Motion

[variant]

It doesn't sound to me as if you and essential are in agreement. But maybe I'm missing something. If there is a circumstance where the motion of the particle is discrete, maybe you could describe it for us.

Having been reading what he has been saying I do not think essential and I are disagreeing rather we are trying to use different wording to explain the same concept.

From there, I don't understand how you could say the particle has a continuous existence without dressing up continuous motion in false clothing.

At time t1 the particle is at Q.
At time t2 the particle is at P.

When time != t1 and time != t2, the particle is neither at Q nor P, and since the motion is discrete, neither is it anywhere else. So where is it?

We are saying that at least according to a QM wave function description of the electron, the particle may not have a single and definite position at any given time.

 

[Resha Caner]

It has no definite position. It might be found anywhere allowed by the wavefunction it has at that time. (But if no one seeks to find it, it is not actually in any one definite place at a given time.)

I thought I addressed that by stating we observed the electron at times t1 and t2 so we knew it was in locations Q and P. I understand you're leaning on the idea it could be at any or none of the locations specified by the wavefunction, but I can't tell if you've noted the situation I describe (or tried to describe) means there are times when it can't be at Q or P.

The discrete change I refer to is the change from "it can't be at P" to "it can be at P", and this is verified by our observing the electron.

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.

That didn't really address my question. In short, this is starting to sound like turtles all the way down.

1) Since there are multiple ways of interpreting QM, there is no 'must' about the interpretation. 2) But there can be, by definition, no evidence about what the electron is doing when you aren't measuring it.

Thanks for clarifying per statement 1, and I understand statement 2, hence I added observation to the example.

Some of the bizarre results of QM, like the two slit experiment, suggest that the electron does not take one path, but all possible allowable paths. And is therefore not in one particular place at one time.

I find your use of terms like "path" very curious. It seems rather than saying the electron takes all paths that you're saying it takes no path.

Because the moon is still there even if you aren't looking at it. Even if nobody is looking at it. I do not believe that if everyone stayed inside, and we turned off all our cameras, the tides would disappear. This is not really any different than the assumption that electrons exist between the times when we actively observe them.

Shrug. At least you admit these are assumptions. I guess we can assume anything we want about the things we aren't observing. Would you disagree with that?

I don't see why you think the moon makes your case. What's special about the moon as an object? Why does the moon have a location when I'm not observing it, but the electron doesn't? That seems inconsistent to me. Just because it's easier to detect the location of the moon when I observe it doesn't mean it always has a location when I don't observe it. It seems to me you should answer the same for both.

Now, I realize you were speaking of existence and not location, but in my previous post I tied those 2 together. I was suggesting that in order for a material thing to exist, it must have a location. And so I'm suggesting that the electron always has a location, you just don't know what it is until you observe it. Anything else suggests to me that it ceases to exist for a time (as a particle). Now, if you're suggesting that the wave nature is material, you'll need to explain to me what it is about the wave nature that exists so we can discuss it.

At this point, I'll be up front that we seem to be going in circles. For example, you seem to use the math (wave function) to defend the peculiar observations of QM that defy classical understandings. When I point out further peculiarities, you fall back on classical references to try to dissuade me (the moon). So when I then start speaking in classical terms, you point out how the math of QM interprets those terms differently and we start round the loop again.

 

[Resha Caner]

We are saying that at least according to a QM wave function description of the electron, the particle may not have a single and definite position at any given time.

Until it is observed.

But, actually what you said is the motion is discrete.

Regardless, as I'm trying to point out in post #42, the key to my example is the change from "it can't be at P" to "it can be at P" as verified by observation.

 

[variant]

Until it is observed.

But, actually what you said is the motion is discrete.

Regardless, as I'm trying to point out in post #42, the key to my example is the change from "it can't be at P" to "it can be at P" as verified by observation.

As I said before, quantum tunneling requires at-least some discrete motion. If it's motion was classical/continuous it would never get to some of the places we observe electrons getting to.

