Register to reply 
3 space and 1 time 
Share this thread: 
#1
May508, 03:11 PM

P: 4

I often feel think that the threedimensional space and the onedimensional time can be viewed as arising due to a basic spinorial structure. I am drawing an analogy with the triplet and singlet states which arise when two spin 1/2 are added. Can we say that space and time basically arise from the coupling of two spinorial structures, the triplet combination giving the 3d space and the singlet combination giving the 1dimensional time?
Please bear with me if my observation looks very crazy. 


#2
May508, 03:45 PM

P: 410

There is a relationship between spacetime and spinors, but it isn't the one that you think (although I will ponder upon it).
You can assign to every 4vector satisfying [tex]v^2 = 1[/tex] a 2x2 special unitary matrix satisfying [tex]\det u = 1[/tex], etc. Now SU(2) matrices transform as two copies of SU(2), whereas spinors transform as one copy. So it is often said that spinors are "square roots" of vectors. There's a related construction for null vectors and this goes by the name of twistors. 


#3
May508, 05:57 PM

P: 27

the basic space time group : Lorentz group can be decomposed into SU(2)XSU(2). So you see all inertial frames are basically connected by a bispinor structure...



Register to reply 
Related Discussions  
Re: timespace... Why the paradoxes of time? (CONFUSED)  Special & General Relativity  10  
Is time, inside an event horizon, timelike or spacelike?  Special & General Relativity  34  
Time and the Time Space Continuum  General Physics  1 