Exploring the Double Slit Experiment - Kev's Amazement

[kkapalk]

Hi guys, I am new to this site and would like to say a little about the double slit experiment.
I find the fact that the electrons or photons choose both paths unless being watched absolutely amazing. But what I find even more amazing to me is this:
The electrons, when fired at the screen one at a time, gradually fill out an interference pattern.
To make myself clearer I will simplify things. Let's say the interference pattern consists of four vertical lines, each line consisting of four electrons stacked vertically. How on Earth does each electron know where to end up? They all go into the correct place. Take the last one for example. Eleven slots are taken up, leaving only one place left to fill out the interference pattern. And when it is fired it goes to the correct space! I find it amazing they fill out an interference pattern in the first place, but to each go to a separate area and gradually make up the pattern like a jigsaw astounds me.
I am not incredibly educated about this subject, so could anyone tell me if what I say is wrong.
Thanks for reading this,
Kev.

 

[muppet]

They don't "know" where to end up. What happens is that there's a certain probability associated with each line (and a probability of near zero in between them) that any particular electron ends up there. The first three electrons might all go to the "least probable" line, for example. But over time it becomes likely to the point of very, very, very near certainty that you see an interference pattern build up as increasing numbers of photons flesh out the probability associated with any particular distribution.

 

[kkapalk]

Thanks for the reply, much appreciated. Could you also answer this for me? Why does the pattern not appear with larger objects? Is the make up of the particle too complex, with too many (atoms?) jostling around? Also, when we observe what happens we collapse the probability wave. Is this because we bounce light off the particle? And if so, why does a detector also collapse the probability wave?
Thanks again,
Kev.

 

[muppet]

The idea of the collapse of the wavefunction is not well understood at all. The standard "treatment" of it is to take it as a postulate that works.
The main thrust of attempts to explain the collapse process centre on the idea of 'decoherence'. The central idea as I understand it is that any thermodynamically irreversible interaction with the outside world is what constitutes a "measurement", but i'd be lying if I said I understood any more than that. Sometime this weekend I'll try and find the time to read up on it properly, which I've been meaning to do for a while. Historically, some people have argued that it is necessary that a conscious mind performs the observation in order to collapse the wavefunction (try googling "Wigner's friend paradox") but I suspect there's very few remaining adherents to that view. There's also a theory put forward known as the GRW (the initials of the surnames of the protagonists which I can neither remember nor spell) interpretation, which postulates that collapse processes can occur randomly in undisturbed systems.

Some people also deny that the wave function actually collapses. The most prominent such theory is known as the "many-worlds" interpretation (MWI). It's commonly described as saying that whenever an observer makes a measurement, all possible outcomes are realized in different "worlds", which can be thought of as a sort of parallel universe. When phrased like that I think it sounds nuts, but Everett's original proposal makes the argument in a much more interesting and elegant way than such a translation into layman's terms suggests. There's also what's called variously "de Broglie-bohm theory" or "Bohmian mechanics" (the subject of some fairly heated debate in a recent thread!). The key idea of that is that particles are described by dynamics influenced by a physically real quantum field, and that the two-slit experiment is explained in terms of real trajectories governed deterministically by this field.

The reason that you don't tend to observe quantum effects on the macroscopic level could be said to depend on what view you take of the idea of a collapse process. Quantum wierdness has its most fundamental origins in the transition from a "superposition of states" (loosely speaking, "the electron goes through both slits at once") to the single outcome of a measurement. One argument would be that as large systems are continually observed/continually interact with their environment they don't exist in a superpostion, so their state is well defined and evolves in a deterministic way.

The other school of thought is that quantum effects still exist for macroscopic objects, but on such small scales as to be inobservable. For example, you may have heard of the concept of a "de Broglie wavelength", which is the wavelength you'd use to predict the diffaction pattern associated with the two-slit experiment. As the momentum of an object increases, this wavelength decreases. So for any macroscopic object moving at a discernible rate, the wavelength is many billions of times smaller than the object. Hence, to see diffraction effects you'd have to pass an object through a slit much smaller than itself! Similarly, there's also a result called the Ehrenfest theorem, which shows that as you move to the macroscopic limit, the expectation values what QM predictions tend towards the description of a particle obeying Newtonian dynamics.

