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[McTraveller]

My explanation, with only some very loose basis on actual study - hopefully the concept comes through in text...

There is another dimension for propagation of events in addition the the usual ones. Call it "hypertime" (in the vein of hyperspace).  The rationale is that when you are time traveling "backwards" in spacetime, your own local clock is still moving forwards.  So rationalize time travel by saying that you always travel forward in hypertime.

Imagine then that events in spacetime are always propagating forward in hypertime.  In fact, all of spacetime history is propagating through hypertime.  So if you travel in hypertime to go "back in time", when you go back you are actually traveling forward in hypertime but slow enough that the propagation of the past spacetime catches up with you.  Then you modify that past.  But the changes you make don't propagate through hypertime faster than the speed of light - so they do not modify the "initial" future. Instead, there is a new "future" that is propagating out from that new change, making a new future, but offset in hypertime from the original frame.  So there are now two universes, both propagating forward in hypertime, but they can't influence each other.

So this means when you travel back to the future, you can travel back to either the "modified" propagation, or to the "original" propagation.

[Starver]

I've been trying to remember the book (series of books?) with this 'model' in it, but haven't been able to.

Multiple worlds are stacked against each other like a set of very similar playing cards. Identical (initially) but skewed by time. A "time travel" event just takes you 'sideways' to the world "500 years ago" (or "500 years in the future", but I'm not sure how they dealt with when (or where on the stack) the first world existed that invented this transit method) but that is their world, and any changes you make to them (by giving the Romans modern automotive techology, e.g.) will never be/never was a change to your own.  Romans can come 'here', check any historic records of their period for 'their' immediate future (though they might be better off checking in a slice opened up to their access that's still more modern than theirs but not much more advanced) and be prepared for things that would happen. So long as it's not something that someone else's travels and travaills has caused to not happen the same.

It's just a more ordered "change a separate timeline" setup, effectively.

(I'm thinking it's a late '70s book. Or earlier, but that's when I read it. Not really the place for a YASID post, so not here asking for that. Just adding it as a solid concept to add to the list.)

[McTraveller]

Ok maybe a dumb question, despite my years of schooling and extracurricular reading.

What does spacetime curve through?  All the examples talk about how spacetime is curved like the surface of a planet or whatever.  But all those examples are surfaces embedded in some other higher-dimensional space.

So is spacetime in some other higher-dimensional construct through which it curves?

Or is it essentially the case that the extra dimension is indeed "artificial" and spacetime really does just curve "through itself"?

Or are these equivalent statements, that if spacetime is curved then there is in fact a way to treat it as in some non-curved frame?

[Maximum Spin]

Essentially, "spacetime is curved" is a shorthand for "geometry doesn't work like it does in a Euclidean space". We call this curved because the only familiar situations in which this happens are on curved surfaces — for example, the largest possible triangle you can draw on the Earth's surface has three 90° angles, which doesn't fly at all in a plane. However, this doesn't actually mean that spacetime is curved in the sense in which we usually understand curvature; there's no reason to assume that that sense applies outside our limited mundane experience.

For an example of how geometry doesn't work like it does in a Euclidean space, if you drew a triangle (using light beams, the only definition we have for "a straight line" in real life) with a neutron star at one vertex, the triangle's angles would add up to considerably less than 180° and the trigonometry would, therefore, be different.

[MetalSlimeHunt]

Much as there isn't really any such thing as an "object" when you really break down the nature of matter to weird probability fields, I don't think there's really any such thing as spacetime in what we think of as existence either. It's just a mathematical representation of what we perceive. Or rather, it's so indistinct that you can't find any discreet part of spacial existence.

So, it's just all math. Extremely important math that blows up stars.

[Starver]

for example, the largest possible triangle you can draw on the Earth's surface has three 90° angles,

Well, technically the asolute largest would have three angles of lim->180°, just short of just being an actual Great Circle...

(Or, if you're going by boring old area covered, not perimeter, internal angles of lim->300°, i.e. all but a tiny-tiny "not in the triangle" bit of the Earth's surface. Going further would wrap over (at least some of) the surface more than once. Which would be cheating, but interesting.)

[McTraveller]

Yeah I know it's just a math model - but since you can represent a curved n-dimensional space with a non-curved n+1 dimensional space with an extra constraint, what is that extra 5th dimension and constraint for space-time?  Even if it is "purely math".

