Temporal Superposition and the Double Slit Experiment

[albroun]

I am confused by an aspect of the infamous double slit experiment. It is said that one way to understand why a succession of single particles can give rise to an interference pattern is that a single particle could be going through both slits simultaneously and interfering with itself. But this would not produce the single point on the screen that each particle produces (as far as I know this is what occurs). It is only after an accumulation of single particle hits that the interference pattern appears. Each particle still only produces a single point. Therefore the description of a particle interfering with itself seems incorrect. There is no superposition for each particle individually, otherwise we would see each individual particle producing an interference pattern.

Surely the interference pattern is really a kind of temporal effect - i.e. each particle is interfering with all the next and/or previous particles and vice versa? In otherwords, it is to do with a process which looks to us as if it is sequential in time, but for the particles in the experiment, simultaneous. Would this not make more sense? Or have I got the understanding of the experimental setup wrong. (I am not a physicist nor have any understanding of maths so I apologise for this rather untechnically framed question).

 

[San K]

I am confused by an aspect of the infamous double slit experiment. It is said that one way to understand why a succession of single particles can give rise to an interference pattern is that a single particle could be going through both slits simultaneously and interfering with itself. But this would not produce the single point on the screen that each particle produces (as far as I know this is what occurs). It is only after an accumulation of single particle hits that the interference pattern appears. Each particle still only produces a single point. Therefore the description of a particle interfering with itself seems incorrect. There is no superposition for each particle individually, otherwise we would see each individual particle producing an interference pattern.

Surely the interference pattern is really a kind of temporal effect - i.e. each particle is interfering with all the next and/or previous particles and vice versa? In otherwords, it is to do with a process which looks to us as if it is sequential in time, but for the particles in the experiment, simultaneous. Would this not make more sense? Or have I got the understanding of the experimental setup wrong. (I am not a physicist nor have any understanding of maths so I apologise for this rather untechnically framed question).

each particle produces one dot


however its position on the screen (probabilistic) is such that suggest its building an interference pattern...


meaning each individual photon tends/likely to "fall/strike" on the fringes and not on the blanks between the fringes...

 

[DrChinese]

I am confused by an aspect of the infamous double slit experiment. It is said that one way to understand why a succession of single particles can give rise to an interference pattern is that a single particle could be going through both slits simultaneously and interfering with itself. But this would not produce the single point on the screen that each particle produces (as far as I know this is what occurs). It is only after an accumulation of single particle hits that the interference pattern appears. Each particle still only produces a single point. Therefore the description of a particle interfering with itself seems incorrect. There is no superposition for each particle individually, otherwise we would see each individual particle producing an interference pattern.

Surely the interference pattern is really a kind of temporal effect - i.e. each particle is interfering with all the next and/or previous particles and vice versa? In otherwords, it is to do with a process which looks to us as if it is sequential in time, but for the particles in the experiment, simultaneous. Would this not make more sense? Or have I got the understanding of the experimental setup wrong. (I am not a physicist nor have any understanding of maths so I apologise for this rather untechnically framed question).

First, it is important to realize that you can in fact send particles through one at a time and get the pattern. The effect is NOT a result of particle 1 interfering with particle 2, 2 with 3, etc. If it were, then there wouldn't be much to discuss because that would be a classical effect.

Second, the idea is that there is a probability function for a SINGLE particle. Just like there is a probability function for the sum of 2 dice (2 to 12), there is a distribution for a particle going through a double slit and it is the classic pattern. When you accumulate enough "hits", the pattern will be clear.

The probability pattern is a result of self interference.

 

[albroun]

First, it is important to realize that you can in fact send particles through one at a time and get the pattern. The effect is NOT a result of particle 1 interfering with particle 2, 2 with 3, etc. If it were, then there wouldn't be much to discuss because that would be a classical effect.

Would it really be classical bearing in mind that the particle hits are separated in time, being fired sequentially? (in the version of the experiment I am describing).

 

[DrChinese]

Would it really be classical bearing in mind that the particle hits are separated in time, being fired sequentially? (in the version of the experiment I am describing).

If they were sufficiently separated as you speculate, then they wouldn't interfere with each other (at least not much).

 

[albroun]

If they were sufficiently separated as you speculate, then they wouldn't interference with each other (at least not much).

So the greater the time interval between the particle hits the less likely you are to see an interference pattern? How close in time do the particles have to be to get the interference pattern?

However if you can fire one photon at a time (even when separated only by very short time intervals) and get an interference pattern emerging after a number of hits, still suggests that the idea of a single particle interfering with itself is NOT the right description.

 

[albroun]

each particle produces one dot
however its position on the screen (probabilistic) is such that suggest its building an interference pattern...
meaning each individual photon tends/likely to "fall/strike" on the fringes and not on the blanks between the fringes...

Again this would not suggest we have a situation in which each individual particle in interfering with itself, but that each individual particle is really part of a total system of particles (i.e. the entire set of particles fired in the experiment being the "total system"), in some sense? Kind of weird, but no more weird than the idea of a single particle going through both slits simultaneously and interfering with itself!

