Instead of hijacking this thread:
Was the universe infinitely large immediately after the Big Bang? - Factual Questions - Straight Dope Message Board
I ask here: Just what makes a dimension “time-like”, and what prevents there being more than one time dimension?
I assume “time-like” refers to an omni-directional nature…moving forward into the future and away from the past at a steady rate.
I’m not a cosmologist. But I think a key factor in the dimension of time is causes and effects. The existence of causes produce the existence of effects so that provides a “direction” in the dimension of time.
Multiple time-like dimensions would create a lot of fundamental problems with reality. If you believe in “multiverse theory” (whatever that actually means) then there are quite possibly some with multiple time-like dimensions but they can’t have any stable causality, and insofar as we can say anything about such a pseudoscientific hypothesis they would likely just collapse upon themselves.
Stranger
Not a physicist, but IIRC a dimension being “timelike” means that it’s impossible to change the order of entities existing in it. Events in 1979 all came before events in 1980, which came before 1981 and so on. In a spacelike dimension however entities can be shuffled around, there’s no “can go only one direction” rule.
To help those not closely following the thread linked by the OP, here is the question that set off the discussion about mutiple time dimensions:
Then there is what appears to be reference to entirely speculative view of the universe from a recollected reading but not something citable, followed by citing of an essay (e.g. a scientific paper on Arkiv not intended for peer review publication) by a fairly well respected philosopher/scientist:
[0812.3869] Multiple Time Dimensions
I confess I don’t follow the scientific arguments, but the final paragraph is a good reminder to not blow scientific hypothesizing into more than that:
The study of multiple time dimensions here is rather preliminary. I have not discussed gauge fields or other massive fields, and on a conceptual level I have not tackled what may be the most difficult question of all, how to characterize observers and observation in such a theory. What I have shown, I hope, is that theories with multiple time dimensions are a live conceptual possibility, and that if nothing else, they serve to stretch our minds as to what may be physically possible.
Why there are however many dimensions of whatever type is going to be a heavy-duty quantum gravity question. Consider something like a path-integral formulation of some theory; you are going to be summing over all possible metrics for a given topology (or something along those lines); but then also sum over all possible topologies. How are you going to do that? Seems like you have some mathematical work to do.
OK, so you’ve probably learned about Cartesian coordinates in school, right? Where every point in a space can be described by an X, a Y, and a Z. And two different people might choose different coordinate systems, so what coordinate labels one person might give to a point don’t necessarily agree with the labels some other person might use (for instance, one person might choose axes that line up with the walls of a particular room, while another might use true north-south-east-west).
What is the same for all coordinate systems, though, is the straight-line distance between any two points. If you measure the change in X coordinates between two points, and also the change in Y coordinates, and also the change in Z coordinates, then you’ll find that \Delta X^2 + \Delta Y^2 + \Delta Z^2 will be the same, no matter what coordinate system you’re using. In mathematical terms, 3-dimensional space has a metric with the diagonal [1 1 1].
Now introduce time. Einstein found that, when two observers are moving relative to each other, that also introduces differences in the coordinates, such that the familiar 3-dimensional distance between two points isn’t actually invariant any more. But what is invariant is -\Delta T^2 + \Delta X^2 + \Delta Y^2 + \Delta Z^2 (it’s conventional to put the time bit before the three space bits), meaning that the metric for four-dimensional spacetime has a diagonal of [-1 1 1 1].
It’s that -1 in front of the time piece that makes it “timelike”. And so far as we can tell, that’s an accurate description of our Universe: One timelike dimension (with a negative in the metric) and three spacelike (with a positive). But physicists like to play around with ideas, so some have explored the implications of what if we had a universe that had multiple timelike dimensions instead of just one, where the metric might be something like -\Delta S^2 -\Delta T^2 + \Delta X^2 + \Delta Y^2 + \Delta Z^2, or -\Delta S^2 -\Delta T^2 + \Delta X^2 + \Delta Y^2, or whatever. It always turns out to be really weird.
I recall reading long ago that a metric with three timelike and one spacelike dimension produces the same result.
In other words, -ΔR2 - ΔS2 - ΔT2 + ΔX2 would be similarly invariant.
Any reality to this?
Yes, but that’s trivial. It turns out to be just a relabeling of the same three dimensions of space and one of time that we have, just with a few arbitrary conventions of notation changed. In fact, I think that particle physicists usually use the opposite convention from astrophysicists.
Really, what matter is that one dimension is different and all the others (however many there are) are the same, and the different one ends up behaving like what we call time.
Greg Egan wrote a whole novel about this–Dichronauts:
There’s a bunch of stuff at the link about how their universe works, including some extended information about the spacetime metric that Chronos described.
Egan also wrote a trilogy in a universe where the interval signature was +1,+1,+1,+1 (though there was still one time dimension) - in that universe the travelling twin aged more than the stay-at-home
Yep. And putting that together with what Chronos said, that covers all the bases (for 4-dimensional spacetime, that is). The metric can be (+, +, +, +), (+, +, +, -), or (+, +, -, -). Permutations of these are all equivalent, as is swapping + with -. So there’s just the three.
What about putting some imaginaries in the signature?
(ducking and running)
I just can’t help remarking on how beautifully this common expression maps to the context here.
What if it turns out that there is some kind of Everettian Multiverse with an almost infinite number of parallel worlds stacked next to each other. Would the ‘space’ they are stacked in count as a dimension? Or would it be called something else?
What ‘space’? No.
However, you can try to construct a quantum field theory where your space-time is “stacked” via a product geometry of your usual 4-manifold times a subtle finite geometry. That has nothing to do with time, though, as far as I understand, just trying to make sense of the Standard Model.
The way I see it, it’s not that a dimension is “time-like,” but time itself is a dimension just as the three (that we are aware of) dimensions of distance are. Each dimension is linear, just as time is. Presumably, someone postulated, “Well, you can move forward and backward in the physical dimensions; why not do so with time?” I also remember one book where someone’s “proof” that it was a dimension was, “If it exists for zero seconds, then it doesn’t exist.”
How would you even define a second time dimension?
I for one think that if time is a dimension, then traveling back in time is impossible, as (a) it is impossible to move from one point to another without moving through a continuous path of points between the two, and (b) just as you cannot move through a solid object, you cannot move backwards in time as you will run into a solid object - namely, yourself. who was already occupying that space at the time one very, very small fraction of a second ago.
Yes but as you move east a tiny bit, your moving through space you occupied a fraction of a second ago.
I’ve lost track of which model the Everettian one is, but yes, there are models where there’s an extra spatial dimension with multiple universes displaced from one another along that dimension.
There’s the radial dimension inside the event horizon of a blackhole. Everything is continually moving towards the center, just as they’re moving forward in the usual time dimension.