Motion

[GrowingSmaller]

Continuous or discrete? I think that they are two sides of the same coin. Their definitions are interrelated, both dependent on the concept of "line" and "number" and "extension" etc???

 

[Resha Caner]

I'm just going by Resha's set-up from page one. He posits an infinite number of "points" between A and B.

I don't know that I did posit this, other than to suggest it as one of several possibilities.

Obviously, point B can never be reached. Which raises the question "can any point be reached?" No, there could really be no motion.

Are you sure? Isn't this only true when the number of intermediary positions is infinite and the object to be moved is only allowed a finite number of steps?

Even if motion was continuous, Zeno's paradoxes don't work because the time portion of the model distance/time to target will get to zero when you use basic calculus to deal with the problem, thus so will the distance.

We can indeed add the infinite series 1/2 + 1/4 + 1/8 ... = 1

I did mention Zeno early on, but I didn't specifically point to the "half of a half" thing.

Regardless, can you really add the infinite series? Has anyone actually sat down and demonstrated the sum of an infinite series by adding up all it's members? Or do we demonstrate what would happen if we could?

So when it comes to real motion, is the electron actually traversing an infinite number of points? Or is this some Platonist type of thing where the mathematical proof of convergence to a finite result "exists" and so the electron can use that "form" for its traversal? Or is it something else?

We do not know this. If space itself is quantized, there are not an infinite number of possible locations.

Yes, I know. "If" can cover a lot of possibilities.

 

[Chesterton]

I don't know that I did posit this, other than to suggest it as one of several possibilities.

I specifically asked you about it and yes, you've stated it at least twice in the thread. But if you're just mentioning it as a possibility, that's fine.

Are you sure? Isn't this only true when the number of intermediary positions is infinite and the object to be moved is only allowed a finite number of steps?

Yes I'm sure you can't reach the end of infinity. By definition there isn't an end.

 

[Resha Caner]

I specifically asked you about it and yes, you've stated it at least twice in the thread. But if you're just mentioning it as a possibility, that's fine.

I wasn't trying to back out of anything. Your phrasing that I had posited something seemed to indicate you thought I was claiming a position. I've not tried to claim any position here.

I did mention it as a possibility, but that was all.

Were I to take a position, my expectation is that if science ever reaches a conclusion, it will decide space is grainy - i.e. that there are only a discrete number of possible locations.

Yes I'm sure you can't reach the end of infinity. By definition there isn't an end.

Yes, but that's not what I was really asking. Let me break it down for you:

The distance traversed is not infinite. The possibility you were discussing involved dividing that distance into an infinite number of steps. So, the first question is whether there are, in reality, an infinite number of steps?

If you would answer in the affirmitive, we must then consider the scope of what variant was suggesting - the sum of a convergent infinite series, L'Hopital's rule in calculus, etc. Do those have analogues in motion? In other words, is there some infinite process that can traverse a finite distance in an infinite number of steps?

 

[Loudmouth]

The higher the energy of the photon, the shorter its wavelength, and the more narrowly you can determine the location of the electron you bounce it off. But the higher the energy, the more the photon disturbs the electron's wavefunction.

Just to make sure I am remembering things correctly, what you describe above relates to the uncertainty principle, does it not? If you use short wavelength photons you can more accurately find the position, but the energy of the photon disturbs the electron which makes for a less accurate measurement of momentum. Using a long wavelength photon is just the opposite, a less accurate measurement of position but a more accurate measurement of momentum. Is that correct?

 

[Loudmouth]

Or are you saying you think light requires no medium? I thought quantum foam was the latest fashion. If so, we've never observed light actually pass through a pure vacuum.

From what I understand, photons pass through a vacuum until they hit something.

Maybe I should have said "sequence" rather than "stream." I wasn't implying interactions between the electrons, if that's what you're getting at. Only that it takes more than one electron to make the pattern.

Just to make sure that you understand the implications of the experiment, you get interference with a single electron. You don't need multiple electrons passing through the two slits in order to get interference. The wave of the single electron passes through both slits and interferes with itself.

 

[Resha Caner]

Just to make sure that you understand the implications of the experiment, you get interference with a single electron. You don't need multiple electrons passing through the two slits in order to get interference. The wave of the single electron passes through both slits and interferes with itself.

