Two-slit experiment and The Truth

[GreatBigBore]

Two-slit experiment and "The Truth"

I've heard the two-slit experiment described over and over, but there's still something about it that seems unclear to me.

When experimenters fire the first, single particle toward the screen, they don't get an interference pattern, do they? The interference pattern shows up only after lots of particles are fired, right? So the interference pattern doesn't indicate that a single particle is a wave that interferes with itself. It just shows that the behavior of large numbers of particles can be described with a wave function.

It seems that saying that a single particle goes through both slits and interferes with itself is about the same as saying that a coin flipped once can be both heads and tails, rather than saying that repeated coin-flip results can be described with a wave function.

If I'm making any sense at all, could someone please shed some light on my confusion? I really just want to know if we really think that a single particle behaves like a wave that can interfere with itself, and maybe a link to a site that makes it clear to interested laypeople.

 

[Vanadium 50]

You get an interference pattern if you fire particles one at a time, with arbitrarily long spacings between them. There's a nice picture of this in French and Taylor's textbook.

 

[Demystifier]

I've heard the two-slit experiment described over and over, but there's still something about it that seems unclear to me.

When experimenters fire the first, single particle toward the screen, they don't get an interference pattern, do they? The interference pattern shows up only after lots of particles are fired, right? So the interference pattern doesn't indicate that a single particle is a wave that interferes with itself. It just shows that the behavior of large numbers of particles can be described with a wave function.

It seems that saying that a single particle goes through both slits and interferes with itself is about the same as saying that a coin flipped once can be both heads and tails, rather than saying that repeated coin-flip results can be described with a wave function.

If I'm making any sense at all, could someone please shed some light on my confusion? I really just want to know if we really think that a single particle behaves like a wave that can interfere with itself, and maybe a link to a site that makes it clear to interested laypeople.

But if a single particle does not interfere with itself, how would you explain the fact that a single particle never appears at some places (at which the supposed interference is completely destructive)?

 

[faen]

I've heard the two-slit experiment described over and over, but there's still something about it that seems unclear to me.

When experimenters fire the first, single particle toward the screen, they don't get an interference pattern, do they? The interference pattern shows up only after lots of particles are fired, right? So the interference pattern doesn't indicate that a single particle is a wave that interferes with itself. It just shows that the behavior of large numbers of particles can be described with a wave function.

It seems that saying that a single particle goes through both slits and interferes with itself is about the same as saying that a coin flipped once can be both heads and tails, rather than saying that repeated coin-flip results can be described with a wave function.

If I'm making any sense at all, could someone please shed some light on my confusion? I really just want to know if we really think that a single particle behaves like a wave that can interfere with itself, and maybe a link to a site that makes it clear to interested laypeople.

The thing is that the "particle" is not a particle. There simply is no particle somewhere within the wave. Our perception of the particle is just an illusion. Its just waves. And when you measure the wave, it can become defined over a smaller position area, or defined over a smaller velocity area. Each wave is a superposition of other waves, since each state is a linear combination of the solution to any schr equation. So perhaps one can say that those waves in the superposition interfere with each other..?

The perception about the particle or particle characteristics comes from that the waves react with each other by forces. But that means that they just exchange energy somehow, not that a particle exist.

 

[Zarqon]

I've heard the two-slit experiment described over and over, but there's still something about it that seems unclear to me.

When experimenters fire the first, single particle toward the screen, they don't get an interference pattern, do they? The interference pattern shows up only after lots of particles are fired, right? So the interference pattern doesn't indicate that a single particle is a wave that interferes with itself. It just shows that the behavior of large numbers of particles can be described with a wave function.

Not sure what you exactly mean by "fire lots of particles", but maybe you are helped by the following:

You can build up statistics to the see the interference pattern in many ways. You can take a single slit and fire a million (or how many you want) particles at it. However, you can equally well build up a million different slits (which may be separated by a large distance), and fire only a single particle through each one. When summing up the events, both experiments will yield the same interference pattern, and it should be fairly clear that the second experiment indicate that it is indeed necessary to describe every single particle in a way that contains the interference effect. Or in other words: The particle does act like it interfers with itself.

 

[zonde]

When experimenters fire the first, single particle toward the screen, they don't get an interference pattern, do they? The interference pattern shows up only after lots of particles are fired, right? So the interference pattern doesn't indicate that a single particle is a wave that interferes with itself. It just shows that the behavior of large numbers of particles can be described with a wave function.

If it's not single particle that interacts with itself (or rather two superpositions of single particle) then it should be that particles within ensemble should interact (even when there is considerable delay between them). I suppose that this seems so counterintuitive that almost no one is considering that.

