Questions over Quantum Physics

[haloshade]

Hello! High school physics student here.

I have some quantum physics questions for you. I am currently doing various studies through Wikipedia right now over quantum physics and I find it extremely fascinating, but I am a bit confused when it comes to the quantum probability areas.

The wave function, if I understand correctly, is a function use to describe the probability of a particle being in certain place at a certain time. I also understand that this involves superposition, but I am a bit confused of what exactly superposition is.

Also I have a problem with the wave function collapse, how exactly does it work? I think I have a mild understanding of what it is, but I'm still confused. I have read up on Schrodinger's Cat and Wigner's Friend, and I do get it, but I'm still a bit confused.

Thank you for any help you can provide!

 

[jwk]

So you were reading, The principle of superposition states that if the world can be in any configuration, any possible arrangement of particles or fields, and if the world could also be in another configuration, then the world can also be in a state which is a superposition of the two, where the amount of each configuration that is in the superposition is specified by a complex number.

When it is this bad, the author does not understand either.

Let's try, if a particle can be in any state, A, B, C, D, E, F, G, H, I, J, K, and L, then write a function that includes all these possible states. That function represents a superposition of states. Rules like spin, reduce the number of states a particle can be found. Now when an observer looks at the situation, the particle is in only one of those states. The superposition function must collapse to the state it is in. Which one? You only know when you look. When you aren't looking, it can be in any of them.

Take this situation, as an example, where you are in an elevator and the door closes, a person looking in sees you standing to the side pushing a button. When you get to your chosen floor, a person sees you leaning on the rail at the back. Each person sees you in a different location, so they write out a function that allows you to move in a variety of positions in the elevator car, representing a superposition. You, however, know what you did, but you are not telling, and you collapse to a position only when observed.

It seems rather contrived and seems to allow too much freedom in the situation. The particle did not really jump into every possible state, but it is a way to deal with the situation. There is a lack of knowledge that is causing the problem. I look at it as a mathematician's trick rather than a real effect.

 

[haloshade]

So you were reading, The principle of superposition states that if the world can be in any configuration, any possible arrangement of particles or fields, and if the world could also be in another configuration, then the world can also be in a state which is a superposition of the two, where the amount of each configuration that is in the superposition is specified by a complex number.

When it is this bad, the author does not understand either.

Let's try, if a particle can be in any state, A, B, C, D, E, F, G, H, I, J, K, and L, then write a function that includes all these possible states. That function represents a superposition of states. Rules like spin, reduce the number of states a particle can be found. Now when an observer looks at the situation, the particle is in only one of those states. The superposition function must collapse to the state it is in. Which one? You only know when you look. When you aren't looking, it can be in any of them.

Take this situation, as an example, where you are in an elevator and the door closes, a person looking in sees you standing to the side pushing a button. When you get to your chosen floor, a person sees you leaning on the rail at the back. Each person sees you in a different location, so they write out a function that allows you to move in a variety of positions in the elevator car, representing a superposition. You, however, know what you did, but you are not telling, and you collapse to a position only when observed.

It seems rather contrived and seems to allow too much freedom in the situation. The particle did not really jump into every possible state, but it is a way to deal with the situation. There is a lack of knowledge that is causing the problem. I look at it as a mathematician's trick rather than a real effect.

Thank you so much! I understand it way better now (I found the elevator analogy helpful).

Damn Wikipedia for not being reliable... Any suggested sites for this topic?

 

[meopemuk]

Hi haloshade,

reading Wikipedia is the most terrible way to study quantum physics. No wonder you are confused. Get yourself an undergraduate-level textbook on QM (there are plenty of them in any physics library), read it, solve problems, and you'll be fine.

 

[haloshade]

Hi haloshade,

reading Wikipedia is the most terrible way to study quantum physics. No wonder you are confused. Get yourself an undergraduate-level textbook on QM (there are plenty of them in any physics library), read it, solve problems, and you'll be fine.

Thank you, just the only problem right now is that I don't have the money to buy myself anything like that until I get a job this summer. Do you recommend any websites?

 

[meopemuk]

Thank you, just the only problem right now is that I don't have the money to buy myself anything like that until I get a job this summer. Do you recommend any websites?

My general advise is to stay away from websites when you want to learn such hard-core stuff as quantum mechanics. Websites will confuse you. Go to a library and get a textbook. Even regular city libraries may have a few good QM textbooks. If necessary, you can also use interlibrary loan. All this should be free of charge.