 

[DrChinese]

Thanks for the reply, much appreciated. Could you also answer this for me? Why does the pattern not appear with larger objects? Is the make up of the particle too complex, with too many (atoms?) jostling around? Also, when we observe what happens we collapse the probability wave. Is this because we bounce light off the particle? And if so, why does a detector also collapse the probability wave?
Thanks again,
Kev.

Actually, it does work for larger objects. All kinds of molecules have been sent through double slit setups, and interference patterns do result. I think this has even been done with Buckyballs (C-60 atoms, more properly called fullerene).

 

[muppet]

Actually, it does work for larger objects. All kinds of molecules have been sent through double slit setups, and interference patterns do result. I think this has even been done with Buckyballs (C-60 atoms, more properly called fullerene).

I'm pretty sure it has DrChinese- I just took "larger" to mean something considerably bigger than 60 atoms...

 

[lightarrow]

Hi guys, I am new to this site and would like to say a little about the double slit experiment.
I find the fact that the electrons or photons choose both paths unless being watched absolutely amazing. But what I find even more amazing to me is this:
The electrons, when fired at the screen one at a time, gradually fill out an interference pattern.
To make myself clearer I will simplify things. Let's say the interference pattern consists of four vertical lines, each line consisting of four electrons stacked vertically. How on Earth does each electron know where to end up? They all go into the correct place. Take the last one for example. Eleven slots are taken up, leaving only one place left to fill out the interference pattern. And when it is fired it goes to the correct space! I find it amazing they fill out an interference pattern in the first place, but to each go to a separate area and gradually make up the pattern like a jigsaw astounds me.
I am not incredibly educated about this subject, so could anyone tell me if what I say is wrong.
Thanks for reading this,
Kev.

According to a theory, called Bohmian Mechanics, the electrons follows the path established by a "quantum potential" which is, in practice, a wave, called "guiding wave":
http://en.wikipedia.org/wiki/Bohm_interpretation

We can formulate the pilot wave's influence using a wavefunction-derived potential called the quantum potential, which acts upon the particles in a manner somewhat analogous to the interaction of particles and fields in classical physics.

It's not the most accepted interpretational theory in QM, however.

 

[kkapalk]

Thanks for all the useful replies. I am going to study the subject in more detail as it truly fascinates me. Thanks again for the great input,
Kev.

 

[reilly]

Something to think about: when Davisson and Germer shot electrons through crystal lattices they found interference patterns, just like those expected with light, in the number of electrons observed at a point and the rest is history. This was a bit of a surprise, as by the knowledge of the day, such a result was impossible. Their experiment was critical to the development of QM, and to the ensuing weirdness of the theory.

If you look carefully, the theories of light and electrons going through two or more or less slits are virtually identical.

Quantum mechanics gives an excellent description of electron diffraction. It says that the probability of an electron to go through one or the other slits is 1/2. What does this mean? If we measure which slit, will find half go through one, half go through the other, to a good approximation -- given a reasonable sample size. Does this mean that, unmeasured, an electron goes through both? First, the question has no answer; unmeasured means unknown.

However, inspection of the symmetry of the problem, the linear nature of the Schrodinger Eq., and Huygens' Principle shows that there is a way of formulating the problem AS IF the electron went through both slits. Let the mid-line of each slit act as a wave source, so that the relative source strengths are equal. But again, what QM tells us is that the probability of finding the electron in either slit is 1/2. So, however, if someone wants to do the two-places-at-the-same-time thing, well, OK. But, how, could one determine the probability of the electron being in each slit at the same time?

The ultimate why of all this is a mystery, just as are Newton's Laws and Maxwell's Eq's..
Nature ain't easy.
Regards,
Reilly Atkinson

 

[rezwar]

i'm still a bit confuzzled on why trying to observe the particle has any effect on the outcome of the experiment? why does observing the particle collapse the wave function?

