Is entanglement just a mathematical construct or is it a real phenomenon?

[olcay]

Hi,

In some books and sites it's said to be nothing but physical wave packet for physical particles. They says a real-physical wave packet can exhibit all the features of a massive particle.

Is it true(shown with experiments?), or is it one of the interpretations?

 

[jtbell]

What is a "physical wave packet" or "real-physical wave packet?" Is this something different from a Schrödinger wave function $\Psi(x,t)$ that is constructed as a wave packet (superposition of many plane waves), e.g.

$$\Psi(x,t) = \frac{1}{\sqrt{2 \pi \hbar}} \int^{+\infty}_{-\infty}{\phi(p)e^{i(px - Et)/\hbar} dp$$

 

[olcay]

Shortly, I read about stg. on wave-only view. It says particle concept of electron is wrong and could be understood as wave-packets. "Physical" means these waves are real in contrary to Born's statistical interpretation.

In 1926, Born was debate with Schroedinger about reality of wavefunction, as you know. His and Heisenberg's main argument about wave-packets reality was dispersion of wave packets with time, while particle did not. The other argument was discrete detection of detectors which shows particle features instead of waves.

But nowadays there're a lot of critics about this refutations. Some scientists say a wave packet don't have to disperse with time, and may have exhibit particle properties which in turn means particle concept may be wrong.

Carver Mead and Atilla Gurel(www.physics-qa.com[/URL]) are one of them.

So I wanted to ask about this view, "wave-only view".

 

[Ken G]

My take on this differs from the usual "wavicle" interpretation. I would say that the wave properties and particle properties are quite clearly distinct, as long as one is clear what one means by "particle properties". By that phrase, I mean "shows up in a quantized form in a detector"-- that's a particle, and quantum mechanics doesn't compromise that attribute, it is built on that attribute. The problem comes in when people automatically associate "particles" with "trajectories". So I would say the lesson of quantum mechanics is not that we don't have particles, it's that particles don't actually follow trajectories. The concept of a trajectory is an approximate notion that must be replaced by the action of a wave function for more precise calculations. So the "wave function" is how you predict where a particle will go-- not a trajectory. But, it's a particle all the same. I think Lande is the person who I first saw describe this approach, and it always just made a lot of sense to me.

 

[peter0302]

So I would say the lesson of quantum mechanics is not that we don't have particles, it's that particles don't actually follow trajectories.

The problem with that view is that it contradicts relativity.

 

[Ken G]

You may wish to expound on how relativistic quantum mechanics requires the concept of a trajectory. For example, relativistic electrons can still make a two-slit diffraction pattern, can they not?

 

[peter0302]

Of course they can but Relativity tells us that space is a real thing with real properties, that things move through it, and that things cannot move from one point to another without passing through the space in between. All of those things are destroyed by saying particles "have no trajectory." They can't just teleport from point A to point B, and since they're _never_ detected at more than one point at one time, the only logical conclusion is that they traveled _some_ trajectory between A and B.

 

[Ken G]

Of course they can

But of course trajectories cannot do that. So how then is saying that quantum mechanics liberates us from the concept of trajectories is inconsistent with relativity?

but Relativity tells us that space is a real thing with real properties, that things move through it, and that things cannot move from one point to another without passing through the space in between.

I think we just ruled that out when we noted that we could get a double slit diffraction pattern from relativistic electrons. So you must be claiming that quantum mechanics is inconsistent with relativity, which I do not think is correct. Perhaps the problem is that you have something different in mind for the word "trajectory" than I do. You seem to think to not have one is to "teleport from point A to point B", whereas I mean to not have one is to not follow a unique path through spacetime, but rather receive amplitudes from many paths. So when I say that we still have particles, but not trajectories, I mean that we have path integrals instead. There never really was such a thing as a trajectory, we kind of made that up as a good but incorrect approximation. I still don't see how relativity changes that.

 

[peter0302]

Your interrpetation of QM is what is inconsistent with Relativity.