 

[essentialsaltes]

The discrete change I refer to is the change from "it can't be at P" to "it can be at P", and this is verified by our observing the electron.

I see no reason why the situation you describe cannot occur, if quantum states are prepared and modified appropriately.

I guess we can assume anything we want about the things we aren't observing. Would you disagree with that?

Well, you can assume anything. But some assumptions are in line with observation and others are not.

I don't see why you think the moon makes your case. What's special about the moon as an object? Why does the moon have a location when I'm not observing it, but the electron doesn't?

In some formulations of QM, it requires a conscious observer to 'make an observation'. i disagree with that. I think that physical interactions count as observations. Lots of things other than you or me are interacting with the moon. Light from the sun is bouncing off it. The moon's gravity affects the tides. It doesn't go away when people are not looking at it.

In the case of the particle in the box, we've made impenetrable walls, and placed the particle in some particular quantum state. In order for it to stay in that state, it can't interact with anything. Nothing is observing it. The standard interpretation of QM says it has no particular position. This is not the same as saying it's not there in the box.

I was suggesting that in order for a material thing to exist, it must have a location.

Due to the Uncertainty Principle, its location (and momentum) can only be known approximately. The standard interpretation of quantum mechanics is that this is not simply a limitation on our ability to measure things, or a limitation on human knowledge. The particle's location does not exist (with zero uncertainty).

Now, if you're suggesting that the wave nature is material, you'll need to explain to me what it is about the wave nature that exists so we can discuss it.

Elementary 'particles' have both particle and wavelike characteristics that are physically real. Waves exhibit interference, and so do 'particles'. Our classical concepts of particle and wave are distinct. But quantum reality defies them.

 

[Chesterton]

That didn't really address my question. In short, this is starting to sound like turtles all the way down.

It's great to discuss difficult things, but don't get too flustered when there are (at a certain point in time, anyway) no concrete answers. I'm reminded of the quote from the great physicist/philosopher Niels Bohr:

There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how nature is. Physics is concerned with what we can say about nature...

 

[Resha Caner]

Elementary 'particles' have both particle and wavelike characteristics that are physically real. Waves exhibit interference, and so do 'particles'. Our classical concepts of particle and wave are distinct. But quantum reality defies them.

Lovely. But if you're going to distinguish between a particle and a wave, then at least one of those must have a property that the other doesn't. What might that property be?

Further, are you saying that location is not a necessary property of existence?

Due to the Uncertainty Principle, its location (and momentum) can only be known approximately. The standard interpretation of quantum mechanics is that this is not simply a limitation on our ability to measure things, or a limitation on human knowledge. The particle's location does not exist (with zero uncertainty).

Well, you can assume anything. But some assumptions are in line with observation and others are not.

Uh huh. So what observation supports the standard interpretation of QM that an unobserved particle's location doesn't exist?

 

[essentialsaltes]

Lovely. But if you're going to distinguish between a particle and a wave, then at least one of those must have a property that the other doesn't. What might that property be?

That's just it, I'm not distinguishing between particles and waves. Although we think of them as separate things in the classical realm, when we go to quantum mechanics, they are the same. The argument that Newton and his contemporaries had about whether light is a wave or a particle has been answered. It is both, and they are the same thing.

Further, are you saying that location is not a necessary property of existence?

I'm saying that the location of a thing is ill-defined. it is not the case that you could give the x,y,z, location of a particle as three real numbers with inifinite decimal places. At best you could do that with some uncertainty in each of the three numbers.

Uh huh. So what observation supports the standard interpretation of QM that an unobserved particle's location doesn't exist?

The two slit experiment. If a particle was in one location, it can only go through one slit, and no interference pattern could form. But the interference pattern does form.

(If you make an observation to see which slit a particle goes through, you will find it going through one slit or the other. But by doing that, the interference pattern disappears.)

 

[Resha Caner]

That's just it, I'm not distinguishing between particles and waves. Although we think of them as separate things in the classical realm, when we go to quantum mechanics, they are the same. The argument that Newton and his contemporaries had about whether light is a wave or a particle has been answered. It is both, and they are the same thing.

