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Author Topic: 2D complex time  (Read 2630 times)
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Yesiamjames
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« on: October 06, 2011, 05:50:56 PM »

I'm sure some smart ass has come up with this before but I've come up with a hypothesis which could have some interesting implications to M theory.

I was talking to a friend of mine earlier who mentioned that since time was created at the big bang the definition of "before" the big bang is meaningless. I personally think that there has to be a cause and Occam's razor implies that a God at least in the theistic sense isn't the answer as an all-knowing, all-powerful, all loving being by necessity would have to be more complex than the universe itself and couldn't have simply have spontaneously formed without evolving. Since there should be a cause and cause is only possable with time we are left with a real problem which I think I may be on the way to solving.

1. The universe had a cause.
2. Time started at the big.
3. Causality only appears possible because of time.
4. therefore there could be another dimension of time making causality possible which didn't start with the big bang and therefore exists independently.
5. We will call this "imaginary time" and we will call time that we perceive as "real time".
6. Since imaginary time exists independently of real time we can plot a collection x, y points for what I would call "complex time".

Ok I'm sure everyone can see where I'm headed with this! Steven Hawking describes time as a "half dimension" in a brief history of time so prehaps plotting points of complex time would have to start with an absolute zero values, effectively limiting us to 1 quadrant of a graph from 0, 0i to inf, infi. If my premises turn out to be accurate and we can figure out the right formular to use we could in theory render a fractal using real and imaginary time as x and y which would tell us something about our universe or even the nature of the multiverse itself.

Prehaps the Mandelbrot version would be a set of all stable universes with low itteration bands representing the most unstable of universe, whereas all the "connected and nearly connected" Julias represent something about individual stable universes (one of them would even describe our own.

Prehaps the "seed value" of a given universe could determine the strength of the universal constants for example. And individual points could represent the state of a particular x,y,z possition at a given point in complex time.

Or prehaps they would represent something else about the nature of reality which I haven't thought of.

Could I be on to something or am I just talking non-sense?
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DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #1 on: October 06, 2011, 10:54:08 PM »

If your theory scares your cat, it surely works. 1st axiom of the fractal sound relativity snore grin
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No sweat, guardian of wisdom!
fractower
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« Reply #2 on: October 06, 2011, 11:02:59 PM »

I am not sure about god, but I can shed some light on the physical implications of imaginary time based on simple quantum mechanics.

The wave function for a free particle can be written as \Psi(t,r) = F(r,t) exp^{i(Et -kr)}. Where E is energy and k is the wave number. The envelop function F(r,t) must meet the normalization requirement <\Psi|\Psi>=1 (a short hand for the integeral over all space of |\Psi(r)|^2 and  |\Psi(r)|^2 is the spacial probability density of the particle.)

If time is allowed to be complex, then the wave function will will either exponentially explode or contract. This can be interpreted in two ways. Either the complex component of time must be zero, or the time component of envelop function F(r,t) must have a balancing exponential term. Either way it does not appear to create an observable.

There are known cases where the wave number k can become complex. Writing energy as the sum of kinetic energy and potential energy E = E_k + E_p where kinetic energy E_k = k^2/(2m). In a classical system such as a ball rolling toward a hill, the ball will stop and roll back when E_k becomes zero. In a quantum system however E_k can become negative giving an imaginary k. This imaginary k causes the wave function to exponentially decay as it enters the classically forbidden region. Normally no-one would be the wiser, but if the hill happens to be tall and narrow, some of the probability can leak through the hill into the classically allowed region on the other side. This is known as tunneling.

The energy term can also become imaginary at least from a mathematical sense if not in reality. Energy can also be written as E=Mc^2 where M = m/sqrt{1 - v^2/c^2} is the relativistic mass. The mass becomes infinite when v = c but when v>c the mass becomes imaginary. Maybe the recent neutrino findings will have something to say about this.



« Last Edit: October 06, 2011, 11:10:01 PM by fractower » Logged
Sockratease
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« Reply #3 on: October 06, 2011, 11:11:34 PM »

I recall seeing one of those tv documentaries about weird physics where some guy  (yes, THE some guy of many obscure theories fame)  claimed that time did not exist at all.

By removing time from his calculations, he was able to complete a Grand Unification Theory of a sort.

It was rejected because most people believe time exists.  But others claim time is just an illusion.  Like god!

If your theory scares your cat, it surely works. 1st axiom of the fractal sound relativity snore grin

My cat scares easily.  Could have something to do with our living conditions...



Bigger: http://www.sockrateaze.com/stuff/meowza.png
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Life is complex - It has real and imaginary components.

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Yesiamjames
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« Reply #4 on: October 07, 2011, 02:23:16 AM »

Fractower: I hadly understood any of that, except for the last 2 paraghaphs. I appreciate the effort though. This is the first forum I've joined where most people can pwn the crap out of me at maths and physics.

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fractower
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« Reply #5 on: October 07, 2011, 10:37:16 PM »

I did not mean to pwn anyone. OK maybe a little.

Quantum mechanics also has something to say about causality. It turns out that quantum mechanics includes an random or non-causal process. This is independent of the uncertainty principle but is instead related to the collapse of the wave function. Consider a hydrogen atom whose electron has just be excited out of the ground state. It will eventually return to the ground state and emit a photon. The statistics are well defined, but no known mechanism exists to predict the exact time. One could imagine a small timer that tells the photon when to leave, but Bell's theorem rules out a local mechanism.

If one accepts that causality is not fundamental on the microscopic scale, it is quite possible that macro causality is just an emergent property. This could be like fluid dynamics is an emergent property of atomic theory, which is an emergent property of quantum field theory, which is an emergent property of... It's turtles all the way down.

 
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Yesiamjames
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« Reply #6 on: October 08, 2011, 01:08:06 AM »

Don't worry I'm hear to learn. That does make a lot of sense but I do need to learn a LOT more about quantom theory.
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