/sci/ - Science & Math

Also, I don't know if that picture is bullshit or not and I partly don't understand it at all. Can someone explain why there is even a temporal dimension in our universe? Is it because of causality?

ITT: Discuss time

bonk

>>6359266
Umm, I would say it is the other way around: there is causality because there is a temporal dimension.

Don't try to imagine other dimensions or how it would look if we could experience other dimensions. Use the equations which describe n-dimensions to get a better picture. For example an n-sphere:
<span class="math"> S^n = \left\{ x \in \mathbb{R}^{n+1} : \|x\| = r\right\}. [/spoiler]

>>6359330
Then the question remains.

>Would it be the same?

No, it will be cyclic, more like a helix.
Transition to 4d will start soon,
will appear as 'cataclysm'.

>>6359263
>>6359330
As far as why? I wouldn't hazard a guess...

>a better picture

how does it look like?

>>6359336
And what am I looking at here?

>>6359353
http://en.wikipedia.org/wiki/N-sphere

Why are we traversing the 4th dimension in one direction?

>>6359380
You're talking about the arrow of time, and nobody really knows. Our best answer is something vaguely to do with entropy. It's one of the biggest problems in physics.

>>6359384
Well I have some thoughts that I certainly wouldn't call scientific but thoughts nonetheless.

Would it have to do with entropy because of the fact that entropy exists in our universe and is time-irreversible?

This is kind of what I was getting at when I asked if the temporal dimension is a result of causality in our universe @ >>6359266.

Another thought I had is that it is all due to the big bang setting our universe in motion which results in change between the states of physical systems, ie time.

But this thought makes me wonder if it is the universe progressing through a temporal dimension or if it is only our perception. It's hard to say because we can map time and it is empirically consistent without our observation. It is not our perception that measures time in standard increments. However, it IS our perception that dictates actions and events occurred in the past. Is perceived time a vector and time otherwise simply a magnitude?

>>6359406
They think it has something to do with entropy in the sense that we perceive time in one direction because we pick up information (due to dS>=0) as entropy of the environment increases. OF course pt symmetry says that time doesn't only flow in one direction, but that is how we perceive it.

>>6359417
There are as many directions for time as there are objects in our universe that move relative to each other.

None of those relative objects or directions for time move backwards.

>>6359266
One explanation is what that picture in the OP is talking about - We have one and only one temporal dimension because intelligent life can't exist in universes with more or less than one temporal dimension. Only universes with one temporal dimension can contain beings capable of asking why there should be a temporal dimension.

>>6359406

>Is perceived time a vector and time otherwise simply a magnitude?

I would think of kind of the other way around. In all of the most important physics equations time enters as a squared value so time reversal does not alter their basic properties. So time can be +t or -t, just like a 1-D vector.

However, for some reason in our universe the symmetry is broken and time only accrues as t+dt, like a magnitude.

>>6359263
time would be the same. (Assuming you meant 4+1 dimension)

the problem is that the kepler problem has no stable orbits. Thus no atoms, no planets, no galaxies etc.

Generally, what the image means:

If don't have exactly one time dimension or space dimension, we find that the equation of motion for fields are not hyperbolic and thus there is no initial value problem with a single solution.
If we have more than three space dimensions, there are no kepler orbits.
If we have more than one time dimensions, we have CTCs which basically mean violation of causality even in flat space.
The only ones left are 1+1, 2+1, and us. 1+1 is just retarded.

2+1 is VERY interesting and a lot has been written (I suggest Dewdney's Planiverse, is a fantastic read) but a lot of shit is very hard to make work, also GR has no local d.o.f.s, which basically means no gravitation. Also spin is not discrete.

>>6359452
Why?

>>6359546
You caught my interest with 2+1, I'll check out the book thanks.

>>6359546
>Dewdney's Planiverse
Another pop-sci bullshit, is it?

>>6359570
>>6359572
no, it's a very nice narrative/essay. It's a sci-fi story of contact between a group of students and their professor and a two-dimensional being in a 2+1 universe. It's not ofc perfectly accurate but dwelves in the technical details and is a nice introduction to the effect different dimensionalities have on physical models (problems of topology, signal propagation, celestial mechanics, chemistry, geography, anthropology etc.) It's not popsci, rather more like recreational physics. It's also a nice story and the main character is so nice.

It's a pretty rare book though, I had to buy it online.

bump I want this to stay alive.

>>6359582
"recreational physics"

Which is pop science.

How would you have more than 1 time dimension? Would the extra time dimension represent a choice?

e.g. if it is deterministic, then universe is 4D static image and we are percieving time as we go trough 3D moments of that image.

>>6361679

A lot hints at out universe being deterministic, it's certainly deterministic to the point that there is no freewill. Whether it's completely static, I think we would need a better understanding of all things quantum first to determine that, but perhaps someone who knows more can chime in.

>>6361629
don't read it. Jesus Christ. Read the original peer reviewed paper from which the image in the OP is from.

>>6361679
Time is a dimension just like space. Worldlines are one-dimensional timelike paths in spacetime. Wordlines are determined by forces acting on the particle.

If you have two or more time dimensions, and we maintain the assumption that worldlines be timelike, a particle can make a closed loop in a time-time plane, returning back to an event where it has already been. This is a CTC and violates causality.

Another possibility for interpreting 1+n dimensions is postulating that worldlines are all spacelike (that's what 'only tachyons' means) but then 1+n is just n+1 in disguise, with time and space mislabeled.

You see, it's just a question of geometry. Our concept of time as a parameter under which the world evolves, step by step, is not fundamental. But this is philosophy.

If you don't have exactly 1 space dimension or exactly 1 time dimension you have no particles, because the equations of motion for fields just don't work like you'd expect them to.

>>6361679

>>6362380
determinism is understood in terms of predictability. Predictability happens if the equations of motion for field operators are hyperbolic; this happens in 1+n and n+1 dimensions. Modern determinism is a probabilistic determinism, coherently with QM being a generalization of probability theory. The connection with free will that you make is unjustified, also it's not science, to nitpick.

Determinism has paradoxically actually very little to do with time. It has to do with the uniqueness and existence in an open set of solutions to a diff eq given a certain type of conditions on a certain kind of boundary. Our modern understanding of (flat space) relativistic QM is that of a theory about correlation of measurements at different events in spacetime. (QM in curved s-t is another kind of beast.) The Universe, in this sense, looks pretty much deterministic.

However.

If you have a spacetime with closed timelike curves, determinism looks very very weird. I refer to the works of Novikov and others. Basically the timeline looping on itself it's self consistent, but there are probably always an infinite number of selfconsistent configurations given fixed boundary (read: "initial") conditions. This is difficult to interpret classically; here is where QM has an important effect and solves the paradoxes in terms of interference between paths in configuration space.

The fact that QM has a global, important effect whenever you try to timetravel is in fact why I have a strong gut feeling that time travel is not possible and the chronology protection conjecture is enforced by macroscopic quantum phenomena at the cauchy surface of the boundary of the region with CTCs that destroy the machine. Sorry, digression.