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/sci/ - Science & Math

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the infinite dimensional time-space manifold Anonymous Wed Mar 6 14:36:56 2013 No.5588176 [Reply] [Original]

In relativity space-time is a 4-dimensional manifold. When we define motion on that manifold and allow for motion in the time dimension we can take the derivative to measure change, i.e. velocity. Velocity on the space-time manifold cannot be measured as change in time anymore since time is just another degree of freedom in which we allow movement. The dynamics do thus happen in a a meta-time and adding that meta-time results in a 5-dimensional manifold. Repeating the process inductively ad infinitum adds an infinite number of hierarchically organized time dimensions. The pseudo-riemannian structure is naturally extended.

Why has nobody considered this before and why do we misleadingly work with relativity in only 4 dimensions?

>>	Anonymous Wed Mar 6 14:44:40 2013 No.5588186 Time is not a spatial dimension. /thread

>>	Anonymous Wed Mar 6 14:48:26 2013 No.5588196 >>5588186 Why not? We can treat it like one for example when straightening the flow of a vector field. The difference between time-like and spatial dimensions is nothing but a sign in the metric signature.

>>	Anonymous Wed Mar 6 14:51:55 2013 No.5588203 >>5588176 you are confined to a section with finite dimension because of the equations of motion eliminating most degrees of freedom.

>>	Anonymous Wed Mar 6 15:14:41 2013 No.5588236 >>5588176 >Velocity on the space-time manifold cannot be measured as change in time anymore Yes it can.

>>	Anonymous Wed Mar 6 15:59:57 2013 No.5588320 Universe isn't 4 dimensional or something faggot. Stop watching pop-sci shows and media monkeys.

>>	Anonymous Wed Mar 6 16:15:11 2013 No.5588351 >>5588320 What is the Minkowski metric, Alex?

>>	Anonymous Wed Mar 6 16:18:42 2013 No.5588360 considering tangent vectors (even in an euclidean 3-space) does not magically create an additional time dimension into existence

>>	Anonymous Wed Mar 6 16:21:12 2013 No.5588367 >>5588320 Oh look, its one of these faggots who dont believe in dimensions! Lets laugh at him!

OP Wed Mar 6 16:22:28 2013 No.5588370

>>5588203
When accounting for meta-time and higher time dimensions the equations of motion can look very different from what you might expect.

>>5588236
Time itself is subject to movement in the infinite dimensional time-space manifold. Movement in time must happen with respect to meta-time because with respect to time the derivative will be constant and doesn't allow for change in velocity.

>>5588320
The dimensions of string thoery are spatial and their number is finite. An infinite number of time dimensions is what I propose.

>>	Anonymous Wed Mar 6 16:25:27 2013 No.5588376 >>5588367 > that one guy samefagging 'muh dimensions' ssshhh...only dreams now kid...

>>	OP Wed Mar 6 16:26:12 2013 No.5588378 >>5588360 A vector field generates a flow, thus naturally making time a new dimension.

>>	Anonymous Wed Mar 6 16:26:26 2013 No.5588379 i thought it was bcuz of all de fish and planktons

>>	Anonymous Wed Mar 6 16:28:41 2013 No.5588382 >>5588370 >with respect to time the derivative will be constant and doesn't allow for change in velocity. wat

>>	Anonymous Wed Mar 6 16:29:27 2013 No.5588383 >>5588378 rather a 1-dimensional submanifold of the whole thing than an additional one

>>	Anonymous Wed Mar 6 16:39:42 2013 No.5588397 >>5588383 The flow can be used to construct the n+1 dimensional product manifold MxR

>>	Anonymous Wed Mar 6 17:05:43 2013 No.5588449 >>5588397 yes, and ?

>>	Anonymous Wed Mar 6 17:06:56 2013 No.5588453 >>5588449 And ... we can repeat to add infinite time dimensions.

>>	Anonymous Wed Mar 6 17:06:56 2013 No.5588454 >>5588176 >Why has nobody considered this before Because it's wrong, obviously. You understand that, right?

>>	OP Wed Mar 6 17:08:27 2013 No.5588456 >>5588454 Why is it wrong? It might lead to a unified theory. Consider how the state space of quantum mechanics is infinite dimensional as well.

>>	Anonymous Wed Mar 6 17:10:11 2013 No.5588461 >>5588453 unless you specify some pseudo-riemannian structure on that MxR, nothing happens, you keep adding useless dimensions for the hell of it

Anonymous Wed Mar 6 17:14:57 2013 No.5588469

>>5588456
>Why is it wrong?

All of it is wrong.

>Velocity on the space-time manifold cannot be measured as change in time anymore

is wrong.

>The dynamics do thus happen in a a meta-time and adding that meta-time results in a 5-dimensional manifold

is nonsense.

>>	OP Wed Mar 6 17:22:43 2013 No.5588482 >>5588461 What structure do you want me to define? My unified theory is not yet completed. >>5588469 >All of it is wrong. Why? >is wrong. Why? >is nonsense. Why?

>>	Anonymous Wed Mar 6 17:25:11 2013 No.5588486 >>5588482 >how do I into burden of proof "Why is it wrong" would be much easier to answer if you would try to tell us why it is correct.

