Hot and cold

[Resha Caner]

Your logic is flawed .

(1) says v = v[sub]1,f[/sub] + v[sub]2,f[/sub].

This means v[sup]2[/sup] = v[sub]1,f[/sub][sup]2[/sup] + v[sub]2,f[/sub][sup]2[/sup] + 2v[sub]1,f[/sub]v[sub]2,f[/sub].

Which contradicts (2), which states: v[sup]2[/sup] = v[sub]1,f[/sub][sup]2[/sup] + v[sub]2,f[/sub][sup]2[/sup].

No, my logic is just fine. Whether v[sub]1,f[/sub] = 0 or v[sub]2,f[/sub] = 0, the term you have placed in bold is zero. Therefore, 1) and 2) equate. There is no contradiction.

Again, though, this makes the choice between v[sub]1,f[/sub] = 0 or v[sub]2,f[/sub] = 0 arbitrary without some further postulate. I say there is an alternate postulate to the classical, which would be the same as the tunneling postulate.

The example could go on from there. Assume, rather than one particle at rest, there are 3 particles at rest. So, initially, 1 is in motion and 2,3,4 are at rest. The classical result would be that after the collision, 1,2,3 are at rest, and 4 is in motion. But again, that is an arbitrary result. I could pick any one of the 4 to be in motion. I could claim 1 tunneled through 2,3,4 (the barrier).

I don't actually believe that. I believe the classical solution to be correct. And, at a macroscopic level, it could be confirmed through experiment (even if the collisions aren't perfectly elastic, we can make them pretty darn close).

It is for quantum tunneling that I don't believe the result. The "barrier" in tunneling is something physical. Why must we assume it is the original particle that tunnels? What has always troubled me is that all the "tunneling" explanations require extra energy. And physicists do this "presto, chango, wave the wand and the particle appears on the other side of the barrier". I've always tried to reserve the possibility that there is something I don't understand, but my that seems like crap.

Why must it tunnel? What if the "particle" were an electron and the "barrier" were 3 electrons? Then wouldn't the impact of electron 1 on the barrier dislodge electron 4 on the opposite side? Sure, some particle appears on the other side of the barrier, but its not the original particle. And it seems to me that explanation doesn't require the particle to escape the well. It doesn't require any "presto chango" of mysterious energy hiding in the quantum uncertainty.

Now, an example that lines up electrons isn't very realistic. So, I've been thinking of taking on something more realistic, but the math is likely to bury me. I've been thinking of trying my explanation with something like the simple example of tunneling given in Razavy's book, but I haven't gotten there yet.

 

[Resha Caner]

Hmm, wait. I'm thinking back on inertial frames.

No, actually, I think the result would be the same even in a different inertial frame. It's just that the numbers would be different. So, if you're still game, before we move on to the quantum example, maybe you could help me try a different inertial frame.

Or maybe the details are getting to be too much for a casual forum chat.

 

[Wiccan_Child]

No, my logic is just fine. Whether v[sub]1,f[/sub] = 0 or v[sub]2,f[/sub] = 0, the term you have placed in bold is zero. Therefore, 1) and 2) equate. There is no contradiction.

Again, though, this makes the choice between v[sub]1,f[/sub] = 0 or v[sub]2,f[/sub] = 0 arbitrary without some further postulate. I say there is an alternate postulate to the classical, which would be the same as the tunneling postulate.

This only works if the particles are identical. Get two, non-identical particles (e.g., a proton and a neutron, which only really differ in charge), you can quite easily determine which particle when where - the fact that the positively charged proton hit the stationary neutron, and then itself became stationary, shows that no such 'tunnelling' occurred, despite the exchange of velocities.

Mathematically, this 'arbitrary' assumption comes from the framework of the system itself: we've already stated a priori that the first particle has an initial velocity of v; if its velocity doesn't change, then you're still calculating its velocity before the collision.

