first, and it was actually to solve paradoxes relating to fast-moving magnets. Maxwell's equations always produced a fixed speed of light, which breaks Galilean relativity, and has Lorentz symmetry baked in. Just gluing that on to Newtonian mechanics causes problems.
His solution was to work out a weird, different but observationally equivalent mechanics that would work. Decades later, it was realised matter is waves which internally move at the speed of light as well, so it's not that weird after all.
Weirdly, the math at the quanta level works in both directions (time-wise).
I guess something happens when you get a few atoms together that changes this.
Maybe AbouBenAdam has some insight.
It still can't be rigorously proven that thermodynamics works - if you look at the statistical mechanics papers on it they basically assume something is random that is not to do it. TBF, the empirical evidence is convincing, and the assumptions they do make are small, even infinitely small.
The second law probably relates to pseudorandomness and P=NP, in the end, but that's a big unsolved problem.
Isn't that when people always start talking about entropy and how that gives us an arrow of time?
And I think whether math "works" within an incomplete model isn't really proof. I mean I can calculate a negative amount of people on the bus... But that alone doesn't make it possible/real.
Get 3 sticks, try and arrange them all perpendicular to each other. You can do it. Now try with 4, you can't. We live in 3D space.
Time is a line, at least as we experience it. Just one, it's hard to even figure out what 2D time would mean, although physicists have thought about it.
So, 3+1=4. It turns out they're kind of interchangeable, though, in that swapping time for a kind of angle made up of some space and some time, if done in a certain way, leaves the predictions of physics the same. That's special relativity, and it is itself connected to the way everything is a wave.
If I had to guess, what you're referring to is how higher dimensions are "orthogonal" (at right angles) to the dimensions below it.
How can you arrange 3 sticks orthogonally using 2 dimensions of space?
The same idea can be applied to arranging 4 sticks orthogonally using 3 dimensions of space.
Maybe to a flatlander, a theoretical being that only experiences 2D space, they'd have a different word for the third dimension like we have a different word for the fourth. That wouldn't mean the third dimension isn't spacial.
Soo what are you wondering? I'd expect it's obvious in our everyday experience that time is a bit different from space.
If you want a something more mathematical, pick an equation from physics. It probably treats time separately from space. The only kind-of exception I can think of is general relativity, and even it ends up producing metrics that give time the opposite sign, like the flat space example the other poster mentioned.
The directionality of time is a bit more subtle and emergent, but you don't need it to look at a double light cone and observe that while a slice of it is a sphere, the whole thing is not a hypersphere. That just follows from Maxwell's equations or the other wave equations in nature.
If somebody here knows their way around QFT they might have something to add, but for all the rest it's just kind of built in.
The spatial dimensions are related to each other via the Euclidean metric (AKA the Pythagorean formula): d2 = x2+y2+z2.
The time dimension is related to the spatial dimensions via the Minkowski metric, which differs only by one sign: d2 = x2+y2+z2-t2. So it’s kind of the same thing as a spatial dimension, but with a difference.
Among other things, the change in sign means that, where spatial rotations result in circular transformations, spacetime rotations with a time component (AKA acceleration) result in hyperbolic transformations. And the asymptotes of the underlying hyperbola are the light cone of the center of the transformation—which is why no amount of acceleration can cause an object’s future path to leave its current light cone, and why faster-than-light travel is impossible.
That…actually made sense