And yes, particles with trajectories can make a two-slit interference pattern. Just bend their trajectories. What particles with trajectories CANNOT do is show up in two places at once, which quantum particles never do.

 

[peter0302]

What I agree with you on is that a particle does not have a well-defined, PREDICTABLE trajectory before it is detected. However, once the particle has been detected somewhere, we can say with certainty precisely what path that particle took, and no experiment will result in a particle having taken an "impossible" trajectory. The Afshar experiment tried to show this and ruled it out.

 

[Ken G]

Your interrpetation of QM is what is inconsistent with Relativity.

I'd like to understand why, but so far you have not established that in the least.

And yes, particles with trajectories can make a two-slit interference pattern. Just bend their trajectories.

You are incorrect, you cannot make an interference pattern by "bending a trajectory". You must admit that a trajectory must pass through one slit or the other, would you not? Of course, if you assert that, you will not get an interference pattern.

What particles with trajectories CANNOT do is show up in two places at once, which quantum particles never do.

Again, I already pointed out why what you are talking about here is the attribute of a particle, it is not a sufficient attribute to define a trajectory.

 

[Ken G]

What I agree with you on is that a particle does not have a well-defined, PREDICTABLE trajectory before it is detected. However, once the particle has been detected somewhere, we can say with certainty precisely what path that particle took, and no experiment will result in a particle having taken an "impossible" trajectory.

You are mixing two claims, one that the path can be known after the fact, and the other that impossible trajectories may be ruled out. The latter is correct, the former is not. There is no way you can determine the path taken by a particle that is undergoing interference by multiple amplitude contributions (i.e., "interference"), even after the fact of having detected it. How can you even identify which slit it went through? It is well known that any effort to do that will eliminate the interference.

 

[peter0302]

The interference pattern disappears if which-path information is known, and reappears after the fact if which-path information is destroyed. But in either case there is the ability to determine the path if desired. This is well documented in DCQE, the Dopfer thesis, and other experiments. The interference pattern only emerges as a result of the lack of information. Assuming the past is not being altered (which if you want to believe that, be my guest, but then our conversation is over) then the only other interpretation is that there always _was_ a fixed path, and that other parameters of the experiment simply determined whether it is knowable or not.

You are incorrect, you cannot make an interference pattern by "bending a trajectory". You must admit that a trajectory must pass through one slit or the other, would you not? Of course, if you assert that, you will not get an interference pattern.

You are incorrect. You can make an interference pattern with classical physics. Shoot bullets through a double slit and put magnets at the interference maxima. Guess what - you'll get an interference pattern that looks almost exactly like a quantum one if you do it correctly. Do you think those bullets had no trajectory either?

[Edit]I indeed admit that a trajectory passes through one slit or the other, never both. I do not admit that quanta pass through both slits. The only thing that we know is that there is a probability amplitude that it will pass through both slits. If you do something downstream to find out which slit it passed through, then that ampltiude is changed so that there is now a probability that it passed only one slit. That doesn't mean the trajectory was changed, or that it had no trajectory to begin with. All it means is that knowing what the trajectory was alters the probability amplitudes as to which slit it passed through, thereby eliminating the interference pattern. This does not prove that not knowing the trajectory, thereby resulting in an interference pattern, meant there was none.

 

[Ken G]

The interference pattern disappears if which-path information is known, and reappears after the fact if which-path information is destroyed.

Which-path information never "appears", you have to create it with your experimental setup. In other words, your statement is unresponsive to the issue of whether or not the particle possesses a trajectory, and that this concept is in any way useful in predicting its behavior. My claim is that the concept of trajectory is imposed on the particle by us, based on outdated classical thinking, and only appears in experiments expressly designed to expose this bias of ours. The most natural way to interpret path-integral approaches to making predictions, or indeed any approach involving interference, is that the particle does not possesses a trajectory unless our experiment forces it to satisfy that desire on our behalf. You may describe an experiment to the contrary if you feel that is an unfair characterization of the situation.