In other words, the solutions, v[sub]1[/sub] = 0, v, correspond to the two cases: pre-collision and post-collision. Which one is which depends on our mathematical premise: did the first particle start at rest, or at v? From that, we can easily deduce that, if it started at rest, the v[sub]1[/sub] = 0 solution corresponds to the pre-collision state. Thus, v[sub]1[/sub] = v corresponds to the post-collision state.

In any case, this is a mathematical quirk given that the particles are identical. You could easily use two non-identical particles and observe either a normal, elastic collision, a 'close miss', or genuine quantum tunnelling.

The example could go on from there. Assume, rather than one particle at rest, there are 3 particles at rest. So, initially, 1 is in motion and 2,3,4 are at rest. The classical result would be that after the collision, 1,2,3 are at rest, and 4 is in motion. But again, that is an arbitrary result. I could pick any one of the 4 to be in motion. I could claim 1 tunneled through 2,3,4 (the barrier).

I don't actually believe that. I believe the classical solution to be correct. And, at a macroscopic level, it could be confirmed through experiment (even if the collisions aren't perfectly elastic, we can make them pretty darn close).

The point about Quantum Mechanics is that Classical Mechanics is an intuitive over-simplification; the Correspondance Principle ensures that, at large scales, QM gives basically the same results as CM - it's only at small scales that QM phenomena arise.

Moreover, a mathematical quirk isn't the reason we talk about quantum tunnelling; it's a little more complex than a simple 'Newton's Cradle' effect.

It is for quantum tunneling that I don't believe the result. The "barrier" in tunneling is something physical. Why must we assume it is the original particle that tunnels? What has always troubled me is that all the "tunneling" explanations require extra energy. And physicists do this "presto, chango, wave the wand and the particle appears on the other side of the barrier". I've always tried to reserve the possibility that there is something I don't understand, but my that seems like crap.

The point of quantum tunnelling is that an identifiable particle exists in a potential well, which, classically, it cannot escape; then, the particle escapes. Quantum Mechanics tells us how this happens: it tunnelled through the barrier.

Why must it tunnel? What if the "particle" were an electron and the "barrier" were 3 electrons? Then wouldn't the impact of electron 1 on the barrier dislodge electron 4 on the opposite side? Sure, some particle appears on the other side of the barrier, but its not the original particle. And it seems to me that explanation doesn't require the particle to escape the well. It doesn't require any "presto chango" of mysterious energy hiding in the quantum uncertainty.

OK, but what if the barrier isn't made of electrons? What if the barrier is made of neutrons, and there's an electron trapped in the middle? What happens then?

 

[Resha Caner]

This time your answer is very convincing - though I will maintain that your statements are still unproven assumptions. Part of the reason your answer to my puzzle is convincing is because I believed that to be the answer before we even began. What I'm doing is playing devil's advocate. It seems to me there is an inconsistency here. The statement being made is: in a classical model, the particle can't escape. Why? The answer to that boils down to an assumption. So, cutting to the quick, the answer is that it can't escape because we assume it can't escape.

Something similar happens at the quantum level, but now the answer is: it escapes because we assume it escapes. There is some observational evidence that seems to support those assumptions, but I'm pushing deeper. I'm asking if those observations could be misleading.

So, let me address the challenge you've raised:

This only works if the particles are identical.

OK, but what if the barrier isn't made of electrons? What if the barrier is made of neutrons, and there's an electron trapped in the middle? What happens then?

As I said, I haven't really worked through a quantum example yet - and maybe it won't work if I try. So, I'll have to start simple. Rather than a barrier of neutrons with trapped electrons, let's start with just a proton and neutron.

For my classical example, remember that I considered a case where 1 particle collides with a barrier of 3 identical particles. The next step would be to consider that the 3 particles are somehow "bonded" so that they appear as a single particle. The idea was to show that the collision causes particle 1 to be absorbed by (i.e. bonded to) the barrier, and the result is to release (i.e. break the bond) of particle 4. Of course in a real such collision, there are other by-products, but I was moving from the simple to the complex. I think the same would apply at the quantum level. The initial cases we speak of will be pretty simple, and as we increase the complexity, we'll have to deal with the other by-products.

