Conversation with @GlenTheUnderboat

T Abraham

Jan 2, 2015 19:43

Ok, I have been trying to figure out the probability of a quantum particle to go thorugh the most optimized path.. similar to the lagrangian..

Glen The Udderboat

Such probability is exactly zero.

T Abraham

meaning?

Glen The Udderboat

I have an answer somewhere explaining that. Looking it up...

Here's one, with zero uproots: physics.stackexchange.com/a/56180/17609

^upvotes

T Abraham

so I can't figure the probability of the particle taking the optimized path bcos it's zero?

Glen The Udderboat

6

A: How light know which path is smallest?

A way to understand this, is to imagine that light actually follows all paths. However, most paths experience destructive interference with other paths. The only paths that do not experience destructive interference are those in the neighbourhood of paths with stationary (e.g., minimal) action (t...

T Abraham

Jan 2, 2015 19:50

Thanks so much!!!!

Glen The Udderboat

The earlier answer was better (for your purposes).

T Abraham

Well the thing was I was trying to answer this question that I asked myself:

5

Q: Plants and Quantum Mechanics!

So, I have been working on quantum biology and found something interesting that I would like to write an equation for: Scientists have wondered how plants have such a high efficiency in photosynthesis... They always thought that the photons' energy (needed for photosynthesis) reach the "reaction...

So would that question you linked answer my question as well?

Glen The Udderboat

Very similar stuff. Read the mentioned QED book. You'll figure it out. And much more. Kind regards, Glen Path The Integral Udderboat III.

T Abraham

@GlenTheUdderboat is there an online resource?

Glen The Udderboat

@TAbraham It's a cheap book, probably $7 or so. And sure, there must be plenty of it online.

T Abraham

Jan 2, 2015 19:55

1

Q: Probability of a path

Let's say I have quantum particle and I wanted to find the probability that this particle goes through a chosen path. Is this practically possible?

quantum-mechanics

Glen The Udderboat

QED: The Strange Theory of Light and Matter

QED: The Strange Theory of Light and Matter is an adaptation for the general reader of four lectures on quantum electrodynamics (QED) by Richard Feynman (1918-1988). QED was designed to be a popular science book, written in a witty style, and containing just enough quantum-mechanical mathematics to allow the solving of very basic problems in quantum electrodynamics by an educated lay audience. It is unusual for a popular science book in the level of mathematical detail it goes into, actually allowing the reader to solve simple optics problems, as might be found in an actual textbook. But unlike...

T Abraham

any help on this question?

Glen The Udderboat

Paths have amplitudes, not probabilities. They'll tell you that.

That's the whole beauty of it.

Probability amplitude

In quantum mechanics, a probability amplitude is a complex number used in describing the behaviour of systems. The modulus squared of this quantity represents a probability or probability density. Probability amplitudes provide a relationship between the wave function (or, more generally, of a quantum state vector) of a system and the results of observations of that system, a link first proposed by Max Born. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. In fact, the properties of the space of wave functions...

T Abraham

@GlenTheUdderboat so path integrals have nothing to do with this stuff?

Glen The Udderboat

Sure they do. Except you can understand the whole thing without knowing integrals too much.

Path integral formulation

The path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique trajectory for a system with a sum, or functional integral, over an infinity of possible trajectories to compute a quantum amplitude. The basic idea of the path integral formulation can be traced back to Norbert Wiener, who introduced the Wiener integral for solving problems in diffusion and Brownian motion. This idea was extended to the use of the Lagrangian in quantum mechanics by P. A. M. Dirac...

T Abraham

Jan 2, 2015 20:00

Thanks so much... You have been so helpful!

oh, you think you can answer this:

5

Q: Plants and Quantum Mechanics!

So, I have been working on quantum biology and found something interesting that I would like to write an equation for: Scientists have wondered how plants have such a high efficiency in photosynthesis... They always thought that the photons' energy (needed for photosynthesis) reach the "reaction...

quantum-mechanics quantum-information path-integral superposition

Thanks again!

