Some doubts understanding wave nature experiment for electrons

[paka]

hello everybody, I'm new here and new to the field of QM also. I have a few doubts regarding the double slit experiment. I know that there are other threads also here about the same thing, and you must be fed up seeing another one pop again, but I'm less brainy than those guys and have more than 1 or 2 questions on this experiment. So please bear my stupid(maybe) questions and try to explain to me with patience. Also i have read Feynman's lectures on the experiment(i saw one guy telling the OP to do that in one of the threads).So here goes.

1. Feynman says that if we don't measure which hole a certain electron is going through and just observe the probability distribution graph of many such electrons, they make the interfernce pattern. But if we do measure it, then it becomes a normal additive probability graph of the probability distr. of the two slits' separate graphs. i understand that 'measuring' by shining light on it for example disturbs the elctron's path, but why should it be disturbed in such a way only that the new behaviour is similar to a particle's? why shouldn't the distr. just become more random?
2. is it true that a single electron also, if not disturbed or measured as to which hole it went through in any way, will interfere with itself? In that case the interference is not visible, because the electron will be detected only at a single point on the screen. how can we be sure now that it is showing wave nature, it cud just as well be a particle, getting deflected randomly to where it was detected. From what i understand of wave nature, if there is interference,there shud be lots of detections with maximas and minimas, even wid a single electron. Now on the contrary if we say that a single electron behaves like a particle, then there isn't any reason why all the other e- sent after it shouldn't do the same, and hence why a normal, interference-free pattern shouldn't be formed. sorry if this sounds stupid, I am terribly confused.
3.what does the imaginary part of the probability amplitude signify? Can anyone please explain what it is and what relation it has, or not with the many-worlds theory?
4.Feynman cites the uncertainty principle when saying that it is not possible to simultaneously know which slit the e- went thru and still observe the interference pattern in the prob. distr.. I know what the Hburgs' UP is, but i couldn't grasp how exactly it could be related with this. Of course there is the same you can't know one thing accurately while knowing the other, but how does momentum and position come into the slit experiment? Please help.
5. Feynamn says that when the observer observes which hole the e- went thru, its wavefunction collapses and the obs. and e- are now entangled. I am sorry, bt what the heck is that supposed to mean?

Many thanks in advance!

 

[etamorphmagus]

1. The randomalities add up to "classical particle distribution" = mess up the interference pattern.

2. The single e diffracts at the slit as a wave, it doesn't "deflect" like a "bullet" - the bullet deflection experiment is just a way to show that single slit particle distribution and single slit wave distribution will be similar - it's a somewhat confusing feynman thing.
Anyways, if you refer to the single electron as a wave, then the wave-intensity on the screen will correlate to the probability of detection as a "particle". that is the way to deal classically with the quantum-behavior. You can detect an electron only at a single location, you "collapse" it to a single state from the variety of states it had before it collapsed in the measurement.

3. Imaginary numbers are a math tool. If you read the chapter in the Feynman lectures about imaginary numbers (I guess you have it, because you talk about stuff from the chapter "quantum behavior") you understand it's just easier to do math with them, instead of cosines and what-not. anyway, the probability in the end is a REAL number, not imaginary.

4. When the e goes thru the slit you know exacatly it's y-location - so there's a spread in the y-momentum - bigger distribution of wavelengths (wavelength=h/momentum). So when you DONT know what slit the e went thru, both slits are coherent sources of the electron-wave - they are of the same wavelength. when you know the y-location - they are no longer coherent and the interference image is messed up, the randomalities will give "classical particle curve" and not "pretty maxima and minima".

5. No idea. Where does he say that?

I know the answers don't sound like poetry - sorry. However I am too very interested in this, and glad to help the curious like me. I did a lot of internet and book reading, but I am not an expert, so whatever sounds weird, open further discussion about it.

 

[paka]

^^
thanks a lot for ur quick reply, and clearing any doubts i had about no.4, no.3 and no.1.

As to no.5 you are right, he doesn't say that(i don't know why i thought that) but i definitely saw this somewhere, and would like if you could explain to me what these terms meant. I have read it up on various sites and i from what i cud grasp, wavefunction collapse is the attainment of a particular state out of many possible states because of disturbance due to measurement etc. and entanglement seems to be the phenomena in which due to laws of conservation in the decay of a constituent body, the natural [roperties of a pair or group pf particles are related to each other and hence when one is known the other is simultaneously determined, leaving us unable to measure(definitely) any other prop of the second particle due to HUP. Maybe you cud tell me more.

no.2 i still don't understand why we are so certain that a single electron, if not measured as to what slit it passes through, exhibits wave nature. it is ejected as a single particle, and detected at some place on the screen as one, then how do we infer that wave like behaviour is being shown? it is only after we do many such experiments and plot the prob. distr. graph that we get the interference pattern.