Anyway, to start simple, consider just the proton (2 up quarks and 1 down quark) and the neutron (1 up quark and 2 down quarks). At the moment of collision, what we really have is 3 up quarks and 3 down quarks. Are you really going to say you can trace which quarks appear on the other side of the barrier? Or is all we really know that 3 quarks stay behind (and they happen to form a neutron) and 3 continue on (and they happen to form a proton). I don't think (due to uncertainty) that you can trace the quarks through the event. All you really know is "before" and "after."

My point is, I have this intuitive part of me saying that (had I the time and ability to wrestle though the math), I could conclude that what really happened is some exchange with the barrier and that what comes out the other side is not really - in totality - the original particle. (Edit: I'm not saying the tunneling conclusion is invalid. I'm saying there are alternative conclusions of equal validity, and that this other conclusion matches with observations of classical mechanics (i.e. of macroscopic observation), and is, therefore, more intuitively correct.)

In getting the case of the electron (i.e. in dealing with collisions of leptons and quarks), I think what I would really face is getting down to wave packets of quanta of energy.

 

[Wiccan_Child]

This time your answer is very convincing - though I will maintain that your statements are still unproven assumptions. Part of the reason your answer to my puzzle is convincing is because I believed that to be the answer before we even began. What I'm doing is playing devil's advocate. It seems to me there is an inconsistency here. The statement being made is: in a classical model, the particle can't escape. Why? The answer to that boils down to an assumption. So, cutting to the quick, the answer is that it can't escape because we assume it can't escape.

Something similar happens at the quantum level, but now the answer is: it escapes because we assume it escapes. There is some observational evidence that seems to support those assumptions, but I'm pushing deeper. I'm asking if those observations could be misleading.

So, let me address the challenge you've raised:

This only works if the particles are identical.
...
OK, but what if the barrier isn't made of electrons? What if the barrier is made of neutrons, and there's an electron trapped in the middle? What happens then?

As I said, I haven't really worked through a quantum example yet - and maybe it won't work if I try. So, I'll have to start simple. Rather than a barrier of neutrons with trapped electrons, let's start with just a proton and neutron.

For my classical example, remember that I considered a case where 1 particle collides with a barrier of 3 identical particles. The next step would be to consider that the 3 particles are somehow "bonded" so that they appear as a single particle. The idea was to show that the collision causes particle 1 to be absorbed by (i.e. bonded to) the barrier, and the result is to release (i.e. break the bond) of particle 4. Of course in a real such collision, there are other by-products, but I was moving from the simple to the complex. I think the same would apply at the quantum level. The initial cases we speak of will be pretty simple, and as we increase the complexity, we'll have to deal with the other by-products.

Anyway, to start simple, consider just the proton (2 up quarks and 1 down quark) and the neutron (1 up quark and 2 down quarks). At the moment of collision, what we really have is 3 up quarks and 3 down quarks. Are you really going to say you can trace which quarks appear on the other side of the barrier? Or is all we really know that 3 quarks stay behind (and they happen to form a neutron) and 3 continue on (and they happen to form a proton). I don't think (due to uncertainty) that you can trace the quarks through the event. All you really know is "before" and "after."

Again, you're taking a very specific event, trying to 'refute' quantum tunnelling on a case-by-case basis.
As it happens, neutrons do indeed turn into protons - through a specific process called beta-decay, so called because for a neutron to become a proton requires it to shed a beta-particle (i.e., an electron). This notably doesn't happen when protons collide with neutrons.

Indeed, protons and neutrons interact perfectly normally without swapping quarks - quarks cannot even be isolated or separated from the host particle. That is, if even the LHC cannot break a proton into its constituent quarks, simply bumping them together is unlikely to break their bonds.

