The problem is, faster than light travel violates causality in some reference frames [1]. This is a big problem. Forget grandpa-killing travellers; even several bits of time travelling information allows one to easily solve NP-complete problems (it's an even more powerful mode of computation, actually) [2]
Any new physics that allows for FTL must be very weird, even in a logical sense.
To be clear, it breaks causality in every reference frame. It is the definition of causality and derived from the definition of reference frames. In fact, c is not really the speed of light, it’s the speed of causality. Light itself could theoretically go slightly slower.
Causality is always hard for me to understand. Imagine an MRI, where you take a 3D object and slice it into a sequence of 2D slices. When you view the 2D slices, is it really true that slice N has any causal relationship to slice N+1? No, of course not. However, when we view a 3D slice of the universe, which is a 4D object in space-time, we want the slices to have a causal relationship.
The big difference that makes causality work is that there is only one timelike dimension (but three spacelike ones).
A purely spacelike curve can wrap back around and close on itself like a circle. But a purely timelike curve just can't turn around: it's like a person on a tightrope who's not allowed to slow down. So it's stuck going to later and later times forever (or to earlier and earlier ones, depending on orientation). (Yes, changes in reference frame broaden that 1D tightrope to a whole "future light cone", but that only allows limited changes of "heading": the time coordinate is guaranteed to be increasing no matter what.) And, roughly speaking, it would cost infinite energy to change from a timelike path to a spacelike one.
You can perform the same thought experiment by pretending you can only “see” in 2 dimensions. Using the MRI example, pretend you “see” sequential slices of the MRI. Prior slices still don’t cause later slices even though one of the dimensions (the axis along which the MRI was taken) is special. And notice, your observation that 3D objects can loop back on themselves is still correct. But that doesn’t really impact how you see the 2D slices.
This could have been an interesting video, but PBS had some nutty production values. Why did they insist on filling half the screen with some guy waving his arms to distract you? I hope the producer moved on to his true calling - gasoline pump videos.
They have toned that down a bit over the years since that video was recorded six years ago. The videos are really informative, and you can always close your eyes and listen if you like.
As if we didn’t have weird physics already. You’re basically saying that the problem with magic is that it works weirdly. But isn’t that the whole point of it?
I understand that it would be TROUBLE at the mathematical and logical level, but that is exactly a box here we’d like to jump out of. Also, aren’t you bothered by the unexplainable fact that the universe somehow adheres to some rules and not the other. What has set them in the first place? Are they even “rules”, or we just accept them naturally, because our most primitive interactions were based on them for few ages?
I guess then causality will be broken if some external force introduces FTL/time travel to our handful of dimensions. Looking at our 4D hypercube of space time, any point in that x|y|z|t space becomes mutable, whats the problem? ;) (I know you need at least one new "time" dimension then to have mutability, this is difficult to talk about. And then somebody in 6D will find that very cute..)
Except that 6D mathematics, and even physics, is routine. Mathematicians and physicists solve problems in more dimensions that that without breaking step these days, and in fact have done for generations at this point. A lot of things like that, which non-specialists think are spooky and weird and unknown, are actually old hat.
Right, it's boring and routine maths, but there's no evidence that sort of mathematics will somehow bypass the rest of mathematics and physics. It's like suggesting that long division might solve quantum non-locality.
Or it could all match up - aren't several dimensions the very core of e.g. field theory? No idea, really, as you can tell I'm not an expert, just throwing around random words in a thread that is ultimately based on a SF story.
Yes it is, like I said it's very well known and understood. It's not a wild poorly understood frontier full of unimaginable possibilities. The actual maths of n-dimensional geometry is dull as ditchwater. There's no magic lurking there.
Everything in the universe is connected to, and influences everything else. Suppose I hit the cue ball on a very low friction billiard table really hard and cause a cascade of collisions, such that some of the balls undergo 20 impacts. That's a lot, but not inconceivable.
Even extremely tiny variations in the initial movement of the cue ball or configuration of the balls can cause the final configuration on the table to be completely different. How tiny? Well, even the removal of a single electron from an atom over ten billion lightyears away could cause a measurable change in the position of some of the balls when they come to rest. That's how interconnected everything is, and how small changes are vastly magnified by cascades of events.
Breaking causality is basically time travel. It would in theory allow future events to change the conditions that lead to our present. Timelines are extremely unstable. Even the most minuscule change could make our present utterly impossible or unrecognisable. A stable consistent universe isn't possible in the presence of causality violations.
So it just makes it very unlikely, right? If I think about the universe as a spreadsheet, there is a large number of formulas, but they are never cyclic, and only look “up” and to the sides, through some lorentz addressing so to say. And dependencies in it are massive, every cell looks at everything up-around it.
We could definitely make a spreadsheet that is circular in parts, e.g. make it find low, middle and high solutions to some cyclic equality group that only resolves to e.g. 1, 2 and 3. But then we have to include all other parameters from up-around and it is ~~ unlikely to solve, makes sense. But I’m curious if that’s correct or provable. The universe seems to have no trouble solving things which we struggle with even at the basic level. Maybe there are coincidences in this spreadsheet that lead to possible dependencies on the future, and then they become a true dependency? We just have no idea how to catch these events.
We observe causality in our universe and day-to-day lives. If FTL movement is possible, you might expect at least some particles to be doing it, and that there'd be closed timelike curves or causality breaking happening already in nature, and we don't.
It's not clear what 'breaking causality' would look like. It's like saying what if you made 0 equal 1?
Well that’s relatively easy. Some object (or particle if you like) appears out of nowhere and causes the events to happen that make it go time travel and appear out of nowhere and cause… you get the idea. Something caused the entire universe, before “time” was even a thing (or there is much more to it). Why couldn’t that something cause few events to cause themselves in an already “deployed” spacetime?
We observe causality
If we can’t observe something it may just mean it’s rare and/or hard to detect.
I understand that probability of me asking this first time is zero and people definitely brought that up and analyzed why this is not the case. I’m interested in reasoning and whether it’s just a rule, like conservation of information (is it so?), or if there is something fundamental preventing it completely.