Motion

[essentialsaltes]

I could be wrong, but I think that quantum tunneling is thought to be the mechanism that allows for nuclear decay.

That's true for alpha decay, yes.

 

[Resha Caner]

I don't know. Time to consult the philosophers again.

Hence my reason for posting the question in the philosophy forum.

The original question looks like a case of making up artificial bins that reality must fit into (discrete vs. continuous) rather than looking at reality and explaining what we see - in this case, wave nature of particles, the uncertainty principle, and so on.

The question was not specifically addressed to the quantum level. If quantum physics applies to larger bodies where classical physics is typically used, I'd be happy to learn about that. Please proceed.

Or, if other descriptors better apply at the quantum level, feel free to offer a suggestion. At this point, as best I know, position is still a parameter that applies to electrons in spite of their wave nature. And, due to the fact that momentum also seems to be a parameter that still applies, the position can change. So, it seems to me the question still applies.

I realize some classical ideas don't really apply to electrons anymore. For example, as I understand it, classical radius doesn't really apply, hence I didn't refer to the extent of the electron, but rather the point about which it's properties are centered ... it's position.

Also, I said nothing of barriers. Barriers or not - tunneling or not - wave function or not - I think the question remains the same. If that is not the case, feel free to offer a modification.

I ask because it seems there are issues no matter how one answers: discrete or continuous. I'm interested in discussing those issues. Those who aren't need not participate.

 

[Resha Caner]

The electron would (at least some of the time) move the same way through space as it does through the barrier, discreetly.

So, does the electron cease to exist for that time when it is in neither position? Or are you saying there is no time between. It instantaneously moves from one position to the other?

 

[Loudmouth]

The question was not specifically addressed to the quantum level. If quantum physics applies to larger bodies where classical physics is typically used, I'd be happy to learn about that. Please proceed.

I kind of addressed that earlier, but in an indirect manner. Again, if my memory serves, it comes down to the DeBroglia wavelength for a given object. For massive objects with little velocity the wavelength is so long as to be ignored. In this case, particle effects dominate and massive, slow objects act in a continous manner with respect to movement.

It's been 20 years since Q-chem and physicis class, so feel free to correct me.

 

[Loudmouth]

So, does the electron cease to exist for that time when it is in neither position?

I believe the correct term is superposition.

"Quantum superposition is a fundamental principle of quantum mechanics that holds a physical system—such as an electron—exists partly in all its particular theoretically possible states (or, configuration of its properties) simultaneously; but when measured or observed, it gives a result corresponding to only one of the possible configurations (as described in interpretation of quantum mechanics)."
Quantum superposition - Wikipedia, the free encyclopedia

 

[Resha Caner]

In this case, particle effects dominate and massive, slow objects act in a continous manner with respect to movement.

As best I know, in classical physics it was believed motion is continuous, but I believe Liebniz may have challenged that notion. Still, I would ask if today's physicist is saying the motion is continuous or if it's just that the more practical approach is to model the motion as continuous.

It's an important distinction, because if we are saying the motion is continuous, then we're saying something emergent happens to motion at larger scales that isn't happening at smaller scales ... and there are other issues as well.

I believe the correct term is superposition.

That's not what I'm really getting at. I also understand the issue of observation. I think this link explains it well: Basic bonding concepts in organic chemistry | Electron, orbital, bond

The probability function isn't saying where an election might actually be, but rather where we might observe it to be. Regardless, it is possible for the probability to be zero at some point. There are places where we know we won't observe the electron.

But those probabilities are centered around some location. In the example, they are centered around the nucleus of the atom. From that point, we can identify a location where we know we won't observe the electron. And, there are an infinite number of places where the probability is vanishingly small.

But the center of that probability is not fixed for all time. That center location may be different for times t1 and t2. So, suppose we observe the electron at times t1 and t2. Given the locations are different, was the change over that course of time discrete or continuous? Or are you trying to tell me that, even with my further clarification, it is still a nonquestion?

 

[Loudmouth]

As best I know, in classical physics it was believed motion is continuous, but I believe Liebniz may have challenged that notion. Still, I would ask if today's physicist is saying the motion is continuous or if it's just that the more practical approach is to model the motion as continuous.

It's an important distinction, because if we are saying the motion is continuous, then we're saying something emergent happens to motion at larger scales that isn't happening at smaller scales ... and there are other issues as well.

Astrophysicists are working on this question by looking at wavelength dependent interactions with the "graininess" of spacetime. Any effect should show up the most in short wavelengths, so they are looking at gamma rays.

Einstein's General Theory of Relativity describes the properties of gravity and assumes that space is a smooth, continuous fabric. Yet quantum theory suggests that space should be grainy at the smallest scales, like sand on a beach.

One of the great concerns of modern physics is to marry these two concepts into a single theory of quantum gravity.