I'm open to explanations that will clarify my understanding, but it seemed the explanations were diverging away from the OP rather than supporting it.

So, there is a detail that confuses me.

As I understand it, if you place a detector anywhere between the source of the electrons and the screen that absorbs them, you cause a deterioration in the interference pattern. IOW, the more detecting you attempt to do, the more the pattern deteriorates. If you try to detect which slit an electron actually passes through (per particle behavior), you mess up the pattern (and I think essential said that earlier). So, you can't trace the paths the electrons are following. In fact, you can't really even say that the electron emitted at the source is the same one that shows up as a dot on the screen.

That all makes sense. I'm fine with that. But if that is true, this is what confuses me: The electron supposedly makes a single dot on the screen when it's absorbed (it behaves like a particle). If that's true, you would need multiple electrons to make a pattern on the screen.

So exactly how are you seeing the wave pattern of a single electron? What is detecting, or showing that? Is this more a hypothesis (per the picture you posted) than an actual observation?

 

[essentialsaltes]

Just to make sure I am remembering things correctly, what you describe above relates to the uncertainty principle, does it not? If you use short wavelength photons you can more accurately find the position, but the energy of the photon disturbs the electron which makes for a less accurate measurement of momentum. Using a long wavelength photon is just the opposite, a less accurate measurement of position but a more accurate measurement of momentum. Is that correct?

Yes, exactly. See also.

 

[Resha Caner]

Yes, exactly. See also.

That is interesting. When this is taught at the undergraduate level, it always sounds like a discrete choice: location or momentum but not both. I've never heard it presented as a spectrum: as the accuracy of location increases, the accuracy of momentum decreases.

That makes much more sense, so thanks for the clarification.

 

[Chesterton]

I wasn't trying to back out of anything. Your phrasing that I had posited something seemed to indicate you thought I was claiming a position. I've not tried to claim any position here.

I did mention it as a possibility, but that was all.

Were I to take a position, my expectation is that if science ever reaches a conclusion, it will decide space is grainy - i.e. that there are only a discrete number of possible locations.

Looks like we're in agreement then.

Yes, but that's not what I was really asking. Let me break it down for you:

The distance traversed is not infinite. The possibility you were discussing involved dividing that distance into an infinite number of steps. So, the first question is whether there are, in reality, an infinite number of steps?

You're flip-flopping. I don't care which you believe, or if you believe both or neither, but for the sake of discussion, stick to one at a time please. I was only discussing an infinite number of points because that's what you were discussing.

 

[Loudmouth]

I'm open to explanations that will clarify my understanding, but it seemed the explanations were diverging away from the OP rather than supporting it.

So, there is a detail that confuses me.

One of the common misconceptions is that there are two electrons, one passing through each slit, which produces the interference pattern. This isn't the case. A single electron passes through both slits simultaneously and interferes with itself.

As I understand it, if you place a detector anywhere between the source of the electrons and the screen that absorbs them, you cause a deterioration in the interference pattern.

It needs to be between the source and the slits. A detector between the slits and the screen will just act as another screen. What will differ is the spacing between the "peaks and valleys"

If you try to detect which slit an electron actually passes through, you mess up the pattern (and I think essential said that earlier).

Correct. You get two round diffraction patterns. When you try and observe which slit the electron is going through you collapse the wave function.

So, you can't trace the paths the electrons are following. In fact, you can't really even say that the electron emitted at the source is the same one that shows up as a dot on the screen.

It is the same electron. Others can correct me, but I would assume that you can use a detector on one side of the slits to measure the time it takes for the electron to travel the distance between the detector and the screen. The important bit is that the detector and screen need to be on opposite sides of the slits.

The electron supposedly makes a single dot on the screen when it's absorbed (it behaves like a particle). If that's true, you would need multiple electrons to make a pattern on the screen.

If you wanted to visualize the pattern, you would need many electrons. However, you can calculate the wave function ahead of time to calculate the probability of where a single electron will end up on the screen.

We can use the game of craps as an example. The probabilities in craps kind of form a wave pattern:

The most probable roll is a 7, and the two most improbable rolls are 2 and 12. These odds are the same for 1 roll or 1 million rolls. However, if you have just a few rolls you will probably not see the pattern in that graph. With a million rolls, you will. The same for the wave pattern on the screen.

