trying to understand Feynmann diagrams ?

[Widdekind]

Do the following "rules" apply, to interpreting FDs ?

 

1. each & every emission, or absorption, of a force-carrying boson, represents a "forceful interaction", i.e. wave-function "collapse", which "conforms" fermions "emerging from the interaction", into eigenstates, of the force, of the interaction, e.g. EM, W, S (er go, "ghosted out" super-position states can only exist, in between wave-function "collapses", i.e. in between interactions)
   
2. when force-carrying bosons decay, into "con-joined fermion pairs", e.g. [math]g \rightarrow \bar{q}q[/math], those fermions emerge from the interaction, in an entangled state (which is also an eigenstate, of the force, of the interaction), cp. Cooper pairs, i.e. one boson (force-carrier) decays into one boson (entangled fermion pair)
   
3. when boson-like, fermion pairs interact with other fermions, via other bosons, entanglement is "broken", and the "conjoined fermion pair" separates, into (mutually consistent) separate fermions
   

 

[Widdekind]

If neutral pions [math]\pi^0 = (\bar{d}d)[/math] can decay into "positronium" [math]P^0 = (\bar{e}e)[/math], via gluon exchange between the incident quarks; then, by time-reversal symmetry, can leptons also exchange gluons (when exposed to their anti-particles) ?

 

[Widdekind]

I understand that

 

each quantum mechanical object is joined through its interactions with all it touches...

 

quantum entanglement...gives quantum-mechanical objects which have common roots a non-local connection (dickau)

Now, in the beta-decay, of cobalt-60 nuclei, the electrons are preferentially ejected anti-parallel to the nuclear spin. And, for a down-quark, in a neutron, to decay, into an up-quark, in a newly-restructured proton, presumably requires that the down-cum-up quark undergo a "spin flip". Er go, to conserve angular momentum, when the emitting down-cum-up quark undergoes a [math]\Delta S = 1[/math] transition, presumably requires that the electron & anti-neutrino emerge with parallel spins. But, beta-decay is a Weak interaction, which only couples to LH leptons, and RH anti-leptons. So, if the electron & anti-neutrino are spin-parallel, then they are presumably momentum anti-parallel. Er go, the anti-neutrinos presumably emerge, from the decay, in the direction of the nuclear spin, opposite the direction of the electrons, i.e. "they fly apart", "[math]\bar{\nu}[/math] up, [math]e[/math] down":

 

Now, according to the Lepton mixing matrix, the "electron-like" lepton quantum states, that couple to, and are generated by, Weak interactions, are mixtures, of the two lowest-mass lepton generations, vaguely [math]|l_e\rangle \approx 0.9 |l_1\rangle + 0.5 |l_2\rangle[/math].

 

Therefore, I understand, that what emerges from the beta-decay, of a cobalt-60 nucleus, are a "Weak electron" [math]|e_W\rangle \approx 0.9 |e\rangle + 0.5 |\mu\rangle[/math]; and a "Weak anti-electron-neutrino" [math]|\bar{\nu}_e\rangle \approx 0.9 |\bar{\nu}_1\rangle + 0.5 |\bar{\nu}_2\rangle[/math]. And, I vaguely understand, that, arising from a common [math]W^{-}[/math] boson, the electron & anti-neutrino emerge in an entangled state:

 

[math]\approx 0.9 |e\rangle|\bar{\nu}_1\rangle + 0.5 |\mu\rangle |\bar{\nu}_2\rangle[/math]

If so, then when the "Weak electron" interacts with the environment, e.g. electro-magnetically (EM); the "Weak electron" will undergo wave-function collapse, into an eigenstate, of the EM interaction, i.e. a "physical" or "canonical" or "mass" eigenstate. If so, then approximately 3/4^ths of the time, the "Weak electron" would collapse into an electron; and approximately 1/4^th of the time, into a muon. Meanwhile, the entangled anti-neutrino would collapse, into corresponding-and-complimentary states.

 

Is this true ? If so, could the decay of cobalt-60, coupled with a quantum 'measurement' of the emerging electrons, generate neutrino beams, in "physical mass" eigenstates, not "Weak flavor" eigenstates ?