Glen The Udderboat

@TAbraham I've read about it. Years ago. So the idea isn't new. The difference here, I think, it that the paths are forced to be discrete, as opposed to 'normal' light.

T Abraham

meaning?

Glen The Udderboat

But the point probably remains that you're not supposed to look at which path is taken, because then the whole interference thing stops working.

T Abraham

@GlenTheUdderboat i don't get it, what do you mean?

Glen The Udderboat

@TAbraham Meaning a countable number of paths (summing) vs an uncountable number (integrating).

T Abraham

Jan 2, 2015 20:05

@GlenTheUdderboat oh.. so all the info you gave me doesn't really apply? can't I justt make it discrete?

Glen The Udderboat

Sure, that should be easier. But you still can't tell which path was taken.

Double-slit experiment

The double-slit experiment is a demonstration that light and matter can display characteristics of both classically defined waves and particles; moreover, it displays the fundamentally probabilistic nature of quantum mechanical phenomena. This experiment is sometimes referred to as Young's experiment. The experiment belongs to a general class of "double path" experiments, in which a wave is split into two separate waves that later combine back into a single wave. Changes in the path lengths of both waves result in a phase shift, creating an interference pattern. Another version is the Mach–Zehnder...

T Abraham

@GlenTheUdderboat but it should still explain the phenomenon.. correct?

I just want to write an equation for this phenomenon to explain it... I thought to do so we would have to know which path was taken but i guess not...

Glen The Udderboat

@TAbraham I think so. At least that's how I read it at the time.

T Abraham

@GlenTheUdderboat Thanks for the help...

Glen The Udderboat

@TAbraham No, you have to describe the probability amplitude for each path instead.

T Abraham

Jan 2, 2015 20:09

@GlenTheUdderboat oh yeah.. that's what I meant... but I am not sure how to do that.. that's why I was talking about path integrals as someone adviswed me to use themm.

Glen The Udderboat

You'll have the compute the length (or rather: time) of each path. That's the crucial ingredient.

T Abraham

@GlenTheUdderboat how?

Glen The Udderboat

Well, time = length.

T Abraham

@GlenTheUdderboat I still don't see what your trying to say.. first you said to compute the length rather than time but now you said time is length...

Glen The Udderboat

Yes, if one path is half a wave-length longer then another path, then these paths will destructively interfere, and probability will be zero for the two combined.

However, if the difference is a multiple of the wavelength, then they will constructively interfere.

T Abraham

Jan 2, 2015 20:14

so how do take every single path and their probability amplitudes into account?

Glen The Udderboat

I suppose you get an idea of all possible paths from looking at the cell structure of a leaf through a microscope.

And if you don't have a microscope, you just make up a structure. A crystal or raster perhaps.

T Abraham

@GlenTheUdderboat ok, so after the strucutre is figure out, from that is there a technique to figure out the possible paths light could travel?

that's the tricky part..

Glen The Udderboat

@TAbraham The structure defines all possible paths. Just like all the paths that the king can take on a chess board.

A path is nothing more than a series of steps from one cell to a neighbouring cell, I would suggest.

T Abraham

Now, since there are so many chemicals and particles, many sugggest to describe like an open quantum system.. what do you think on that?

Glen The Udderboat

Not much. Don't know enough about them. Anyway, the answerers to your question do seem to have a good clue. What's not sufficient in their answers?

T Abraham

Jan 2, 2015 20:27

@GlenTheUdderboat nothing, their answers are great, I just want many opinions on the question...

do you think you can answer my question with the info you gave me? I just want to have it for documenting purposes so I can quickly refer to it...

Glen The Udderboat

Certainly not. I'm just making this up on the spot. :)

T Abraham

@GlenTheUdderboat but the ifno you gave me was pretty helpful...

Glen The Udderboat

@TAbraham Hopefully, but not an answer to the question.

The h Bar

Participants