 

[DrChinese]

Again this would not suggest we have a situation in which each individual particle in interfering with itself, but that each individual particle is really part of a total system of particles (i.e. the entire set of particles fired in the experiment being the "total system"), in some sense? Kind of weird, but no more weird than the idea of a single particle going through both slits simultaneously and interfering with itself!

OK, I don't think the part is getting through about the ONE at a time. You could put an hour between the individual hits and it would make no difference. There is no evidence whatsoever for what you describe.

Ask yourself this: why does the interference pattern disappear in some cases? That should help you see what is going on.

 

[DrChinese]

So the greater the time interval between the particle hits the less likely you are to see an interference pattern? How close in time do the particles have to be to get the interference pattern?

No. There is no such effect. I was just trying to show you that your idea does not fit the facts.

 

[albroun]

which means that what I have read in a lot of books about getting an interference pattern even when particles are fired one-at-a-time is totally incorrect??

 

[albroun]

Here is a quote from the Wikipedia article on the subject:

The most baffling part of this experiment comes when only one photon at a time is fired at the barrier with both slits open. After many photons are emitted one at a time, and recorded on the same sheet of photographic film, the pattern of interference remains the same, even though each photon produces only a dot on the film.

http://en.wikipedia.org/wiki/Double-slit_experiment

 

[DrChinese]

which means that what I have read in a lot of books about getting an interference pattern even when particles are fired one-at-a-time is totally incorrect??

One at a time, many at a time, they all produce interference patterns. One following the other is not part of the equation as to what does or does not cause it.

 

[DrChinese]

Here is a quote from the Wikipedia article on the subject:



http://en.wikipedia.org/wiki/Double-slit_experiment

Yes, this is good. So do you now understand that your idea of the cause of this - interference between successive particles - is incorrect?

 

[albroun]

Yes, this is good. So do you now understand that your idea of the cause of this - interference between successive particles - is incorrect?

No, I am not saying that there is classical interference between successive particles, but that somehow there may be a non-classical (weird!) temporal superposition going on that might be necessary to account for the interference pattern occurring when particles are fired one-at-a-time.

 

[albroun]

In otherwords, there is a breakdown of the distinction between "one-at-a-time" and "simultaneous", and that THIS may be the way to understand what is going on. Whichever way one interprets the double slit experiment, one is going to end up with a breakdown of classical assumptions.

 

[DrChinese]

In otherwords, there is a breakdown of the distinction between "one-at-a-time" and "simultaneous", and that THIS may be the way to understand what is going on. Whichever way one interprets the double slit experiment, one is going to end up with a breakdown of classical assumptions.

True enough, but where does "simultaneous" enter into it? One at a time means there is just one particle to consider for each individual dot.

 

[albroun]

Simply because in order for the interference pattern to emerge over time, (in the experimental situation we are describing in which each photon is fired one at a time, and each individual hit is a dot not an interference pattern), it will not do to say that each individual photon is interfering with itself as is commonly maintained. There has to be some other explanation as to how the interference pattern emerges.

 

[albroun]

True enough, but where does "simultaneous" enter into it? One at a time means there is just one particle to consider for each individual dot.

What I am challenging is the commonly held notion that we have to think of a single particle splitting into two and interfering with itself. If that were so, each single particle would yield an interference pattern. However each single particle arrives as a dot on the screen!

 

[DrChinese]

Simply because in order for the interference pattern to emerge over time, (in the experimental situation we are describing in which each photon is fired one at a time, and each individual hit is a dot not an interference pattern), it will not do to say that each individual photon is interfering with itself as is commonly maintained. There has to be some other explanation as to how the interference pattern emerges.

Why is 7 the most common result of the sum of 2 dice? One throw has nothing to do with the next, still a pattern emerges. The same thing is true of an interference pattern. But the individual "throws" are independent. They have nothing to do with it. The actual explanation is properly described by Quantum Mechanics. For example:

http://arxiv.org/abs/quant-ph/0703126

 

[albroun]

Sorry, the paper you cite is way beyond my knowledge - I am just a layperson trying to get my head round this stuff as far as I can!

Perhaps we don't need to maintain some kind of temporal superposition theory, but then neither do we need Many Worlds or Path Integral (Sum over Histories) or Hidden Variable explanations either?

What baffles me is why so many explanations say that we have to assume that in some sense each particle is splitting in two and interfering with itself, when there seems to be nothing in the experimental data to suggest that is so - each particle arrives as a point, not as an interference pattern, the latter only emerging as a result of multiple hits over time. I am utterly baffled as to why it is so commonly suggested that we need to think of individual particles interfering with themselves. Am I missing something?

This seems to have led to extremely counter-intuitive theories such as Many Worlds or Sum over Histories. I was suggesting that we could instead go for a kind of Temporal Superposition interpretation which I think is a bit like some forms of Systems Theory in which you have to understand parts in terms of the whole rather than the other way round. In otherwords, the ensemble of particle hits over time produces an interference pattern because the whole - the aggregation of hits - explains the part - the individual hits, rather than the other way round.

Is what you are suggesting that we assume the wave to be a probability wave, rather than a "physical" wave? Does this avoid having to evoke such counter-intuitive hypotheses?