 

[Landru]

I have watched a couple YouTube videos about the double slit experiment and I've read a few web pages about it but I can't find any specifics about how the detectors work. I'd like to know more about the process of detection because it seems like they blame it on the light and not the detectors, going so far as to say the light has a psychic ability to read the observer's mind.

They say it's curious that the light acts like a wave or particle depending on wether a detector is detecting or not, but to me it just seems that the electrons and photons carry some kind of field with them that extends beyond their boundries so that even though the photon might go through one slit its accompanying field goes through both, then on the other side the field spreads all over the screen and the photon hits somewhere within that area. Is that half way right?

 

[mal4mac]

I'm just coming to the end of reading Gribbin's two cat books and I wouldn't recommend them -- in the first one he pushes the "many world's" interpretation. In the second a weird "transactional" interpretation that involves effects traveling backwards in time.

Muppet's explanation of decoherence is more lucid than anything I've read in Gribbin. Any recommendations for reading up on this muppett?

Gribbin mentions in passing that Penrose suggests it is the concentration of gravitation that might initiate decoherence (in Emperor's new mind) and that Bohm suggested the thermodynamic origin of decoherence. But he mentions them only to dismiss them. But, to me, decoherence due to the wave function interacting with a macroscopic body seems entirely reasonable. At least it doesn't entail an infinite number of universes splitting off every instant, effects traveling backward in time, or weird Bohmian pilot waves.

Anyway "Ghost in the Atom" by P.C.W. Davies next. I'm sure it will all be clear after reading that :-)

 

[Count Iblis]

The MWI does not say that there are "an infinite number of universes splitting off every instant". That is the MWI version for dummies :rofl:

Anyway MWI or no MWI, decoherence is well established both theoretically and experimentally, see these articles:

http://arxiv.org/abs/quant-ph/0204129

http://arxiv.org/abs/quant-ph/0205108

http://arxiv.org/abs/quant-ph/0006117

 

[mal4mac]

The MWI does not say that there are "an infinite number of universes splitting off every instant". That is the MWI version for dummies

Can you justify that statement? Gribbin says this is the "original version" on p.162 of his kittens book. I can see no reason to label this as "for dummies". Thanks for the links.

 

[Count Iblis]

Can you justify that statement? Gribbin says this is the "original version" on p.162 of his kittens book. I can see no reason to label this as "for dummies". Thanks for the links.

In quantum mechanics, time evluton is a so-called "unitary" transformation. This is, in layman terms, analogous to rotations. It preserves distances, volumes etc.

In the MWI, you assume that time evolution is always unitary, also after measurements. In the Copenhagen Interpretation, you assume that measurements are not unitary, the wavefunction collapses.

Let's use the following analogue for quantum mechanical time evolution. Imagine a three dimensiona space in which we difine an x, y, and z direction. An observer can find himself in the x, y, and z state which are described by vectors that point in the x, y, and z, directions, respectively.

Now, if you are in state x and then under time evolution, you "rotate" to a vector that has components in all three directions, then that means you have certain finite probabilites of finding yourself in the three possible states. So, if you find yourself in state y you know that you have copies that are in states x and z. So, you could say that you have been split into three parts.

However, I think you would agree that the picture of the universe splitting all the time does not really convey very well how this simple theory works. The universe in this theory is a three dimensional space and there is a tme evolution which amounts to some rotation in this space. You could say that this is a multiverse and the three projections in the x, y and z directions are the three possible universes the observer can see. But the multiverse as a whole does not split, it simply rotates which is a mapping onto itself.

Also, it is natural to assume that you "already" have three copies in this setting, instead of assuming that at some time you only have one copy which then becomes three after the time evolution.

Real quantum mechanics works in the same way, except that the space in infinite dimensional and that rotations are now replaced by unitary transformations (unitary transformations are generalizations of rotations to complex vector spaces).