How observation leads to wavefunction collapse?

[Mr Virtual]

Hi all

I know I raised a similar question in the thread "Wave particle duality", but it is already so full of many other questions, that I'd not be able to discuss this topic fully there.

So, in the double slit experiment, if a photon observes an electron, the interference pattern vanishes. Why is this so? What does a photon do to an electron? Also, can anybody explain to me as to how a single electron creates an interference pattern in reality? I am completely at sea as far as understanding this phenomenon is concerned. I know that in theory we have wavefunctions, but how can all the paths that can be followed by the electron, consist of one in which it passes through both the slits?

thanks
Mr Virtual

 

[olgranpappy]

a single electron does not create an interference pattern

 

[olgranpappy]

...I suppose I should explain further... quantum mechanics can tell you how to predict the probablity that (in your double slit experiment) the electron will hit the detecting screen at a point 'x'.

If you shoot a single electron thru the double slits at your detecting screen it will hit the screen and be recorded in only *one* place because it is only *one* electron. If you shoot lots and lots of electron then they will each hit the screen (once each) but the distribution of hits will look like an interference pattern. Indeed, it will look like the probability density to hit the screen at 'x' which you calculated using quantum mechanics.

 

[chessforce]

When a photon interacts with an electron, it changes the electron's momentum.

 

[Mr Virtual]

If you shoot a single electron thru the double slits at your detecting screen it will hit the screen and be recorded in only *one* place because it is only *one* electron. If you shoot lots and lots of electron then they will each hit the screen (once each) but the distribution of hits will look like an interference pattern. Indeed, it will look like the probability density to hit the screen at 'x' which you calculated using quantum mechanics.

I agree. But my question is that why this distribution on the screen resembles to a wave interference pattern, instead of the usual pattern observed when bullets are hit through two slits? This interference pattern can result only when some of the electrons are passing through both the slits at the same time, which is impossible to be done by a particle. If, then, an electron is a wave, then what is the nature of this wave? A wave consists of quanta, but electron itself is a fundamental particle. Then what type of quanta does this electron-wave consist of, and does it actually consists of any quanta at all or not? How is mass distributed in this wave? Why does a photon collapse this wave? As far as I know, waves normally do not collapse into particles on interaction with other waves.

thanks
Mr V

 

[Mr Virtual]

When a photon interacts with an electron, it changes the electron's momentum.

That's quite true. But why does a photon collapse an electron-wave into a particle?

Mr V

 

[olgranpappy]

I agree. But my question is that why this distribution on the screen resembles to a wave interference pattern

...and the answer is that it simply does as it does. You might as well question why light makes an interference pattern. The experimental facts are that electrons *are* diffracted in the same way that photons are diffracted. In some instances it is more useful to think of conglomerations of photons as waves and in some instances it is more useful to think of photons as particles; and in some instances it is more useful to think of conglomerations of electrons as waves and in some instances it is more useful to think of electrons as particles. Do not stray into metaphysics.

 

[Demystifier]

That's quite true. But why does a photon collapse an electron-wave into a particle?

Within the conventional interpretation of QM, an answer that would satisfy you does not exist. An answer exists within the Bohmian (pilot wave) interpretation, if you are willing to accept the idea that the wave and the particle are two separate but coexisting things.

 

[Mr Virtual]

The experimental facts are that electrons *are* diffracted in the same way that photons are diffracted.

Yeah, you are quite right.

...and the answer is that it simply does as it does. You might as well question why light makes an interference pattern.

Indeed, it will be nice of you if you could explain just that, because knowing how light gets diffracted will automatically explain diffraction of electrons.

warm regards
Mr V

 

[Mr Virtual]

Precisely, I would like to know as to what happens to a photon when it is fired at the two slits (and we are not looking at it). How does a single photon interfere with itself (as is told by many)?

 

[Mr Virtual]

Also, what do we mean by observation (which causes wavefunction collapse)? Suppose, there is a box full of light and we are performing the two slit experiment inside it. Now, though we are not seeing the electron, the photons inside the box are "seeing" it (in other words, the photons are colliding with it). So, will there be a wavefunction collapse?

EDIT: Is photon the actual cause of collapse? If it is, then does it also lead to the collapse of wavefunction of photons also?

 

[rewebster]

Hmmmmm--for some reason (I really can't say why I get that feeling), I get the idea that you're not satisfied with the answers you're getting.

---I'm guessing (hoping really) that you've looked all over the internet for the answers?

 

[Gza]

Wavefunction collapse is a postulate of QM supported by experimentation.

 

[olgranpappy]

101

Indeed, it will be nice of you if you could explain just that, because knowing how light gets diffracted will automatically explain diffraction of electrons.

