# Question on some basic principles of quantum theory [closed]

I asked a physicist (former head of the physics department in a university) about some of the basics of quantum theory and the double slit experiment. Here is his reply. Are any of these points incorrect?

1. Electrons and light are always particles and never waves. There is no such thing as an electron wave. Ditto for light. However, electrons are quantum particles which behave very differently from classical particles.

2. In the two-slit experiment, the electron does not go through both slits at the same time. This can be confirmed experimentally by placing detectors at both slits and then sending an electron toward the slits. One finds that only one detector goes off. Both detectors never go off, confirming that the electron did not go through both slits.

3. A particle cannot be in two places at the same time.

4. The interference pattern for electrons (through a double slit) does not indicate that electrons are waves. Electrons are particles, but they are quantum particles, and quantum particles can produce an interference pattern.

5. The solution to the Schroedinger Equation is a probability amplitude, and not a wave function because there is no such thing as an electron wave.

6. Superposition does not mean that the particle is in, say, two energy states E1 and E2 at the same time. Superposition means that the particle has a non-zero probability (say 40%) to yield energy E1 and a non-zero probability (say 60%) to yield energy E2 upon performing a measurement. One obtains this result because quantum theory is a probabilistic theory of nature. It is impossible to know the energy of the particle before a measurement is performed. There is one exception to this rule, but I will not discuss it here.

edit: regarding what is a particle he replied: A particle is a localized entity that can pass through only one slit. A wave is an extended entity that can pass through both slits at the same time.

• This post (v4) seems too broad. – Qmechanic Sep 12 at 16:36
• That's a lot of opinions, mostly about things where opinions and interpretations are the only available currency, but also in areas where some opinions do require some strenuous defense to be viable. This particular set would be extremely hard to defend in a professional setting with quantum-foundations specialists in attendance. Not necessarily impossible, but it would require a lot of very careful argumentation, extremely careful handling of definitions (not in evidence here), and a bunch of epistemological concessions (also not in evidence here). – Emilio Pisanty Sep 12 at 21:18
• 1. is false. See Davisson-Germer experiment. – ZeroTheHero Sep 12 at 22:50
• He seems to like being a contrarian. Pretty much everybody else is happy to call a wavefunction a wavefunction. – G. Smith Sep 12 at 23:55

To answer 2 for you, I think that this explanation is not correct.

It is indeed true that if you place detectors close to the slits, only one of them will go off for each electron. However, when you do this, you will not get a interference pattern. If you remove the detectors you will. Hence, there is a difference between the two situations. In the case where you do get the interference pattern (no detectors), you have to at least calculate like the electron actually goes through both of the slits.

It might be that the person you asked are into the pilot wave interpretation. In that case the electron actually goes through one of the slits, but the actual pilot wave (which determines the probability of the electron position) is affected by whether or not you have the detectors in place.

• ok thanks.+1... – michael Sep 12 at 10:52

Ask your friend "What is a particle?" The term is not defined in what you wrote. There isn't any meaning in his ideas until we know the meaning of that word.

Richard Feynman, a Nobel laureate in physics, once said unequivocally that a photon is a particle, not a wave. Willis Lamb, a Nobel laureate in physics, argues that photons are not particles. So what are mere mortals like me to think?

The mathematical model that represents photons (and electrons) is that of a quantized excitation of a field. To me, that's neither a wave nor a particle. It's something that doesn't have a name in physics today. And that's a shame, because it leads us to endless discussions about the nature of our elementary entities. We are left with the concepts "wave" and "particle", and I think everyone agrees that the elementary entities do not behave the way a tiny marble does, or the way a wave on a pond does. Wait ... sure they do. We observe interference. Wait ... no they don't. In interactions they transfer energy and momentum at a specific location, just like a tiny marble. Here we go again.

To me, it seems that we are trying to understand these entities by fitting them into the ideas we have in our head, ideas that developed over millions of years of evolution in a macroscopic world where particles were particles and waves were waves, and there was nothing at all that behaves like the elementary entities. I think our brains are not up to the task of having an true intuitive understanding, of groking exactly what the elementary entities are. The best we can do is try to make the best of two imperfect metaphors: wave and particle.

I don't know if your friend is right or wrong, because I don't know what he means by "particle". But if he means "a tiny, localized bit of stuff" I fear he might be trying to fit a square peg in a hole that's not round, but not square either.

• by particle i think he means in the sense that it cannot go through both slits simultaneously like a wave. it is a single particle with a probability function of where to be found as he said in point 6. we discover its correct probabiltiy when measuring it – michael Sep 12 at 11:02
• asked him. please see edit. – michael Sep 12 at 16:29
• @michael Thanks for the edit. I think my point of view is relevant, and that your friend has an overly narrow view. – garyp Sep 12 at 17:31

Summary: I think your friend's summary is not bad for a summary aimed at a non-expert in a "train ride" conversation about quantum physics.

