Understanding the Measurement and Interaction of Electrons: A Beginner's Guide

[bhobba]

Considering the double slit experiment, during the passing of the electron through both slits,

That's Feynman's sum over histories interpretation - its an interpretation - the QM formalism is silent on what happens when not observed.

If you want to make progress in QM that's something that needs to be indelibly imprinted into your understanding.

Here is the explanation of the double slit using only the formalism:
http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

Thanks
Bill

 

[BvU]

Bhobba is perfectly right, but in view of posts #1 and #32 I suggest you don't try to work your way through this article yet. Just keep an open mind and remain as critical as you have thus far proven to be. Do as many exercises as you can. And be glad that the introductory ones are fairly simple

 

[bhobba]

Bhobba is perfectly right, but in view of posts #1 and #32 I suggest you don't try to work your way through this article yet. Just keep an open mind and remain as critical as you have thus far proven to be. Do as many exercises as you can. And be glad that the introductory ones are fairly simple

I agree wholeheartedly. For now simply keep it in mind and a bit later as your understanding progresses then go though it. There is a reason beginner books don't teach it that way. The issue is they don't go back and redo the earlier ideas in light of the new knowledge you have gained. The purpose of the paper I linked to was to correct that.

Thanks
Bill

 

[durant35]

How does the microscopic (quantum) /macroscopic transition happen? I red that microscopic effects like a range of locations for an electron average out in one interpretation so let's say the Moon is almost precisely where we see it because of it small wavelength? What about molecules, do they average out the atomic and subatomic behavior so it can be said that their position is in a localized region?

 

[durant35]

I got to add, I am starting to suffer from a kind of existential anxiety because of the lack of knowledge and confusion from examining quantum physics. I've red that 5 years ago a scientist made a superposition of 'vibrating-non vibrating' states of a 60 micrometer thing. Can somebody explain that and the relation to macroscopic phenomena. Any help and constructive advice would mean so much to me.

 

[bhobba]

How does the microscopic (quantum) /macroscopic transition happen?

Basically in the macro world everything is observed by everything else.

At the lay level here is the book to get:
https://www.amazon.com/dp/0465067867/?tag=pfamazon01-20

Thanks
Bill

 

[bhobba]

I got to add, I am starting to suffer from a kind of existential anxiety because of the lack of knowledge and confusion from examining quantum physics. I've red that 5 years ago a scientist made a superposition of 'vibrating-non vibrating' states of a 60 micrometer thing. Can somebody explain that and the relation to macroscopic phenomena. Any help and constructive advice would mean so much to me.

Here is the experiment:
http://www.nature.com/news/2010/100317/full/news.2010.130.html

What they did is remove the environment that would usually observe it so quantum effects can manifest.

Thanks
Bill

 

[durant35]

So can we describe let's say bacteria and cells with adequate determinism, so those entities behave classically and without superpositions (unless we go radical and induce an experiment like the Schrodinger's cat experiment?

 

[bhobba]

So can we describe let's say bacteria and cells with adequate determinism,

Yes - they are classical.

Thanks
Bill

 

[UncertaintyAjay]

That's exactly what Schrodinger's Cat demonstrates. That if you remove the environment that observes it, the cat becomes a quantum object.

 

[durant35]

Could a Scrodingers cat be constructed in principle in everyday life? Is the random event, the atomic decay obtainable in our level? Basically I want to know why don't random quantum events trigger something on the macro scale and how would the Schrodinger cat experiment be obtainable in practice, in what conditions?

 

[bhobba]

Could a Scrodingers cat be constructed in principle in everyday life?

The set-up is easily constructed.

What you can't do is have the cat in a live-dead superposition because the cat breaths air that decoheres it. And it is not the only thing in the set-uo that does that - even sitting on the stool will do it.

And no, from many many discussions on this I can assure you there is no way around it - a cat can't be in a superposition - end of story. So please, please, do not go down that path - do a search here on other threads. It will go nowhere just like those other threads. A cat is entangled with its environment by the definition of a cat - no escaping it. Don't ask - but if you could do it what would happen - you can't - forget it.

Thanks
Bill

 

[durant35]

The set-up is easily constructed.

What you can't do is have the cat in a live-dead superposition because the cat breaths air that decoheres it. And it is not the only thing in the set-uo that does that - even sitting on the stool will do it.

And no, from many many discussions on this I can assure you there is no way around it - a cat can't be in a superposition - end of story. So please, please, do not go down that path - do a search here on other threads. It will go nowhere just like those other threads. A cat is entangled with its environment by the definition of a cat - no escaping it. Don't ask - but if you could do it what would happen - you can't - forget it.

Thanks
Bill

But decoherence isn't an instanteneous process, right? So upon what do you think that a can't be in the mixture of states for an instant?

 

[bhobba]

But decoherence isn't an instanteneous process, right? So upon what do you think that a can't be in the mixture of states for an instant?

A cat is decohered from the moment of its existence as a cell in its mothers womb. There is no way to avoid it from what a cat is.