It's freshman physics. Go get any physics textbook (I suggest "Fundementals of Physics" (Fifth Ed.) by Halliday Resnick and Walker) and lookup "Young's Experiment" in the index. Interference maxima occur on the viewing screen for
$$d \sin( \theta ) = n \lambda$$
where d is the distance between the slits, theta is the angle of observation, n is any integer and lambda is the wavelength of the light.

 

[olgranpappy]

...so, from this discussion it appears that you do not yet understand how the *classical* scattering of light works... if you don't understand how this works then how can you expect to understand how diffraction of electrons works?

 

[Mr Virtual]

...so, from this discussion it appears that you do not yet understand how the *classical* scattering of light works... if you don't understand how this works then how can you expect to understand how diffraction of electrons works?

You misunderstood me. When I said,

Indeed, it will be nice of you if you could explain just that, because knowing how light gets diffracted will automatically explain diffraction of electrons.

I was actually asking for an explanation of diffraction of light considering light to be made of photons, not waves. I actually wanted to know how to explain interference in terms of photons. If that is explained, then it would obviously be easy to understand diffraction of electrons.

And as far as I know, *classical* explanation of diffraction of light is based on wave nature of light, not particle nature. So that is not what I asked.

regards
Mr V

 

[Mr Virtual]

Hmmmmm--for some reason (I really can't say why I get that feeling), I get the idea that you're not satisfied with the answers you're getting.

Yeah, you are quite right about that. I am very frustrated about this dual nature of matter. I know that until and unless I understand this duality, I am not going to understand anything. What makes my head spin is my complete inability to forge any relation between these two entirely different concepts. For example, we say that light consists of photons, and the energy of the photon depends on the frequency of light. It doesn't make sense to me. We are trying to describe the particle-behaviour of light in terms of its wave-nature. The word 'frequency' has no meaning for a photon, even then its energy depends solely on frequency.

I hope one day I will be able to understand this paradox (oops! not a paradox, but this funny behaviour of nature), like most of you already have.

 

[rewebster]

Yeah, you are quite right about that. I am very frustrated about this dual nature of matter. I know that until and unless I understand this duality, I am not going to understand anything. What makes my head spin is my complete inability to forge any relation between these two entirely different concepts. For example, we say that light consists of photons, and the energy of the photon depends on the frequency of light. It doesn't make sense to me. We are trying to describe the particle-behaviour of light in terms of its wave-nature. The word 'frequency' has no meaning for a photon, even then its energy depends solely on frequency.

I hope one day I will be able to understand this paradox (oops! not a paradox, but this funny behaviour of nature), like most of you already have.

WE have?

If you are wanting to know WHAT happens with light and the double slit, etc., that is extremely well documented (ie interference patterns). IF you are looking for the reasons behind WHY it happens (and it sounds like you are), it also sounds like you are thinking that WE know and are keeping it from you (not explaining it to you for some reason--keeping it a secret).

 

[Mr Virtual]

No, no. That's not the case. Actually, all of you are trying to explain to me in every way you can; as I said, it is my inability to comprehend it in the way that you are trying to make me understand it.
And yes, I am interested in looking for reasons as to WHY it happens. I have searched almost everywhere I can, but nowhere they give any explanation. At best, they will just say, "Even the most experienced physicists do not know the exact reason as to why these things happen in nature". That is why I thought that I may get help from this forum. No doubt I have received plenty of help, suggestions and new ideas. But I think there are some things which you can't understand just by sitting at the computer and firing questions at others. You have got to see them yourself to find answers.
Most of you are physicists, professors, grads or undergrads, who have spent a large amount of time studying these mystifying things, and I can't expect to learn all of this in a day or two.


Mr V

 

[olgranpappy]

You misunderstood me.

But my point still stands. You either do or you do not understand interference of light from a classical point of view. If you do, then good for you. If you don't, then I encourange you to look into it.

I already explained that a single electron does not make an interference pattern on a detecting screen. The same holds for a single photon. Thus it is a matter of semantics as to whether or not you want to say the single photon (or electron) "interferes with itself."

 

[rewebster]

No, no. That's not the case. Actually, all of you are trying to explain to me in every way you can; as I said, it is my inability to comprehend it in the way that you are trying to make me understand it.
And yes, I am interested in looking for reasons as to WHY it happens. I have searched almost everywhere I can, but nowhere they give any explanation. At best, they will just say, "Even the most experienced physicists do not know the exact reason as to why these things happen in nature". That is why I thought that I may get help from this forum. No doubt I have received plenty of help, suggestions and new ideas. But I think there are some things which you can't understand just by sitting at the computer and firing questions at others. You have got to see them yourself to find answers.
Most of you are physicists, professors, grads or undergrads, who have spent a large amount of time studying these mystifying things, and I can't expect to learn all of this in a day or two.


Mr V

It still sounds like you think we (or I) are not telling you the secret.

 

[Mr Virtual]

I already explained that a single electron does not make an interference pattern on a detecting screen.

