Feynman discussion of electron diffraction

[elou]

TL;DR Summary

Feynman measures particles and waves differently. Isn't that a problem?

Feynman, in the third volume of his Lectures on Physics, chapter 1, presents bullets and waves in two different diagrams, Fig 1-1 and 1-2 respectively.
https://www.feynmanlectures.caltech.edu/III_01.html

It is obvious that bullets are counted individually, the detector registering each hit separately, while waves have their intensity measured, whereby the effect is cumulative: two waves arriving more or less at the same time do not get registered as two separate events, as is the case with bullets, but as a single event with a higher intensity.
The same way, what is registered is not the number of hits by electrons, but the intensity achieved at each location by consecutive hits.
In other words, electrons are measured just the way waves are. I am therefore not surprised by the results.

 

[pines-demon]

The same way, what is registered is not the number of hits by electrons, but the intensity achieved at each location by consecutive hits.

It is not clear to me what difference you are making between measuring the intensity and measuring "single events". What would be the intensity of a bullet?

Remark that you can perform the double-slit experiment, one electron at a time, and count the detection of single electrons in localized parts of the screen. So you measure both single events and the intensity of the wave.

 

[elou]

It is not clear to me what difference you are making between measuring the intensity and measuring "single events". What would be the intensity of a bullet?

Remark that you can perform the double-slit experiment, one electron at a time, and count the detection of single electrons in localized parts of the screen. So you measure both single events and the intensity of the wave.

single events are not cumulative. When you add them up, there is no surprise at all. It is simple arithmetic.
Cumulative events, even if they also can be counted individually, change the end results. When you add two colors, the result is not the original numbers added together.

 

[elou]

I would like to add that Feynman, not having performed the experiment, is probably wrong concerning the adding of the hits by electrons. There is no reason, if he is counting the number of times a detector reacts to an electron, to get results different from those of bullets. It only makes sense if we consider the intensity attained by the hits.

 

[pines-demon]

single events are not cumulative. When you add them up, there is no surprise at all. It is simple arithmetic.
Cumulative events, even if they also can be counted individually, change the end results. When you add two colors, the result is not the original numbers added together.

Single events are cumulative if they are cumulative. Imagine that we have three different places where the bullets can land (left, right and middle). If a bullet hits right, and the next bullet hits right, then we count two bullet in the right spot.

Same happens with electrons, if the first electron hits the right spot, and a second electron hits it again, we count two electrons in the right spot. It is not like an electron will remove the previous count.

However, for the double slit experiment, when we look at the overall distribution (counting how many right, left, middle and points in between) after having sent a large number of electrons (sent individually one by one) the distribution looks like a wave interference (intensity) pattern.

 

[pines-demon]

I would like to add that Feynman, not having performed the experiment, is probably wrong concerning the adding of the hits by electrons.

I do not want to be snarky, so I will recommend you to read more about Feynman. He is not the kind of person who will get these introductory topics wrong.

Edit: here is a video of Feynman's explanation, maybe he can make it more clear:

 

[Ibix]

I would like to add that Feynman, not having performed the experiment, is probably wrong concerning the adding of the hits by electrons.

The experiment has, of course, been done many times since and individual electrons appear as spots and the cumulative pattern is a diffraction pattern. https://en.wikipedia.org/wiki/Double-slit_experiment

 

[elou]

The experiment has, of course, been done many times since and individual electrons appear as spots and the cumulative pattern is a diffraction pattern. https://en.wikipedia.org/wiki/Double-slit_experiment

Yes, I am aware of that. I was referring specifically to the number of hits in P1 and P2, and whether P1+P2 # P12.
Do you know if that has ever been checked?

 

[pines-demon]

Yes, I am aware of that. I was referring specifically to the number of hits in P1 and P2, and whether P1+P2 # P12.
Do you know if that has ever been checked?

Feyman's $P_1$ and $P_2$ are sketches, but even if they were true clearly $P_1+P_2\neq P_{12}$ as $P_1$ and $P_2$ have no nodes. This is also confirmed experimentally, I think somebody showed a picture of it in a previous thread where you were involved.

 

[elou]

Feyman's $P_1$ and $P_2$ are sketches, but even if they were true clearly $P_1+P_2\neq P_{12}$ as $P_1$ and $P_2$ have no nodes. This is also confirmed experimentally, I think somebody showed a picture of it in a previous thread where you were involved.

First. I should have said P'1, P'2 and P'12. Second, It is not a matter of whether electrons create an interference pattern, but whether the number of clicks do not add up, as Feynman suggests.
IF I am correct, Feynman is assuming that they would not add up. Remember, this was a thought experiment. If it turns out that his assumption was correct, I will stand corrected.

 

[pines-demon]

First. I should have said P'1, P'2 and P'12. Second, It is not a matter of whether electrons create an interference pattern, but whether the number of clicks do not add up, as Feynman suggests.
IF I am correct, Feynman is assuming that they would not add up. Remember, this was a thought experiment. If it turns out that his assumption was correct, I will stand corrected.

By P prime do you mean the experiment with a light source (Fig. 1–4)?