 

[Sillyboy]

For just a single particle, its state also behaves as a wave. That is to say, a single particle also is a wave. just emsamble of particles behave stasitically. Maybe we could comprehend this this way. for a coin, |state> = 0.5|up>+0.5|down>. But once the measurement happens, its states either goes into |up> or |down>, a large number of coins at the same sate can work out the probability or wave hehaviors!
If there is some wrong in my statement, please point them out. We can talk about them!

 

[DevilsAvocado]

When experimenters fire the first, single particle toward the screen, they don't get an interference pattern, do they?

No, it’s obviously impossible to get any 'pattern' with just a single dot...

The interference pattern shows up only after lots of particles are fired, right?

Yes.

So the interference pattern doesn't indicate that a single particle is a wave that interferes with itself. It just shows that the behavior of large numbers of particles can be described with a wave function.

Wrong. In QM there is this 'weird' (for none scientist) http://en.wikipedia.org/wiki/Particle-wave_duality" , meaning an electron can be regarded as both a wave and particle – simultaneously. When you perform any measurement on the electron, the wave–particle duality is lost.

When a single electron is fired towards the http://en.wikipedia.org/wiki/Double-slit_experiment" , it passes as a wave, thus creating an interference pattern on the way out, towards the measuring screen.

If someone is 'sneaky', and try to measure which slit the electron actually passes; the wave–particle duality (and thus the interference pattern) is lost!

The position where the electron is measured on the screen is (mostly) random, with one very important exception – the interference (of the two waves coming out of the double-slit) increases the possibility for the electron to hit the screen where the waves are in phase (constructive/destructive interference).

https://www.youtube.com/watch?v=<object width="480" height="385"><param name="movie" value="http://www.youtube.com/v/FCoiyhC30bc&hl=en_US&fs=1&rel=0&color1=0x006699&color2=0x54abd6"></param><param name="allowFullScreen" value="true"></param><param name="allowscriptaccess" value="always"></param><embed src="http://www.youtube.com/v/FCoiyhC30bc&hl=en_US&fs=1&rel=0&color1=0x006699&color2=0x54abd6" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="480" height="385"></embed></object>

 

[LostConjugate]

The confusion is in the fact that if the electron is a wave packet how is it that after detection the rest of the wave(s) suddenly no longer exist. It is as if though we held the detector in place for an infinite amount of time until it absorbed the entire wave across all space.

So the question becomes more about time, and our perception of time.

Perhaps the individual wave functions of different momentum are traveling at an infinite relative speed to the detector so that when we place a detector all the waves are absorbed instantly. Since only the group velocity can transfer energy this would obey the laws of special relativity. Just a thought.

 

[DevilsAvocado]

Just another thought:

Would it be possible to use 'entangled' electrons (as entangled photons in EPR) to make a "sneak preview" on which slit the entangled electron passes – thus knowing that the partner is passing the opposite – without breaking the wave-particle duality...??

 

[Antiphon]

Just a point of clarification: different photons cannot interfere with one one another. Any given photon can only interfere with itself.

If you only shoot one photon in the whole experiment it will create an intereference with itself. Not a pattern because (as noted) one dot doesn't make a pattern. But it will never land in the node of what will become an interfetence pattern should you ever decide to shoot additional photons. (photons interfering with one another would result in a non-linear theory.)

 

[LostConjugate]

Just another thought:

Would it be possible to use 'entangled' electrons (as entangled photons in EPR) to make a "sneak preview" on which slit the entangled electron passes – thus knowing that the partner is passing the opposite – without breaking the wave-particle duality...??

Not possible, you can't send information via entanglement. For one it would violate special relativity, though there is a QM explanation as well.

 

[LostConjugate]

Just a point of clarification: different photons cannot interfere with one one another. Any given photon can only interfere with itself.

If this is the case why did the scientists even experiment with only sending one photon at a time through the slits. The experiment of sending large amounts of photons at once would be just as convincing if they could not interfere with each other.

 

[ThomasT]

I really just want to know if we really think that a single particle behaves like a wave that can interfere with itself ...

Or that an (emitted) expanding wavefront passes through both slits (thus transmitting two expanding, interfering wavefronts), but only produces a single pointlike detection.

Maybe the passage through the slits produces two slightly different wavefronts which subsequently interfere with each other leaving only a small area with enough energy to produce a detection. Or maybe not.

