Phase of a probability

Guest254 said:
There is no topic. We have one guy who insists on copying things down from wiki and MIT notes and pretending to understand them. We have another that alludes to being a government funded physicist who does no research and doesn't know about Hamiltonian mechanics.

I have no idea why these people make up the stories they do, but I imagine that pandering to their need to sprout rubbish only serves to perpetuate their habit.
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Apologies BenTheMan, this post was uncalled for. Your forum, your rules, to which I should abide.

Vkothii has moved onto gauge theory and topology now, so I'm quite eager to see how the thread unfolds.
 
Vkothii said:
K.
How would you rewrite that to get it into an action integral formulation - there are at least two. One mass and one charge integral.
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Why would you want to write the action as integrals over charge and mass? That would tell you how the solutions varied with charge and mass, but you aren't interested in that - we want to know how the Dirac particles behave as it moves in space time. The action is integrated over space time and it is

$$S = \int d^4 x \left(m \overline{\psi} \psi - \frac{i}{2} \overline{\psi} \gamma^\mu \left(\partial_\mu \psi \right)- \frac{i}{2} \left(\partial_\mu \overline{\psi}\right) \gamma^\mu \psi\right)$$

Vkothii said:
This "exercise" I thought has an interesting angle on the AB effect; you can do a gauge transformation that shows:
"... The gauge transformation is the gradient of a scalar function, and that gradient corresponds to the gradient in the probability of an interaction.

Thus by means of a variable index of refraction resulting from the absorption and emission of photons the probability density is transformed into a function of the local density of matter and energy, and so are the coordinates! ..."

Hint: there is a bit more to do than just derive the action for the EM field, but that's a detail of this I want to work through - see if it commutes with another view of the physical rep. (of information entropy).
Thing is, information has to be 'conveyed' in a classical sense which is necessarily irreversible.
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Are you talking about the Aharonov-Bohm effect? I don't see what this has to do with quantum information theory. It's about showing the gauge field $$A_\mu$$ is a more fundamental object that the electric and magnetic fields $$E$$ and $$B$$.

Vkothii said:
Oh yeah, the actual Dirac form:
$$ \psi_\pm(x,p)\, = \, \varsigma^{\script l}(p) \exp [{i \over \hbar} p^{\alpha} g_{\alpha\beta} {\chi^\beta}]
$$
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I presume you're using the greek letter chi for your space time coordinates here, despite the fact that psi is a function of x and p. This is quite an odd way of writing it, since chi is often used to write the Dirac spinor like this
$$\psi_s = \left(\begin{matrix}\phi \\ \chi \end{matrix}\right) $$
where phi and chi are 2 component Weyl spinors. I would write your solution like this:
$$ \psi_\pm(x^\mu)\, = \, \left(\begin{matrix}\phi \\ \chi \end{matrix}\right) \exp [\pm i p_\mu x^\mu]
$$
 
Final warning.

Either help Vkothii answer his question about Wilson lines, or go take your trolling to "About the Members".
 
prometheus said:
psi is a function of x and p. This is quite an odd way of writing it, since chi is often used to write the Dirac spinor like this
$$\psi_s = \left(\begin{matrix}\phi \\ \chi \end{matrix}\right) $$
where phi and chi are 2 component Weyl spinors. I would write your solution like this:
$$ \psi_\pm(x^\mu)\, = \, \left(\begin{matrix}\phi \\ \chi \end{matrix}\right) \exp [\pm i p_\mu x^\mu]
$$
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There's a way of writing it as a $$ \psi_\pm(x,p) = ? $$ You have to find a wave solution..? So you want the spinors in there - or the correct solutions for them..?

This is more a way to see the topology from another angle - the gauge transform. Is the Schwarzschild frame the only possibility here?
Do Dirac electrons as free particles, require that frame as a given, I mean are there other candidates (I haven't done any gauge stuff)?
 
Hang on just a minute! Since when are we talking about the Dirac equation in curved space? The machinery for quantum field theories in curved space is pretty limited compared to minkowski space QFT. The Dirac equation in Schwarzschild space is a highly non trivial problem - classically there are probably known solutions but quantum mechanically I doubt anything is in the literature. About the best we can do right now is QFT on a plane wave.
 
OK, I had some idea this guy's paper is going down a bit of a strange path.
I was more interested in the math, than the result itself.

I think the idea is to derive a relativistic eqn, do a gauge transform and assume a zero local curvature, to then derive a nonrelativistic form.
I don't want to get buried in it, just look at what's being done and why, hence the question about using a different metric for 'spacetime'.

The notion of a path integral is tied to the notion of 'communication' and irreversible changes, or events in spacetime. Right, it's a big subject and lots of ways to see the field/particle models.
I'm at the start of a QIS course, on my own bat I want to explore the basics, if I get a handle on the ideas then the math just seems to come more easily (I prefer to know why to derive something than how to just 'get a result').
I also realise some of this will bump into various ontological objections, etc.

