# Slit problem

1. Mar 23, 2006

### R34p3r

I have a question about an expirement that i saw yesturday in my physics class. They were shooting electrons one at a time at a wall on a video. They watched it and it showed a wave pattern on the sheet and it said that even when one electron goes throught it still goes through both slits and so on. Now when they observed it though it behaved like it was solid matter like a marble that made a two slit pattern on the wall. Now why does the observer change the situation for the electron to act so differently. I asked my physics teacher and he said that it required a 400 lvl class and about three weeks. So basically he didnt know. I was wondering if any of you knew why this happened i dont need to understand it right now i just want to know how that happened that the observer changed it. Thankyou tell me if you need it to be clearer.

2. Mar 23, 2006

### LnGrrrR

Reaper, good luck understanding that one...I don't know if anyone understands exactly "why" it happens. :) We know it does though, and there are different theories/explanations regarding it.

Others who are more-versed (and actual physicists) will give more informational words than I could though, I'm sure. :)

3. Mar 24, 2006

### koantum

The behavior of the electrons does not depend on observers. It depends on the setup, regardless of the presence of observers. If the setup makes it possible to learn through which slit each electron went, then each electron went through a single slit, either left (L) or right (R). If the setup doesn't permit this, then each electron went through both slits.

Note that saying "the electron went through both slits" cannot have the same meaning as the conjunction "the electron went through L and the electron went through R". For if the electron goes through both slits (as a whole, without being thereby divided into parts that go through different slits) then "the electron went through L" and "the electron went through L" are each neither true nor false. These propositions are then meaningless. So what can saying "the electron went through both slits" possibly mean? Think about it!

As for understanding, that is in a completely different league...

4. Mar 25, 2006

### R34p3r

and for the going throught both slits is actually exaculy what happens it goes through both until you add the observer then it goes through one. and i need to know im just starting to become obbsessed so if anyone out there knows using mahamtics words whatever i dont care if i dont understand it ill learn to understand it.

5. Mar 25, 2006

### -Job-

I like to think of a photon as a tiny particle, or some amount of energy, being displaced by some wave. Like a grain of rice on top of a water wave. The grain of rice only goes through one slit, but the wave goes through both slits. The water wave will interfere with itself at the region of the slits. Because the grain of rice is displaced by the water wave and the water wave interferes with itself, the final destination of the rice will exhibit interference. The reason why adding an observer at one of the slits might prevent the interference pattern might be because the wave doesn't go through slit A at the same time as it goes through slit B. Even a slight difference, considering that this wave is propagating at the speed of light could mean no interference. But if a quantum computer works then this can't be right, there must be superposition.
 On a second thought why wouldn't a quantum computer work in this scenario? The effect is the same. I have to ask my teacher this.

Last edited: Mar 25, 2006
6. Mar 25, 2006

### Hurkyl

Staff Emeritus
If we're given the fact we saw the electron pass through the left slit, then its subsequent behavior should be as if it passed through the left slit.

If we're given the fact we saw the electron pass through the right slit, then its subsequent behavior should be as if it passed through the right slit.

However, if there's nothing to determine which slit the electron passes through, then its subsequent behavior should be as if it passed through both slits (and thus you get interference).

(The following is based on my preferred interpretation of QM, which I will shamlessly plug with vanesch's favorite phrase: it's the one that takes QM seriously!)

Let's first analyze why interference happens: the state of the electron is the sum of what happens when it passes through the left slit, and what happens when it passes through the right slit. At some points P, the "electron strikes point P" parts of the left and right slits are out of phase, and they cancel each other out. Therefore, it's impossible to strike at point P.

However, when you have a device capable of "observing" through which slit the electron passes, the electron becomes entangled with the device. Then, at the point P, we have that the "device says left and electron strikes point P" and "device says right and the electron strikes point P are still completely out of phase. However, now they are different states (they're distinguished by the result of the measuring device), so they cannot cancel each other out!

(For the same reason "electron strikes point P" and "electron strikes point Q" don't cancel each other out when P and Q are different points)

7. Mar 25, 2006

### -Job-

If there were multiple slits in random positions, and we didn't know which way the photon/electron was fired, would its behavior still be as it if had passed through all slits? It's not like photon knows about the slits.

Last edited: Mar 25, 2006
8. Mar 25, 2006

### Staff: Mentor

While the photon is propagating, you can't think of it as being like a tiny pellet, localized in space at any given instant and following a well-defined classical trajectory. Its propagation is determined by a wave that spreads over a large volume of space, and is influenced by whatever obstacles are in that volume.

9. Mar 25, 2006

### -Job-

I understand that that is the view adopted by Quantum Mechanics. I'm wondering if there is a classical view that explains why the photon/electron exhibits its strange behavior. Just seeing if there can be an explaination there is more familiar, and consitent with experience.