>>	Anonymous Wed Mar 6 17:31:41 2013 No.5588503 >>5588482 ITT: we add real dimensions to things

>>	Anonymous Wed Mar 6 17:44:58 2013 No.5588534 >>5588378 No. In elementary terms, a vector is just a magnitude and a direction. It doesn't mean anything is flowing.

>>	Anonymous Wed Mar 6 17:46:12 2013 No.5588537 >>5588534 Fuck off, high school retard. Obviously you don't know shit about differential geometry.

>>	Anonymous Wed Mar 6 17:51:12 2013 No.5588557 >>5588537 If you think you can explain a proper formal definition of vectors to someone who thinks a vector means something is flowing, be my guest.

OP Wed Mar 6 17:52:56 2013 No.5588561

>>5588486
Didn't you say it was wrong? Science is all about disproving theories, "falsifiable". My theory is consistent and generalizes general relativity with a possible extension to quantum mechanics.

>>5588503
String theory does the same only with spatial dimensions.

>>5588534
>>5588557
http://en.wikipedia.org/wiki/Vector_field#Flow_curves

>>	Anonymous Wed Mar 6 17:55:27 2013 No.5588570 >>5588176 you can consider the cotangent bundle of a 3 dimensional riemannian manifold foliated over time with its natural symplectic structure, I think that's what happens here: http://en.wikipedia.org/wiki/ADM_formalism It is not my area of expertise.

>>	Anonymous Wed Mar 6 17:56:41 2013 No.5588574 >>5588482 "wrong" = a false statement "nonsense" = an incoherent statement If you don't give your reasoning, nobody can say where your reasoning is flawed. "2+2=5" "No it doesn't." "Why not?"

>>	Anonymous Wed Mar 6 17:57:56 2013 No.5588577 >>5588482 a (pseudo-)metric would help

>>	Anonymous Wed Mar 6 17:58:57 2013 No.5588579 >>5588574 If you really think explaining his reasoning would change the fact that "2+2=5" is false, you are fucking retarded. Math doesn't give a shit about your reasoning, if the result is wrong.

Anonymous Wed Mar 6 17:59:56 2013 No.5588582

>>5588176
>Why has nobody considered this before

Clearly it's because you easily noticed something that everybody else in the world missed and will revolutionize all of science. That's far more likely than you being the one who misunderstands something.

>>	Anonymous Wed Mar 6 18:01:27 2013 No.5588588 >>5588579 >If you really think explaining his reasoning would change the fact that "2+2=5" is false, you are fucking retarded. What. Who... why... what are you talking about?

>>	Anonymous Wed Mar 6 18:03:42 2013 No.5588594 >>5588588 I'm talking to you, pseudo-intellectual high school retard. You said >"2+2=5" "No it doesn't." "Why not?" If you knew a minimum of math, you'd know how to answer the "Why not?" Same goes for OP's "theory".

OP Wed Mar 6 18:06:42 2013 No.5588604

>>5588570
Thanks, interesting.

>>5588574
>a false statement
Why is it false?
>an incoherent statement
Why is it incoherent?

>>5588577
I can define whatever pseudo-metric I want. Let's say for the sake of simplicity we extend the Minkovski metric to a (-1,...,-1,+1,+1,+1) metric.

>>	Anonymous Wed Mar 6 18:08:12 2013 No.5588608 >>5588604 >Why is it false? Because it's not true. >Why is it incoherent? Because it conveys no meaning.

>>	Anonymous Wed Mar 6 18:09:42 2013 No.5588612 >>5588604 that would then give different field equations, once you define a new stress energy tensor

Anonymous Wed Mar 6 18:14:42 2013 No.5588619

>>5588594

I think you misunderstood me and now are just trolling.

OP has concluded that 2+2=5. Since this is wrong, there must be some flaw in his reasoning. One could explain why 2+2=4 from first principles, but that would almost certainly be needlessly complicated and confusing compared to correcting a simple misunderstanding.

>>	Anonymous Wed Mar 6 18:16:42 2013 No.5588623 >>5588561 I stand by my statement. A flow does not mean anything is flowing. 0/10, kindergarten-level trolling

Michio Kaku Wed Mar 6 18:22:26 2013 No.5588636
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HERRO DER!

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VERY GOOD BOOK ABOUT HOW WE NEED 10 DIMENSION TO SIMPRIFY FORCES OF NATURE INTO EQUATION ABOUT AN INCH LONG! VERY GOOD READ.

>>	Anonymous Wed Mar 6 18:24:27 2013 No.5588642 File: 26 KB, 369x450, hurp.jpg [View same] [iqdb] [saucenao] [google] >>5588623 >A flow does not mean anything is flowing.

>>	Anonymous Wed Mar 6 18:31:41 2013 No.5588651 >>5588623 a vector field (it has to be a field) gives, on each co-ordinate patch, an ODE which can be solved locally and then the solutions can be patched together. Locally, dy/dt (t,x) = v(y(t,x)), with y(0,x) = x.

>>	Anonymous Wed Mar 6 18:48:56 2013 No.5588686 >>5588651 and now finally I know what flows are!

>>	Anonymous Wed Mar 6 22:04:56 2013 No.5589120 We're always moving at c in the 4d space

>>	Anonymous Wed Mar 6 22:21:27 2013 No.5589172 File: 202 KB, 432x520, laughing man.png [View same] [iqdb] [saucenao] [google] >>5588636

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