What is the true nature of path in quantum mechanics?

[SimonA]

What actually is "path" in QM

Marcus posted an intersting point here;

https://www.physicsforums.com/showthread.php?t=7245

"here's another piece of the jigsaw puzzle

in classical mechanics things move along trajectories---curved paths
parametrized by time---and when you quantize the trajectories go away.

the curved paths things travel along don't exist any more, you have to erase
the trajectories (or in Feynman sum over histories you "integrate" all
possible ways of getting from here to there---in any case the clear picture
of a path loses reality and dissipates)"

So in effect the "path" is something we (and our instruments) 'see' from the perspective of "being inside" Minowski spacetime.

In reality we have x in a state ready to expel energy and y receiving that energy. And we know that the receiving y will be the system that has the first 'relatavistic locality' to x.

Am I missing something there ?

 

[Antiphon]

A path is a mathematical device and is not a physical reality.

Path integrals are not exclusively QM. Classical physics uses them
to determine which "path" a ray of light will take when it reflects
from a shiny curved object (physical optics, asymtoptic evaluation
of integrals.)

In fact, the light takes all "paths" but you only see one shiny spot
because that's the spot where the nearby paths didn't cancel one
another.

Ultimately this path integral business in QM is just the same as physical
optics only the fields are quantum fields instead of classical em or acoustic
ones.

 

[SimonA]

Thanks Antiphon

My question is more about the nature of what's going on "behind the scenes". If light takes "all paths", and is particulate in nature, does the "photon" do its "path integral" calculations and then decide its destination ? I know I'm being simplistic, of course the ball you throw does not check up on Newton and then decide where to land. I'm looking for mechanism though.

Light can indeed take all paths if it is a wave. And then we say the wave function collapses here and the particle magically appears. So where exactly was the particle of energy observed ? It did not take a specific path at the start. But when it ran as a wave against something that absorbed its energy it became a particle (with frequency imbued from wave to particle in a magical kind of way).

How do we distinguish the process between emission and detection independantly ? I have to admit my undoubtedly ignorant suspicion that Einstein got the Nobel for his only significant mistake.

Simon

 

[reilly]

SimonA -- Einstein got it right. See Wolf and Mandel's Optical Coherence and Quantum Optics for an exhaustive discussion of the photoeletric effect and photoeletric detectors. That Einstein got it right has been accepted for almost a century. What's to argue?

Except under classical-limit circumstances, there's no such thing as a trajectory in QM. QM deals in probabilities, and that's exactly what the path integral formulation is about. Not that it is necessarily relevant to this discusion, but recall that the basic idea of the QM path integral is due to Dirac, as Feynman acknowledged. Further, if you will study the subject, it is based on computing the basic transition probability,
<X,T|x,t>. At best the idea of traversing all paths is a metaphor, a rather inexact one.

Among Feynman's many gifts was the ability to formulate great metaphors, which he used to make his profound mathematics a bit easier to understand. If you want to understand this stuff, you have a lot of work to do. Read Lanczos The Variational Principles of Mechanics, and Dirac's Quantum Mechanics. And that will just get you started. This stuff is not easy, takes most people several years of intense study to get to the point of minimal comfort with QM. That's just the reality of it. In my opinion at least, to have any chance of understanding QM, you must master QM's mathematics, and be highly familiar with the history of, at least, atomic physics.

Good luck and regards,
Reilly Atkinson

 

[SimonA]

Thanks Reilly for such a great reply. I am truly humbled by it. I mean that as someone who knows more than me on the subject treating my views with a kind of respect I doubt I would give anyone where I was confident I knew more than them on the subject, with reason.

And I do realize I have so much work to do to catch up on the basic formalism mathematically. But I'm still having problems understanding minowski space properly :)

But I'm also hungry to know and so I'm curious what you mean by;

At best the idea of traversing all paths is a metaphor, a rather inexact one.

Do you really consider that a photon travels as a particle between these two points ? I have my own reasons why I rekon the idea of quantisation in terms of EM is purely a theoretical construct driven by the nature of our instruments of observation.

