Complex time?

[dirkjently]

Forgive me if someone has discussed this befor but there has been somethign that i've been thinking about for a while.

Time is not the fourth spacial dimention and i would debate that time is a spacial dimention at all.

Could it be possible that time is the complex part of the plane of the universe where spacial dimentions are the real part.

It hard to explain i'm trying to campare reality to the graphs where space = x and time = i, where i = root(-1)

could we not also have time being multidimentional which would explain parralell universes.
it wouldalso explain why we can't explain the apparant paradoxes associated with time travel, becasue while we are 3-spacial dimentional beings we are only 1-time dimentional beings.

[thigle]

surely time is not of same dimensional quality as space. to claim that is a grave reductionism.

check this out (and don't get terrified by the technical mumbo-jumbo, or if you do, then the last link is math-free version):

http://www.valdostamuseum.org/hamsmith/ ... #liesphere
http://www.valdostamuseum.org/hamsmith/BlackHole.html
http://www.valdostamuseum.org/hamsmith/play456.html

there you can see that physical spacetime is represented as RP1xS3, and the same goes for internal symmetry spaces.

anyway, if the above seems not relevant, check out the TimeMaster as i like to call him: Metod Saniga. he is an astrophysic, who came up with one of the most refined and flexible theories of time ever. you can check it out at:

http://www.astro.sk/~msaniga/ - his homepage
http://www.ta3.sk/~msaniga/pub/ftp/ARWmtd.pdf - on geometry of time and dimensionality of space
http://www.ta3.sk/~msaniga/pub/ftp/ZiF_05_san.pdf
http://www.ta3.sk/~msaniga/pub/ftp/gamu.pdf

[moonlord]

Um, RP1 is the same with S1 so why use it? And who said the universe is glomar-shaped (S3)?

[thigle]

RP1 is not S1 fully. what about the ideal point ?

and the universe is not as someone says. though many have proposed glomar shaped universe. like Riemann. or M. R. Feltz. or Tony Smith, for whom spacetime corresponds to RP1xS3, and timespace to another RP1xS3.
the geometry at the level of macrospace of manyWorlds, or multiverse, or pluriverse, or whathaveyou, is RP1xS7.

so each point of RP1xS3 spacetime corresponds to a whole internal symmetry space with same structure RP1xS3. and each whole spacetime(of a given universe) is only one point in RP1xS7 pluriverse.

now that's far out, isn't it ?

still this model of tony smith gives all that a physics model needs and unifies all the forces. it was blacklisted by Cornell. pity for them.

[bo198214]

In special relativity, time occurs always in ict, where i is the imaginary unit, c the light speed and t the time.
(Note that "complex" denotes real and imagenary part, I understood you as time not being complex but imaginary.)
In that way you can regard time as imaginary part in a certain way.
But, note also that the complex numbers have only 1 real part and not 3 (and only 1 imaginary part).

If you have an additional time dimension then you can explain time travel in the previous time dimensions. Though you also get paradoxes if you involve all time dimensions. Time travel assumes implicitly an additional time dimension: First I am in time t1 and then I am in time t2, this "first" and "then" indicate an additional time dimension.

[moonlord]

thigle, you'll need to point out the difference between S1 and RP1... :?

[bo198214]

The real projective plane can be obtained from a square by identifiying edges (look at the pictures here or here)

The real projective plane is not embeddable in 3d. The sphere is.

[moonlord]

Well I know these. I meant, what's the difference between S1 - a circle, and the real projective line (that is, RP1).

[thigle]

S1 - a circle, is embeddable in 2d
RP1 is not embeddable in 2d, because the span of flat euclidean dimension is +- potential infinity, while one of the points of RP1 is ideal point, thus dwells in 'actual' - projective infinity, just beyond the potential infinity where E1.

perhaps i am wrong, but i would consider S1 with r=infinity and centre at ideal point at infinity to be same as RP1, but that's very special case of circle - horocircle in wendy's terms.

RP1 spans both ways from one ideal point and both ends meet at origin, while S1 is centrifugal - all the points at equal distance from centre.

[bo198214]

oops, i am too high in dimension.

The only closed 1-manifold is S₁, as far as I know.

[houserichichi]

The only closed connected 1-manifold, anyway.

[jinydu]

When I was studying special relativity, after I was shown the formula for spacetime distance, my professor said something along the lines of:

"Minkowski looked at this and said: "Oh, time is imaginary!" People soon realized it doesn't work." (I'm not as sure about the last sentence).

He then went on to talk more about Special Relativity, without explaining why time cannot be regarded as imaginary.

[thigle]

The only closed connected 1-manifold, anyway.

what about trefoil-knot ?

[houserichichi]

The trefoil is homeomorphic to S1, it's just not deformable to it in R3. However, in R4 all knots can be deformed to circles so there are no knots in four dimensional real space.

[bo198214]

I tried to explain the difference between homotopic and homeomorphic in this thread.

[thigle]

i tried to understand it but how does it relate to S1 / trefoilKnot issue ?

in that thread you mention there is written that something is homeomorphic to something only if it's homotopic. so S1, being homeomorphic to trefoil, is also homotopic with it, by simple syllogistic logic.

so, what is the important difference between S1 & trefoil, if any ?

[bo198214]

If you embed S₁ as circle in R³ and embed S₁ as trefoil (or any other non-trivial) knot in R³ they are not homotopic.

No, I mention that if two embeddings are homotopic then they are also homomeomorphic not the other way around.

[steelpillow]

The spacetime of general relativity is called Minkowski spacetime. ISTR that in the maths, time behaves somewhat like an imaginary dimension of space. Quite why we experience thiings the way we do is a mystery.

But other kinds of spacetime have been proposed. The most famous are the 10-dimensional string theories and the 11-dimensional M-theory. A typical string theory adds three more real dimensions of space and three imaginary ones (the six together are called a Calabi-Yau space).

Steven Hawking suggested that time might itself have both a conventional "real" and a second "imaginary" dimension (I use quotes due to the difficulties of interpreting Minkowski spacetime). This would be truly "complex time" in the mathematical meaning of complex. I hope one day to come across an accessible discussion of how this would work.