Thanks
Bill

 

[durant35]

So what's the difference between the cat and the small item which that the scientist used in the article you posted about?

 

[bhobba]

So what's the difference between the cat and the small item which that the scientist used in the article you posted about?

It was isolated from the environment ie no atmosphere, at near absolute zero, shielded from vibrations etc etc. Even then its not entirely isolated - its impossible to do that. From QFT the particles of whatever obect you are considering is entangled with the quantum vacuum that pervades all space. Since that vacuum is the ground state of all fundamental particles I can't see how you can stop that entanglement, but won't rule it out with future progress. Certainly you can't do it now. It this that leads to the strange phenomena of spontaneous emission so that even the human body is a black body source:
https://en.wikipedia.org/wiki/Black_body

Thanks
Bill

 

[durant35]

Ok Bill, thank you. One more question regarding the Schrodingers cat in theory, once the cat gets entagled with the radiation emitter from the beginning of the experiment, it still behaves classically until the moment it gets hit/doesnt get hit by poison, then it enters the superposition? Conceptually and theoretically speaking of course.

 

[durant35]

Does the experiment imply that there are more than two possibilities depending on the time the atom decays? So on a time scale cat is in a superposition at t1, cat is in a superposition at t2 and so on as possibilities?

 

[mfb]

One more question regarding the Schrodingers cat in theory, once the cat gets entagled with the radiation emitter from the beginning of the experiment, it still behaves classically until the moment it gets hit/doesnt get hit by poison, then it enters the superposition?

Our ideal non-breathing and in general non-interacting (not even with itself) cat would have to be isolated all the time - the point of the experiment is that you cannot determine from outside if the radioactive decay happened or not. As long as you observe the cat, you know that.
The state changes gradually from "the cat is alive" to "the cat is in a superposition of alive and dead" where the dead contribution increases over time.

By the way: the past tense of "read" is "read".

 

[bhobba]

Does the experiment imply that there are more than two possibilities depending on the time the atom decays? So on a time scale cat is in a superposition at t1, cat is in a superposition at t2 and so on as possibilities?

Their is a lot of rubbish written about Schroedinger's Cat. The purpose of the thought experiment was to highlight a subtle problem with the then prevailing Copenhagen interpretation to do with where to place the Von Neumann cut. No one seriously considered the cat in a superposition of alive and dead. As a living macro object that's impossible. With our better understanding of decoherence that issue is now resolved - the most natural place to put the Von Neumann cut is just after decoherence which in the Schroedinger Cat experiment is at the particle detector. I have read that from the way particle detectors work its actually a bit before the flash or click or whatever indicates the radioactive decay but that is neither here or there. From that point on everything is common-sense classical. Cats can never be in a superposition of alive or dead.

In fact due to the set-up its entangled with the radioactive source. You can analyse it from that viewpoint and it shows it can't be in a superposition of alive and dead:
https://www.physicsforums.com/threads/is-the-cat-alive-dead-both-or-unknown.819497/page-3

See post 43.

But you know that anyway from what cats are.

Thanks
Bill

 

[durant35]

Their is a lot of rubbish written about Schroedinger's Cat. The purpose of the thought experiment was to highlight a subtle problem with the then prevailing Copenhagen interpretation to do with where to place the Von Neumann cut. No one seriously considered the cat in a superposition of alive and dead. As a living macro object that's impossible. With our better understanding of decoherence that issue is now resolved - the most natural place to put the Von Neumann cut is just after decoherence which in the Schroedinger Cat experiment is at the particle detector. I have read that from the way particle detectors work its actually a bit before the flash or click or whatever indicates the radioactive decay but that is neither here or there. From that point on everything is common-sense classical. Cats can never be in a superposition of alive or dead.

In fact due to the set-up its entangled with the radioactive source. You can analyse it from that viewpoint and it shows it can't be in a superposition of alive and dead:
https://www.physicsforums.com/threads/is-the-cat-alive-dead-both-or-unknown.819497/page-3

See post 43.

But you know that anyway from what cats are.

Thanks
Bill

So neither the detector nor anything macroscopical is in a superposition, decoherence occurs during the transition and washes away the effects so that everything is classical?

 

[bhobba]

decoherence occurs during the transition

I don't know what you mean by that. It occurs in the particle detector. Exactly what happens there you will need to consult how such detectors work.

Thanks
Bill

 

[durant35]

Can an atom decay in everyday life have similar influences to transfer randomness to other stuff? Does macroscopic radiation emerge from the quantum microscopic randomness?

 

[bhobba]

Can an atom decay in everyday life have similar influences to transfer randomness to other stuff? Does macroscopic radiation emerge from the quantum microscopic randomness?

You are getting way off topic - if you want to pursue it start a new thread or threads.

But yes in real life atomic decay can lead to macro effects eg it can cause cancer. EM is the classical limit of QED.

Thanks
Bill

 

[durant35]

I didn't mean to get off topic, I was wondering can an random atomic decay in normal circumstances cause a superposition on a macro level. You must've meant that radiation emerges from decay of atoms with your last sentence, and that the cancer is caused with the radiation in general as a classical concept, since you mentioned that classical ED emerges from QED. Thanks in advance.