Nevertheless, consider my other proposal: an electron trapped in

Finally, you're missing one of the key aspects of quantum tunnelling: it's not that the particle tunnels through a physical barrier, but that it tunnels out of a potential barrier. Neutrinos have no trouble zipping through physical media, because they just don't interact. But electrons, for instance, can be trapped in very specific, very finely tuned, magnetic wells. They can be trapped within the electromagnetic grip of an atom - yet, perversely, can fly away under conditions at odds with CM.

The reason we say that, classically, the particle cannot escape, is because the potential gradients are such that the particle requires energy to traverse the distance (the quintessential analogy being: the particle is at the bottom of the hill. You have to push it to the top to get it over).

In other words, there doesn't actually need to be a physical particle with which the trapped particle can be 'exchanged'.

My point is, I have this intuitive part of me saying that (had I the time and ability to wrestle though the math), I could conclude that what really happened is some exchange with the barrier and that what comes out the other side is not really - in totality - the original particle. (Edit: I'm not saying the tunneling conclusion is invalid. I'm saying there are alternative conclusions of equal validity, and that this other conclusion matches with observations of classical mechanics (i.e. of macroscopic observation), and is, therefore, more intuitively correct.)

In getting the case of the electron (i.e. in dealing with collisions of leptons and quarks), I think what I would really face is getting down to wave packets of quanta of energy.

Indeed. If you're willing to come up with a quantum mechanical model that explains how leptons can become quarks, and vice versa, contrary to the Standard Model, your Nobel Prize is ready and waiting...

It also should be stated that, however intuitively appealing a classical 'particle exchange' interpretation of quantum tunnelling may be, CM has still been superseded by QM. QM regards these phenomena as instances of quantum tunnelling, given the nature of particles within that paradigm (i.e., blurs of probability that coalesce down upon observation).

 

[Wiccan_Child]

Let's start simpler.

If you have a particle in a potential well, the particle's wavefunction nonetheless exists over all space. In other words, you can calculate the probability of measuring the particle as existing at any given point.

Within the well, the particle is very likely.
Outside the well, the particle is much rarer.

But the point is that there is a finite, non-zero probability of finding the particle outside the well.
Thus, using QM, we can calculate the probability of finding a trapped particle outside the barrier that held it.

This is something we can measure. We can directly measure the rate at which electrons are emitted. It's one thing to offer alternative explanations for the mechanics involved, but quite another to come up with empirical evidence that prefers one mechanics over another - in this case, the reliability with which we use the tunnelling effect is, in my opinion, proof enough.

 

[mzungu]

My bets are on WICCAN CHILD

 

[Resha Caner]

Again, you're taking a very specific event, trying to 'refute' quantum tunnelling on a case-by-case basis.

Mmm. Actually, it's been more of a journey ... an ironic statement based on what I'm about to say. I'm thinking I need to change my position ... one of those gestalt things. I never really expected to refute tunneling (i.e., it's not as if I thought the math was wrong), I just didn't accept it as a reality. From the beginning I've considered it a model (and not a very good one), and what I was trying to do was ponder what alternative models might be viable.

It's been interesting. Back before I knew of QM I remember proposing something to my teacher that I called an "entron" - which was essentially a quantum, but a more childish form. It seemed right to me, but the idea got squished and I never chased the implications of it. What always hung me up about QM was its probabilistic nature - because I was taking it as a total randomness. My shift was to look at it from a more Eleatic perspective. In other words, though I'd long accepted particles as manifesting in distinct states, I was still thinking of space as a continuum. In fact, it was just this past summer that I gave up the idea of space having dimension. I've since been thinking of space as a literal nothing with neither substance nor attribute. So, saying we live in 3-space would be erroneous as I see it. If the physical construct were correct, we could make a model with as many degrees of freedom as we chose. There isn't some "hidden" dimension for Trekkies to locate. It took awhile for that idea to catch up with the rest of my mental contortions.