I went off and did a bit of reading. My conclusion is use of the terms "particle" and "wave" are ambiguous. They're not really saying what you want to say about the behavior of an electron. There should be a better way to describe the behavior, though it seems unlikely you would accept any changes I might suggest.

The term "particle" implies discrete location, and as such without a location there can be no particle. But it seems when you refer to an observed location of the particle, what you really mean is an observed interaction with the electron, and the location of that interaction can occur anywhere within a space described by a probability distribution.

The term "wave" implies a transfer of energy through some continuous media, and so without a continuous media there can be no wave. But it seems when you refer to the interference of waves, what you really mean is the double slits constitute an interaction with a stream of electrons that accumulate as a set of points at locations which form a pattern equivalent to an interference pattern.

Maybe I haven't expressed myself well enough yet - this is a new tac for me. And even if I have, as I said, I'm not sure you'd accept my suggested changes.

But let me try again. Even if the location of a particle doesn't exist (or is ill-defined - those are 2 different things) - I still think the electron has a position. It is an arbitrary position. To say the moon is located at (x,y,z) because that is the location of its CG is not explicitly accurate. There are practical reasons for saying that is its location, but we all know there are bits of the moon located at places other than its CG.

Likewise with the modes shown for the electron in a box example. We could devise a reason for saying those modes are located at the left end, the center, or the right end of the box. And while that is not explicitly true, it establishes a reference for describing the properties of the electron inside the box. And in that sense, I would say it has a location. And until the box moves it is a fixed location. That the location of our interaction with the electron may be unknown until the interaction occurs doesn't impact the reference location.

 

[essentialsaltes]

The term "wave" implies a transfer of energy through some continuous media, and so without a continuous media there can be no wave.

Classically, light is a wave that requires no medium.

But it seems when you refer to the interference of waves, what you really mean is the double slits constitute an interaction with a stream of electrons that accumulate as a set of points at locations which form a pattern equivalent to an interference pattern.

No 'stream' is necessary, if I'm understanding a distinction you're making. If you fire electrons one at a time, an interference pattern will form.

But let me try again. Even if the location of a particle doesn't exist (or is ill-defined - those are 2 different things) - I still think the electron has a position.

Are you drawing a distinction between location and position?

Likewise with the modes shown for the electron in a box example. We could devise a reason for saying those modes are located at the left end, the center, or the right end of the box.

I don't understand this at all. Are we talking modes or nodes? As you go on I understand even less what you're trying to say, I'm afraid.

 

[Resha Caner]

Classically, light is a wave that requires no medium.

Of what relevance is that? Another ancient theory was that light was a beam emitted from the eyes and reflected off objects.

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.

No 'stream' is necessary, if I'm understanding a distinction you're making. If you fire electrons one at a time, an interference pattern will form.

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.

Are you drawing a distinction between location and position?

No, I used them synonomously. It was unconscious on my part. I should have stuck with "location" for consistency's sake.

I don't understand this at all. Are we talking modes or nodes?

Both. In my classical training, a mode contains the node, the anti-node, and everything in between. In QM-speak the better term might be "wavefunction", but I'm not well-versed enough to say.

I'm trying to loop back to my example of the change from "it can't be at P" to "it can be at P" as verified by observation. You seemed to think that a reasonable example per the following quote:

I see no reason why the situation you describe cannot occur, if quantum states are prepared and modified appropriately.

But I've come to the conclusion we don't have the language to understand each other as I proceed from there. So, I've introduced a (possibly) new term: reference location.

The reference location would be the origin indicated in the diagram at this site explaining the particle in a box.
http://plus.maths.org/content/schrodingers-equation-action

So, the modes of the electron have a reference location at x = 0, and the modes extend from x = 0 to x = L. As before, when I suggested moving the box, the motion I refer to is the motion of the reference location.