Yes, that's right. But eventually, you are going to get an interference pattern (when a large number of electrons have hit the screen), which defies common-sense experience (of course, QM goes beyond common-sense experiences). And if that is true ( it is ), then this means that the electron/photon is showing wave-nature. I want to understand what type of wave nature is this, in which the electron/photon still hits the screen like a particle, not a wave?
A wave makes an interference pattern on the screen at once, whereas the electron/photon builds it gradually. This means that though, it is not a wave, it is still following all the paths followed by a wave (defined by QED), and this wave ( the probability wave function, to be precise), predicts that a photon/electron has the probability to pass through both the slits and interfere with itself. This is what confuses me. How can such a probability exist?

regards
MR V

 

[Mr Virtual]

When I said

though, it is not a wave, it is still following all the paths followed by a wave

I meant that each of the electron which "passes through both slits" follows "any one" of the paths usually followed by interferring waves.
Let me expand a bit more. The interference pattern is bulit up only by those electrons that follow the probability path defined through both the slits. The rest of the electrons ( which pass through either slit or pass through neither) will follow the macroscopic laws we observe, and help in forming the two main lines ||.

 

[Mr Virtual]

It still sounds like you think we (or I) are not telling you the secret.

Then please, reveal that secret.
Just joking. I don't know what words to write to convince you that I am not blaming anyone of keeping any secret. Believe me, I haven't got any complaint of such a kind.

 

[rewebster]

Then please, reveal that secret.

NOPE--it's not going to happen---you're going to have to wait for book or the movie to come

 

[Mr Virtual]

NOPE--it's not going to happen---you're going to have to wait for book or the movie to come

Oh My! How long do I have to wait for the movie? You won't charge anything from me when I go to see it, would you? I will give you the name of the cinema hall. Please inform them about this special discount you are going to give me ( You are, aren't you??).

 

[olgranpappy]

and this wave ( the probability wave function, to be precise), predicts that a photon/electron has the probability to pass through both the slits and interfere with itself.

No. To be precise, this wave (the "wave function" $$\Psi(\vec x)$$) does not tell you that; what the wave function tells you is this: If the *position* of the electron is measured then the result of the measurement is within $$d^3x$$ of
$$\vec x_0$$
with probability
$$|\Psi|^2(\vec x_0)d^3x$$.

When the electron hits the screen this *is* the act of measuring and we now know where the electron is. We have measured it's position. The distribution of *many* repeated measurements will show the distribution predicted by quantum mechanics. I.e., the distribution given by $$|\Psi^2(\vec x)|$$. And, yes--yes, $$\Psi(\vec x)$$ does obey an equation which is called a "wave equation." Yes. That is true. But, so what? The facts are simply what I have just presented. No more and no less. The rest is either metaphysics or semantics.

 

[Mr Virtual]

Am I right if I say this: that the electron's (and photon's) wave-nature is actually this probability distribution. The electron/photon itself is not a wave. The interference pattern we observe just shows the probability density area filled by individual electrons over a period of time?

Mr V

 

[olgranpappy]

Yes, this is a fine perspective.

 

[Demystifier]

Yeah, you are quite right about that. I am very frustrated about this dual nature of matter. I know that until and unless I understand this duality, I am not going to understand anything. What makes my head spin is my complete inability to forge any relation between these two entirely different concepts. For example, we say that light consists of photons, and the energy of the photon depends on the frequency of light. It doesn't make sense to me. We are trying to describe the particle-behaviour of light in terms of its wave-nature. The word 'frequency' has no meaning for a photon, even then its energy depends solely on frequency.

I hope one day I will be able to understand this paradox (oops! not a paradox, but this funny behaviour of nature), like most of you already have.

You have not responded to my post, so I will try again, more explicitly:
Have you tried with the Bohmian interpretation? Yes or No?
If yes, why don't you like it?
If no, what are you waiting for?

 

[Mr Virtual]

If no, what are you waiting for?

For a link to a good site which explains Bohmian interpretation in detail and accurately. It would be nice if you provide one.

Thanks
Mr V

 

[Mr Virtual]

Is wikipedia a good place to start?

Mr V

 

[Demystifier]

Is wikipedia a good place to start?

Mr V

Wikipedia is fine, although probably not perfect.
You may try also with this:
http://xxx.lanl.gov/abs/quant-ph/0408113
For a somewhat wider context, some sections of
http://xxx.lanl.gov/abs/quant-ph/0609163
may also be useful, e.g. Sec. 2 and especially Sec. 4.2.

 

[Mr Virtual]

Thanks. I will have a look at these sites.

Mr V

 

[Demystifier]

For a very concise, but accurate, introduction to the Bohmian interpretation see also the section "Nonrelativistic Bohmian interpretation" of
http://xxx.lanl.gov/abs/quant-ph/0512065