[simiones]

> we perceive as Dark Energy in our 4D world

This is a bit of a technicality, but we don't live in a 4D world, we live in a 3+1D world - the 3 spacial dimensions are interchangeable, but the 1 time-related dimension is not interchangeable with the other three (the metric is not commutative).

I'm bringing this up because a lot of people seem to think that time and space are completely unified in modern physics, and this is very much not the case.

[pwatsonwailes]

To expand on this a little for those interested, time has properties space doesn't. For example, you can turn left to swap your forward direction for sideways in space. You cannot turn though, in a way that swaps your forward (as it were) direction in space for a backward direction in time.

Equally, cause always precedes effect. If time were exactly like space, you could bypass a cause to get to an effect, which would break the fundamental laws of physics as we know them.

There's obviously a lot more, but that's a couple of examples to hopefully help someone.

[mxkopy]

Related: https://en.wikipedia.org/wiki/Causality_conditions

[jamincan]

I had always thought that the fundamental forces were largely the same regardless of whether time was reversed or not.

[Pet_Ant]

Can you expand on this? I’m guessing that it’s something to do with preservation of mass & energy? Like mass doesn’t have to be preserved over a spatial dimension (eg rotating an object) but does over time.

[simiones]

I explained in another comment, but it's more fundamental than that.

In pure mathematical terms, the vector space used in special relativity (and in theories compatible with it, such as QM/QFT), while being 4 dimensional, is not R^4, it's not a 4D cartesian vector space.

Specifically, the scalar product of two vectors in R^4 (4D space) is [x1,y1,z1,h1] dot [x2,y2,z2,h2] = x1x2 + y1y2 + z1z2 + h1h2. You can order the coordinates however you like - you could replace x with h in the above and nothing would change.

However, SR space-time is quite different. The scalar product is defined as [x1,y1,z1,t1] dot [x2,y2,z2,t2] = c^2 * t1t2 - x1x2 - y1y2 - z1z2. You can still replace x with y without any change with the result; but you can't replace x with t in the same way. This makes it clear from the base math itself that the time dimension is of a different nature than the 3 space dimensions in this representation. This has a significant impact on how distances are calculated, and how operations like rotations work in this geometry.

[Lerc]

How is the difference between them characterised in physics?

It seems like it would be hard to distinguish from the point of view of a 4D unit vector XYZT if T was massively larger. Is it distinguished because it's special or is it just distinguished just because the ratio to the other values is large.

Imagine if at the big bang there was stuff that went off in Z and XY and T were tiny in comparison? What would that look like? Part of me says relativity would say there's no difference, but I only have a slightly clever layman's grasp of relativity.

[simiones]

The difference is this: in regular 4D space, the distance between two points, (X1 Y1 Z1 T1) and (X2 Y2 Z2 T2) is (X1-X2)^2 + (Y1-Y2)^2 + (Z1-Z2)^2 + (T1-T2)^2), similar to 3D distances you may be more familiar with.

However, this is NOT the case in Special Relativity (or in QM or QFT). Instead, the distance between two points ("events") is (cT1-cT2)^2 - (X1-X2)^2 - (Y1-Y2)^2 - (Z1-Z2)^2. Note that this means that the distance between two different events can be positive, negative, or 0. These are typically called "time-like separated" (for example, two events with the same X,Y,Z coordinates but different T coordinates, such as events happening in the same place on different days); "space-like separated" (for example, two events with the same T coordinate but different X,Y,Z coordinates, such as events happening at the same time in two different places on Earth); or light-like separated (for example, if (cT1-cT2) = (X1 - X2), and Y, Z are the same; these are events that could be connected by a light beam). Here c is the maximum speed limit, what we typically call the speed of light.

This difference in metric has many mathematical consequences in how different points can interact, compared to a regular 4D space. But even beyond those, it makes it very clear that walking to the left or right is not the same as walking forwards or backwards in time.

Edit to add a small note: what I called "the distance" is not exactly that - it's a measure of the vector that connects the two points (specifically, it is the result of its scalar product with itself, v . v). Distance would be the square root of that, with special handling for the negative cases in 3+1D space, but I didn't want to go into these complications.