Now, Integral has placed stringent new limits on the size of these quantum 'grains' in space, showing them to be much smaller than some quantum gravity ideas would suggest.

According to calculations, the tiny grains would affect the way that gamma rays travel through space. The grains should 'twist' the light rays, changing the direction in which they oscillate, a property called polarisation.

High-energy gamma rays should be twisted more than the lower energy ones, and the difference in the polarisation can be used to estimate the size of the grains.
Quantum 'graininess' of space at smaller scales? Gamma-ray observatory challenges physics beyond Einstein -- ScienceDaily
​

The probability function isn't saying where an election might actually be, but rather where we might observe it to be.

The concept of quantum superposition is that the electron is at all of those positions prior to observation. Once the observation is made, the wave function collapses to just one position.

 

[essentialsaltes]

The probability function isn't saying where an election might actually be, but rather where we might observe it to be. Regardless, it is possible for the probability to be zero at some point. There are places where we know we won't observe the electron.

But those probabilities are centered around some location. In the example, they are centered around the nucleus of the atom.

Let's take a simpler example, a particle in a 'box'.

Classically, a 'ball' would just bounce back and forth between the walls, and you could follow its continuous motion.

The quantum wavefunction has nodes where it is zero. As you say, the probability of finding the particle at those points is zero.

In the simple case (labeled C in the animated diagram there), there's a node in the middle of the box. The particle can't be found in the middle.

If we shine a light on it to see where it is, we might find it in the left half of the box. We shine it again, and find it in the left half again. We shine it again and find it in the right half.

OK, somehow it got from the left side of the box to the right side of the box. Did it do that by 'moving through' the node?

It depends what you mean by move.

I would say no. The standard interpretation just says that you can measure the position of the particle at various times, and you will find it at various places with frequencies corresponding to the wavefunction. Position is a measureable quantity, but 'motion' is just not a quantum variable.

You could also measure momentum and find that the velocity was so and so much, but this is not the same as measuring 'motion'. If we found it was moving 10 mph to the right, and was in the right half of the box, you can't extrapolate and say that if you backtrack the particle, it must have gone through the midpoint.

I think motion, in the sense you mean it, is a macroscopic human description that just does not apply to the quantum level. Just like particle and wave.

 

[Resha Caner]

Let's take a simpler example, a particle in a 'box'.

Thanks. I think this will help ... if you're willing to endure several questions.

I think motion, in the sense you mean it, is a macroscopic human description that just does not apply to the quantum level. Just like particle and wave.

OK, then I would pose the same question to you as the one Loudmouth answered in post #27 about emergence ... or at least comment on the sufficiency of his answer.

If it is the case that we're waiting to synthesize GR and QM in order to answer that question, then give me some odds (based on your opinion). What are the odds the answer will be that space is grainy vs. smooth?

The quantum wavefunction has nodes where it is zero. As you say, the probability of finding the particle at those points is zero.

But what is the wavefunction outside the box? That's more pertinent to my question. Assuming no tunneling happens here (based on the way the problem is described), I would assume it is zero everywhere outside the box. Is that correct?

If so, my next question is: Can the box be located in different places?

If we shine a light on it to see where it is, we might find it in the left half of the box. We shine it again, and find it in the left half again. We shine it again and find it in the right half.

But what does this really mean that you observe it in a location? I'm not sure I understand what you mean by that anymore.

In my classical understanding, energy is a scalar. So what does it mean now that energy has real & imaginary parts? And how does energy relate to the probability of location? I would think energy would relate more to it's momentum (in connection with it's mass ... further depending on what terms like mass and velocity now mean in QM) ... though I suppose you could maybe then use some stochastic integral to find position?

 

[variant]

The probability function isn't saying where an election might actually be, but rather where we might observe it to be. Regardless, it is possible for the probability to be zero at some point. There are places where we know we won't observe the electron.

But those probabilities are centered around some location. In the example, they are centered around the nucleus of the atom. From that point, we can identify a location where we know we won't observe the electron. And, there are an infinite number of places where the probability is vanishingly small.

But the center of that probability is not fixed for all time. That center location may be different for times t1 and t2. So, suppose we observe the electron at times t1 and t2. Given the locations are different, was the change over that course of time discrete or continuous? Or are you trying to tell me that, even with my further clarification, it is still a nonquestion?

The take away message from quantum tunneling is that if the electron can get places in the universe it should be fundamentally excluded from via classical physics (which assume continuous motion).

The only current working explanation/description we have for this is the quantum wave function description of the electron, which does not assign a specific "place" to the electron at any given time but merely a probability.

If some non zero probability exists for an electron to be behind any barrier it will be able to go through it, which means that the electron probably moves in a non-continuous way.

 

[essentialsaltes]

OK, then I would pose the same question to you as the one Loudmouth answered in post #27 about emergence ...