But in either case there is the ability to determine the path if desired.

Again, such an "ability" is unresponsive to the issue of whether or not unique trajectories are actually useful concepts in experiments not expressly designed to exercise that "ability".

The interference pattern only emerges as a result of the lack of information.

Interference patterns are physical manifestations of the physics of the situation, and hence cannot "emerge as a result of the lack of information". They emerge as a result of information-- they are information. Obviously, they only convey the information that they do not lack, that is a safe statement about all of reality. The point is, quantum mechanics allows you to imagine, if you are dead set on doing so, that the particle behavior is consistent with it having a trajectory, but that imagined concept won't mean anything unless you design an experiment to force it to have a trajectory-- in which case you will be doing a different experiment and will get a different result.

Assuming the past is not being altered (which if you want to believe that, be my guest, but then our conversation is over) then the only other interpretation is that there always _was_ a fixed path, and that other parameters of the experiment simply determined whether it is knowable or not.

This claim has not been supported in your argument as it stands (I will grant you the past has not been altered, but you may be applying an unworkable meaning for both the words "past" and "altered", based on outdated classical pictures of what those words mean. More on that below.).

You are incorrect. You can make an interference pattern with classical physics. Shoot bullets through a double slit and put magnets at the interference maxima. Guess what - you'll get an interference pattern that looks almost exactly like a quantum one if you do it correctly. Do you think those bullets had no trajectory either?

You are saying I am incorrect only by claiming I said something other than what I did. What I actually said is you would not get interference, obviously you can mock up something that looks like an interference pattern but isn't (I don't need magnets for that, paint would work fine). If we run your experiment again, but I close one or the other slit at random each time, I will of course get the exact same pattern you do after twice the number of trials, so obviously the presence of interference is not determined by the shape of the pattern. Or is it your claim that we are in fact seeing interference between the slits, even though there is never more than one slit open? You are not describing interference-- can you think of a situation where you know the trajectory of each particle, yet the resulting detections exhibit interference? (The way to tell is, close one slit at random each time and see if the pattern changes.)

I say, you will not be able to do that, and that is the reason that a "trajectory" is a reverse-engineered concept that should be discarded in quantum mechanics, whereas "particle" is the crux of quantum mechanics. That's why there is no contradictory "duality" between waves and particles, as long as one does not make the mistake of thinking that a trajectory is a manifest attribute of a particle.

I indeed admit that a trajectory passes through one slit or the other, never both. I do not admit that quanta pass through both slits.

Note that I never said the quantum passes through both slits. I am saying that the question "which slit did the quantum go through" is unanswerable, and therefore meaningless scientifically, unless the experimental setup is expressly designed to answer that question. That is a clear sign of a concept that we are imposing on reality, rather than one that is manifestly real.

If you do something downstream to find out which slit it passed through, then that ampltiude is changed so that there is now a probability that it passed only one slit.

True, but here's the key point: the only amplitude that is ever changed by something you do "downstream" is a downstream amplitude! There are no examples of upstream amplitudes (i.e., amplitudes that can be used to make a prediction about an upstream measurement) that are changed by anything that is done downstream. That is the issue your argument about "not altering the past" is overlooking. Indeed, I see that misconception in a lot of quantum entanglement arguments, you might say it's a pet peeve of mine because it suggests all kinds of mystery that is not in evidence. Jettison "trajectories", and the mysteries evaporate, other than the usual "why" mystery.

All it means is that knowing what the trajectory was alters the probability amplitudes as to which slit it passed through, thereby eliminating the interference pattern.

We can certainly agree that if we force the particle to conform to our preconceptions about trajectories, it will alter the outcome of the experiment. But the issue I want to address is, what happens if the experiment is not expressly designed to create a concept of a trajectory? Answer: there are then no physical manifestations of a need for that concept. Thus by Occam's razor, we are compelled to avoid creating that useless concept. We would merely be writing a story ourselves, instead of reading nature's.

