Hidden variable in SR and GR Relativity?

  • Thread starter Karlisbad
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"Hidden variable" in SR and GR Relativity??..

My question is, since we live in a 3-D world, what would happen for an "alien" living on a 4-D world??..if we suppose that space-time has only 4 dimension, and that after a Wick rotation then [tex] X_{0} =it [/tex] then what we think is just a time component for this being would be only an spatial component... then this "being" to describe the evolution and dynamics of its world would need to insert an extra parameter "s" (unphysical??) that we can't see or measure so [tex] X_{\mu}(s)=X_{\mu} [/tex], in this case i think that the "evolution" of a quantity in GR should depend on this "s" and hence:

[tex] g_{ab}(x(s),y(s),z(s),t(s)) [/tex] and [tex] L_{E-H}=\int_{a}^{b}ds\(-g)^{1/2}R(s)ds [/tex]
 

Hurkyl

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No we don't; we live in a 3+1-D universe.
OK,OK Hurkyl..but if we make a "Wick Rotation" (from real to complex plane) the Lorentz metric becomes just [tex] g_{ab}x^{a}x^{b} [/tex] where all the diagonal components are just 1 and the rest 0 (Euclidean 4metric) in fact:

- To describe the dynamic of a particle in one dimension we define two parameters [tex] (x,t) [/tex]
- To describe the dynamic of a particle in 2 dimension we need to define [tex] (x,y,t) [/tex]
- Hence to define the dynamic of a particle in 4-dimension we need ¡¡5 parameters¡¡ [tex] (x,y,z,t) [/tex] However we only can define x,y,z and t physically
 

Hurkyl

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There is no notion of time in a 4+0-D universe. It's just space. Why would there be dynamics?
 
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The Question Hurkyl..from the Physical point of view is that Physicist always need to look at the "Dynamic" of everything (space-time, particles, and so on) we always look in quantization expressions of the form:

[tex] i\hbar \frac{\partial \Phi}{\partial t}=H\Phi [/tex]
 

Hurkyl

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Physicists only look at dynamics because they're studying a 3+1-dimensional universe. When you change the problem to a 4+0-dimensional universe, you study it in a way appropriate for a purely spatial universe. e.g. in (it, x, y, z) coordinates, you'd use a "quantization expression" of the form

[tex] -\hbar \frac{\partial \Phi}{\partial (it)}=H\Phi [/tex]
 

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