[Widdekind]

As a general rule, do all 'particles', emerging from any forceful interaction, emerge into a co-mingled entangled state, until one (or more) of the particles, undergoes a subsequent interaction ?? I.e. the "natural state" of quanta, is to be entangled, in between interactions ??

 

E.g. the mean-free path, through inter-stellar space, is ~10 Glyr for photons; and <1 lyr for H atoms (assuming [math]d \sim 1 \aa[/math]). Converted into times, t=d/v, yields ~10 Gyr, and ~10 Kyr, respectively. If so, then photons, emitted by processes within our galaxy, could possibly arrive at earth, in still-entangled states; and, the fraction of still-entangled photons could possibly provide range-to-source information. Could astute measurement techniques, cp. "weak measurement", distinguish between still-entangled, and already-collapsed, photons ??

 

Human scientists have generated entangled matter-energy, electron-photon, states, from artificial atoms (Quantum Dots), that "can emit photons one at a time, such that photons are entangled with [the artificial quantum atom]":

 

"[entangled quantum states] can communicate with one another over long distances...

 

Quantum entanglement...is a fundamental property of quantum mechanics. It allows one to distribute quantum information over tens of thousands of kilometers, limited only by how fast and how far members of the entangled pair can propagate in space" (SD 2010)

Indeed:

 

In the quantum mechanical phenomenon of "entanglement", two quantum systems are coupled, in such a way, that their properties become strictly correlated. This requires the particles to be in close contact... Entanglement which is generated in a local process [can] be distributed among remote quantum systems... One way to achieve this is to use photons for transporting the entanglement... Entangled quantum states are extremely fragile, and can only survive if the particles are well isolated from their environment.

And, stimulated Rubidium atoms emit photons, with which they are entangled:

 

a laser pulse stimulates the single atom [of Rubidium] to emit a single photon. In this process, internal degrees of freedom of the atom are coupled to the polarisation of the photon, so that both particles become entangled

However, when quantum systems are entangled, all of their past interactions are reversible:

 

The photon is transported through a 30 m long optical fibre into a neighbouring laboratory where it is directed to the BEC. There, it is absorbed by the whole ensemble. This process converts the photon into a collective excitation of the BEC. "The exchange of quantum information between photons and atomic quantum systems requires a strong light-matter interaction... For the single atom, we achieve this by multiple reflections between the two resonator mirrors, whereas for the BEC, the light-matter interaction is enhanced by the large number of atoms."

 

In a subsequent step, the physicists prove that the single atom and the BEC are really entangled. To this end, the photon absorbed in the BEC is retrieved with the help of a laser pulse and the state of the single atom is read out by generating a second photon (SD 2011).

What constitutes a "strong light-matter interaction" ?? Would an isolated atom, in deep space, emit coherent & entangled photons ?? For, information can be transferred, to-and-from energy-and-matter, with sufficient precision to reconstitute the original information; but without, seemingly, involving entanglement (SD 2007).

 

 

Decay product particles emerge entangled ?

 

the Bose-Einstein condensate is left with only one single way to dispose of its energy: emitting pairs of atoms... The emitted twin atoms cannot be understood in the same way as classical particles, such as debris scattered into all directions in an explosion. They are quantum mechanical copies of each other and only differ by their direction of motion. They form one common quantum object. One atom cannot be mathematically described without also describing the other (SD 2011)

Edited January 30, 2012 by Widdekind

[Widdekind]

I understand, that in the Feynmann path integral approach, all possible paths are attributed phase factors [math]e^{\frac{1}{\hbar}\int p dx}[/math]. Relativistically, [math]p \rightarrow \infty[/math] as [math]v \rightarrow c[/math], which drives the phase factors to oscillate "wildly", and so tend to cancel out, i.e. destructively interfere. Does that, then, limit possible paths, to the future light-cone, of some starting "event" (t,x) ??

 

(I.e. the Classical limit corresponds to [math]c \rightarrow \infty[/math], so that the future light-cone "opens out" until the cone "lies flat", and admits paths over arbitrary distances, at arbitrary velocities, throughout the "entire future" of that even (t>0, x="anything"), in Classical QM ??)