Can Quantum Waves Really Have Mass?

[Hoku]

I don't usually consider "waves" to have mass. They're just energy that moves THROUGH mass. Light waves, sound waves, ocean waves... They are all massless energy. But I'm thinking about quantum wave/particle dualities. Electrons have mass and I'm having some trouble accepting how waves can have mass. Any insights or ideas for this seemingly trivial road-block?

 

[Matterwave]

Matterwaves, as they are called, aren't physical waves like sound, nor are they EM waves like light...they are probability waves. The probability wave itself does not have any "mass", it just tells you the probabilities of finding the particles at specific places. The particle has mass, not the wave. The wave simply describes the particle.

 

[Hoku]

How funny! You're more famous than I though, Matterwave.

So, you're saying that it's not just a "wave/partice" duality when it comes to electrons, it's also a "mass/massless" duality? So when an electron hits the film in the double slit experiment, it records mass when it's a particle and no mass when it's a wave?

 

[LostConjugate]

Err not exactly. The wave/particle duality is a bit of a different subject where the electron( or particle ) sometimes acts like a wave and sometimes acts like a particle. The wave equation was developed when we started looking at the idea that all matter is made up of waves, however there are still particle like aspects. So now we have these waves with no medium that are peculiar in that the entire wave seems to collapse when it is measured at anyone position.

The wave equations give scientists all the information they need to know about a particle even though there is no physical explanation for it. In some ways it is like a computer program trying to figure out what makes its bits flip.

 

[Matterwave]

Hmm, I think we should be very careful when discussing wave/particle duality and what exactly this means.

Wave-particle duality generally means that the electron acts like a particle for some experiments and like a wave for others. This means, in simplified terms, if I am looking for particle-properties such as mass, the electron will act as a particle. If I am looking for wave-like properties such as diffraction, the electron will act like a wave.

If you try to measure the mass of the electron, you get a definite mass because you are looking for a particle-tied property and the electron will act as a particle for this test! You will never measure the electron to have zero mass, because the electron will NOT act like a wave for a mass measurement.

I'm trying to keep this discussion close to High-school level, so at higher levels of understanding, the picture is more complicated. I will digress a little bit into the more complicated picture, but if you don't understand it at this point, don't worry. You will, once you study QM at a deeper level. The wave is, as I mentioned, a probability wave. The particle is described by a wave-function, and this wave-function is NOT physical in any sense. You can't make any measurements on this wave-function. So it doesn't make sense to try to measure the "mass" of this wave-function. All you can do is measure many electrons prepared in the same state to try to get a feel for the probability distribution of the electrons. The double slit experiment, for example if you release one electron at a time, each detection event is particle-like. You see 1 electron at one detector, and then 1 electron at another detector. You never detect some sort of "wave". Where the wave characteristics come in is when you get many detections, you will see a diffraction pattern IN your detections which would not arise classically for particles. It is therefore easier to describe the sum total diffraction phenomenon in terms of waves.

 

[LostConjugate]

It is therefore easier to describe the sum total diffraction phenomenon in terms of waves.

However a single particle must be described by a wave equation in a tunneling equation.

 

[Matterwave]

Sure, but when you make measurements in tunneling, you always measure the electron as either having tunneled or not having tunneled. You never measure an electron as "half-tunneled" or some such.

Only when you get many electrons together, can you find that X% of them tunneled and 100-X% of them didn't.

There is a definite disconnect between how electrons are described and how electrons are measured. They may be described by a wave-function, but they will inevitably be measured as electron particles.

 

[LostConjugate]

Sure, but when you make measurements in tunneling, you always measure the electron as either having tunneled or not having tunneled. You never measure an electron as "half-tunneled" or some such.

Only when you get many electrons together, can you find that X% of them tunneled and 100-X% of them didn't.

There is a definite disconnect between how electrons are described and how electrons are measured. They may be described by a wave-function, but they will inevitably be measured as electron particles.

Another example of the wave-particle duality. I wouldn't expect you would need many electrons though. You could setup an experiment so that the potential allowed for a 90% chance of tunneling even though V > p_e. Do one experiment and if the single electron tunnels then you just proved wave like nature without any statistics. If it happens not to tunnel then wait 5 years, well you get the point.

 

[Matterwave]

?

First of all, how does 1 data point make any proof? Second of all, you are STILL detecting the electron AS AN electron.

Perhaps I am not understanding your scenario correctly...

 

[LostConjugate]

Just imagine you did an experiment once and got "lucky" and the electron tunneled. The wave equation describes the result and the "wave" is not based of a statistical collection of results.