 

[peter0302]

And we're now back to your interpretation that a trajectory is just a man-made construct without physical meaning, and I said that contradicts relativity. I can't prove that the opposite is true but you certainly cannot prove you're right either, for many reaosns I cited. All I can say is that I would prefer an interpretation of QM that preserves the most important tenant of the other most important physical theory of the 20th century, i.e., the reality of spacetime and locality.

 

[Ken G]

All I can say is that I would prefer an interpretation of QM that preserves the most important tenant of the other most important physical theory of the 20th century, i.e., the reality of spacetime and locality.

We would probably all prefer that-- but science is not about what we prefer, it is about getting our preconceptions out of the way of nature and choosing the minimal intellectual interface that allows our predictions to function correctly. That's basically Occam's razor in a nutshell, which I would reinterpret as "letting nature speak for itself".

 

[peter0302]

Occam's razor is possibly the most overused and misunderstood concept in all of science.

Your interpretation offers no advantages over others and conflicts with a very widely accepted, experimentally verified theory. Copenhagen and MWI pose no such conflicts. I think it's clear which one is preferable.

 

[reilly]

Of course they can but Relativity tells us that space is a real thing with real properties, that things move through it, and that things cannot move from one point to another without passing through the space in between. All of those things are destroyed by saying particles "have no trajectory." They can't just teleport from point A to point B, and since they're _never_ detected at more than one point at one time, the only logical conclusion is that they traveled _some_ trajectory between A and B.

The space you describe goes back at least to Newton, and probably well before.
In QM we deal with wave equations and wave functions, not trajectories. But both phenomena require spaces with the same properties, so we usually take their intersection -- basically the condition is one with a continuous metric and uniform measure, a Hausdorff space, ... Somethings have trajectories, some don't. How do you know that radio station signals don't skip some space, or don't have trajectories?- we assume that's so, much to Occams delight. Nothing teleports in QM, cf. Feynman's Path Integral formalism.

Vacuums are not always empty, Hawking radiation for example. There's a big literature on Vacuums in QFT. It's easy to see that there is no such thing as an empty interacting vacuum. QED provides non zero matrix elements of the interaction vacuum <-> electron, positron, photon, and vice versa. Look at the consequences of {1/(E -Ho)}<e p g|H|0> with a non zero matrix element (the |epg> is te electron, positron, photon state.

(Some of the work in superfluidity and superconductivity plays around, to good effect, with different types of vacuums; great physics, good to study. Also , check out the connection between the eikonal approach to optics and the use Of Hamilton's Principle to generate wave fronts in classical mechanics. see Lanczos -- Variational Principles of
Mechanics.In fact there are some very strong parallels between mechanics and optics, but to show that's so requires some sophisticated math and reasoning.
Regards
Reilly Atkinson

 

[peter0302]

All I'm saying is we should not be so eager to throw the baby out with the bathwater. Just because wave functions don't need trajectories to work doesn't mean they don't exist. The fact that other very successful theories DO need them is good reason NOT to throw them out.

 

[Ken G]

Occam's razor is possibly the most overused and misunderstood concept in all of science.

On the contrary, it is the very beating heart of science. You see, the point of science is to gain power and understanding over the world around us by identifying simplifying principles that can actually fit in our ape-sized brains. Can any deny the truth of this remark? So given that this is what science is, it should not come as a surprise that the core principle of that science is to seek the simplest working description.

Furthermore, in addition to that principle, the history of science is rife with examples of the fault in over-interpreting what we currently believe to be an absolute description of reality, prior to experimental verification. Some of our principles have led us to new physics, and others have led us down blind alleys-- they are all just guesses until we actually have some experimental reason to hold that they are true. If that is not the core lesson of science, I sure don't know what is.

Your interpretation offers no advantages over others and conflicts with a very widely accepted, experimentally verified theory.

That is flatly untrue. There is no aspect of my interpretation that contradicts a single experiment-- indeed, the whole motivation of my interpretation is to add no more than what can be verified by experiment.