Many of his statements would (will) cause a lot of unhappiness with people who know a bit more about it as they are very simplistic and "cartoon-ifying".

His most contentious claim is probably "electrons and photons are always particles and never waves". This is a problematic statement. In classical physics we have some things that are waves, and some things that are (billiard ball) particles. In quantum physics their is only one type of thing (lets call it a "wavefunction") - it has many of the properties of a classical wave, and many of those of a classical particle. In quantum physics the term "particle" comes to have a completely different meaning from what it would imply otherwise (it in no way implies a billiard ball).

My preferred "train ride conversation" of quantum physics aimed at a non-expert would instead be:

Quantum Physics - Not-too-mathematical non-expert summary:

Quantum physics is a theory about probability. The "weirdness" of quantum physics comes mostly form a single fact - that in quantum mechanics we only track things called "probability amplitudes", which when squared give probabilities. Note that the probability amplitude -0.5 and that for 0.5 both square to give 1/4.

When their are two (or more) ways a particular final state can be reached we have to add the probability amplitude of each possible way we can get into that state.

In the two-slit experiment (for some locations beyond the two slits) their is destructive interference between the two routes. Simplistically going through the left slit gives a p-amplitude of +X and the right slit -X so that the overall probability of finding the electron at that location is zero. Probilities cancel out! This is why some places the electron CAN be found with only 1 slit it cannot be found when you have two.

But what about if we put detectors to check which slit the electron actually went through?

This is where it gets really cool. You can only add the probability amplitudes for two sequences of events that lead to the same final state (state of everything).

So the left slit gives us a +X p-amp for producing the final state: "Electron here, and left detector saw an electron".

And the right slit gives us a -X p-amp for producing the final state: "Electron here, and right detector saw an electron".

These two p-amps do not add (cancel), because the text in ""'s is different between the two cases. (In more precise settings people would put the text inside a "ket" instead of quotes but the meaning is the same.)

So you just find an X-squared chance of each of those two events - no cancelling.

This "de coherence" is why we don't "see" quantum physics in everyday life. Their may be two different ways for me to get to work, but the two do not cancel because if I take one route I will push one set of air molecules around, and if I take a different route I will push different air molecules around in a different way.

Their is no (known) upper bound for how big a thing can be and still act quantum, so long as it is very well isolated from interacting with other things that (like the air molecules) stop its various possible paths from cancelling properly.

How you calculate these "probability amplitudes" is the mathematics of the theory. (Hamiltonians, master equations ....)

(but I am just some weirdo on the internet and my explanation will rile the knowledgeable as much as your friends).

• he's actually a professor of physics at a university. former department head – michael Sep 12 at 17:55
• I didn't mean to say that HE was a "non expert", (I am sure he is). I just meant to say that his explanation was intended for a non-expert. Will edit to clarify. – Dast Sep 12 at 18:02

These claims are neither true nor false. This person is either making statements without defining his terms, or he's offering these statements as implicit definitions of his terms. In general this just seems like a catalog of aphorisms of someone who has a shallow understanding or is not good at the kind of critical thinking needed in order to decide how to make and evaluate meaningful claims about a physical theory.

That's an interesting somewhat non-standard interpretation.

I'd disagree with 5. "The solution to the Schroedinger Equation is a probability amplitude, and not a wave function because there is no such thing as an electron wave."

If you consider $$|\psi|^2$$ the solution rather than $$\psi$$ you will loose information. The full information, both the magnitude and phase are needed to describe the system.

• The probability amplitude is $\psi$, not $|\psi|^2$. (The latter is termed a probability density instead.) – Emilio Pisanty Sep 13 at 7:38
• I could believe that $|\psi|$ would be a probability amplitude. In this case, it does not change the fact that phase is lost. – bert Sep 13 at 12:29
• That's simply not how the term is used in the broader literature: the term 'probability amplitude' means the wavefunction $\psi$, together with its phase information. Any usage different to that is non-standard. Whether that coincides with what OP's acquaintance meant by the term is anyone's guess, but that aspect is ultimately moot with regards to this answer, which is definitely wrong. – Emilio Pisanty Sep 13 at 12:33
• So what I'm learning from this thread is that probabiltiy amplitude and wavefunction are synonymous. Okay, I'm concluding that either it is a very obscure term or that I've subconsciouly blocked the true definition since I've always thought of amplitudes as non-negative real values. If this is broadly used in the literature is there any paper or author that you could suggest that's a good read where I could encounter the term or definition? – bert Sep 14 at 16:20
• The term is in no way obscure. If you want to find examples, I would suggest a simple Google Scholar search. – Emilio Pisanty Sep 14 at 18:12