P.S. This from the intro to the paper:

" ..the attempt is made where possible to translate the fluent geometrical language of General Relativity into the less rigorous, but more intuitive language of electrical engineering. A basic understanding of Quantum Mechanics, vectors and the index notation of General Relativity are required... The equivalent circuit for the transmission of probability waves through space-time is shown to be analogous to the transmission of waves through wave guides in quantum optics, or along transmission lines in electrodynamics. With this interpretation it is shown that the relationships between gravitation and electrodynamics compliment each other in the same fashion that the components of an electronic circuit compliment the sources of electrical energy.

What is presented here shows how the gravitational field can be modeled by variable component values in the equivalent circuit. In a linear circuit the component values do not depend on the strength of the sources."

So he assumes a completely linear "circuit" in each case (no corrections are assumed).

Looks like it could be an EE students attempt to explain the AB effect in GR terms. Maybe it makes some stretches that don't stretch that far?
Or it's an insight into gauge and spin, in terms of particle momentum - path integrals.

The question, ultimately, is WHAT is information? Well, it's what we say it is, essentially.
So how or why do we? (Maybe that's too simplistic for you guys)
 
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Vkothii---

What are we discussing here? I am completely confused (which may be little surprise to some people here).

We started talking about Wilson Lines, and now we're doing Dirac equation in curved space-time?

What do you want to talk about? What is the question you want to answer with this threaD?
 
I didn't say enough in that last post?

Start at step #1, the derivation of Taylor's expansion of an exponential product with complex exponents.
Why do you get an order 3 approximation, and of what?

How come? The expansion 'oscillates', is how come. It drives the time-evolution of a 'discrete' precession angle. The algorithm is the spin wavefunction.
An applied potential isn't "just some number". It's the equivalent of what drives a digital computer's CPU - the system clock.
So gauge theories are the geometry/topology of this EM field which is QFT.
 
Vkothii said:
I didn't say enough in that last post?

Start at step #1, the derivation of Taylor's expansion of an exponential product with complex exponents.
Why do you get an order 3 approximation, and of what?

How come? The expansion 'oscillates', is how come. It drives the time-evolution of a 'discrete' precession angle. The algorithm is the spin wavefunction.
An applied potential isn't "just some number". It's the equivalent of what drives a digital computer's CPU - the system clock.
So gauge theories are the geometry/topology of this EM field which is QFT.
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Now I'm more confused. You do know that the probability is the absolute square of the wavefunction, which kills the complex phase, right?
 
Yes, it's about (this thread is) looking at the engine - the field and what it "does" to fermionic spin.

Electrons aren't the only quanta in the field and we know how to play with a lot of 'quasiparticle' equivalents of wavefunction 'algorithms'. Measurement, or recovering a classical result is not trivial.
Understanding why/why not is another part of this QIS thing.

You guys have not ever done any algorithmics, huh? How about those topological gates, anyons in 2d?
 
What are you talking about? What field are you talking about?

Probabilities are real numbers, true or false?
 
BTM said:
Probabilities are real numbers, true or false?
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When we measure something, it's real, true or false?

I'm talking about the EM field - the one with electrons in it.

So what's the big problem with the phase 'collapsing' because it has to be the square integral of the wavefunction's amplitude?
 
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Well, is an event real, do we assign a real value to it?
Any observable is modeled as being selected, from a space; these 'spaces' are quite different classically and non-classically (i.e. in the quantum views of fields).
There are real probabilities assigned to classical variables, but not to quantum variables, observables evolve differently.
Or "we can't observe a wavefunction".
 
How about this question:
Are we talking about probability??

If we are, is an apple that's growing on an apple tree a probability?

Or does it "have" a probability, and what is "the real probability", since someone wants to know if a probability is a real number?

Did the question not go: "is a probability a real number?"

So, if it is, is an apple a real number? Or is something the apple "has", a real number?
Or, if it isn't, is an apple an imaginary number? Is whatever it "has" also imaginary, or WHAT??

Answer: apples are real, but they aren't "real numbers". Apples have a probability - actually several 'probabilities', which are events we associate with apples.
But the resident plonker would rather avoid that little mathematical problem, it bumps into way too much reality for them to handle, obviously.
 
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So electrons are in a different field, you mean? Not the EM field?
How about neutrons, what field are they in?

Don't you mean to say: "the quantum of the EM field is the photon".
The electron interacts with the bloody thing doesn't it? So electrons, protons, neutrons, any particle with electromagnetic charge, is "in the EM field" then.
 
Here's another obvious fuck-up that illustrates how opinionated you math-fucks are.

"The AB effect has nothing to do with quantum information, the same way QM has nothing to do with quantum information, or QFT, or QED, actually no quantum theory is remotely connected to information".

According to some expert here at this fucking pathetic forum.
I sure hope all that is sufficiently "semantically void manipulation" of the requisite symbology. Ben didn't fucking ask any FUCKING question.
What he did was bat my question away, because he is ignorant of what a quantum event is. Which means he's ignorant of what quantum information is.
Which means I am wasting my time asking any of you oh-so assured math types a bloody thing. Because you all have a fundamental lack of understanding of the goddam subject.

Most of them seem to think it isn't a subject, so much for that one, huh.
 
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