Anyway, it's (whatever it is) only a particle on detection, otherwise it's treated as a wave. So, if you have two-slits open, then you (eventually) get an interference pattern, and with just one slit open you get a diffraction pattern.

The truth of the two-slit experiment is still a mystery.

 

[DevilsAvocado]

Not possible, you can't send information via entanglement. For one it would violate special relativity, though there is a QM explanation as well.

The actual 'decision' to go left or right is of course 100% random, as in 'normal' double-slit, analogous to EPR spin up/down.

And EPR is not regarded as a violation of information FTL...?

 

[LostConjugate]

They actual 'decision' to go left or right is of course 100% random, as in 'normal' double-slit, analogous to EPR spin up/down.

And EPR is not regarded as a violation of information FTL...?

I am not too familiar with entanglement or EPR entanglement, though I read somewhere that no information can be found until both entangled particles are measured. How would the spin or the paramagnetic resonance of the electron tell you about which slit it went through?

 

[DevilsAvocado]

I am not too familiar with entanglement or EPR entanglement, though I read somewhere that no information can be found until both entangled particles are measured.

No real information can be transmitted in EPR, the outcome 100% random (up/down), but you don’t need to measure both particles – if P1 is measured 'spin up', then P2 must be 'spin down', even if P2 is on the other side of the universe.

How would the spin or the paramagnetic resonance of the electron tell you about which slit it went through?

Good question, I have absolutely no idea, that’s why I asked!

Maybe it’s impossible… when thinking more about it, a measurement on an entangled twin breaks the superposition by measurement, and the other twin is now 'forced' to 'choose' it’s opposite state instantly = measurement = breaking the wave-particle duality... maybe...

 

[jeblack3]

Just another thought:

Would it be possible to use 'entangled' electrons (as entangled photons in EPR) to make a "sneak preview" on which slit the entangled electron passes – thus knowing that the partner is passing the opposite – without breaking the wave-particle duality...??

When two particles are entangled so that they both go through the left slit or both go through the right slit, then neither particle by itself creates an interference pattern. You only get an interference pattern when you compare the two particles; select only the events where the first particle lands at a given place, and the places the second particle is detected form an interference pattern. Thus if you measure which slit one particle goes through, you cannot detect any interference pattern. Experiments of this type are called "quantum eraser" experiments.

 

[RUTA]

Just another thought:

Would it be possible to use 'entangled' electrons (as entangled photons in EPR) to make a "sneak preview" on which slit the entangled electron passes – thus knowing that the partner is passing the opposite – without breaking the wave-particle duality...??

The short answer is "no." See "Time and the Quantum: Erasing the Past and Impacting the Future," Y. Aharonov & M.S. Zubairy, Science 307, 11 Feb 2005, 875-879.

 

[LostConjugate]

No real information can be transmitted in EPR, the outcome 100% random (up/down), but you don’t need to measure both particles – if P1 is measured 'spin up', then P2 must be 'spin down', even if P2 is on the other side of the universe.

.

So what is to stop you from configuring a series of entangled particles of spin up and spin down, then flip the spin at one location of specific particles to send a message to another location. I read about this and why it was impossible many years ago.

 

[zonde]

The confusion is in the fact that if the electron is a wave packet how is it that after detection the rest of the wave(s) suddenly no longer exist. It is as if though we held the detector in place for an infinite amount of time until it absorbed the entire wave across all space.

I think confusion here is in the fact that ground state of the (electron) field has zero excitation level. But it is not the case.
If you assume that ground level of field is in coherent state and electron wave packet too is in coherent state then interference of ground state with different waves from electrons wave packet can create situation that wave packet probability is increased at one place and lowered at other without the need to absorb the entire wave across all space.

 

[DevilsAvocado]

So what is to stop you from configuring a series of entangled particles of spin up and spin down, then flip the spin at one location of specific particles to send a message to another location. I read about this and why it was impossible many years ago.

I’m not sure what you’re questioning here... are you saying that EPR is impossible??

Then you’re up against a whole bunch of very smart people (including Einstein), and some very serious physical experiments all verifying EPR.

In 1964, John Bell showed that there are no local hidden variables involved.

Wikipedia: "The Geneva 1998 Bell test experiments showed that distance did not destroy the "entanglement". Light was sent in fibre optic cables over distances of several kilometers before it was analysed."


P.S.
This is clearly wrong: "then flip the spin at one location of specific particles to send a message to another location"

It’s impossible to (deliberately) choose the superposition outcome.

 

[DevilsAvocado]

The short answer is "no." See "Time and the Quantum: Erasing the Past and Impacting the Future," Y. Aharonov & M.S. Zubairy, Science 307, 11 Feb 2005, 875-879.