 

[Hoku]

This is interesting, and you haven't lost me at all. You're definitely bringing to light some simple, missing pieces in laymans literature. Let me pick through some of this for clarification. Are you saying that a single electron will never display a "wave" pattern, even if we try to measure it as such? Are you also saying that an electron cannot tunnel unless it is in a group?

 

[LostConjugate]

? Are you also saying that an electron cannot tunnel unless it is in a group?

No, he is saying that the wave nature described in QM is based off a statistical collection of results. We can never say exactly what single particle will do, just what many of them will do, though in the end if 5 million electrons tunneled, they each tunneled.

As for your first question, I think that a single electron can display wave nature when measured only once. MatterWave might have more to say on that though.

 

[LostConjugate]

You never measure an electron as "half-tunneled" or some such.

You can find the electron within the area of space where V > p_e though. The probability wave is a gaussian here. Not sure that's what you meant though.

 

[Matterwave]

So you are saying, by virtue of the electron having tunneled, it must have wave-characteristics because particle characteristics cannot account for tunneling?

Perhaps I should make my point clearer.

When you make a measurement, e.g. a measurement of mass, you invariable are measuring the particle. Even in the tunneling example, you are measuring the position of the particle. You are not measuring a wave like you could measure a physical wave (like waves on a pond). With waves on a pond, I could measure the amplitude by using a ruler, for example; however, I can make no such measurements on the electron's wave-function (or the absolute square of the wave-function). I can only get an idea for the amplitude, if I get many measurements of identically prepared electrons.

With your tunneling example, with 1 electron, I certainly can't measure the amplitude, or the wavelength, or any other wave-characteristic of the wave-function. All that I may be able to tell is that something weird is happening in that the electron moved through a region it shouldn't be able to move through.

Perhaps I am wrong. And indeed, it is often hard to reconcile high-school level explanations with "real" explanations. But in any case, this is a digression from the OP's discussion. I think the main point as far as the OP is concerned is that if I measure the mass of an electron I will always measure a mass because the electron behaves particle-like for such a measurement.

 

[Matterwave]

You can find the electron within the area of space where V > p_e though. The probability wave is a gaussian here. Not sure that's what you meant though.

Actually you can never find the electron in a classically forbidden region (V>E). You can only find it on one side or the other.

The rough proof is that if you tried to measure the electron in the classically forbidden region, you must necessarily boost the energy of the electron such that that region is now classically allowed. You can't tell that originally the electron didn't have enough energy. This is intricately intertwined with the HUP.

I don't have a very good proof, but there are rigorous proofs available, and you can search for them. =)

 

[LostConjugate]

I agree with everything you say MatterWave, but not sure how it contradicts the fact that there are wavelike-characteristics with emphasis on "like". I am not saying it disproves the particle theory, just that there is wavelike nature describing the experiment.

Just trying to say that wave equations are not all based off statistical results, otherwise it would be a boring subject and talk of a single particle borrowing energy, or interfering with itself would no longer be a subject.

 

[LostConjugate]

The rough proof is that if you tried to measure the electron in the classically forbidden region, you must necessarily boost the energy of the electron such that that region is now classically allowed. You can't tell that originally the electron didn't have enough energy. This is intricately intertwined with the HUP. )

Oh. Didn't know that. Understandable.

 

[Hoku]

I appreciate your input, LostConjugate. I hope my continued questioning doesn't bother you. I do have a few layman's books on the subject and I feel pretty comfortable with things like probability distributions.

I know that, in a non-controlled environment, particles will do (essentially) whatever they want without us being able to track exact locations or states (uncertainty principle). I also know that, in more natural environments, many electrons are required to "fulfill" a probability distribution. Without enough electrons, it's a free-for-all. I think even WITH enough particles it's still a free-for-all, but we only care how they perform as a group.

I think I'm most interested in controlled experiments, like the double-slit one. What I'm picking up here is that the wavelike properties of electrons are described from the group that collectively display the wave pattern. Is that right? But a single photon CAN display both wave and particle dualities. Is this right?

 

[LostConjugate]

A photon and electron both display wave particle dualities the same. A photon is a particle, it is not an electro magnetic wave.

So with the double slit you can work with either one, shouldn't matter.

Either way in order to see the wave nature you must send more than one particle through the slits. Though you can send them with great amounts of time between. Like 1 photon every year and still see the interference pattern.

 

[Matterwave]

Discussing this topic can become quite sticky. I myself prefer the Ensemble interpretation of QM...but in discussing this topic I tried to not allow interpretation-dependent aspects through, and just describe standard quantum mechanics. It's difficult because the topic we are discussing is beginning to push onto the interpretation level...haha.

