Regarding one single electron, how about one lone, albeit inflated, photon as well?

Hi Chipper, my man! :-)
Well, it was a theoretical attempt, and I don't think it worked well!

What Feynman picked up and worked upon were the flavours of the day, and out of it grew his 'path integral' approach. This prescribed that despite only single/complete/'lumpy' electrons ever being detected ( in say a double slit type experiment ), the mathematical behaviour of the wave function ( which gave terrific accuracy between calculations and experiment ) implied that this same electron travelled an infinite number of paths from source event to target event. Each individual path had a certain 'weighting' ( a complex number ) so that adding up ( 'integrating' ) all of the paths finally yields a probability distribution for events ( on say the target screen ) which is increasingly closely approximated for progressively larger numbers of electrons.

These clever complex numbers basically store amplitude and phase information 'orthogonally', and by adding such numbers gives a vectorial type addition which yields behaviour like interference ( crests & troughs stuff ).

Several points of interest:

- between events, or detections if you like, we are not 'looking' at the electron so we can't actually say where it is during that travel. If we did, say by shining a photon on it, that would constitute an extra event and we would have to recalculate to include that. In fact is not the same experiment as , thus it is not required that they agree. This is often quoted as a result of Heisenberg's Uncertainty Principle, and you can view it that way, but this is classically true too. What is important in quantum mechanics ( QM ) is that one can't arbitrarily reduce that photon influence and also retain the character of the experiment. This amounts to not being able to determine which slit an electron went through and also maintaining an interference pattern. Or alternatively if you maintain the pattern you lose path information.

- the double slit experiment can, and has, been performed over long time periods so that one can be confident that only a single electron is present in the apparatus at any one time. The result is identical to the higher flux scenario, and only depends on the total/cumulative statistics and not on how long it took. The interference is not between distinct electrons. The interference is between the multitude of potential paths for a single electron! Any given electron arrives at the screen unpredictably, but the accumulation reflects a precise outline. This is the mind-blowing bit of QM, the part that Feynman meant when he said that no one understands it ( QM ). There is not, yet, any deeper explanation. It bloody well works famously though!

- one 'squares' the wave function to get a measure of probability. This yields a real number from a complex one. Probability includes a denominator which encompasses all those real numbers from the total ensemble of interest. This is called 'normalisation' and is crucial to get measurable numbers. It has often been difficult to calculate this bit - many of the infinities that Mr Hawking speaks of, for instance, arise from this.

- for alternate paths/events which we can't distinguish, even in principle, you add the complex amplitudes then square to get a probability. This will exhibit interference, and corresponds to the photon-less double slit arrangement.

- for alternate paths/events that you can distinguish, you square the amplitudes to get probabilities and then add those. This will not exhibit interference, and corresponds to the double slit with photons.

So there's another of my long winded potted ( potty? ) summaries. :-)
Cheers, Mike.

( edit ) Another really weird bit is that closing a slit can cause more electrons to appear at certain screen positions. Also opening a slit can cause more than double the number of electrons at certain places. It's all comes out of the mathematics, and is found very true by experiment. But hey! Go figure ........ :-)

I have made this letter longer than usual because I lack the time to make it shorter.Blaise Pascal

[â€¦] the other forum uses square brackets too, calls the protocol 'BBCode', and employs the exact same set of tags (e.g., to emphasize text, provide links, images, code, etc.).

I donâ€™t think the code tag works here eitherâ€”and itâ€™s on the â€˜cheat sheetâ€™!

Apparently it does force line-breaks, but has no effect on character formatting.

## RE: Regarding one single

)

Hi Chipper, my man! :-)

Well, it was a theoretical attempt, and I don't think it worked well!

What Feynman picked up and worked upon were the flavours of the day, and out of it grew his 'path integral' approach. This prescribed that despite only single/complete/'lumpy' electrons ever being detected ( in say a double slit type experiment ), the mathematical behaviour of the wave function ( which gave terrific accuracy between calculations and experiment ) implied that this same electron travelled an infinite number of paths from source event to target event. Each individual path had a certain 'weighting' ( a complex number ) so that adding up ( 'integrating' ) all of the paths finally yields a probability distribution for events ( on say the target screen ) which is increasingly closely approximated for progressively larger numbers of electrons.

These clever complex numbers basically store amplitude and phase information 'orthogonally', and by adding such numbers gives a vectorial type addition which yields behaviour like interference ( crests & troughs stuff ).

Several points of interest:

- between events, or detections if you like, we are not 'looking' at the electron so we can't actually say where it is during that travel. If we did, say by shining a photon on it, that would constitute an extra event and we would have to recalculate to include that. In fact is not the same experiment as , thus it is not required that they agree. This is often quoted as a result of Heisenberg's Uncertainty Principle, and you can view it that way, but this is classically true too. What is important in quantum mechanics ( QM ) is that one can't arbitrarily reduce that photon influence and also retain the character of the experiment. This amounts to not being able to determine which slit an electron went through and also maintaining an interference pattern. Or alternatively if you maintain the pattern you lose path information.

- the double slit experiment can, and has, been performed over long time periods so that one can be confident that only a single electron is present in the apparatus at any one time. The result is identical to the higher flux scenario, and only depends on the total/cumulative statistics and not on how long it took. The interference is not between distinct electrons. The interference is between the multitude of potential paths for a single electron! Any given electron arrives at the screen unpredictably, but the accumulation reflects a precise outline. This is the mind-blowing bit of QM, the part that Feynman meant when he said that no one understands it ( QM ). There is not, yet, any deeper explanation. It bloody well works famously though!

- one 'squares' the wave function to get a measure of probability. This yields a real number from a complex one. Probability includes a denominator which encompasses all those real numbers from the total ensemble of interest. This is called 'normalisation' and is crucial to get measurable numbers. It has often been difficult to calculate this bit - many of the infinities that Mr Hawking speaks of, for instance, arise from this.

- for alternate paths/events which we can't distinguish, even in principle, you add the complex amplitudes then square to get a probability. This will exhibit interference, and corresponds to the photon-less double slit arrangement.

- for alternate paths/events that you can distinguish, you square the amplitudes to get probabilities and then add those. This will not exhibit interference, and corresponds to the double slit with photons.

So there's another of my long winded potted ( potty? ) summaries. :-)

Cheers, Mike.

( edit ) Another really weird bit is that closing a slit can cause more electrons to appear at certain screen positions. Also opening a slit can cause more than double the number of electrons at certain places. It's all comes out of the mathematics, and is found very true by experiment. But hey! Go figure ........ :-)

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

## RE: [â€¦] the other forum

)

I donâ€™t think the

`code tag`

works here eitherâ€”and itâ€™s on the â€˜cheat sheetâ€™!Apparently it does force line-breaks, but has no effect on character formatting.

(End of interruption. Sorry.)

## RE: @Misfit: Sorry that

)

Talk about whatever you want. I'm popular that way. ;)

me-[at]-rescam.org