[semi-extrinsic]

No. Entropy can be used to explain the direction of time, as a kind of symmetry breaking of all the microscopic laws that are symmetric in time. But it does not say anything about the "speed of time". Relativity does tell us the speed of time - it's the speed of light.

[Balgair]

To be suuuuuuper pedantic here: Relativity tells us that time is a dimension, one that is a bit unique. In that it has a constant attached to it. So, the 3 dimensions you're used to are just normal, they have no constants.

(x,y,z)

Meters of x are meters of z and meters of y. Relativity (and I'm really simplifying a lot by just saying 'relativity'), well relativity comes along as says that time is also a dimension, just with the constant of 'c' attached (the speed of light). That way you can convert seconds into meters.

(x,y,z,ct) not just (x,y,z,t).

So now the time dimension is much larger than the spatial dimensions. About 300,000,000 times larger, a third-ish of a billion. So a meter of x is ~1/3 of a billion meters of time.

Now, there is a lot more about relativity, like, just tons. And I skipped most of it. And trying to just say that time is a simple little conversion away from meters is just wrong. And how that all relates to entropy is a mess that we really haven't figured out yet.

[contravariant]

That constant is immaterial, it's just the conversion constant between two different units. It just turns out that for the units we're used the time unit is a lot larger than the space unit.

The real difference has to do with the metric on spacetime, but that gets tricky to explain. Suffice it to say that a rotation involving 2 of the spatial dimensions, and the equivalent of a rotation for time and a spatial dimension are quite different.

[trenchgun]

Is it because of th minus sign?

[contravariant]

Pretty much yeah. A metric like x^2 - t^2 is quite different from one like x^2 + y^2 (and to some extent those are the only possible in 2d)

[cubefox]

The last sentence surprised me.

[kergonath]

And yet… If you want to get properly depressed, there is a lot we don’t understand about gravity, either.

[klabb3]

> Relativity does tell us the speed of time - it's the speed of light.

I forget the name of the book, but it was trying to convey intuitions about relativity (first special, then general).

It’s very easy to make the mistake of trying to understand space and time first, concepts we think we intuit, but in relativity these are somewhat higher-level concepts. Instead, start with what the most fundamental part of the theory and go from there: the speed of light is constant. Accept that first. It’s the comfort zone. You can always return safely to this point.

So, when moving to space and time, the book explained it like this: everything moves at the speed of light, at all times. It’s just that instead of x,y,z – we add t, time, as well. So for an object that’s still, all it’s movement is through the time dimension. Conversely, an object that moves incredibly fast, like a photon, already “used” it’s speed in the spatial dimensions, so it doesn’t “age” in terms of time.

This is just special relativity, but I liked this approach. It’s basically embracing the theory first instead of trying to shoehorn it into the world we have so many misconceptions about.