# Is this person right about particle wave duality?

## Main Question or Discussion Point

Here is the conversation

Person 1: Here is my favorite hit off a quick google search for an equation intensive look at QM: http://www.physics.sfsu.edu/~greensit/book.pdf [Broken]

Starting with De Broglie wavelength since it's the most fun part of the topic. Imagine going out to dinner and convincing your friends that they are in fact a wave, and when you're not looking at them they fluctuate like this " "

Person 2: Just be careful in your understanding of this, the particle isn't traveling like a wave, the probability of finding the particle in a certain location is what is waving...it's weird.

Me: Something about [Person 2's statement] doesn't seem right. Particles also behave as waves. Particle-wave duality doesn't stem from the shape of the probability function which seems to be what you are saying.

Person 2: The particle isn't really traveling as a wave, think of it more as a cloud that travels that when you look at it, it collapses to a certain point with regards to the uncertainty principle. The location that it collapses to is dependent upon the wave function for that particle which describes the probability of it being in any location as it moves through space and oftentimes time.

The de Broglie wavelength is really the wavelength of the probability function. It behaves like the particle travels as a wave but current physics doesn't see it that way.

Me: I understand how the wave function collapses and the probability function. But I take issue with the idea that it isn't really traveling as a wave. Take the double slit experiment for example. Particles in this case behave as a wave, so to say that they are not waves seems puzzling.

Person 2: (this is compiled from a couple posts)

The double slits affect the wave functions because the area around the slits are potential barriers, this causes the probability function to take on the form of the interference pattern. It isn't that one electron (in this example) is forming the pattern on its own, it is that all the electrons have certain probabilities to end up at certain points and they are more likely to end up at the center of each fringe.

With light, the actual electomagnetic waves are interfering. With particles, its the probability waves that interfere and change the wave function due to the potential barriers that make up the slits.

Light is different because light is a wave that has particle like properties and things like electrons are particles that have wave like properties. Just because they have similar properties to each other does not mean they are the same thing.

Also, it isn't that the electron is interfering with itself, its that the slits alter the wave function.

Me: I don't get the distinction between "a wave that has particle like properties and particles that have wave like properties." Defining something that has both wave and particle properties as either a wave or particle seems meaningless and ambiguous in the context of quantum mechanics.

Sorry that is a lot, but that is our conversation. I feel like what he is saying may not be correct.

TLDR:

The argument is basically that he says light is massless and "is" a wave. It can behave as a particle, called the photon, which is also massless.

An electron has mass and "is" a particle. It can behave as a wave, but it's really a probability function that describes the possible locations of the particle, because a wave can't have mass. It is not the electron that is waving, it is the probability.

I say that distinguishing between an electron as a wave or particle is meaningless. It has properties of both. It is not the illusion of acting as a wave, it is indeed actually acting as wave. Any semantics around this issue is wrong.

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Simon Bridge
Homework Helper
I've singled out one quote as indicative of the core understanding:
I understand how the wave function collapses and the probability function.
That is highly unlikely - but if you do, then you'd be the first :)
But I take issue with the idea that it isn't really traveling as a wave. Take the double slit experiment for example. Particles in this case behave as a wave, so to say that they are not waves seems puzzling.
person 2 is correct here - quantum mechanics is really great at making predictions about the conditions of systems we do experiments on - but it is really bad at telling us how a system goes from one state to another. In your case - we can tell that a particle left some source, and gets detected someplace else, but we don't know how it got there.

You are broadly correct to assert that it makes no sense to talk of, say, an electron as being a classical particle or a classical wave but incorrect to say it has properties of both... experiments can be performed with electrons which show results that can be modeled by either - depending on the experiment. However, there are important distinctions which lead to the convention of referring to the electron (or any QM particle) as a particle rather than a wave.

In the two slit experiment, the electron wave-function does not "pass through the slits". In a classical interference experiment, say with water waves, an actual physical wave passes through the slits.

Instead - the electron wave-function is calculated from the properties of the apparatus - the source-slit apparatus prepares the initial quantum state of the electron. The whole thing is statistical.

All the measurable properties of the electron are partical-like ... eg. the electron energy all arrives in one lump in one place. In the classical version, the wave energy is distributed through the interference pattern.

In the end we have to view QM particles as being their own object. Ideally we should give them a different name, "quarticle" or something, to distinguish the QM particle model from the classical particle model: but that is not what happened.

Part of the confusion comes from poor treatments of interference in QM classes ... quantum interference is seldom actually modeled from the POV of quantum mechanics. Instead, some sort of shortcut is taken through ray optics and the relationship is asserted.

A proper treatment would start with the wavefunction - which must be a solution to the schrodinger equation ... eg.
http://arxiv.org/pdf/quant-ph/0703126]

A place to see a decent lay treatment is in Feynmans QED lectures on youtube.

we can tell that a particle left some source, and gets detected someplace else, but we don't know how it got there.
This sunk in for me when I looked at Feynman and Kac's path integral formalism. In that (as far as I could tell, I'm no authority) the path of each particle is a fractal. I thought, doesn't that mean the path is of infinite length? No wonder this didn't catch on. But the interpretation was accepted, so I guess it really is possible to look at it that way. Maybe it is even true. It is hard to tell. I concluded that no one really knows what the mechanism is and I should not worry about it.

I think that quantum objects are neither particles nor waves and trying to impose these ideas doesn't work. Once I started to think of them as something completely unfamiliar then things got easier.

Simon Bridge
Homework Helper
This sunk in for me when I looked at Feynman and Kac's path integral formalism. In that (as far as I could tell, I'm no authority) the path of each particle is a fractal.
Nope - not at all. What it says is that just knowing the endpoints of a path is not enough to know what happened in between - but knowing the endpoints does tell you enough to start making predictions about what kind of thing to expect.

Feynman et al provided a useful way to assign probabilities to the various possible paths based on what you know about the physics.

You don't need the "sum over many paths" formalism though - did you read the paper I linked to? That is plain ordinary year 1 wave mechanics.
I thought, doesn't that mean the path is of infinite length?
Google for "self energy" and "renormalization".
I think that quantum objects are neither particles nor waves and trying to impose these ideas doesn't work. Once I started to think of them as something completely unfamiliar then things got easier.
Well that can help - you just want to add the term "classical" in there.

According to everything we can measure - they are particles enough to be called that as a preference. It's like a coin - the distribution of heads and tails is discrete but it only comes down heads or tails ... one side or the other. You only see the distribution if you throw a lot of coins and you count heads and tails in a special way.

What you wouldn't do is try to combine the statistics and the coin into some sort of meta-object combining the features of both.