We know that quantum objects behave like particles AND waves. At the macro scale, collections of quantum objects *appear* to behave like particles or waves. The de Broglie wavelength of a thrown baseball is immeasurably small, but it exists, the baseball does have wave properties.

So behaving like a 100% particle is not an emergent property of the macroscale. The earth behaves a little bit like a wave. So does the sun, etc.

I would say that the continuousness of motion that we experience on the macroscale is the same. The discontinuities are immeasurable, but we have reason to believe they must exist at the quantum level.

If you ask a physicist, out of the blue, "Is the motion of a baseball continuous." she'd probably say yes. But if you then said, "But isn't it true that at the quantum level, blah blah blah..." she might well say, "Well, if you're going to split hairs, sure at some level something goes on that is not what we think of as continuous motion."

If it is the case that we're waiting to synthesize GR and QM in order to answer that question, then give me some odds (based on your opinion). What are the odds the answer will be that space is grainy vs. smooth?

The grainy/smooth question is not identical with the continuous/discontinuous motion question. If space is grainy, then I think motion has to be discontinuous. If space is smooth, then I still think these quantum weirdnesses of atomic orbitals and particles in boxes show that motion is not continuous in the usual sense.

But what is the wavefunction outside the box? That's more pertinent to my question. Assuming no tunneling happens here (based on the way the problem is described), I would assume it is zero everywhere outside the box. Is that correct?

Yes, but this depends on the simplifying assumptions of the scenario, namely "(also known as the infinite potential well or the infinite square well) describes a particle free to move in a small space surrounded by impenetrable barriers"

One cannot actually build such a box with infinitely tall walls. If you built a reasonably strong box, the solution would be approximately correct, but there would be some bleed of the wavefunction into the walls.

If so, my next question is: Can the box be located in different places?

The thought-experiment box can't be built at all, so it can't be moved. An approximate box could conceivably be moved. This would presumably cause some change to the wavefunction that I can't easily intuit (some sort of Doppler shift effect as the walls move with respect to our particle), but I expect the particle to stay in the box.

But what does this really mean that you observe it in a location? I'm not sure I understand what you mean by that anymore.

Sitting in our easy chair, next to our impossible box, we can derive the wavefunction of the particle in the box. From the wavefunction, we don't know very much about where the particle is. Its average position is in the middle of the box. To actually see where it is, you have to bounce a photon off it (or make some other measurement). Alas, this will screw up the wavefunction, but from judging the angle the photon comes off at, you can determine (with some range of uncertainty) where the particle was at the exact moment the photon hit it.

In my classical understanding, energy is a scalar. So what does it mean now that energy has real & imaginary parts?

The wavefunction has real and imaginary parts, but the energy of the particle in the box is a real number.

 

[Resha Caner]

The wavefunction has real and imaginary parts, but the energy of the particle in the box is a real number.

OK, that's a relief. But can't the energy be determined from the wavefunction? If so, how?

And I'm not quite there on location. What if the photon you shoot into the box misses the particle? Since you don't know the location, you don't know where to shoot it, so couldn't you miss?

And is that the only way to know it's location? To interact with it? It seems the wavefunction, energy, etc. can be determined from some calculations, but are you saying you can't calculate location? You have to test for it?

... I still think these quantum weirdnesses of atomic orbitals and particles in boxes show that motion is not continuous in the usual sense.

OK. Your answers all seem to have a common theme - that you think motion of the particle is discrete. At the same time I'm aware of all the qualifiers, so I realize it's not something you would say is a solid claim of physics. Again, that's why we're in the philosophy forum.

One cannot actually build such a box with infinitely tall walls. If you built a reasonably strong box, the solution would be approximately correct, but there would be some bleed of the wavefunction into the walls.

That's fine. I don't think it will affect where I'm trying to go with this.

The thought-experiment box can't be built at all, so it can't be moved. An approximate box could conceivably be moved. This would presumably cause some change to the wavefunction that I can't easily intuit (some sort of Doppler shift effect as the walls move with respect to our particle), but I expect the particle to stay in the box.

What I wanted to get to is the phrase in bold: the wavefunction changed. Let's consider mode C in the example, and let's label the center node as point P. Initially we can't observe the particle at P, so let's name the point where we do observe it as Q.

Once the wavefunction changes the node probably won't be located at P anymore. So let's say the new location of the node is Q, where we had observed the particle. Since the particle can no longer be located at Q, and since you appear to indicate the changes are discrete rather than continuous, the particle must make a discrete change in location from Q to some other point. Let's say the next time we observe the particle it is now at P.

Did the particle cease to exist during that discrete time when its location changed from Q to P?

 

[variant]

And is that the only way to know it's location? To interact with it? It seems the wavefunction, energy, etc. can be determined from some calculations, but are you saying you can't calculate location? You have to test for it?