I've been pointed to all these studies where the the reality of a quantised nature of EM is apparently described and even proven. But all of them seem easily explainable in terms of the frequency and nature of the wave, and the quantised nature of our instruments.

I actually rekon EM is in effect particulate from our perspective, but only due to a property of the energy band jump between spacetime and the extra dimensions. But that's irrelevant to this thread, I'm just curious why exactly people are convinced EM has a quantised nature independant of emiiter and detector. I just want someone to make a go at putting that in their own words.

Thanks

Simon

 

[reilly]

SimonA -- I appreciate your kind words. Indeed, you have brought up a very difficult and profound issue. I happen to belong to the "Shut up and calculate" school -- I was trained this way, and temperamentally agree. What that really means to me is that you learn QM by doing it. In practice, what that means is a suspension of belief or judgement, as is necessary to enjoy a Harry Potter flick or an opera, or a novel. As you do it, your intuition grows, you see how powerful a tool QM is. I'm still blown away by the success of QM, Balmer to Lamb, in dealing with the hydrogen atom, in dealing with superconductivity, with the Standard Model, and on and on. Given its extraordinary success, QM is by no means built on a flimsy facade. Understanding comes with application.

During my student days, Bohm's work on hidden variable was becoming known. My profs told me: stay on course, and worry about Bohm when you know what you are doing. And, as it turns out, once I began to know what I was doing, I'd lost interest in Bohm's hidden variable work and other alternative approaches to QM.

My take on paths, particles, waves and all that is: Nature puts us in the awkward position of understanding empirical phenomena that seem impossible, wave? particle?, by conventional notions. So, physicists must cope with very difficult conceptual and descriptive notions -- photoelectric effect vs. diffraction, electron scattering from crystals vs scattering from a proton and so forth. Each experiment is different, and requires different computations, and we are, I think, very fortunate to have a scheme that allows us to do these computations, even if we are troubled by some matters of interpretation. The plain fact is, that Born's idea of QM probability, Fermi's Golden Rule, and other basic approaches work extraordinarily well, so what's to worry?

We don't fully understand measurement? Well, we understand it well enough to keep physics going with experimental data, and to keep theoreticians busy.

I think to infer much of anything about "photon paths" is an exercise in futility -- if we don't measure, how can we know? We compute probabilities for specific measurements. Note the same thing is done in classical physics, say in the kinetic theory of gases. Einstein himself in the prelude to Special Relativity, see his little big book, Relativity, stresses the overwhelming importance of measurements.

If I'm honest, I'm not at all sure how the photon gets to the atom and then kicks out an electron. But I know it gets there. And, for the time being, the best I can do is to compute probabilities, and lo and behold, they, so far, are always correct.

With computation comes understanding. With experimentation comes understanding. Nature has tossed us a high, hard one, and no one has yet learned how to turn on an inside 200 mph fastball.

Regards and good luck,
Reilly

 

[NEOclassic]

SimonA --
During my student days, Bohm's work on hidden variable was becoming known. My profs told me: stay on course, and worry about Bohm when you know what you are doing. And, as it turns out, once I began to know what I was doing, I'd lost interest in Bohm's hidden variable work and other alternative approaches to QM.

Hi reilly and Simon,

David Bohm too, lost interest in a "hidden variable" that would help him to quantify the atomic electrons as being particles rather than being wave-like. In my opinion, Bohm had been wrongly persuaded that the HUP applied to all atomic electrons while it really applied only to those unpaired valence electrons and not to the co-called configurational Pauli-pairings nor to the Pauli-type molecular bonds which are mixed classical/quantum structures. Bohm's final straw was his apparent belief that the EPR (he called it ERP) had been shown to be valid although the Bell/Aspect thing was still in the future.
There is at least one real hidden variable and that is the Coriolis condensation force that collapses the 6 "p" electrons around the neon nucleus into a triple Planck spherical "onion" layer orbital. Cheers, Jim

 

[Antiphon]

Thanks Antiphon

I know I'm being simplistic, of course the ball you throw does not check up on Newton and then decide where to land. I'm looking for mechanism though.