Thanks! I’ll check that.

 

[LostConjugate]

It’s impossible to (deliberately) choose the superposition outcome.

I thought you could force the spin to be up or down with a strong enough magnetic field.

 

[DevilsAvocado]

I thought you could force the spin to be up or down with a strong enough magnetic field.

Nope, in the case of EPR most http://en.wikipedia.org/wiki/Bell_test_experiments" with photon polarization measurements.

In QM there are no 'fixed values'; we have to rely on statistical http://en.wikipedia.org/wiki/Probability_distribution" which states that certain pairs of physical properties, like position and momentum, cannot both be known to arbitrary precision.

Basically QM is a 'complete mess' for anyone who wishes 100% control (on lowest level)...


Edit: Of course, when you measure one property of an elementary particle, it is a fixed value. But then the rest of the 'superposition magic' (or wave-particle duality) is gone...

 

[DevilsAvocado]

... How would the spin or the paramagnetic resonance of the electron tell you about which slit it went through?

I've found proof for working double-slit experiment with two entangled photons:

...But as RUTA notes in post https://www.physicsforums.com/showpost.php?p=2669143&postcount=19" – it doesn’t work for a "sneak preview".

 

[edgepflow]

This is an interesting topic.

Could someone give a me link for a mathematical treatment of the wave function for this single particle, double slit experiment?

 

[LostConjugate]

This is an interesting topic.

Could someone give a me link for a mathematical treatment of the wave function for this single particle, double slit experiment?

http://www.physics.sfsu.edu/~greensit/book.pdf

Page 38

 

[DevilsAvocado]

... Could someone give a me link for a mathematical treatment of the wave function for this single particle, double slit experiment?

LostConjugate’s link is fine, but mainly deals with electrons, and ends in not describing "The wave-like behavior of electrons".

It all boils down to the http://en.wikipedia.org/wiki/Complementarity_(physics)" sets the rules: "When position is relatively well defined, the wave is pulse-like and has a very ill-defined wavelength (and thus momentum). And conversely, when momentum (and thus wavelength) is relatively well defined, the wave looks long and sinusoidal, and therefore it has a very ill-defined position."

In modern QM, all information about a particle is encoded in its http://en.wikipedia.org/wiki/Wave_function" describes how the wave function evolves over time.

$$i\hbar\frac{\partial}{\partial t} \Psi = \hat H \Psi$$

"The values of the wave function are probability amplitudes — complex numbers — the squares of the absolute values of which give the http://en.wikipedia.org/wiki/Probability_distribution" that the system will be in any of the possible states."

[PLAIN]http://upload.wikimedia.org/wikipedia/en/thumb/e/e7/Hydrogen_Density_Plots.png/500px-Hydrogen_Density_Plots.png
The electron probability density for the first few hydrogen atom electron orbitals shown as
cross-sections, for the wave function of the electron.

All quotes from Wikipedia


Edit: And of course, https://www.physicsforums.com/library.php?do=view_item&itemid=203"!

 

[edgepflow]

Thanks LostConjugate and DevilsAvocado for the link. I will work on these.

For the single particle case, I was reading that the "Many Worlds" interpretation of quantuum mechanics suggests that an electron from "our universe" goes through one slit and an electron from a "parallel universe" goes through the other.

I wanted to try to figure out the probablity density of the wave function that it goes through both slits at the same time. I think this might be called degeneracy but I am not sure. I studied basic quantuum mechanics in my undergraduate engineering studies but this was awhile back. I have been reading "Quantuum Mechanics DeMystified" to try to get back into it (a good book for its purpose in my opinion). Maybe some others more versed in this area could give me some hints.

 

[DevilsAvocado]

(Disclaimer: I’m only a layman and I could be wrong.)

For the single particle case, I was reading that the "Many Worlds" interpretation of quantuum mechanics suggests that an electron from "our universe" goes through one slit and an electron from a "parallel universe" goes through the other.

In the Copenhagen interpretation we have a process called http://en.wikipedia.org/wiki/Wave_function_collapse" , i.e. in the case of the Double-slit experiment the wave function of the photon (or electron) collapse, after interaction with an observer (measurement), to one determinate outcome, to 'explain' the observation.

In MWI there is no wave function collapse. The observer and the observed (particle) have become http://en.wikipedia.org/wiki/Quantum_entanglement" ; i.e. the state of the observer and the observed are correlated after the observation is made.