Let us try to make everything as clear as possible. First, let's stay with the double-slit experiment. When you make a specific measurement of position, i.e. where the particle is on the screen, you necessarily measure only the particle-like aspect - position (waves are spread out!). When you combine many many measurements of position, you start to see a diffraction pattern occur in the distribution of these electrons and from this you can infer a wave-like property. Be absolutely certain that you did not measure this wave-like property, but you inferred it from your measurements. This applies to both electrons and photons. You can ever only measure 1 aspect at a time.

Now onto the tunneling example. In fact, it is analogous because when you measure the 1 electron, you are in fact measuring a particle-like aspect (position). You may be able to infer from this 1 electron the wave-nature but you certainly did not measure the wave-nature.

I admit, this topic is getting to the limits of my QM knowledge.

The main point to make here is that the wave-function is not a physical reality (except perhaps in the Many-worlds interpretation...which I'm not familiar with). The wave-function cannot be measured like position or mass or the amplitude of a real physical wave.

 

[Hoku]

Just trying to say that wave equations are not all based off statistical results, otherwise it would be a boring subject and talk of a single particle borrowing energy, or interfering with itself would no longer be a subject.

This is what I'm trying to get at. I learned that the wave aspect of the duality was documented in the double slit experiment by a single particle interfering with itself after it passed through both slits, simultaneously. So you're saying that I learned this wrong? Where did this "interfereing with itself" thing come from?

I think the main point as far as the OP is concerned is that if I measure the mass of an electron I will always measure a mass because the electron behaves particle-like for such a measurement.

I think I understand your point here. You cannot measure mass when it is in wave form, so we don't/can't really know the answer. But the best assumption is that it doesn't. Right?

 

[LostConjugate]

The main point to make here is that the wave-function is not a physical reality (except perhaps in the Many-worlds interpretation...which I'm not familiar with). The wave-function cannot be measured like position or mass or the amplitude of a real physical wave.

The waves are not an observable, agreed. I guess what I was thinking you were saying was that a wave function was nothing more than a convenient way to collect data.

 

[LostConjugate]

This is what I'm trying to get at. I learned that the wave aspect of the duality was documented in the double slit experiment by a single particle interfering with itself after it passed through both slits, simultaneously. So you're saying that I learned this wrong? Where did this "interfereing with itself" thing come from?

The particle is interfering with itself when passing through the slit, this is the result of getting a diffraction pattern.

We can't detect a single particle going through both slits though, because each time we detect a particle the wave function collapses, which means a function which used to exist over all space now exists only in one spot, the slit it was detected at.

Edit: By exists I mean has a value other than 0 at each position.

 

[Hoku]

Discussing this topic can become quite sticky. I myself prefer the Ensemble interpretation of QM...but in discussing this topic I tried to not allow interpretation-dependent aspects through, and just describe standard quantum mechanics. It's difficult because the topic we are discussing is beginning to push onto the interpretation level...haha.

It seems that even "infering" wavelike properties in "standard quantum mechanics" is in the realm of interpretation.

 

[Matterwave]

This is what I'm trying to get at. I learned that the wave aspect of the duality was documented in the double slit experiment by a single particle interfering with itself after it passed through both slits, simultaneously. So you're saying that I learned this wrong? Where did this "interfereing with itself" thing come from?

Think about it, if you just detected 1 electron, how could you tell that it had diffracted/interfered? 1 electron is just a dot on the screen...by looking at this dot how can I possibly tell that diffraction/interference occurred? Only when you get a lot of dots can you tell from the interference fringes that interference occurred.

What people mean when they say that "interference happens even for 1 electron" is that even if you sent 1 electron through the the slits at a time so that it couldn't possibly be interfering with another electron, once you collect many data points, you still see a interference pattern!

I think I understand your point here. You cannot measure mass when it is in wave form, so we don't/can't really know the answer. But the best assumption is that it doesn't. Right?

We necessarily can't measure a mass for the wave because waves are entities which we defined which we can't attribute a mass to...it does sound very much like circular reasoning. We attribute mass to particles. So the argument is going to sound something like "waves don't have mass because they aren't particles"...somewhat of a tautology.

The best I can tell you is that this attribute we call "mass" is something that only is attributed to particles. So asking whether waves have mass is kind of like asking whether my baseball has an amplitude...

 

[Hoku]

We can't detect a single particle going through both slits though, because each time we detect a particle the wave function collapses, which means a function which used to exist over all space now exists only in one spot, the slit it was detected at.