Thanks for the help, keep it coming please.

 

[etamorphmagus]

No problem, you're actually helping me, but still don't take what I say too seriously.

As to no.5 you are right, he doesn't say that(i don't know why i thought that) but i definitely saw this somewhere, and would like if you could explain to me what these terms meant. I have read it up on various sites and i from what i cud grasp, wavefunction collapse is the attainment of a particular state out of many possible states because of disturbance due to measurement etc. and entanglement seems to be the phenomena in which due to laws of conservation in the decay of a constituent body, the natural [roperties of a pair or group pf particles are related to each other and hence when one is known the other is simultaneously determined, leaving us unable to measure(definitely) any other prop of the second particle due to HUP. Maybe you cud tell me more.

A very important thing about QM is that it is all about semantics and philosophical interpretation that doesn't really mean anything physically. Nothing is derived from HUP, but everything is derived from quantum-mechanical behavior. This behavior is weird, but to us, classical creatures, we care about classical things. So the way the QM behavior exhibits itself to us is thru the HUP, which talks about [uncertainty in x-p, spread of results, etc] for classical particles and waves. Another semantic is the wave-function-collapse, and interpertations.
From http://en.wikipedia.org/wiki/Wave_function_collapse" :

The reality of wave function collapse has always been debated, i.e., whether it is a fundamental physical phenomenon in its own right or just an epiphenomenon of another process, such as quantum decoherence.[2] In recent decades the quantum decoherence view has gained popularity.[citation needed] Collapse may be understood as a change in conditional probabilities.

So basically, it's easier to say collapse, but when you say it you go into philosophical semantics. it really is just decoherence, the particles (be it in entanglement or 2 slits) lost coherence and you force them to give you a "particle result", a single location, or single momentum. I am not sure about the process itself and the math at all. Decoherence is another interpretation maybe, but the whole point is that you get classical result from many available QM-options.

no.2 i still don't understand why we are so certain that a single electron, if not measured as to what slit it passes through, exhibits wave nature. it is ejected as a single particle, and detected at some place on the screen as one, then how do we infer that wave like behaviour is being shown? it is only after we do many such experiments and plot the prob. distr. graph that we get the interference pattern.

The electron is quantum-mechanical, but when it reaches the screen the interaction causes it to lose coherence (decoherence), and you get "collapse" to a single location.
So yes, you have to plot a graph of many results, since you can't measure the QMness of stuff, only classical stuff that QM creates.

In this thread there's discussion about HUP, I think it's important in the whole "understanding QM quest".
https://www.physicsforums.com/showthread.php?p=2910519#post2910519

 

[paka]

so wavefunction collapse is just a manifestation or classically understandable phenomenon leading from the decoherewnce phenomenon? is that it?
the link was very informative..i now think of hup as leading from qm and just an easily understandable(in classical terms) effect of qm. But surely the OP was wrong in the presumption that exact position and momentum do exist, but are just simultaneously not measurable? from what i have read on various sites, hup is not due to the measurement distrurbance but in faact a quantum system cannot have definite position and momentum at the same tiime. That was what i think feynnman showed thru that example of the short wave train. Do correct me if I am wrong, or if u can add something to these topics, it wud be great too.

 

[etamorphmagus]

so wavefunction collapse is just a manifestation or classically understandable phenomenon leading from the decoherewnce phenomenon? is that it?
the link was very informative..i now think of hup as leading from qm and just an easily understandable(in classical terms) effect of qm. But surely the OP was wrong in the presumption that exact position and momentum do exist, but are just simultaneously not measurable? from what i have read on various sites, hup is not due to the measurement distrurbance but in faact a quantum system cannot have definite position and momentum at the same tiime. That was what i think feynnman showed thru that example of the short wave train. Do correct me if I am wrong, or if u can add something to these topics, it wud be great too.

Yep everything you said is pretty much the way I see it.

If you mean a wave-train = http://en.wikipedia.org/wiki/Wave_packet" then uncertainty on momentum is great because it changes in different points - you can only get average momentum, and so the "length" of the packet shows you where the location of particle is most probable when measured (highest amplitude is highest probability). if the quantum is represented as a perfect sine wave - momentum is exactly known because wavelength gives you the momentum, and location is not known, it is "smeared" all over infinity.

What I said with pictures on http://hyperphysics.phy-astr.gsu.edu/hbase/uncer.html#c2".