In MWI this means that if the observer tries to measure which slit the photon passes through, then the observer is split into observer₁ that measures left slit, and observer₂ that measures right slit. These two observers are now in separate worlds, and can never interact again (after the observation).

I don’t have the full understanding of MWI to explain what happens when the interfered wave hits the detector screen... Logically the observer ought to be split into every possible position that the photon can have on the screen. But that would mean no single MWI observer can ever see the full interference pattern!? (In case where photons arrive one by one) If a pro could explain this it would be great...

I wanted to try to figure out the probablity density of the wave function that it goes through both slits at the same time. I think this might be called degeneracy but I am not sure. I studied basic quantuum mechanics in my undergraduate engineering studies but this was awhile back. I have been reading "Quantuum Mechanics DeMystified" to try to get back into it (a good book for its purpose in my opinion). Maybe some others more versed in this area could give me some hints.

Well, as I understand this, the photon must go through both slits at the same time – otherwise there would not be any interference pattern...??

http://en.wikipedia.org/wiki/Photon_dynamics_in_the_double-slit_experiment#Probability_for_a_single_photon"

"Some time before the discovery of quantum mechanics people realized that the connexion between light waves and photons must be of a statistical character. What they did not clearly realize, however, was that the wave function gives information about the probability of one photon being in a particular place and not the probable number of photons in that place. The importance of the distinction can be made clear in the following way. Suppose we have a beam of light consisting of a large number of photons split up into two components of equal intensity. On the assumption that the beam is connected with the probable number of photons in it, we should have half the total number going into each component. If the two components are now made to interfere, we should require a photon in one component to be able to interfere with one in the other. Sometimes these two photons would have to annihilate one another and other times they would have to produce four photons. This would contradict the conservation of energy. The new theory, which connects the wave function with probabilities for one photon gets over the difficulty by making each photon go partly into each of the two components. Each photon then interferes only with itself. Interference between two different photons never occurs."

http://en.wikipedia.org/wiki/Photon_dynamics_in_the_double-slit_experiment#Probability_amplitudes"

The probability for a photon to be in a particular polarization state depends on the fields as calculated by the classical Maxwell's equations. The photon probability density of a single-photon Fock state is related to the expectation value of the energy density of the equivalent E and B fields.

Simplified version of Maxwell's equations, written in terms of either the electric field E or the magnetic field B:

$$\nabla^2 \mathbf{E} \ - \ { 1 \over c^2 } {\partial^2 \mathbf{E} \over \partial t^2} \ \ = \ \ 0$$

$$\nabla^2 \mathbf{B} \ - \ { 1 \over c^2 } {\partial^2 \mathbf{B} \over \partial t^2} \ \ = \ \ 0$$

where c is the speed of light in the medium

 

[JohnnyGringo]

Seems to me, this is simply a mapping issue.

We're taking a N dimensional object(photon) and passing it through 4D (space-time) slits onto a 2D screen.

 

[GreenLantern]

WOW so i really read through that entire thing to just have the principle of complementarity talked about by one person? (thanks DevilsAvocado in post #29 you got it pretty on) and then its generally just brushed off... Schrodinger/heisenburg/complementarity is really at the heart of this whole "the truth" about the double slit experiment. These three things pretty much (I dare say with 100% certainty ;)) exhaust what you should be getting out of the slit experiments.

People keep confusing the whole particle-wave duality concept that is really right near base of QM. Everyone gets confused because they are attempting to describe, say electrons, from a QM stand point with a classical mind set. Principle of complementarity + Schrodinger wave eq. + Heisenburg all put together makes the entire particle-wave duality picture. In QM its quantum objects that exhibit particle behavior in some cases and wave behavior in others. There is not just particle and just wave.

"Is light a particle or a wave?" answer: YES
"Is an electron a particle or a wave?" answer: YES

no "or" just "and" lol

-GL

 

[DevilsAvocado]

... no "or" just "and" lol

Glad it worked for you GreenLantern!

Yeah, it’s really at the core of QM, and it has been listed as the http://physics-animations.com/Physics/English/top10.htm" by physicists in NYT.

And things move on, and now Shahriar S. Afshar is claiming that his http://en.wikipedia.org/wiki/Afshar_experiment" invalidates the complementarity principle, although this claim has not been published in any peer-reviewed journal.

But the "or" is clearly hanging loose, as his paper has been peer-reviewed and was published in Foundations of Physics in January 2007:

[PLAIN]http://www.sciencefriday.com/images/shows/2004/073004/AfsharExperimentSmall.jpg

 

[Mu naught]

Sorry if this is off-topic a bit, but do electrons show diffraction patterns when fired through a single slit?