But you can control how many particles are shot from the gun, right? So if you KNOW you shot just one particle, and if you don't try to "detect" it, then the particle shows an interference pattern as if it went through both slits. That's how I learned it from all of my resources. Is this totally wrong??

 

[Matterwave]

Haha, I think we are getting a bit confused on "detection". In the 2 slit experiment, you MUST detect at the screen, this is the detection event I have been talking about. However, if you shined a light at either of the slits to try to tell which slit the electron went through, that is a separate detection event. Don't confuse the 2 detections.

 

[Hoku]

Alright, then! Guess I'll put my flashlight away. Unfortunately, I don't have any more time for this today. I will get out my resources, pick out exactly what I've "learned" from them and post it here tomorrow. Hopefully that will help get to the heart of the problem.

 

[Hoku]

Here is a quote from Wikipedia entry "double slit experiment":

The most baffling part of this experiment comes when only one photon at a time is fired at the barrier with both slits open. The pattern of interference remains the same, as can be seen if many photons are emitted one at a time and recorded on the same sheet of photographic film. The clear implication is that something with a wavelike nature passes simultaneously through both slits and interferes with itself — even though there is only one photon present. (The experiment works with electrons, atoms, and even some molecules too.)

The part in bold is really what's confusing me here. Are we talking about ONE photon or a GROUP of photons?? I know they're saying that you shoot one at a time, but it is still a collective of the GROUP. So why do they talk about "only one photon present"?

 

[LostConjugate]

Welcome back Hoku :)

What the article is stating is that after sending a large number of photons through the slit we can determine from the results that a single photon must have wavelike nature.

We can't deduce this from sending only one photon, though it is true that single photon has wavelike nature.

 

[Hoku]

My computer won't let me watch the video (time for a new one). Since the discusion has changed direction from my initial question, which has essentially been resolved, I think I'll begin a new thread to continue. I'll call it, "understanding waves". Hope to see you there!

EDIT: It's called "understanding duality".

 

[GreenLantern]

I don't usually consider "waves" to have mass. They're just energy that moves THROUGH mass. Light waves, sound waves, ocean waves... They are all massless energy. But I'm thinking about quantum wave/particle dualities. Electrons have mass and I'm having some trouble accepting how waves can have mass. Any insights or ideas for this seemingly trivial road-block?

I'm guessing you are referring to the age old question that many (as well as myself had initially before some more consideration) have asked when starting into QM and that is, "what happens to the properties, like mass, that are associated with particles, like electrons, when they are behaving as waves?" because as you said, waves do not have mass. But one thing you are over looking is, they have MOMENTUM! You should recall that due to its momentum light ( EM radiation/waves) actually exerts a pressure, hence why a solar sails and Crookes radiometers etc... do what they do ;) (check out Poynting vector section of physics texts. Usually this concept is talked about round about there)

The same idea goes for electron's and other quantum objects with non-zero rest mass when they are exhibiting wave behavior (are "being" waves).

Mass associated with particles <===> Momentum associated with wave

I hadn't read all the pages of this thread but I'm quite sure this is accurate and may resolve some confusion here (as always someone please politely correct me if I am wrong so I may correct my words)

-GreenLantern

<edit> I just looked at a few of the most recent posts above and noticed, WHY for the love of quanta and all that is empirical are we citing wikipedia?!?? and this what you say your "resources" are?? NO WONDER WHY YOU'RE CONFUSED! If you want to learn something and not have nearly as large of a probability that you will get crap stuck into little folds of your brain, don't read wiki. Stay away from wiki. READ A PUBLISHED TEXT! where, you know, those awesome people called editors with some credit to their name are checking the information... I could go in wiki and, as i have said before, tell you that when an electron is exhibiting particle behavior, it is really just in two dimensions, leaving our four (or 11, which ever you feel like citing) for just a moment so it can go through the single/double slit barriers... or some other stupid crap like that. ugh...i sware, a large majority of nonsense in this world wouldn't be if it weren't for wiki</edit/rant>

 

[LostConjugate]

A classical wave of some medium could be said to have mass which is proportional to the integral of the function.
For example \int e^{ikx} = ke^{ikx}

The mass is proportional to the frequency, this is because the amount of the medium per unit area is higher with higher frequency. If the wave is traveling at a constant speed the momentum increases because the mass per unit area increases.

In a wave where there is no medium the momentum remains proportional to the frequency just as if though you were adding up more medium per unit area in a classical wave. Strange connection.