10. Mar 25, 2006

### Hurkyl

Staff Emeritus
I'm not sure if you meant it that way, but I still feel the need to point out that QM is consistent with (most people's) experience.

In fact, since most people have zero experience with the microscopic world, just about any theory would be consistent with their experience.

What you meant, I think, is that you want to extrapolate the experience you do have into this domain where you have no experience.

11. Mar 25, 2006

### -Job-

I suppose.

12. Mar 26, 2006

### koantum

The same interference fringes have been observed with http://thisquantumworld.com/images/c60a.jpg" [Broken] and diffraction gratings containing thousands of slits.

Last edited by a moderator: May 2, 2017
13. Mar 26, 2006

### koantum

If it looks like a duck, walks like a duck, and quacks like a duck, then it is duck. In science we can never say more than "it's as if", so we may as well drop the "as if".
Before one can take quantum mechanics seriously, one has to have an interpretation!
The "state of the electron" is a probability algorithm. According to this algorithm, the probability of electron detection at the backdrop is either the sum of the absolute squares of two amplitudes (http://thisquantumworld.com/2rules.htm" [Broken]), depending on the setup.
Entanglement, like interference, is not a physical state or process but a mathematical feature of the quantum-mechanical probability algorithm. Without interference (Rule A) we have p = |A1|2+|A2|2, with interference (Rule B) we have p = |A1|2+|A2|2 + an "interference term". We speak of constructive interference if the interference term is positive and of destructive interference if it is negative. We speak of entangled systems if the probability algorithm for a composite system does not factorize into separate algorithms for the component systems.
If you treat the device as capable of indicating the slit taken by the electron, then there is no question of phases – you have one outcome, not two. As long as the phases of the amplitudes (associated with the alternatives) matter, the appropriate probability algorithm is a superposition, and in this case the device cannot indicate anything.
The proper definition of an alternative is a sequence of measurement outcomes.
• The actual outcome of the initial measurement determines how probabilities are assigned to subsequent outcomes.
• The possible outcome of the final measurement is the one whose probability we are calculating.
• Alternatives that may interfere differ neither in the initial nor in the final outcome. They differ in the possible outcomes of intermediate measurements.
• Rule A applies if the intermediate measurements are made (or if it is possible to infer from other measurements what their outcomes would have been if they had been made).
• Rule B applies if the intermediate measurements are not made (and if it is not possible to infer from other measurements what their outcomes would have been).

Last edited by a moderator: May 2, 2017
14. Mar 26, 2006

### woodsy2k

I was led to believe that the electron has with it an associated wave of probability. And it is this that passes through the slits. Thus there is a "quantum jump" (Ref - The New Quantum Universe. Hey & Walters, Cambridge university) after the slits, whereby the electrons' function of probability suddenly takes a specific form and the electron is detected once only at the detector.

15. Mar 26, 2006

### Hurkyl

Staff Emeritus
The interpretation is "QM is right, let's take it seriously" -- you view the world as quantum. :tongue: In particular, there is no need for the collapse postulate, since its purpose in life is to get classical answers out of a quantum theory.

Fine -- allow me to revise my comment to say:

The ket denoting the state of the electron is the sum of the ket denoting the state we'd get if we knew the electron passed through the left slit, and the ket denoting the state we'd get if we knew the electron passed through the right slit.

It's certainly not a state -- "entangled" is an adjective that describes states.

I don't see why you would say "entanglement" is not a process: surely the verb "to entangle" applies to any interaction that took unentangled states as input and produced entangled states as output?

And, incidentally, the state here does not factor. The probability that the electron strikes a particular point on the screen is not independent of the outcomes of the measuring device.

In other words:

P(|left slit, point X>)

is not equal to

p(|right slit, point X>)

Yes, it's in a superposition! An unnormalized ket denoting the state would look like:

|left slit>|left amplitudes> + |right slit>|right amplitudes>

Where |left amplitudes> is the ket that denotes the state of the electron if we knew it had passed through the left slit.

Your (rule A) is then derived by taking the partial trace to discard the information provided by the measuring device.

(for clarity, I'm going to assume that the distribution on the screen is discrete, not continuous.)

The whole point I'm trying to make is this: if |left amplitudes> looks like:

|left amplitudes> = ... + |P> + ...

and |right amplitudes> looks like:

|right amplitudes> = ... - |P> + ...

then without a measuring device in the middle, the ket denoting the state of the electron looks like:

|left amplitudes> + |right amplitudes> = ... + 0|P> + ...

which completely kills off the |P> component.

But with the measuring device, it looks like:

|left slit>|left amplitudes> + |right slit>|right amplitudes>
= ... + |left slit>|P> - |right slit>|P> + ...

and since |left slit>|P> and |right slit>|P> are different outcomes, they cannot interfere and cancel each other out.

