# Do we really need physical/real waves to explain single particle interference?

1. Feb 16, 2012

### San K

in explaining the interference pattern that happens in double slit, single particle interference -

some of the interpretations, for example De Broglie–Bohm interpretation:

assumes that (some sort of) "waves" travel through both slits simultaneously and interfere with each other

the question is that do we really need waves to explain the interference?

for example let's discard waves and look at the below explanation:

when the photon starts its journey towards the slits -

the photon/electron can be anywhere within the small narrow say 99% cloud....also it can only be in certain orbitals (separated by some multiple of planks length)

now some would be at one edge and others at other edge...of the 99% probability distribution

now some photons will strike edge of slit A,
others will strike edge of slit B,
while others will pass right in middle of slit A,
while others will pass right in middle of slit B,
while others will be slightly to the left of the middle of slit A,
while others will be slightly to the right of the middle of slit A,
while others will be slightly to the left of the middle of slit B,
while others will be slightly to the right of the middle of slit B,

etc......

isn't this fact alone sufficient to cause an interference pattern?

the one striking the edges of the slits would form a dark band further away from the middle of the screen ......and so on......

thus the single particle never interferes with itself.....it simply hits the slits at slightly different angles....and gets deflected....

when we cover one of the slits, we actually constraint the photon paths/behavior....the photons that were to cause the interference pattern never go through because the other slit was closed....there was only one slit available.....

and thus the interference pattern disappears

side note:there will still be slight bit of interference......i.e. single particle, single slit interference....(with the edges of the slit or related).....

the mach zehnder (which i think is simply a more elaborate form of the double slit experiment) can be explained similarly

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http://en.wikipedia.org/wiki/Mach%E2%80%93Zehnder_interferometer[/URL] [Broken]

so even if we took tennis balls (one by one) and shot them through a double slit we would get an interference pattern.....assuming that the tennis ball starting position is similar to the probability distribution of the photon/electron (...i.e. the ball can only be in certain positions which correspond to the energy levels of the electron/photon.....the planks length)

or mathematically if we were to substitute the probability distribution of the photon into the Schrodinger wave equation we would get the patterns.....without having to consider two physical waves (one wave that split into two at the slits) and their interference

note: the wave and amplitude are simply talking about probabilities or their derivatives and are not actual physical waves.....we don't need actual physical waves to explain the interference pattern..

Last edited by a moderator: May 5, 2017
2. Feb 16, 2012

### Antiphon

Let's put it this way; the mathematics of the wave explanation are incredibly accurate when compared to experimental results.

If you can come up with a linear phenomenology that isn't mathematically equivalent to waves but reproduces their dynamical qualities it would be impressive.

3. Feb 16, 2012

### nonequilibrium

First off, your post confuses me, at least starting from "the photon/electron can be anywhere within the small narrow say 99% cloud....also it can only be in certain orbitals [....]". You seem to be juggling with words out of context and I don't see them making a coherent picture. It implies, to me at least, that your knowledge of QM doesn't go beyond a first introductory, phenomenological course in university, am I right? If so, I think the main problem is that you're misunderstanding what QM is actually about.

But I think one big misunderstanding you're having is that you seem to think QM is talking about real waves, while you prefer mathematical distributions which aren't necessarily literally manifested in the real world. Well, the thing is, QM doesn't imply that there are really waves, and most probably conforms to your idea of abstract distributions, not "actual physical waves", as you call them.
That being said, the distinction between "real" and "purely mathematical" is not clear when it comes to QM, cause we have no way of verifying what is truly there and what is not, and a lot of people argue we can't even sensibly define "real" when it comes to quantum phenomena (pretty much the natural philosophical view of "Positivism").

4. Feb 16, 2012

### DennisN

I also think it was confusing, but I think I understand what San K meant, at least I think so . He probably meant that the photons get deflected when they pass the slits, due to interactions with the electrons in the plate material (at the edge of the slits) (San K, please correct me if I misinterpreted you).

There is however, AFAIK, no such interaction between a single photon and an electron (even though light can be influenced by e.g. magnetic fields; polarization rotation in the Faraday effect).

Concerning discussions for/against wavefunctions, my standpoint is that the most simple model that works best is the best model, even if it might be counterintuitive.

5. Feb 16, 2012

### San K

Thanks Antiphon.

Question:

isn't the mathematics about probability distributions rather than waves?

correct me if i am wrong:

the mathematics (that we are talking about above) does not deal with "waves" just probability distributions (and their derivatives)

the word "waves" is sort of a misnomer

the mathematics is correct, however we don't need to assume physical/real waves passing through both slits as some interpretations do....to explain the fringes....

6. Feb 16, 2012

### San K

thanks Mr. Vodka. some of the (popular and not so popular) interpretations of QM assume that: "real/physical waves" pass through both slits......

Last edited: Feb 16, 2012
7. Feb 16, 2012

### San K

thanks DennisN.

Question:

if we assume slightly different starting/initial conditions of the photon (prior to leaving for its journey towards the slits). Initial conditions like: co-ordinates, angle of strike at the slit, spin etc....

i.e. every time we send a photon (one by one) towards the slits.....their initial position, coordinates are really not the same as the previous/next photon.....

then could the emergence of interference fringes/pattern be explained that way?

or in other words:

the fringe pattern is already hidden/embedded in the initial conditions of the photon (which vary according to a probability distribution) and gets amplified by the slits

8. Feb 16, 2012

### ZapperZ

Staff Emeritus
9. Feb 16, 2012

### San K

Thanks so much ZapperZ. I never read it earlier, and, as chance would have it, never came across it earlier.

However the summary/abstract in the start seems to be saying what I was thinking. Thanks for sending the link, will go over the entire paper.

The paper says" Interference effects, if any, are inherent in the probability function"

Question: can the behavior of photon/electron in mach-zehnder be explained this way too? (i.e. photon detection always at only one detector when both paths available and photon randomly landing up at one of the detectors when one path blocked....)

http://en.wikipedia.org/wiki/Mach%E2%80%93Zehnder_interferometer

Last edited: Feb 16, 2012
10. Feb 19, 2012

### DennisN

San K, concerning your question to me:
Not really; those initial conditions of the photon do not explain how (or why) the interference pattern appears with its maxima/minima. The interference pattern depends on the wavelength of the particle being fired (photon, electron etc.), so I see no classical, particlelike way how to explain the interference.
In a sense, yes; what's hidden/embedded is the wavelength of the particle.

Today, we can with the wavemodel calculate how the interference pattern will appear. Why is another question. The same thing happens when you fire single electrons, one by one, against the slits. The common explanation is that the particle interacts with itself at the slits, due to the wavelike behavior of the particle (see e.g. Interference of individual particles).

ZapperZ, many thanks for that paper! I had not read that before, I'm new on this forum.

11. Feb 19, 2012

### Drakkith

Staff Emeritus
The key is that single particles bouncing off of the edges of the slits would NOT form an interference pattern like the one we see in the experiment. They would form two bands like this video shows.

Last edited by a moderator: Sep 25, 2014