 

[haloshade]

I'll be sure to run to the library this week and get some books then.

Thank you so much everybody.

 

[jtbell]

For someone in your situation (assuming you're in the USA), a straight-up QM textbook probably isn't a good idea. They're usually aimed at third- and fourth-year students, usually assume a good amount of mathematical sophistication, and don't usually cover much of the historical and experimental background.

A better choice would probably be an "introduction to modern physics" textbook. Students in the USA usually take this kind of course as sophomores (second year), right after the first-year "general physics" course. It covers the historical and experimental background, and has an introduction to the basic concepts and mathematics of QM itself (the wave function, Schrödinger's equation, calculating probabilities, etc.). As far as the math is concerned, it usually assumes only that you know basic calculus (derivatives and integrals), and provides a brief introduction to more sophisticated math (e.g. partial derivatives) as needed.

I think "real" QM textbooks tend to assume that the student has already been through a course of this type.

 

[Fredrik]

The wave function, if I understand correctly, is a function use to describe the probability of a particle being in certain place at a certain time.

This is what we all thought when we were first introduced to wavefunctions, but you will eventually get over it. The above should be "...the probabilities of the possible results of position measurements". It's a mistake to think that the particle is somewhere between measurements.

 

[0xDEADBEEF]

[...]
Take this situation, as an example, where you are in an elevator and the door closes, a person looking in sees you standing to the side pushing a button. When you get to your chosen floor, a person sees you leaning on the rail at the back. Each person sees you in a different location, so they write out a function that allows you to move in a variety of positions in the elevator car, representing a superposition. You, however, know what you did, but you are not telling, and you collapse to a position only when observed.

It seems rather contrived and seems to allow too much freedom in the situation. The particle did not really jump into every possible state, but it is a way to deal with the situation. There is a lack of knowledge that is causing the problem. I look at it as a mathematician's trick rather than a real effect.

I am sorry but this is false. This analogy will take you quite far, but there are many effects that cannot be explained unless one assumes that the particle is actually in all states at once. Take the double slit for an easy example. You cannot explain what happens if you assume that the electron goes through one slit but we simply don't know which one, since it goes through both slits at the same time and interferes with itself. Macroscopic objects like people in elevators are another matter. They raise questions about the independence of observers. Can Schrödingers cat look at itself to check if it is alive? These questions remain very problematic and we will probably necessitate a quantum description of the brain (of which we don't even have a good classical one yet)

 

[mn4j]

I am sorry but this is false. This analogy will take you quite far, but there are many effects that cannot be explained unless one assumes that the particle is actually in all states at once. Take the double slit for an easy example. You cannot explain what happens if you assume that the electron goes through one slit but we simply don't know which one, since it goes through both slits at the same time and interferes with itself. Macroscopic objects like people in elevators are another matter. They raise questions about the independence of observers. Can Schrödingers cat look at itself to check if it is alive? These questions remain very problematic and we will probably necessitate a quantum description of the brain (of which we don't even have a good classical one yet)

Actually, it is the above which is false. It has not been demonstrated experimentally that a single electron/photon goes through both slits, nor has it been demonstrated experimentally that a single electron/photon interferes with itself. It is merely a conjecture.

 

[mn4j]

This is what we all thought when we were first introduced to wavefunctions, but you will eventually get over it. The above should be "...the probabilities of the possible results of position measurements". It's a mistake to think that the particle is somewhere between measurements.

I think this is taking it too far, since in QM all observables are results of measurements, it only makes sense to say it is a mistake to think the particle has a measured position when it is not measured. Rephrasing this statement the way you did takes it beyond what QM can say about any system. In other words, it IS a mistake to think that the particle is not somewhere even when it's position has not been measured. A theory is supposed to explain nature rather than dictate to nature what it must be.

 

[meopemuk]

A theory is supposed to explain nature...

This is a dangerous proposition. When you try to "explain" things that are not directly observable (like how the electron passes through the slits), you immediately lose a contact with experiment, and you may be tempted to introduce speculative non-verifiable notions, like "pilot waves" and "many worlds". These notions can give you a cosy feeling that you have "understood" nature, but, in fact, they are pseudo-scientific.

I would formulate the goal more cautiously: "A theory is supposed to predict results of measurements". To be even more cautious: "A theory is supposed to predict probabilities of results of measurements".