In other words, though I can now say that I could accept tunneling as a viable model, there are implications behind that acceptance that mean we probably still disagree. For example, I've long considered time to be a mere invention of the mind to give reference to motion, and that it is without any real metaphysical meaning (as much as people try to assign it such meaning). I was of the opinion that "time" depended upon the system under consideration, and, therefore, trying to reference it to something external (like cesium) was a serious error. As such, I don't accept the whole space-time thing. Again, it's not that the math is wrong, but it seems a very poor model of reality - despite its support from observation. I agree with Smolin's statement that there is this strong intuitive inclination to say that the reason physics is having problems (conflicts between GR and QM for example) is due to an erroneous concept of time. Accepting tunneling, then, actually moves me farther from the space-time idea, rather than closer to it.

Like the Eleatics, it would lead me to say that "motion" is impossible. Therefore, "time" becomes totally irrelevant. There is no motion, then, as in the movement of a particle through space. Rather, a particle has a probability of existing. That probability is different for different locations, and that probability is affected by the other particles in the system. So, while it might be convenient to say the particle has moved from here to there, what in fact has happened is that it ceased to exist here and began to exist there. The "barrier" then, simply decreases the possibility of it existing in certain locations ... but the probability is never zero. The reason the barrier changes the probability is because it also has a possibility of existing in that self-same location. Further, the existence of the particle in different locations would not be a movement in space, but a change in its extent (a somewhat Cartesian idea).

As such, another disagreement we might have would be in regard to the macro level. Or, maybe it would only be a semantic issue that could now be resolved. I would think, that, if the possibility of tunneling exists at the quantum level, it also exists at the macro level, but it is much reduced. For example, suppose the probability of a particle appearing outside a well is 0.5. If 2 particles are in the well (and ignoring all the complications of their mutal interaction), then each has a probability of 0.5 and the probability that both will appear outside the well is 0.25. Therefore, if the 2 particles bond into a single, larger particle, the probability of the larger particle appearing outside the well is smaller. As such, the number of particles involved in a billiard ball tunneling through the cushion on the pool table is so astronomical as to make the possibility practically zero ... but it is not actually a zero probability.

Therefore, my classical example still stands as a possibility.

As it happens, neutrons do indeed turn into protons - through a specific process called beta-decay, so called because for a neutron to become a proton requires it to shed a beta-particle (i.e., an electron). This notably doesn't happen when protons collide with neutrons.

Indeed, protons and neutrons interact perfectly normally without swapping quarks - quarks cannot even be isolated or separated from the host particle. That is, if even the LHC cannot break a proton into its constituent quarks, simply bumping them together is unlikely to break their bonds.

Unlikely, but I would say it is still possible. As such, though I would now agree that the most likely result is that a particle appearing outside a well is the same as the one that was in it, it cannot be definitely known. The possibility exists that it is a different particle.

In other words, there doesn't actually need to be a physical particle with which the trapped particle can be 'exchanged'.

Saying "particle" may be a semantic problem. Surely there must be some physical manifestation that creates the potential barrier. If not, then we have something interesting to talk about.

Indeed. If you're willing to come up with a quantum mechanical model that explains how leptons can become quarks, and vice versa, contrary to the Standard Model, your Nobel Prize is ready and waiting...

If you would help me, we might get there. So far you've seemed unwilling to joust with the windmill of established physics. Maybe you are willing to do that, but if so, I haven't seen you express in what regard that would be. That's where the everlasting fame lies. Everything else is a predestined refinement of existing math ... kinda boring.

 

[Wiccan_Child]

Mmm. Actually, it's been more of a journey ... an ironic statement based on what I'm about to say. I'm thinking I need to change my position ... one of those gestalt things. I never really expected to refute tunneling (i.e., it's not as if I thought the math was wrong), I just didn't accept it as a reality. From the beginning I've considered it a model (and not a very good one), and what I was trying to do was ponder what alternative models might be viable.