Yes. The only way to observe a particle is to interact with it, that is what detectors of all sorts do.

It becomes pronounced when looking at very small things, the detectors we use necessarily effect our results more on a smaller scale.

OK. Your answers all seem to have a common theme - that you think motion of the particle is discrete. At the same time I'm aware of all the qualifiers, so I realize it's not something you would say is a solid claim of physics. Again, that's why we're in the philosophy forum.

It is a solid claim of the theory of quantum mechanics at least in some circumstances.

Did the particle cease to exist during that discrete time when its location changed from Q to P?

No.

 

[essentialsaltes]

OK, that's a relief. But can't the energy be determined from the wavefunction? If so, how?

The energy would be the expectation value of the Hamiltonian. In the particular case of the particle in a box, the Energy values are known quantized values.

And I'm not quite there on location. What if the photon you shoot into the box misses the particle? Since you don't know the location, you don't know where to shoot it, so couldn't you miss?

Sure you could miss. So you'd have to keep sending them in there, until the electron interacted with a photon. If your detector picks up the photon after the interaction, you'd be able to make an estimate of the location.

And is that the only way to know it's location? To interact with it?

Yes. 'Seeing' it involves bounding photons off it.

It seems the wavefunction, energy, etc. can be determined from some calculations, but are you saying you can't calculate location? You have to test for it?

That's right, the wavefunction will tell you the probability of finding it in one place or another, but there's no way to say where it is.

In my (fairly standard Copenhagen-ish) view of QM, the location of the electron does not exist unless and until it is measured.

OK. Your answers all seem to have a common theme - that you think motion of the particle is discrete.

Really, I think I agree with earlier posters who said that the concept of continuous and discrete motion do not apply very well to the quantum world. As I said above, I think the electron's very location is undefined unless it has been measured, so it's hard to see how you would define motion. You can't measure it's position continuously, so you can only ever see random snapshots of location, and between them you cannot say anything about where the electron is.

It defies the usual idea of what continuous motion is. But I'm not sure it makes it discrete.

Once the wavefunction changes the node probably won't be located at P anymore. So let's say the new location of the node is Q, where we had observed the particle. Since the particle can no longer be located at Q, and since you appear to indicate the changes are discrete rather than continuous, the particle must make a discrete change in location from Q to some other point. Let's say the next time we observe the particle it is now at P.

Did the particle cease to exist during that discrete time when its location changed from Q to P?

I do not believe particles cease to exist when it is not being actively measured. The moon is still there, even if no one is looking at it.

But we only know about a quantum particle's location when we measure it. At one time, we measured its location at Q. At another, P. We cannot say anything about its location between those times. If you like, it's location is not defined in the meantime. But that doesn't mean it disappears.

 

[essentialsaltes]

dp

 

[Resha Caner]

It is a solid claim of the theory of quantum mechanics at least in some circumstances.

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.

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?

 

[Resha Caner]

Yes. 'Seeing' it involves bounding photons off it.

Interesting. But how do you know where the photon is? Doesn't it have similar wave/particle QM behavior?

Really, I think I agree with earlier posters who said that the concept of continuous and discrete motion do not apply very well to the quantum world. As I said above, I think the electron's very location is undefined unless it has been measured, so it's hard to see how you would define motion. You can't measure it's position continuously, so you can only ever see random snapshots of location, and between them you cannot say anything about where the electron is.

It defies the usual idea of what continuous motion is. But I'm not sure it makes it discrete.

OK. I get that (I think). But I still think we're making some (philosophical) progress here.

In my (fairly standard Copenhagen-ish) view of QM, the location of the electron does not exist unless and until it is measured.

No offense, but this seems a bit silly to me. Why must it be interpreted this way? Why couldn't it be that the particle is constantly randomly changing locations and you just don't know what the location is until you measure it? Why does it have to be that location doesn't "exist" until you measure it - a very philosophical sounding statement there.

If that's what you're going to say, it seems you're saying the particle nature of an electron doesn't exist until you measure it, and that puts you very near to saying the particle doesn't exist until you measure it. How do you know that it isn't the actions of your measurement that create the electron? And once you're done it disappears?

 

[Archie the Preacher]

What I really want to know is this:

If I answer this question wrong, am I condemned to Hell?

 

[essentialsaltes]

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?

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.)

 

[essentialsaltes]

Interesting. But how do you know where the photon is? Doesn't it have similar wave/particle QM behavior?

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.

No offense, but this seems a bit silly to me. Why must it be interpreted this way? Why couldn't it be that the particle is constantly randomly changing locations and you just don't know what the location is until you measure it?

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

Why does it have to be that location doesn't "exist" until you measure it - a very philosophical sounding statement there.

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.

How do you know that it isn't the actions of your measurement that create the electron? And once you're done it disappears?

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.