Copenhagen and MWI pose no such conflicts. I think it's clear which one is preferable.

MWI adds a vast scaffolding of unnecessary and unverifiable additions to the science, in flagrant violation of Occam's razor-- all to give people a false sense of understanding and control that to me is entirely analogous to magical thinking. The Copenhagen interpretation, on the other hand, is only guilty of that when people use it in ways that are not even required in that very interpretation-- to wit, to claim that a cat, or the "universe", can be in a pure state. Relaxing that unfounded claim contradicts exactly what experimental evidence? If you will claim it does, you must "deliver the goods".

 

[reilly]

All I'm saying is we should not be so eager to throw the baby out with the bathwater. Just because wave functions don't need trajectories to work doesn't mean they don't exist. The fact that other very successful theories DO need them is good reason NOT to throw them out.

Sorry, 80 years of experience with QM strongly supports the idea that there are no particle trajectories at the quantum level.And, of course there are theories that do not involve trajectories, Maxwell's Eq. without sources, same for the theory of sound waves or water waves, or ...

The baby grew up a long time ago, and stepped out of the bath on her own terms. Again, go back and read some history of QM.
Regards,
Reilly Atkinson

 

[reilly]

On the contrary, it is the very beating heart of science. You see, the point of science is to gain power and understanding over the world around us by identifying simplifying principles that can actually fit in our ape-sized brains. Can any deny the truth of this remark? So given that this is what science is, it should not come as a surprise that the core principle of that science is to seek the simplest working description.

Furthermore, in addition to that principle, the history of science is rife with examples of the fault in over-interpreting what we currently believe to be an absolute description of reality, prior to experimental verification. Some of our principles have led us to new physics, and others have led us down blind alleys-- they are all just guesses until we actually have some experimental reason to hold that they are true. If that is not the core lesson of science, I sure don't know what is.
That is flatly untrue. There is no aspect of my interpretation that contradicts a single experiment-- indeed, the whole motivation of my interpretation is to add no more than what can be verified by experiment.
MWI adds a vast scaffolding of unnecessary and unverifiable additions to the science, in flagrant violation of Occam's razor-- all to give people a false sense of understanding and control that to me is entirely analogous to magical thinking. The Copenhagen interpretation, on the other hand, is only guilty of that when people use it in ways that are not even required in that very interpretation-- to wit, to claim that a cat, or the "universe", can be in a pure state. Relaxing that unfounded claim contradicts exactly what experimental evidence? If you will claim it does, you must "deliver the goods".

Excellent post, one of the best I've read in a long time.. You have it right.
Regards,
Reilly Atkinson

 

[Ken G]

Thanks Reilly, your earlier posts indicate a profound understanding of physics and I look forward to seeing more of your reactions-- even (especially) when I don't have it right!

 

[peter0302]

There is a difference between professing that "particles have no trajectories" and saying that quantum mechanics doesn't need partilces to have trajectories.

Ken G - if you think Occam's razor is violated by MWI, then you do not understand MWI. MWI, more than any other interpretation, in fact strips away vague, undefined, and/or ludicrious concepts from QM and takes the core, proven concepts to their logical conclusion. It does not advocate things like vitalism or teleportation, solves basically all of the so-called "quantum paradoxes" and actually does have experimentally verifiable aspects (at least in theory). It may not be perfect but it is the best candidate.

The only thing I give Copenhagen credit for is not bothering to get mired in metaphysical babble. At least Copenhagenists know enough to know they don't know. I just disagree with those who say it doesn't matter.

And Reilly, I've read plenty of QM. I'd really appreciate if you knocked off the patronizing.

 

[Ken G]

Ken G - if you think Occam's razor is violated by MWI, then you do not understand MWI. MWI, more than any other interpretation, in fact strips away vague, undefined, and/or ludicrious concepts from QM and takes the core, proven concepts to their logical conclusion.