Is this more a hypothesis (per the picture you posted) than an actual observation?

It is observation. This webpage has a really good run down of the refined experiment where they only use 1 electron per second. The video on the page shows how the wave pattern emerges over time as you get more and more electrons to hit the detector.

Feynman's double-slit experiment gets a makeover - physicsworld.com

 

[Chesterton]

Hope this isn't too dumb a question, but is the single electron "aimed"? From point "a", is it aimed midway between points "b" and "c"?

 

[Resha Caner]

You're flip-flopping. I don't care which you believe, or if you believe both or neither, but for the sake of discussion, stick to one at a time please. I was only discussing an infinite number of points because that's what you were discussing.

I can handle discussing multiple possibilities. I'm sorry if that's confusing for you.

However, I don't see the point in discussing something that no one believes in - that no one wants to defend. So, my first objective was to ask people where they stand.

I never really got an answer on that.

If you lean more toward the "discrete" answer, then that is the one I would prefer you discuss.

 

[Loudmouth]

Hope this isn't too dumb a question, but is the single electron "aimed"? From point "a", is it aimed midway between points "b" and "c"?

My understanding is that the wave function of the electron just needs to cover both slits. If you want a perfectly centered interference pattern with as many peaks and valleys as possible, then you need to get the electrons centered.

 

[Resha Caner]

One of the common misconceptions is that there are two electrons, one passing through each slit, which produces the interference pattern. This isn't the case. A single electron passes through both slits simultaneously and interferes with itself.

That wasn't my issue. I was just asking how much of this you can actually observe.

It is the same electron.

My point is a trivial one, and I have the same question about tunneling. How do you know the first electron doesn't impact the screen, interact with it, and cause the emission of a separate electron? I don't think you do know, but it's a trivial matter not worth arguing.

If you wanted to visualize the pattern, you would need many electrons. However, you can calculate the wave function ahead of time to calculate the probability of where a single electron will end up on the screen.

That is what I had guessed, but you've confirmed my guess. So, that is what I was saying. Observing the pattern requires multiple electrons. Anything else is a calculation - a hypothesis of what the pattern looks like for a single electron.

 

[essentialsaltes]

So exactly how are you seeing the wave pattern of a single electron? What is detecting, or showing that? Is this more a hypothesis (per the picture you posted) than an actual observation?

One could imagine a wealthy physicist (or a well funded one) creating 1,000 identical copies of the apparatus. Each one fires a single electron, detected on the screen. If you overlaid all the results, you would see the interference pattern.

 

[essentialsaltes]

Hope this isn't too dumb a question, but is the single electron "aimed"? From point "a", is it aimed midway between points "b" and "c"?

That's basically right.

 

[Chesterton]

I can handle discussing multiple possibilities. I'm sorry if that's confusing for you.

It's not confusing, it's deceptive (though unintentional I hope). Don't say "we're discussing x", then when I respond to x say "no, that's not what we're discussing".

However, I don't see the point in discussing something that no one believes in - that no one wants to defend. So, my first objective was to ask people where they stand.

That was my first objective also. See below.

I never really got an answer on that.

If you lean more toward the "discrete" answer, then that is the one I would prefer you discuss.

You did get an answer on that from me in my second post. My first post was a question to you to define terms, and you said there are an infinite number of points between two points.

 

[Chesterton]

That's basically right.

Why "basically"? It's an actual single particle right? It has to be aimed somewhere, no?

 

[Loudmouth]

That wasn't my issue. I was just asking how much of this you can actually observe.

Ok, just wanted to make sure we were on the same page.

My point is a trivial one, and I have the same question about tunneling. How do you know the first electron doesn't impact the screen, interact with it, and cause the emission of a separate electron?

If that were happening then you would see a higher rate of detections on the screen than would be allowed by the emission source. That isn't the case. There would be many ways to control for this in the experiment.

That is what I had guessed, but you've confirmed my guess. So, that is what I was saying. Observing the pattern requires multiple electrons. Anything else is a calculation - a hypothesis of what the pattern looks like for a single electron.

The full pattern is also a test of the hypothesis. Whether one or 1 million, it is a test of the same hypothesis. The only difference is statistical certainty.