Parallel Universes

[Guille]

Post 1,111!
Correct me if I'm wrong, but up to what I know, Paul Dirac came along an equation that has his name. This equation impplies, atleast, another universe apart form ours in which the amount of matter/anti-matter are opposite.

Dirac's equation is:

and it is a special case of Shroedinger's equation:

And from dirac's equation we derive the "Dirac Hamiltonian":


Now, I think that, Antonio, still, is probably the only person to answer my question, but if someone can, please do so. My question is:
In what way, or what part or what of Dirac's equation impplies that there is an opposite parallel anti-universe?

[AntonioLao]

Dirac equation is applicable only for fermions (specifically, just the electrons and positrons) and their antiparticles. There are still the bosons and their antiparticles to think about. A theory for bosons is quantum electrodynamics (QED) or quantum field theory of the electromagnetic interactions between fermions and bosons. The extensions of QED are the electroweak standard model and quantum chromodynamics (QCD) of the color charges of quarks and gluons. QCD is still not a complete theory until the Higgs bosons is discovered.

[Guille]

So, then, dirac's equation is of tensors, right? Because tensors are only of fermions.


And, then, if dirac's equation is "spinorized", i.e. made of spinors, then, both fermions and bosons would me managed by the equation? If so,, there are anti-forces for every force!

[AntonioLao]

GUILLE,

Dirac equation is purely spinors. The distinction between fermions and bosons have to do with their wave functions. Symmetric wave functions for bosons and antisymmetric for fermions. These led to two basic spin statistics the Bose-Einstein statistics and the Fermi-Dirac statistics.

[Guille]

GUILLE,

Dirac equation is purely spinors. The distinction between fermions and bosons have to do with their wave functions. Symmetric wave functions for bosons and antisymmetric for fermions. These led to two basic spin statistics the Bose-Einstein statistics and the Fermi-Dirac statistics.

Wait, wait, wait.....

You have mized maths that are so disparate that it doens't make sense.

What does spinors have to do with symetricy and what does this last one has to do with statistics?

And, if birac's equationis spinors, shouldn't it be usefull for fermions and bosons?

[AntonioLao]

GUILLE,

Spinors are 2-component matrices with complex elements. It solved Dirac's linear energy equation.

[Guille]

GUILLE,

Spinors are 2-component matrices with complex elements. It solved Dirac's linear energy equation.

"Complex elements"?

[AntonioLao]

"Complex elements"?

The elements of the matrices are complex numbers.

[Guille]

The elements of the matrices are complex numbers.

What is dirac's linear equation and why/how is it solved?

[AntonioLao]

What is dirac's linear equation and why/how is it solved?

The relativistic form of Schroedinger's original wave equation is quadratic in the partial derivative with respect to time. It was able to demonstrate agreements with the Balmer formula of spectral analyses. However, it failed to account for the correct fine structure of the hydrogen D-doublet spectral lines. At this time, many people were working on this problem. They were working on a scalar wave equation which could basically give a nonpositive definite probability density since squares of all negative and positive densities give positive answers. Dirac believed at the time that the requirement for positive definite probability densities must have their wave equation linear in the partial time derivative.