But that's the whole point-- there's no need to take anything "to its conclusion"-- just leave it alone! The interpretation that does this is well known to be the "ensemble interpretation", the one expressly designed to add nothing to what quantum mechanics is actually required to do, with no "logical conclusions". I maintain what you are calling logical conclusion is exactly what I call "philosophical baggage". Would a Newtonian not say that taking Newton's laws to their logical conclusion yields a deterministic universe? The point is, Occam says neither that Newton's laws imply determinism, nor that we should expect some new complication to arrive in quantum systems. Instead, it says that we should take Newton's laws exactly at face value-- useful approximations in the context of the systems similar to ones where they have been found by experiment to apply. Now, what part of that statement applies to MWI?

It does not advocate things like vitalism or teleportation, solves basically all of the so-called "quantum paradoxes" and actually does have experimentally verifiable aspects (at least in theory).

But I just take science at face value, and I don't have any problem with any of those things, whereas I see MWI as imaginary science that cannot be falsified or supported by experiment.

It may not be perfect but it is the best candidate.

If so, it is a candidate for the post of "best among all the useless and unnecessary tack-ons to scientifically supported theories".

The only thing I give Copenhagen credit for is not bothering to get mired in metaphysical babble. At least Copenhagenists know enough to know they don't know. I just disagree with those who say it doesn't matter.

I'll agree there on all counts. But what matters is to not go farther than is actually supportable, or we become hypocrites when we claim a firmer hold on the truth.

 

[reilly]

Thanks

Thanks Reilly, your earlier posts indicate a profound understanding of physics and I look forward to seeing more of your reactions-- even (especially) when I don't have it right!

Thanks for your kind words. So far, as I see it, you do have it right.
Regards,
Reilly

 

[reilly]

There is a difference between professing that "particles have no trajectories" and saying that quantum mechanics doesn't need partilces to have trajectories.

Ken G - if you think Occam's razor is violated by MWI, then you do not understand MWI. MWI, more than any other interpretation, in fact strips away vague, undefined, and/or ludicrious concepts from QM and takes the core, proven concepts to their logical conclusion. It does not advocate things like vitalism or teleportation, solves basically all of the so-called "quantum paradoxes" and actually does have experimentally verifiable aspects (at least in theory). It may not be perfect but it is the best candidate.

The only thing I give Copenhagen credit for is not bothering to get mired in metaphysical babble. At least Copenhagenists know enough to know they don't know. I just disagree with those who say it doesn't matter.

and very small And Reilly, I've read plenty of QM. I'd really appreciate if you knocked off the patronizing.

I apologize for seeming patronizing; it is not my intent to do so. However, my concern comes from the fact that one of the early and highly important experiments, the Davisson-Germer experiment, destroyed the concept of a trajectory for electrons passing through a crystal. It is the wave-like nature of electron scattering wave functions that explains a great deal of phenomena that cannot be explained by trajectories -- this goes back to the origins of modern QM. Feynman and Dirac's path integral formalism deals with trajectories, but all trajectories in order to capture the basic dynamics of a quantum mechanical transition probabilities from point A at t, to B at t'. Thus it seems to me, that in order for you to make your claim about trajectories you might want to explain how, then, you deal with Davisson-Germer. From a historical perspective, it seems to me that to attempt to incorporate or save trajectories you necessarily must come to grips with the parent of the no=trajectory family.;

Depending on how far you want to push, you might want to consider the notion of trajectories within a system with Brownian motion. At any time, a particle can move with a displacement di with probability p(di) = pi such that the sum of the p's is one. Then over time, the probability to be anywhere, after starting at, say , the origin becomes uniform. There is thus no well defined trajectory. But there is a probability that a certain trajectory is followed; but each realization wiil yield a different path.