Light can indeed take all paths if it is a wave. And then we say the wave function collapses here and the particle magically appears. So where exactly was the particle of energy observed ? It did not take a specific path at the start. But when it ran as a wave against something that absorbed its energy it became a particle (with frequency imbued from wave to particle in a magical kind of way).


Simon

I can't add much to the other top-quality answers in this thread, but I'll try
to add this much: First, balls don't check to decide where to land. If you
study "phase integrals" or these path integrals you'll see that the equations
"decide the issue for the ball". [Note: The unreality of the path is easily
demonstrated in classical optics. Two people will see a distant point of
light reflecting from *different* places on a shiny sphere. So the "path"
of the light ray depends on the oberver. It's just a calulation tool.]

And second, QM *is* bizarre in many ways, and here's one of the most.
When a particle like a photon interacts with an electron, it will impart
a *definite* energy to the electron in a *finite time*. (This itself is
apparently at odds with the uncertainty priciple, no?)

Yet you must treat the lone quantum as if had *many possible* energies
(a spectrum) prior to that interaction or you will get the wrong physical
preditions in your experiments.

 

[SimonA]

Many thanks for those good answers thanks guys. I will ruminate, read, learn and ponder some more :)

Simon

 

[SimonA]

Note: The unreality of the path is easily
demonstrated in classical optics. Two people will see a distant point of
light reflecting from *different* places on a shiny sphere. So the "path"
of the light ray depends on the oberver.

This is something I've found strange for a long time - not so much in sphere's but in that what you see in a reflection in a window has different things in different parts of that window than what others from another perspective see. In some ways it seems to be at the very heart of the QM phenomena, and at the same time I can't help thinking of relativity.

Should I seek proffessional help and accomodation with pin-cushioned padded walls ?

 

[Antiphon]

This is something I've found strange for a long time - not so much in sphere's but in that what you see in a reflection in a window has different things in different parts of that window than what others from another perspective see. In some ways it seems to be at the very heart of the QM phenomena, and at the same time I can't help thinking of relativity.

Should I seek proffessional help and accomodation with pin-cushioned padded walls ?

The good news is there is no need for padded walls due to the window,
SimonA.

Think of it like this: the window actually reflects light in many directions
but you can only see that part of it that is aimed at you. It's a lot less
mysterious when viewed this way.

The bad is news is that the heart of QM is much weirder than mere
wave interference. For the over-contemplation of THAT, you and I may both
end up in adjacent padded cells.

 

[SimonA]

LOL :)

So myself and Fred are looking at an apple reflected in a mirror. And to Fred the apple is in the bottom left of the mirror and to myself its in the top right. Basic stuff - the apple causes light to bounce in many directions and we as observers see the light that was on a direct path between our retinas and the apple - given 'angle of incidence' on the mirror.

So now we put sensors in the mirror that detect the light from the apple. For fred these sensors would see the light incident on one part of the mirror, and for me they would see the light incident on another part. Now these sensors are going to seem confused. The light from the apple is sort of seen in very different places. But the detectors are in a place where they "see" all the possibililities in terms of the observer. Then you turn the wave into a particle in your mind due to its packet like "nature" - and see that an individual wave/particle is seen both here and there. To one person this particle hit one part of the mirror, to another person it hit a different part. Its all to easy to simplify this into some of the many particles went here, and the others went there. But step back and employ the single photon - its far too simplistic to say the "wave function" collapses. We know from Einstein that the observer is crucial to some aspects and completely irrelevant to others.

Why are people so convinced that the formalism describes "actual path" when path is so dependant on observation ? Objectivity sees the "photon" taking many paths like a wave. Subjectivity sees a single path taken. So at what point does Youngs slit see a particle interfere with itself ? The answer is at all points. Cartesian relativity is naturally going to conflict here. Its not so much that EM has a constant velocity to all observers. EM has a constant nature independant of observation. Its not Cartesian nor Newtonian. Its our equiment that is in effect objective.