# Of waves and particles

1. Oct 1, 2011

### TrickyDicky

There is a detail in the 2-slit experiment interpretation that bothers me, when analyzing it for instance in the Cohen-Tannoudji book (pg.13) they say the purely wave interpretation was rejected because "we can expose the photographic plate during a time so short that it can only receive a few photons. We then observe that each photon produces a localized impact on the screen and not a very weak interference pattern."
But aren't localized impacts precisely a very weak interference pattern when this pattern is formed by very many localized impacts?
I mean what determined patterned was expected if you only have a handful of impacts? If you have a pattern made of thousands of points and you erase all the points but 3 or 4 in whatever location surely you can't recover the previous interference pattern, there are simply not enough points.
So what bothers me is that with this kind of set up it can't be decided whether to reject the purely wave interpretation because there is no possible way it could have been not rejected unless you previously decide a minimum number of impacts necessary to produce a given pattern.

2. Oct 1, 2011

### jfy4

I see what you mean. But the localized impacts would be seemingly random. Maybe if we were to look at only a few flips of a fair coin we would say "well, this is a really weak version of half heads and half tails", even if we got all tails in our few flips. I wouldn't be inclined to say that....

The wave properties that this experiment exposes are the interference effects between probabilities. Normally one would expect the distribution of particle impacts to resemble two distributions of the form $|\Psi_{\text{expected}}|^2=|\Psi_1|^2 + |\Psi_2|^2$ but instead what is observed is
$$|\Psi_1 + \Psi_2|^2=|\Psi_{\text{expected}}|^2+2|\Psi_1|| \Psi_2|\cos\theta$$
which has an interference term for the probability amplitudes.

3. Oct 3, 2011

### TrickyDicky

Hi Judah, thanks for that answer; exactly, they would be "seemingly" or apparently random. I find the coin example is a very good one to make my point clear. Certainly when the coin is flipped a few times the fact that by pure chance we might get 5 tails in a row is not used to reject the probabilistic notion that a fair coin has a pure 50% chance of getting tails in every flip of the coin. So why is this done in the case of the wave pattern in the 2-slit experiment?

There seems to be people that confusingly think that the fact that the energy is quantized in QM is incompatible with a purely wave interpretation of the experiment. I would say the opposite is true, the very reason energy radiation appears quantized in the Planck-Einstein equation is precisely that it is expressed in wave terms of frequency in a quantum coherence context.

4. Oct 3, 2011

### Bill_K

Classical electromagnetism predicts a continuous distribution of E and B across the screen, even when the incident wave is made indefinitely weak. The fact that discrete impacts are observed contradicts this, and is evidence that the classical theory is wrong and requires modification. This conclusion does not depend on whether the number of impacts is a handful, several hundred, or several thousand. There is not a "mimimum number of impacts necessary". Maxwell says there should be no discrete impacts at all.

As the intensity of the incident wave is increased the number of impacts increases, and their distribution becomes a better and better approximation to the classical distribution.

5. Oct 3, 2011

### TrickyDicky

I'm aware of this. But why use the fact that classical EM had a wrong intuition about the radiated energy distribution to reject a wave interpretation if we know that in fact energy is quantized.
Classical EM is clearly wrong in this respect but that shouldn't make us reject a purely wave interpretation once we know they had a wrong intuition about the behaviour of waves at the limit of little energy.

6. Oct 3, 2011

### Ken G

It sounds to me like you simply don't like what was meant by a "purely wave intepretation." That's fine, but I don't think you and Cohen-Tannoudji are really disagreeing on anything other than the desired meaning of that phrase. To you, we update what we mean by a wave interpretation as we learn more about it, to them, the qualifier "purely" is intended to mean the "previous" way that waves were interpreted. Perhaps eventually so much time will have gone by that everyone will know this is how waves behave, but even most physics students still go a good 2 years before they find out, even today, so one can certainly see plenty of reason for either way to think about what a "purely wave interpretation" is.

Were I to rethink our physics curriculum, I might teach quantum mechanics before wave mechanics, and gravity-free general relativity before Galilean relativity. Then there's nothing to "unlearn" later. Then again, it isn't the way it's done, and could easily be a dismal failure.

7. Oct 3, 2011

### TrickyDicky

Bold mine.
Thanks Ken, that helps and practically (di)solves my question ;)
But I must say that I have the feeling that a great part of QM postulates and most of QFT is an attempt to create an ontology for the quantum particle that is triggered by the kind of justifications I alluded to in my OP (rejection of the purely wave interpretation).
If a purely wave interpretation (in the way we understand waves currently) is actually not rejected it could mean we don't need an ontology for quantum particles, we'd simply need to acknowledge that certain features of the modern quantum wave theory are in practice visualized better if we think of them as particles since we are used to it from classical physics.For instance the probabilistic view of amplitude as "particle location".

