spin and time axis

[AntonioLao]

There is no distinction between spin and time axis. In quantum mechanics, spin is quantized with values of [math]\pm\frac{1}{2}\hbar[/math]. Since the zero point energy of one harmonic oscillator is given by [math]\frac{1}{2}\hbar \omega_0[/math], it means that the zero point energy is just the product of spin and the fundamental angular frequency. Time axis is dual (showing similarity with spinors), meaning it has a positive and a negative component or positive and negative direction. On the average, the orientation of these two components is nearly opposite. However, their absolute magnitudes have wide differences. These differences are relatively small for bosons, relatively big for fermions. Nevertheless, unlike spinors it is not necessary to represent these magnitudes by complex numbers unless the imaginary parts of the orthogonal space axes (as analogy of phase factor [math]e^{i\alpha}[/math]) are included in the formulation. Real numbers representations are more than sufficient. The maximum magnitude is equivalent to [math]\frac{1}{2}\hbar[/math], the minimum is theoretically zero. In other words, the upper limit of the absolute difference between the magnitude of these dual time axes can never be greater than [math]\frac{1}{2}\hbar[/math]. The lower limit is identically zero, the zero of all zeros. The photon should have its absolute difference magnitude of dual time axis nearly the true zero. It is the wide differences of these magnitudes, which are responsible for double rotations (720 degrees instead of the normal 360 degrees) of fermions returning to their initial quantum states.

The normalized column eigenvectors of the bosonic axes are [math]b_1=\left(\begin{array}{c}+1&-1\end{array}\right)[/math] and [math]b_2=\left(\begin{array}{c}-1&+1\end{array}\right)[/math]

For the fermions, there are four normalized eigenvectors

[math]f_1=\left(\begin{array}{c}+0&-1\end{array}\right)[/math], [math]f_2=\left(\begin{array}{c}-0&+1\end{array}\right)[/math],

[math]f_3=\left(\begin{array}{c}+1&-0\end{array}\right)[/math], [math]f_4=\left(\begin{array}{c}-1&+0\end{array}\right)[/math].

If we are allowed to join two eigenvectors into 2 by 2 matrices then the concatenations of the f’s give two of Pauli spin matrices (except for the one with complex elements), e.g., [math]\sigma_x=f_2 f_3 [/math] and [math]\sigma_z=f_3 f_1[/math]. Furthermore, the concatenations of the normalized column bosonic eigenvectors formed the singular matrices (zero determinants) of quantized space.

[Guille]

If the spin is indentical to the time axis, it means that if one is proved or disporved then the other one also.

Do you mean "equal" in this way'

[AntonioLao]

If the spin is indentical to the time axis

The spin is the measurable part of the time axis. All elementary particles have the property of spin. The hypothesized graviton has a spin of 2. The imaginary part of the time axis eluded measurements. However, a duality theorem says that the real and the imaginary parts of time axis are inseparable. If the positive part exists then the imaginary part must also exists. It is just not detectable.

[pramodmaths]

I would like to ask about the title "spin and time axis"
that "does the electron really spins?"
If not! what we always talk about?Is it really a particle?
no.
only to describe it's degree of freedom we introduce a quantum
number and call this spin .On this concept we describe several
propperties like magnetic moments and so many things,even
without convincing ourselves to the question,"waht electron really is?"
Is it not to hide our incapability??

[AntonioLao]

"does the electron really spins?"

It does. However, the intrinsic spin axes is quantized. There are only two possible directions, say, up or down.

[pramodmaths]

I want to know that "why the bosons are the mediator of all interactions?
why not the fermions?Is it only due to the reason that the coupling of
fermions may give both type of spins(integral and half integral) or there
is some advanced reason behind this?"

[dleviwing]

To offer a less mathematical interpretation:
Bosons should be viewed as measured dimensions of quantum energy increments just as we view the photon as the amount of energy absorbed or emitted.
Calling them particles only create confusion and make the topic seem more complex than it really is.

You may wish to ask: "What is exchanged in these interactions"?

[AntonioLao]

Is it only due to the reason that the coupling of
fermions may give both type of spins(integral and half integral) or there
is some advanced reason behind this?"

Pauli's exclusion principle prohibits the coupling of fermions. They never happens, theoretically or experimentally.