 

[essentialsaltes]

So, the modes of the electron have a reference location at x = 0, and the modes extend from x = 0 to x = L. As before, when I suggested moving the box, the motion I refer to is the motion of the reference location.

Yes, the thing is in the box. The box starts 3 cm from the edge of the desk, with an uncertainty of a micron. If you move the box 4 cm further from the edge, the thing will still be in the box. And the location of the box is now 7cm from the edge, with an uncertainty of a micron. The change in its position is much larger than the uncertainty, so we can be assured that it did, in fact, move. The spectrum of possible locations for the thing inside will have changed accordingly.

 

[Resha Caner]

Yes, the thing is in the box. The box starts 3 cm from the edge of the desk, with an uncertainty of a micron. If you move the box 4 cm further from the edge, the thing will still be in the box. And the location of the box is now 7cm from the edge, with an uncertainty of a micron. The change in its position is much larger than the uncertainty, so we can be assured that it did, in fact, move. The spectrum of possible locations for the thing inside will have changed accordingly.

Yes, so in moving 4 cm there seem to be 2 possibilities: 1) The movement was continuous, touching every infinitesimal point along the way, 2) The movement was discrete, touching only a subset of those points. I suppose case #2 could be further divided to say 2a) the subset of points touched is still infinite, 2b) the subset of points is finite. But, to be honest, since we already have case #1, case #2a seems rather uninteresting to me. So, I'd prefer to only think of case #2b.

 

[essentialsaltes]

Yes, so in moving 4 cm there seem to be 2 possibilities: 1) The movement was continuous, touching every infinitesimal point along the way,

What touches every point? 'The movement' is not a thing.

The geometric center of the box?
A particular electron in the box?
A nonzero value of the wavefunction of the thing inside the box?

What do you mean by 'touch a point'?

Euclidean points are imaginary abstractions. How would something touch a point?

 

[Chesterton]

This thread just reminds me of this song :

WatchTower - The Size of Matter - YouTube

 

[Resha Caner]

What touches every point?

The electron (and note I am purposefully choosing to say "electron" and not "particle"). Or at least that would be my answer. You agreed that "the spectrum of possible locations for the thing inside will have changed accordingly." If the thing isn't the electron we've been discussing, you'll have to tell me what thing you referred to in your statement.

What do you mean by 'touch a point'?

Across the span of the 4 cm you moved the box, there are an infinite number of possible locations. Each location is represented by a point. I would think you already knew that. Does the electron occupy each one of those points (each one of those locations) during the movement of the box?

I don't know why you singled out case 1. I'm not invested in any particular answer here, so even if you say no to case 1, there is still cases 2a & 2b, and you can add cases 3, 4, and 5 if you like.

 

[Chesterton]

Across the span of the 4 cm you moved the box, there are an infinite number of possible locations. Each location is represented by a point.

Then it will take eternity. Or I guess if it has to go halfway to halfway to halfway as in Zeno, it can never get started, can't move at all? Then there's no such thing as motion?

 

[variant]

Then it will take eternity. Or I guess if it has to go halfway to halfway to halfway as in Zeno, it can never get started, can't move at all? Then there's no such thing as motion?

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

 

[essentialsaltes]

The electron

okay. It doesn't matter too much, but is this the electron in the box, or an electron that makes up the box?

Across the span of the 4 cm you moved the box, there are an infinite number of possible locations.

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

Does the electron occupy each one of those points (each one of those locations) during the movement of the box?

What do you mean by occupy a point? The electron itself has some uncertainty in its location (due to the uncertainty principle). Supposing the electron were in a quantum state where its average location was at P, is that what you mean by occupying a point? If it was in that state, and you looked for the electron, you might not find it at P. (Indeed, for some of the wavicle in a box states, the average location is at a node, so you won't find it at P.)

 

[Chesterton]

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'm just going by Resha's set-up from page one. He posits an infinite number of "points" between A and B. Obviously, point B can never be reached. Which raises the question "can any point be reached?" No, there could really be no motion.