 

[mfb]

I was wondering can an random atomic decay in normal circumstances cause a superposition on a macro level.

No. Not even in not normal circumstances.

 

[bhobba]

I didn't mean to get off topic, I was wondering can an random atomic decay in normal circumstances cause a superposition on a macro level.

OK rather than answer the question directly can you define what you mean by superposition?

Thanks
Bill

 

[durant35]

A mixture of states like in the case of Schrodinger's cat. But mfb already answered the question so thanks to both of you sincerely for the patience.

 

[bhobba]

A mixture of states like in the case of Schrodinger's cat. But mfb already answered the question so thanks to both of you sincerely for the patience.

No worries.

Just a technical aside. A superposition is NOT a mixture.

Thanks
Bill

 

[durant35]

No.
The uncertainty principle does not talk about the actual value of position or momentum. It merely says this:
The position and momentum of something cannot be simultaneously measured with arbitrarily high accuracy.
It is a statement about the accuracy with which it is possible to measure momentum and position. If you measure one to a high accuracy, your measurement of the other must necessarily be more inaccurate. The relationship between the error in measurement of momentum ( Δp) and error in position ( Δx) are related to each other by:
ΔpΔx≥h/2π ( equation 1)
where h is Planck's constant ( 6.63 * 10^-34). Let's say your measurement of the electron's position is fairly accurate and the error is tiny. Then the error in position is necessarily larger than h/(2π*Δx). I.e:
Δp≥h/(2π*Δx) ( equation 2).
So if your error in measurement of position is small, you can see from equation 2 that error in measurement of position is large.

So increased momentum does not result in more certainty in position.

It is also important to note that the uncertainty principle does not talk about the accuracy of your apparatus. I could be using the most accurate apparatus ever and this law would still apply. Try as hard as you want. The uncertainty principle is inescapable. The reason for this is because the very act of measurement interferes with the system and changes a state.

For example if you wanted to measure the position of an electron, you could do it by having a light source and observing a flash as the electron goes by. But the interaction between the electron and the photon will result in a change in the momentum of the electron. So the act of measuring changes the system. Only, in macroscopic systems this phenomenon is so small it can easily be neglected.

A quick scroll throught the posts and this gave me a bit of a worry and confusion.

If we increase the momentum, the wavelength becomes smaller, right?
And the small wavelength implies better localization and a smaller region where we can find the object.

Does UncertaintyAjay just mean that the value of the momentum doesn't have any effect on the position/momentum standard deviation in the equation?

 

[UncertaintyAjay]

Yes.

 

[durant35]

Yes.

I'm still confusing myself because I can't conceptualize this so let me try to explain you.

I have imagined wavelength as a boundary which contains all the possible positions of the object. Now the problem is that we can't calculate the precise wavelength because of the velocity uncertainty. So in idealized conditions let's take let say 45 for the momentum which gives us a particular wavelength. Due to uncertainty, it can be a bigger and a smaller number than 45 and if it is bigger than the wavelength also varies and becomed bigger so the boundary gets bigger, which would imply that greater uncertainty in velocity gets greater uncertainty in position which makes no sense. Please correct me because this is confusing me.

 

[UncertaintyAjay]

That thing about a small wavelength meaning that a particle is localised is wrong. Hence the confusion.

I have imagined wavelength as a boundary which contains all the possible positions of the object

Not true.

Due to uncertainty, it can be a bigger and a smaller number than 45

I suppose by 'it' you mean momentum?

if it is bigger than the wavelength also varies and becomed bigger

How?

I cannot stress this enough- the uncertainty principle does not talk about the actual values of momentum and position but the error in your measurement of them.

Here is what I am going to do.Say momentum is y units. Say the error in this measurement is Δp. Say you simultaneously measure the position of the particle and get that it is some distance z from your origin. Then your measurement of position will have an error Δx that must be greater than h/(4π*Δp). That is what the uncertainty principle states. If you see, there is absolutely no mention of z ( the actual position) or y ( the actual momentum) in the uncertainty relation( highlighted in bold just above). There are only the errors in your measurement of the two properties. I don't know where you got the wavelength thing from but I don't think it is true. A mentor or someone better versed in QM than me could tell you more about that.

 

[durant35]

Check out the Broglie wavelength for anything on an observable scale. A dust particle or something. And for a baseball...

I inferred it from this. And on many many websites I've red that because the wavelength of macroscopic objects is small that they are almost exactly where we see them. And on some websites I've red that wavelength represents the boundary for a big object. I hope the mentor will clarify this.

 

[durant35]

"If you explore the wavelength values for ordinary macroscopic objects like baseballs, you will find that their DeBroglie wavelengths are ridiculously small. Comparison of the power of ten for the wavelength will show what the wavelengths of ordinary objects are much smaller than a nucleus. The implication is that for ordinary objects, you will never see any evidence of their wave nature, and they can be considered to be particles for all practical purposes."

Quote from the hyperphysics webpage.