I've not thought this through, but I suspect that QM can, under some circumstances, mimic Brownian motion. Most generally, the fact that both Brownian motion and Schrödinger Eq single particle motion both obey the path integral formalism suggests to me a fairly strong equivalence between the two. My sense is that Huyghen's Principle is appropriate here for the QM case -- start with an electron wave packet with momentum p at t=o, one with a very small standard deviation for p. Wait for t1, and measure the position of the packet -- imagine the space threaded with discrete detectors, tiny potential wells that, when interacting with the particle, emit a low energy "photon". Further, let's assume that the energy loss of the particle is small, so that the particle can go through very many detectors without serious degradation of energy. Oh, yes, let's further assume that each detector has a unique signature. Then I can track the motion of a particle through that space, and find some kind of trajectory. But the next run will equal an earlier run only with an enormously small probability.

Given the history of scattering in QM. it's very hard to see where the idea of trajectory fits in. Perhaps there's one exception, Coulomb scattering in which both classical and quantum approaches yield exactly the same result.

I'm very curious about one aspect of MWI -- given that it has equal applicability to classical and quantum situations -- why was it not invented during the time of Fermat and Bernoulli, or some by some business planning hotshot working on decision chains or portfolio analysis? (I'll be happy to show that MWI refers to probability systems of any kind.)

So, by what reasoning do trajectories play a role in QM? A mere dismissal of standard QM ideas is not sufficient; lack of trajectories is a central point of QM. There is a preponderance of evidence, some circumstantial indeed, to support conventional QM. So, to convince doubting Thomases, more than unsupported claims are required. You need to demonstrate that "usual and customary" professional practices are lacking -- I apologize if my quoted phrase is incorrect, it's been a while since I've been in a courtroom as an expert witness.



RE.MWI -- List the assumptions necessary for MWI, then list the assumptions of practical Born-Bohr; which could be also characterized as Copenhagen without collapse, and without quantum-classical boundaries.(You are aware that most physicists in practice use practical Born-Bohr. Go through any physics journal of the last 80 years or so, and find any but an infitesimal number of authors using something other than the pragmatic approach of practical Bohr-Born.

Regards,
Reilly Atkinson

 

[Ken G]

There is a difference between professing that "particles have no trajectories" and saying that quantum mechanics doesn't need partilces to have trajectories.

The real issue is whether or not trajectories remain as necessary concepts whenever one is dealing with the concept of a particle. So for reasons that become even clearer below, I amend my statement to "in quantum mechanics the concept of a trajectory is subsumed into the concepts of wave mechanics, such that the trajectory concept may or may not retain relevance in any given situation, but those situations that require quantum mechanics are expressly those where the trajectory concept gives out (other than in a multiple-trajectory path-integral sense)". My main point is not that the concept of particle precludes the concept of trajectory, merely that many who talk about wave/particle "duality" seem to assume that the concept of trajectory is an integral and inescapable aspect of the concept of a particle, and that's what I'm saying is the wrong thinking here.

I've not thought this through, but I suspect that QM can, under some circumstances, mimic Brownian motion. Most generally, the fact that both Brownian motion and Schrödinger Eq single particle motion both obey the path integral formalism suggests to me a fairly strong equivalence between the two. My sense is that Huyghen's Principle is appropriate here for the QM case -- start with an electron wave packet with momentum p at t=o, one with a very small standard deviation for p. Wait for t1, and measure the position of the packet -- imagine the space threaded with discrete detectors, tiny potential wells that, when interacting with the particle, emit a low energy "photon". Further, let's assume that the energy loss of the particle is small, so that the particle can go through very many detectors without serious degradation of energy. Oh, yes, let's further assume that each detector has a unique signature. Then I can track the motion of a particle through that space, and find some kind of trajectory. But the next run will equal an earlier run only with an enormously small probability.

Indeed, I think a key issue in this important thought experiment is whether or not the "wells" are connected to macro instruments that can record "a photon was just generated here". If they are, the macro interaction will disrupt the photon coherences, and we are in the situation where we are intentionally coaxing the individual trials to have trajectories, they'll just be trajectories we can only handle probabilistically (indeed like Brownian motion).