 

[Ibix]

First. I should have said P'1, P'2 and P'12.

But the quantities (or distributions, in fact) Feynman calls $P'_1$ and $P'_2$ are predicted to add to $P'_{12}$ (as Feynman says in 1-6 - this is the two slit experiment with "which slit" detectors added). And yes, that has been checked, as discussed in the Wikipedia link I gave earlier.

 

[elou]

Talking about P1 and P2 Feynman says: "the number that arrives at a particular point is not equal to the number that arrives through 1 plus the number that arrives through 2, as we would have concluded from Proposition A"
I was therefore wrong to correct my first statement. It is not P'.
This is what I think is a wrong assumption by Feynman.

 

[Ibix]

This is what is think is a wrong assumption by Feynman.

Again, see the wiki link. Yes, we have checked that electron diffraction happens.

 

[elou]

Again, see the wiki link. Yes, we have checked that electron diffraction happens.

I never denied that.

I will further remark that since Feynman had not done a real experiment, all the numbers he gives, are fictive. By assuming that the numbers did not add up, he was committing a petitio principii: assuming what he meant to prove.

 

[Ibix]

I never denied that.

But "electron diffraction happens" is what $P_{12}\neq P_1+P_2$ means. So if you are questioning that and saying that $P_{12}$ ought to equal $P_1+P_2$ you are saying electron diffraction ought not to happen. Yet now you say you don't deny that. So you agree with Feynman that $P_{12}\neq P_1+P_2$ - am I correct?

 

[PeroK]

Talking about P1 and P2 Feynman says: "the number that arrives at a particular point is not equal to the number that arrives through 1 plus the number that arrives through 2, as we would have concluded from Proposition A"
I was therefore wrong to correct my first statement. It is not P'.
This is what I think is a wrong assumption by Feynman.

You might learn more physics if you didn't assume that most of it wrong!

 

[pines-demon]

Summary:

• Bullets: $C_1(x)+C_2(x)=C_{12}(x)$ (where I am replacing $P$ by $C$ the distribution of counts)
• Waves: $I_1(x)+I_2(x)\neq I_{12}(x)$ (where I am replacing $P$ by $I$ the intensity)
• Electrons $C_1(x)+C_2(x)\neq C_{12}(x)$ and $C_{12}(x)$ looks similar to $I_{12}(x)$ from the wave pattern.

This has been verified experimentally. Also Feynman's account agrees with experiments (and with most textbooks).

Note: Here I am not considering the case of Fig. 1–4.

 

[elou]

But "electron diffraction happens" is what $P_{12}\neq P_1+P_2$ means. So if you are questioning that and saying that $P_{12}$ ought to equal $P_1+P_2$ you are saying electron diffraction ought not to happen. Yet now you say you don't deny that. So you agree with Feynman that $P_{12}\neq P_1+P_2$ - am I correct?

I am afraid you are wrong. That is, it is not what I am saying.
What I am saying is as follows:
When you measure clicks as singular events, whether you are measuring bullets, electrons, OR WAVES, the numbers will always add up.
What comes through one slit, plus what comes through a second slit, will always be equal to what comes through both slits together. This is simple arithmetic, with no possible exceptions. That is why I think Feynman was wrong on this point.
It is only when you use different methods of measurement that differences appear. In the case of Feynman's thought experiment, counting clicks on one hand, and intensity on the other.

 

[PeroK]

It is only when you use different methods of measurement that differences appear. In the case of Feynman's thought experiment, counting clicks on one hand, and intensity on the other.

This is wrong.

 

[Ibix]

It is only when you use different methods of measurement that differences appear. In the case of Feynman's thought experiment, counting clicks on one hand, and intensity on the other.

You are wrong. Single electron diffraction experiments have been done, and you get diffraction patterns when you count clicks. This is discussed in the wiki article I keep referencing and you apparently haven't read.

 

[Nugatory]

The thread title has been changed to reflect what the thread is actually about.
(In quantum mechanics, the “measurement problem” is something altogether different)

 

[berkeman]

And the OP is on a permanent vacation from PF, so this thread is closed.

 

[PeterDonis]

Even though the OP is on permanent vacation, there are a couple of points that should be clarified for future readers:

When you measure clicks as singular events, whether you are measuring bullets, electrons, OR WAVES, the numbers will always add up.

This statement leaves out a key factor, namely, where on the detector screen the individual impacts arrive, and what pattern those impacts form once you have a large number of them. Nobody is saying that the number of electron impacts on the screen is somehow different from the number of electrons that left the source, or that this somehow changes with both slits open vs. one slit open. The key point is that the pattern the electron impacts make on the detector screen when both slits are open is an interference pattern--i.e., the kind of pattern you get with waves, not the kind of pattern you get with bullets.

What comes through one slit, plus what comes through a second slit, will always be equal to what comes through both slits together.

This statement is based on a false assumption, namely, that in the experiment with both slits open and an interference pattern at the detector, we can somehow count individually how many electrons go through each slit. We can't. If we change the experiment so we can, we destroy the interference pattern.