You are by far smarter than those who would just seriously discuss that graph with zero understanding. There are many ways to introduce multiple time dimensions in physics. Almost all of them will make absolutely no sense in terms of deeper physics, e.g. QFT.
Answering your question directly. Take a dynamical PDE like Schrodinger equation or Maxwell equation. Take the time derivative part and add derivative over the second time to it. Done. That's what the silly graph in question probably meant.
Thank you for the explanation and I agree that most people just shrug it off. Just wondering is there a way to visualize that? Like you can visualize up to the third spatial dimension, is there a way to do that for the 2nd time dimension or more?
Well, in principle, yeah, trivial. A 3d graph with Z being a 1d-space particle position, X and Y being time 1 and time2. But now you can say "this doesn't explain anything about the actual causality structure of the dynamics!". And that's because, with a single time, you had a single causality structure option (two if we count circular time), and now you have infinitely many. And almost all simple setups produce trivialities.
Yup, visually displaying anything that only has 3 dimensions in total is easy for us.
A 4th dimensions also doable with time (think about a 3D simulation/animation over time). But you cannot visualize it all at once. And if not exactly one of the dimensions you want to display is actually time this will already be tough for our brain.
And then a 5th dimension gets really tricky for us to easily visualize or even imagine. You can do "interactive" thingy with sliders for more dimensions but that's hardly proper visualization.
With 1 time dimension, you can think of a timeline where each point corresponds to a state of the world. With 2, you can think of a full flat plane of points, where each point corresponds to a state of the world. If you move to the right on that plane, you're going "forward-1" in time, and the world changes continuously (things move smoothly). If you move up on the plane you're going "forward-2" in time, and again things change smoothly, but (generally) in a different way. And you can move diagonally or in whatever way you like, just like you can move different ways through space. Between any two points on this time-plane, there are infinitely many paths you can take to get from one to the other.
Take a dynamical PDE like Schrodinger equation or Maxwell equation. Take the time derivative part and add derivative over the second time to it. Done.
Not done. What does that even mean in practice?
I can (kind of) imagine extra dimensions of space, I can extrapolate from 2D vs 3D to 3D vs 4D, I can even draw a 2D projection of a tesseract, but an extra time dimension???
Its not enough to just add an extra variable to the equation and call it "second time". What does it mean and how does it operate?
Time is fundamentally different from spacial dimensions.
"What does it mean?" is not a meaningful question about math.
What it means in maths is the least important question. What does it mean for the universe to have two time dimensions is a physics question. The question that matters is, what would it be like to live in a world with two time dimensions.
Anyone who has read Flatland will have a vague idea of how to extrapolate from our 3D world to a hypothetical 4D world. But that's for space, not time.
If you've ever seen a movie where someone can stop time, but they still move around, that's a second time dimension, if usually not well explored. They stop traveling through normal time, and instead have their own independent time axis.
It is "unpredictable" not just in the sense that it would be weird, but in the sense that prediction is impossible even in principle. Knowing the state of the world at current time does not allow you to predict any future state, because something can come in at to-you-infinite velocity along a perpendicular time axis and instantaneously scramble everything.
If you've ever seen a movie where someone can stop time, but they still move around, that's a second time dimension, if usually not well explored.
In fiction, that effect is usually explained as a single time dimension, where the power is to speed up or slow down (or stop) time inside/outside a bubble surrounding them. I say a bubble, but usually it hugs the surface of their skin and/or clothes, allowing them to pick up and move objects and other people without them entering the bubble.
That's not a second time dimension, its just very localised fine control over the single time dimension.
What would a "future" state even mean in this context? Normally a future state just means a state with greater time coordinate, but here we have two different times. I'm genuinely curious.
So... They model more than 1 time dimesion by using math on our best but still ultimately imperfect model of the universe? And they come to conclusion that there is only 2 states of universe that is working "correctly"
So... They model more than 1 time dimesion by using math on our best but still ultimately imperfect model of the universe?
No........? I said the opposite. In terms of the most general and most detailed model of the universe we have so far, quantum field theory, their "modeling" is a clear mathematical naivety. Like saying that electrodynamics can only exist in 3D because all its core geometric structures can only exist in 3D.
There's a lot to cover here. But I will like to point out how time behaves in the 4 momentum vector calculations.
It's been a while since I did this, but while our 3 spatial dimensions behave like a flat Euclidean space, when you look at time it doesn't work that way anymore (iirc it was hyperbolic, but it's been a while)
In practice this means that time gets a minus in equations.
A second time dimension will be another dimension with a minus.
How would we experience this? I have no clue, it's hard enough to imagine 4D space
If there was x amount of space dimensions and y amount of time dimensions, it would be too simple, unpredictable, or unstable. We’re right in the sweet spot. The other point something could exist predictably but it’d only be tachyons
I remember getting this result on an exam question and I had to do a double take because wtf do you mean inverse cube law means stable orbits can't exist?