16. Mar 27, 2006

### koantum

What do you think is a "wave of probability"? A wave is a physical entity that has an amplitude and a phase at every point of space and every instant of time (within some region of spacetime). Is a probability something that exists at every point of space and every instant of time (within some region of spacetime)? Is it something that has an amplitude or a phase? Is it something that can pass through slits? Get real, dude! Don't buy all that….

The quantum formalism is an algorithm for calculating the probabilities of possible measurement outcomes on the basis of actual outcomes. The calculation involves complex numbers called amplitudes, and these are functions of space and time in the same sense that probabilities are functions of space and time. The probability of detecting a particle in a region of space monitored by a detector is not something that is located in that region or that gets there after passing through the slits. The probability of obtaining a given outcome in a measurement performed at the time t is not something that exists at the time t. The dependence of quantum-mechanical probabilities on space is a dependence on the location of detectors, and the dependence of quantum-mechanical probability assignments on time is a dependence on the time at which a measurement is performed.

17. Mar 27, 2006

### koantum

Thanks for the explanation that "viewing the world as quantum" means that there are no collapsible states or wave functions. In this sense, I happen to view the world as quantum.

The state we'd get if we knew the electron passed through the left slit is not the ket |L> but the projector |L><L|. The state we'd get if we knew the electron passed through the right slit is not |R> but |R><R|. The state we'd get if we could know through which slit the electron passed but don’t care to is |L><L| + |R><R|. The state we'd get if it's impossible to know through which slit the electron passed is not (proportional to) |L>+|R> but (proportional to) (|L>+|R>)(<L|+<R|).

The "input" is a joint probability algorithm that factors, the "output" is a joint probability algorithm that doesn’t. What transforms that input into this output? Why not simply admit that we don’t know?

You see, it is by definition impossible to find out by experiment what happened between one measurement and the next. Any story that tells you what happened between consecutive measurements is just that – a story. You may tell any story you like about the transformation of the initial algorithm into the final algorithm, but it has nothing to do with physics. What transforms the initial algorithm into the final algorithm is a computation performed in accordance with laws that correlate measurement outcomes. If you want to think of this computation as a physical process and call it "getting entangled" (or whatever), be my guest. I only want to point out that we have precious little hope of ever understanding the relation of the quantum formalism to the real world if we consistently fail to draw the distinction between a computation and a physical process.

??? That's what I wrote. (I said: "We speak of entangled systems if the probability algorithm for a composite system does not factorize into separate algorithms for the component systems.")

It makes no sense to say that a physical system it is in a superposition. It only makes sense to say that the probability algorithm associated with a physical system is a superposition.

As I said, the state of the electron if we knew it had passed through the left slit is not denoted by a ket. Your following argument below is based on a misconception.

Surely this is not what you mean to say. The partial trace discards phase information because it takes into account that a measurement has occurred (without taking into account the outcome of the measurement).

18. Mar 27, 2006

### woodsy2k

The square of the wavefunction gives the electron a probability of appearing anywhere on the screen. Perhaps i was wrong in saying that it has a "wave of probability" that is a physical entity, but there is certainly an element of probability associated with an electron when traveling throught he slits.

19. Mar 27, 2006

### koantum

The wave function is the absolute square of the amplitude. Integrated over a region R, it gives the probability of detecting the electron in R.
Everything in the quantum world is described in terms of probabilities! Put in a nutshell, QM says that everything is possible, and it allows you (in principle) to calculate the probability of it. If this turns out to be zero, then it's impossible.

20. Mar 27, 2006

### Hurkyl

Staff Emeritus
That's not a state, it's a projector. :tongue:

Density matrices, kets, positive linear functionals, points in projective Hilbert space -- they're all just different ways of denoting the same thing. Each one is just as good as the other. (Though some may be easier to use in certain contexts)

I like kets because that's what I'm used to, and they have the nice notational advantage that it's easy to give them verbose labels.

But in any case, your missing the main point of my whole exposition: you ought to look not just at the electron, but the whole system.

In the Hilbert space formalism, I could have just said:

If there's no detector, then the resulting (unnormalized) ket is:

(... + |P> + ...) + (... - |P> + ...) = ... + 0|P> + ...

but if there's a detector, the resulting (unnormalized) ket is:

... + 2|P> + ...

But that begs the question: "Why?" -- and since we can actually answer this question, we might as well, by looking at the system comprised of the electron and the detector.

You could do the same in the density matrix formalism, can't you? When there's a detector, you should write it as:

(|left, L> + |right, R>)(<left, L| + <right, R|)

and if you take the partial trace, you're left with

|L><L| + |R><R|

We don't have to present it as some mystical reason why we do one thing when there's a detector, and another thing when there's not a detector: we can actually give a theoretical reason why there's a difference!