# Wave packets and particles

1. Mar 10, 2008

### 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?

2. Mar 10, 2008

### Staff: Mentor

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.

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

3. Mar 11, 2008

### 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.

Last edited by a moderator: Apr 23, 2017
4. Mar 11, 2008

### 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.

5. Mar 11, 2008

### peter0302

The problem with that view is that it contradicts relativity.

6. Mar 11, 2008

### 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?

7. Mar 11, 2008

### 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 travelled _some_ trajectory between A and B.

8. Mar 11, 2008

### Ken G

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?
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.

9. Mar 11, 2008

### 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.

10. Mar 11, 2008

### 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.

11. Mar 11, 2008

### Ken G

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

12. Mar 11, 2008

### Ken G

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.

13. Mar 12, 2008

### 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 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?

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.

Last edited: Mar 12, 2008
14. Mar 12, 2008

### Ken G

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 possess 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.
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".
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.
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 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.
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.
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.
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.

Last edited: Mar 12, 2008
15. Mar 12, 2008

### 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.

16. Mar 13, 2008

### Ken G

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".

17. Mar 13, 2008

### 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.

18. Mar 13, 2008

### reilly

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

Last edited: Mar 13, 2008
19. Mar 13, 2008

### 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.

20. Mar 14, 2008

### Ken G

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".

Last edited: Mar 14, 2008