8. Oct 3, 2011

### jfy4

I've had a number of discussions about this idea with a friend. It's hard to say. The more I have thought about the current curriculum, shockingly, the more I have come to like it... There are of course aspects that I do disagree with, but there is a certain continuity that is unmistakable. Take GR as an example. why don't we learn GR first? Well Newtonian gravity is easier, is one answer. But maybe a better one is, Newtonian gravity isn't wrong! This is where the notion of "unlearning" comes in somewhat. What we have after introductory physics is the ability to talk about 90% of anything we can think of in 10 seconds, but it comes at the price of conceptual naivete... So as we move on to new more comprehensive topics, our conceptual understanding is constantly challenged. But, one of the conclusions I have come to is that this isn't bad. It's important for us to have be constantly shaken at the core throughout our career's in order to be good physicists. So we constantly have a commencement from a feeling of power and understanding to utter collapse, only to build it up again. So I think the system does do a good job of making good physicists, just as long as students let go of what they hold as absolutely true at each junction, and don't lock out change.

Sorry for the slight digression, but I wanted to say a piece.

9. Oct 4, 2011

### Q-reeus

10. Oct 4, 2011

### TrickyDicky

Thanks Q-reeus I'll look it up.

11. Oct 4, 2011

### vanhees71

Concerning the discussion about the curriculum, I'd keep principally the old-fashioned order of subjects, but with different emphasis. It must start with classical mechanics (where I mean "classical" as opposed to "quantum", i.e., classical includes both non-relativistic (Galilei-Newtonian) and relativistic (Einstein-Minkowskian) space-time. I'd start with Newtonian mechanics, proceed with the formulation with variational principles (Hamilton principle of least action in Lagrange and Hamilton form), leading to the most important notion of symmetry principles (Noether's theorem). Then I'd reanalyse the special principle of relativity. Taken together with some other elementary assumptions on the structure of space time this leads to the two possibilities of such space-times, i.e., Galilei-Newton and Einstein-Minkowski space-time.

The next step is electromagnetism. Here, I'd abandon all non-relativistic approaches from the very beginning. However, this becomes an issue in macroscopic electromagnetics with the introduction of constitutive relatations, so at later stages of the lecture on Maxwell theory. The standard form of the constitutive relations easily follow from the relativistic ones as approximations simplifying the solution of practical problems, but issues that seem to be difficult in the traditional approach (e.g., homopolar induction) come out very naturally.

Then one has to introduce quantum theory. That's a delicate issue since I don't know any really satisfactory approach yet. For sure, one must not start with photons and Bohr's old quantum mechanics. Photons are way too complicated to begin with since they cannot be understood without quite subtle analyses of the Poincare group and relativistic quantum field theory, and Bohr's old quantum mechanics leads to a qualitatively wrong picture of affairs. Also an approach using the idea of "matter waves" is very problematic. Quantum theory teaches us that there is no consistent way to describe matter as either consisting of classical point particles "billard-ball picture" or classical (wave) fields ("fluid-dynamics picture"). That said, the only way out seems to be an approach as given in Schwinger's textbook (Quantum Mechanics. Symbolism for atomistic measurements) or (less detailed) in J. J. Sakurai's "Modern Quantum Mechanics".

General relativity is a special subject, and can be taught easily after a relativity emphasized electromagnetics course since it's of course nothing else than a purely classical relativistic field theory of gravitation, based on the (strong) principle of equivalence, leading to the geometrization of spacetime as detailed in, e.g., The Feynman Lectures on Gravitation.

12. Oct 4, 2011

### Ken G

Yes, that is most likely the best justification for keeping things the way they are. It's kind of like how the higher brain functions are built, by evolution, directly on top of the earlier lower functions. There is a certain workability to that approach, though it can also lead to some evolutionary awkwardnesses that make us reject the concept of intelligent design! We want to end up with a physics curriculum that looks more like an intelligent design than like an evolutionary process, but we should recognize, as you point out, the two may share many of the same gross features.
That's an interesting insight. Indeed, yesterday I told my 7-year-old son about the expanding universe, but even as I did I thought, I hope I'm not robbing him of the chance to be astounded by it later on. He wasn't impressed at all, because he hasn't really thought about any of the alternatives! But on the other hand, maybe we only get so many surprises in a lifetime, so if we stop recreating the same ones in perpetuum for our students, they can start having more fundamentally new ones.

13. Oct 4, 2011

### Ken G

Your approach seems to stress "getting it right the first time", in essence, and then deciding on a developmentally appropriate order that leads to a rigorous understanding. I'm imagining a more "do it simple the first time and add rigor later" kind of approach, but which front-loads the essential concepts that are otherwise introduced as "seed changes" later on in the standard curriculum. For example, I'm imagining introducing wave-particle duality and quantization of action at the same time that waves and particles are introduced, and introducing the purpose of having a form of relativity at the same time that laws of motion are introduced. Kind of a "forest for the trees" approach, but which starts out very simple and not very rigorous. Then we avoid the standard "here's everything you need to know about how particles behave" followed much later by "oh, and by the way, particles don't really behave that way in many contexts." The latter seems too much like "here's how you build a house" and later by "Oh and we could have used rebar in the concrete, so let's knock that house down and do it again."

14. Oct 4, 2011

### Chronos

This my opportunity to whine about math curricula - why teach number theory after calculus I? That rubbed my fur against the grain. Maybe its different now, its just how it was done years ago, and, it was annoying.

15. Oct 7, 2011

### yoron

Am I getting this right?

As the 'photons' doesn't fit a wave pattern, we change the definition of a wave?
Or is there another reason?

16. Oct 7, 2011

### Ken G

Yes, you might say that. We used to think waves and particles were two different things, now we regard them as a single unified phenomenon.

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