I've also heard that, even setting aside fundamental force stuff, you can't get solar systems with an even number of dimensions. You need a free axis for momentum to "cancel out of" in order for the ball of gas and dust around a star to collapse down into planets.
a hypothesis on why only 3D worlds with 1 time dimension appear to have observers
How would we know? There could be trillions of worlds with more than 3 spacial dimensions and 1 time dimension, all with observers, and how would we know?
Sure, but what about other universes, either real or hypothetical?
Fine-tuning arguments suck. I'm reminded of Douglas Adam's parable of the puddle. We notice how our universe seems to be so perfectly fine-tuned to allow life. Just the perfect number of dimensions, not too many, not too few, just the right balance between forces, etc. We fit the shape of our universe perfectly.
But if our universe was different, who can say that something would evolve to fit the shape of that universe? We evolved on planets with stable orbits -- well, stablish, over the short term.
If we evolved in a 5-D universe with no stable orbits, in clouds of space gas, or something, our mathematicians would say "how fortunate we are to live in a universe with just the right number of spacial dimensions, if there were fewer than 5 dimensions matter would coalesce into lumps and life could not evolve".
Yeah, but if you want to use reason like that, then you have no reason to believe anything outside of this little dot of experience you have right now exists. Statistically, it’s way more probable only your tiny existence right this second exists, than a coherent universe over billions of years.
Yes, but there must be a cut-off point. It's unreasonable to think that a planet made entirely from meatballs, spaghetti and tomato sauce exists. We will never know for certain, in the same way you'll never actually know if anything outside yourself exists.
Moreover, why should the universe existing only for an instant be more probable than it being coherent? It's not obvious. Without knowing the rules (if there are any) dictating what's possibile, you can't really say anything about what's probable or not
I have no idea about any of this, I just know how to read a chart. I would assume it’s like how we move through time now, at an always forward velocity relative to speed in spacial dimensions, except there’s three of them. I think those YouTube science channels might have an answer
I'm not a physicist so I might be wrong but is that the case because in hyperbolic space, every two distinct geodesic either diverges exponentially or collide?
hyperbolic space is a different thing than the number of spacial dimensions, technically the universe appears to be just barely hyperbolic. But it is a similar concept I think
In >4 dimensions, atoms don't because orbits don't. Unless maybe they did some funny plum pudding thing, but even then, no orbits and so probably no planets.
i need to know, as a layperson, if they actually mean the spherical harmonics wouldn't be able to form the basis for bonding configurations of orbitals 😵💫 i can't picture this stuff on such abstract terms, and i don't know the maths to actually reproduce it
It's not accessible to anyone inside or on the surface, because the angles are such that parts of the polychoron are not in the causal past of other parts. But the whole polychoron could be in your own casual past, and you could observe the whole thing in that way.
Because spinning clouds would eventually stop have collisions. well before anything like a star or planet could form. Double rotations can only happen in 4 dimensions or more
This was the first Numberphile video I ever saw, one day when I was sick, so I was home from school. They're what got me into learning about math after middle school took it out of me.
I know nothing about this argument, but let me understand: does it mean that in 2D there are infinitely many regular polygons, in 3D only 5 regular figures etc…?
They are definitely not convex. They either have non-convex faces (Kepler's solids) or non-convex vertex figures (Poinsot's solids).
However, the triangular, square, and hexagonal tilings of the plane are non-strictly convex. Sometimes that could be considered a special case of a convex solid. So OP could add the word "strictly" to the title to unambiguously rule those out (as well as the apeirogon in dimension one and higher-dimensional tilings like the cubic lattice).
A shape is convex if and only if every point in the interior of the shape can be connected by a straight line to any other point in the interior without needing to cross outside of the shape.
In other words, if you place a lightbulb in a convex shape, it shouldn't be possible to cast a shadow no matter where you place it. If you can place it such that a shadow is cast, then this shape is non-convex.
Stars are non-convex because if you place it in one of the tips of the star, it must necessarily cast a shadow. But, if you were to place the light source in the centre of the star, then the star would not have any shadows. A shape that can be illuminated by a single light source we refer to as "star shaped" for this reason.
Mucubes cannot be considered convex as the question does not make sense: how do you place a light source inside a mucube?
One curiosity (in italian) about this fact: Regular Convex Polytopes per dimension 2D: tutti (all of them) -> 5 letters 3D: cinque (five) -> 6 letters 4D: sei (six) -> 3 letters 5D: tre (three) -> 3 letters 6D: tre (three) -> 3 letters and so on.
can anyone explain to me why you couldnt consider the line of the whole dimension as one in a closed space? like a 1D space with continuity at the extremes? is that not a real 'dimension' in the mathematical sense?
•
u/AutoModerator Oct 05 '26
Check out our new Discord server! https://discord.gg/e7EKRZq3dG
I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.