Another interesting variant is where the wells make photons automatically without any macro coupling, or any coupling that cannot be explicitly included in the overall time evolution of our description of the system. In that case, the concept of trajectory will not be recovered, because it cannot support the necessary interferences (outside of a path-integral approach, which one might think of as multiple trajectories but that's not what I meant by a trajectory because each of the multiple trajectories are themselves neither unique nor solutions to any dynamical equations).

What may be most important to note is that in many situations, these two experiments will not yield different results, even though the ways we validly conceptualize them will be very different. So the line between waves and trajectories does not need to be drawn in all situations-- but it does in some situations, and when that's true, it is always the trajectory picture that is refuted.

Given the history of scattering in QM. it's very hard to see where the idea of trajectory fits in. Perhaps there's one exception, Coulomb scattering in which both classical and quantum approaches yield exactly the same result.

That's an important example that may be relevant to the thought experiment above. It sounds reminiscent of the way Newtonian gravity can, on occasion, yield the same answer as GR.

I'm very curious about one aspect of MWI -- given that it has equal applicability to classical and quantum situations -- why was it not invented during the time of Fermat and Bernoulli, or some by some business planning hotshot working on decision chains or portfolio analysis? (I'll be happy to show that MWI refers to probability systems of any kind.)

I think this is an excellent point, I have also tried to point out that many aspects of "quantum mechanical interpretations" actually appear after all the quantum mechanics is "over", and the system has already been reduced to a probabilistic "mixed state". It seems to me this is when quantum mechanics hands its results over to classical thinking, and at that point the "interpretations" jump in, but claim that they are somehow interpretations of quantum mechanics! I'm right on your page there.

 

[erastotenes]

On Copenhagen interpretation

The only thing I give Copenhagen credit for is not bothering to get mired in metaphysical babble. At least Copenhagenists know enough to know they don't know. I just disagree with those who say it doesn't matter.

The Copenhagen interpretation is not as humble as as the second sentence implies. Because if this were so, this would mean "There may be some better formulation somewhere to know and that we would achive it some time in the future if we do more experimental and theoretical work".

On the contrary they go so far that they declare "there is no conceptual or scientific problem at all. What you experience as a problem, is not a problem at all. There is nothing else to know (regarding the subject matter) Any sense of discomfort you have regarding our formulation of QM is not because it is incomplete but it is because you cannot adapt your mind to the new form of knowledge as we have formulated it. Thus any attempt to find a better solution is by definition a metaphysical babble"

Copenhagen interpretation (CI) has the major defect of using the concept "measurement" in the axioms of a physical theory by implicitely dividing physical events/processes into two distinct type categories (measurement and non-measurement) without telling us ,(and this is the defect), which criteteria defines the boundary that separates them. This conceptual defect of CI is the reason for all the metaphysical babble. Is measurement the interaction of the measured particle with macroscopical(classical) measuring device. However it is clear that there is no definite natural boundary seperating microscopic (quantum) from macroscopic(classical). Has measurement to do with a conscious being obtains information? But if so what is a conscious being? An human? a cat? a one celled organism that has light sensitive organelles ? A macromolecule?

 

[erastotenes]

All I'm saying is we should not be so eager to throw the baby out with the bathwater. Just because wave functions don't need trajectories to work doesn't mean they don't exist. The fact that other very successful theories DO need them is good reason NOT to throw them out.

However it iseems that it is inevitable that not all the babies can live peacefully together. Copenhagen interpretation is in a sense the desperate attempt to let all the babies (particle, wave, relativity) live together in a bizarr formulation. However it could do this only by containing a major inacceptable conceptual defect that I explained in the previous message.

It is clear we either have to sacrifice the physical reality of the wave function to save the relativity (because it implies faster then light wave propagation during collapse)

or we keep the obscure "probability amplitude for measurement" interpretation of wave function to save the relativity without being able to define what measurement is(see previous message).

Thus by trying to save all the babies together the CI sacrifices the most important baby namely the conceptual clarity and consistency.