 

[Fredrik]

it only makes sense to say it is a mistake to think the particle has a measured position when it is not measured.

That statement isn't really saying anything.

Rephrasing this statement the way you did takes it beyond what QM can say about any system. In other words, it IS a mistake to think that the particle is not somewhere even when it's position has not been measured.

This is wrong. It's certainly a mistake to assume that every measurable quantity has a value at all times. The assumption that they do, has logical consequences called Bell inequalities. QM predicts that some Bell inequalities don't hold, and experiments have been performed to test that prediction. The result was that nature violates Bell inequalities, which means that it's not possible for all observables to have values at all times.

If you don't believe me, take it from someone smarter than me. This is a quote from Rudolf Haag ("Local quantum physics", page 2):

Take the example of a position measurement on an electron. It woud lead to a host of paradoxa if one wanted to assume that the electron has some position at a given time. "Position" is just not an attribute of an electron, it is an attribute of the "event" i.e. of the interaction process between the electron and an appropriately chosen measuring instrument (for instance a screen), not of the electron alone. The uncertainty about the position of the electron prior to the measurement is not due to our subjective ignorance. It arises from improperly attributing the concept of position to the electron instead of reserving it for the event.

A theory is supposed to explain nature rather than dictate to nature what it must be.

What Meopemuk said. (Although I wouldn't go so far as to call pilot waves and many worlds pseudoscientific. I haven't studied Bohm's theory, but it seems to be a well-defined theory that makes excellent predictions. I'm not a fan of many-worlds though. Everett's MWI in particular seems ill-defined to me).

 

[mn4j]

This is a dangerous proposition. When you try to "explain" things that are not directly observable (like how the electron passes through the slits), you immediately lose a contact with experiment, and you may be tempted to introduce speculative non-verifiable notions, like "pilot waves" and "many worlds". These notions can give you a cosy feeling that you have "understood" nature, but, in fact, they are pseudo-scientific.

I would formulate the goal more cautiously: "A theory is supposed to predict results of measurements". To be even more cautious: "A theory is supposed to predict probabilities of results of measurements".

You are right to the extent that the notions above are not verifiable. But that is a different issue that deals with the validity of different theories, it still doesn't change the fact that a theory is supposed to explain things rather than dictate them. The fact that "pilot waves" have not been verified does not mean "pilot-wave theory" is not a theory. I made no claim that all theories were valid.

 

[Fredrik]

it still doesn't change the fact that a theory is supposed to explain things

What we're objecting against is the word "explain". I would replace "explain things" with "make predictions that agree with experiments".

I'm sure we all agree that a theory that explains what "actually happens" would be desirable, but there's no good reason to think that QM can tell us what "actually happens". Does that make QM something less than a theory? I don't think so.

 

[mn4j]

It's certainly a mistake to assume that every measurable quantity has a value at all times.

I agree. Some observables are contextual. Just as it is equally wrong to assume that every measurable quantity has no value unless it has been measured. Not all observables are contextual.

The assumption that they do, has logical consequences called Bell inequalities.

Please, let's not even get into Bell's inequalities and its numerous problems.

The result was that nature violates Bell inequalities, which means that it's not possible for all observables to have values at all times.

You are forgiven for thinking a series of experimentally unverified inequalities can dictate to nature what it can and can not be. This is the same issue I was responding to in the first place, it is called the mind projection fallacy. An apparent discrepancy between Bell's inequalities and nature says more about the validity of Bell's inequality than what nature must be.

If you don't believe me, take it from someone smarter than me. This is a quote from Rudolf Haag ("Local quantum physics", page 2):

Take the example of a position measurement on an electron. It woud lead to a host of paradoxa if one wanted to assume that the electron has some position at a given time. "Position" is just not an attribute of an electron, it is an attribute of the "event" i.e. of the interaction process between the electron and an appropriately chosen measuring instrument (for instance a screen), not of the electron alone. The uncertainty about the position of the electron prior to the measurement is not due to our subjective ignorance. It arises from improperly attributing the concept of position to the electron instead of reserving it for the event.

The quote itself supports my view not yours. If "position" only makes sense when it is measured, the "measured position" means the same thing as "position" , then the following two statements are equivalent:

* an electron has no position unless it is measured
* an electron has no measured position unless it is measured

However, the second statement shows exactly how meaningless such a claim is in the first place (I'm happy you agree it is meaningless). This was exactly my objection to your claim that it is a mistake to think the electron is somewhere between measurements. So then the question for you is, are you sure "position" is ALWAYS contextual? Is there proof that it is?