Maybe this should've been in random thoughts instead...

[Maximum Spin]

for example, the largest possible triangle you can draw on the Earth's surface has three 90° angles,

Well, technically the asolute largest would have three angles of lim->180°, just short of just being an actual Great Circle...

(Or, if you're going by boring old area covered, not perimeter, internal angles of lim->300°, i.e. all but a tiny-tiny "not in the triangle" bit of the Earth's surface. Going further would wrap over (at least some of) the surface more than once. Which would be cheating, but interesting.)

I don't really know why I said "largest", which doesn't even have a consistent meaning in this context, no.

Much as there isn't really any such thing as an "object" when you really break down the nature of matter to weird probability fields, I don't think there's really any such thing as spacetime in what we think of as existence either. It's just a mathematical representation of what we perceive. Or rather, it's so indistinct that you can't find any discreet part of spacial existence.

So, it's just all math. Extremely important math that blows up stars.

Well, "spacetime" has a specific definition under general relativity. It's kind of hard to describe in classical terms, but basically spacetime is a particular coordinate space.

Yeah I know it's just a math model - but since you can represent a curved n-dimensional space with a non-curved n+1 dimensional space with an extra constraint, what is that extra 5th dimension and constraint for space-time?  Even if it is "purely math".

There isn't one. We can confidently prove the lack of any extra dimensions big enough to matter in that sense.

[Il Palazzo]

There is a concept of intrinsic vs extrinsic curvature. The latter requires embedding in a higher-dimensional space, whereas the former doesn't. I.e. the curvature can be defined without referring to a higher dimension. E.g. an open-ended cylinder has extrinsic curvature but is intrinsically flat (i.e. is only curved if embedded) while a sphere is curved intrinsically (i.e. exhibits curvature even without embedding). The curvature in GR is intrinsic - additional dimensions are unnecessary.

Also, I feel like some of the previous posts might be confusing space curvature with space-time curvature. One can have flat space with Euclidean geometry that still has gravity (space-time curvature) in it.

[Maximum Spin]

Also, I feel like some of the previous posts might be confusing space curvature with space-time curvature. One can have flat space with Euclidean geometry that still has gravity (space-time curvature) in it.

Actually can't, as gravity curves space per se, not just space-time. In fact, you can't curve one and not the other!

Actually, just to be sure I've run this by my one friend who's an actual expert on the subject. I think I'm right here but I'll let you know.
Nope, physics backs me up on this one. The linear relationship imposed by c means you can't curve one and not the other.

[Il Palazzo]

Also, I feel like some of the previous posts might be confusing space curvature with space-time curvature. One can have flat space with Euclidean geometry that still has gravity (space-time curvature) in it.

Actually can't, as gravity curves space per se, not just space-time. In fact, you can't curve one and not the other!

Yes you can. Cosmological models with no spatial curvature describe just that.

[Maximum Spin]

Also, I feel like some of the previous posts might be confusing space curvature with space-time curvature. One can have flat space with Euclidean geometry that still has gravity (space-time curvature) in it.

Actually can't, as gravity curves space per se, not just space-time. In fact, you can't curve one and not the other!

Yes you can. Cosmological models with no spatial curvature describe just that.

Pretty sure those models are only globally flat but still have local curvature.

ETA: Asked my astrophysicist friend and he says the same.

[Il Palazzo]

The models assume uniform distribution of matter and energy, so there aren't any local deviations. Obviously, there is a small-scale granularity in reality (at least today, less so in the early universe), but the models ignore that.

[Maximum Spin]

The models assume uniform distribution of matter and energy, so there aren't any local deviations. Obviously, there is a small-scale granularity in reality (at least today, less so in the early universe), but the models ignore that.

With uniform continuous distribution of matter and energy, there is no spacetime curvature (assuming globally flat spacetime). Once gravity is operational, there is local spatial curvature — you can ignore it, but then you're willfully violating both general and special relativity. Obviously it is possible to produce anything you want once you ignore general and special relativity, but that means the model doesn't apply in those domains.

Also I think my physicist friend is personally mad at you now. He's going on a whole thing about models.

[Il Palazzo]

Does a de Sitter universe have no space-time curvature then? Or has localised spatial curvatures? Or is violating GR?