It doesn't make sense to attribute contextual variables to only a part of the context. Yet unless you know for sure that ALL variables are contextual, you can not rule out the existence of non-contextual variables.

 

[Fredrik]

You are forgiven for thinking a series of experimentally unverified inequalities can dictate to nature what it can and can not be. This is the same issue I was responding to in the first place, it is called the mind projection fallacy.

I haven't said anything like that, so you may want to work on your reading comprehension skills.

An apparent discrepancy between Bell's inequalities and nature says more about the validity of Bell's inequality than what nature must be.

"Apparent" discrepancy? They were severely violated, so there's no hope that they can hold. What exactly are you claiming here? That there's a logical flaw in the derivation of the Bell inequalities?

The quote itself supports my view not yours.

It definitely supports my view. If it also consistent with yours, then you haven't been very good at explaining what you meant. (But I think it's getting clearer. See below).

If "position" only makes sense when it is measured, the "measured position" means the same thing as "position" , then the following two statements are equivalent:

* an electron has no position unless it is measured
* an electron has no measured position unless it is measured

However, the second statement shows exactly how meaningless such a claim is in the first place (I'm happy you agree it is meaningless). This was exactly my objection to your claim that it is a mistake to think the electron is somewhere between measurements.

OK, so now you're not saying that particles have positions between measurements. You're saying that the entire concept of position is meaningless between measurements.

Most people would say that to "have" a position implies that a position measurement will yield that result with certainty. Anyway, that's what it means for an observable to have a value in the context of Bell inequalities. When I said that a particle doesn't have a position between measurements, you objected and said that I was wrong. If you meant anything other than that the negation of what I said is true, you should have made an effort to explain that. The negation of my claim is that particle's have positions at all times, so obviously I thought that's what you were saying.

 

[meopemuk]

Although I wouldn't go so far as to call pilot waves and many worlds pseudoscientific. I haven't studied Bohm's theory, but it seems to be a well-defined theory that makes excellent predictions.

I've possibly missed this point. Did "pilot wave" theory have any predictions that are different from ordinary QM? If yes, then I will take back "pseudoscientific" with apologies.

I used the (possibly too strong) word "pseudoscientific" to describe theories which invent artificial "mechanisms" and create a false feeling of understanding. A good example is the ether theory. Originally Maxwell thought that all-penetrating ether is a kind of elastic substance, whose tensions and torsions are seen as electric and magnetic fields. Today we say: "Heck with those substances and "mechanisms". Just solve Maxwell's equations and you'll know the values of the fields. Don't even ask how exactly the changing vector E creates vector B".

In my view, the pilot wave "mechanism" is similar. The "wave", which commands poor electron where to go doesn't explain anything. It just adds an extra level of complexity without adding even a bit of extra predictive power to the ordinary quantum mechanics.

 

[Fredrik]

My point is that all Bohm's theory needs to do in order to qualify as a scientific theory is to make some of the predictions that QM does.

 

[meopemuk]

My point is that all Bohm's theory needs to do in order to qualify as a scientific theory is to make some of the predictions that QM does.

I certainly agree with that. I just wanted to make two points to explain why I dislike Bohm's theory and similar approaches. One point is more technical, and another is more fundamental.

On the technical side, Bohm's theory could be equivalent to QM in simple situations, like one electron passing through the slits. But what about many-particle systems? What about systems with variable number of particles (i.e., QFT)? What about Poincare invariance? All these problems have rather simple resolutions in the Hilbert space formulation of QM. However, in the Bohm's approach they seem to be very cumbersome.

On the fundamental side, it appears that the pilot wave theory suggests some physical mechanism for the quantum evolution of particles. Then it becomes open to a lot of further questions. For example, what is the mechanism for the "guiding" of electrons by the wave? Is there some kind of wave-electron interaction? What is it? Once we started to introduce physical mechanisms, we should go all the way. Are we going to stop somewhere? On the other hand, quantum mechanics simply refuses to provide a physical mechanism for the electron propagation. It simply gives a mathematical recipe for calculating results of measurements. So, it can easily shrug off annoying questions, like "why?" and "how?". I find it kind of neat.