It's been interesting. Back before I knew of QM I remember proposing something to my teacher that I called an "entron" - which was essentially a quantum, but a more childish form. It seemed right to me, but the idea got squished and I never chased the implications of it. What always hung me up about QM was its probabilistic nature - because I was taking it as a total randomness. My shift was to look at it from a more Eleatic perspective. In other words, though I'd long accepted particles as manifesting in distinct states, I was still thinking of space as a continuum. In fact, it was just this past summer that I gave up the idea of space having dimension. I've since been thinking of space as a literal nothing with neither substance nor attribute. So, saying we live in 3-space would be erroneous as I see it. If the physical construct were correct, we could make a model with as many degrees of freedom as we chose. There isn't some "hidden" dimension for Trekkies to locate. It took awhile for that idea to catch up with the rest of my mental contortions.

If space is not 3D, then what are we talking about when we think of height, width, and depth?

In other words, though I can now say that I could accept tunneling as a viable model, there are implications behind that acceptance that mean we probably still disagree. For example, I've long considered time to be a mere invention of the mind to give reference to motion, and that it is without any real metaphysical meaning (as much as people try to assign it such meaning). I was of the opinion that "time" depended upon the system under consideration, and, therefore, trying to reference it to something external (like cesium) was a serious error. As such, I don't accept the whole space-time thing. Again, it's not that the math is wrong, but it seems a very poor model of reality - despite its support from observation.

If it's supported by observation, how is it a 'very poor' model of reality? The preponderance of evidence should make it a very good model of reality, no?

It seems your objection is one of principle - your personal philosophy doesn't allow for QM - rather than any objective veracity of the model.

I agree with Smolin's statement that there is this strong intuitive inclination to say that the reason physics is having problems (conflicts between GR and QM for example) is due to an erroneous concept of time. Accepting tunneling, then, actually moves me farther from the space-time idea, rather than closer to it.

Before, the particle's in the well. After, it's not. If you do not believe in time, then no phenomenon has occurred - what, then, are you trying to explain?

Like the Eleatics, it would lead me to say that "motion" is impossible. Therefore, "time" becomes totally irrelevant. There is no motion, then, as in the movement of a particle through space. Rather, a particle has a probability of existing. That probability is different for different locations, and that probability is affected by the other particles in the system. So, while it might be convenient to say the particle has moved from here to there, what in fact has happened is that it ceased to exist here and began to exist there. The "barrier" then, simply decreases the possibility of it existing in certain locations ... but the probability is never zero. The reason the barrier changes the probability is because it also has a possibility of existing in that self-same location. Further, the existence of the particle in different locations would not be a movement in space, but a change in its extent (a somewhat Cartesian idea).

Which is, by and large, a quantum mechanical idea.

As such, another disagreement we might have would be in regard to the macro level. Or, maybe it would only be a semantic issue that could now be resolved. I would think, that, if the possibility of tunneling exists at the quantum level, it also exists at the macro level, but it is much reduced. For example, suppose the probability of a particle appearing outside a well is 0.5. If 2 particles are in the well (and ignoring all the complications of their mutal interaction), then each has a probability of 0.5 and the probability that both will appear outside the well is 0.25. Therefore, if the 2 particles bond into a single, larger particle, the probability of the larger particle appearing outside the well is smaller. As such, the number of particles involved in a billiard ball tunneling through the cushion on the pool table is so astronomical as to make the possibility practically zero ... but it is not actually a zero probability.

Indeed. In my first year of university, we calculated the probability of one snooker ball tunnelling through another. It was quite remote.

Therefore, my classical example still stands as a possibility.

I think that's something of a non sequitur. Everything you've said points to quantum tunnelling: particles existing as a blur of probability, with a non-zero chance of simply appearing outside their potential well. Not some sort of phantom clone particle, but the real deal.

Your classical example has yet to explain how particles can surmount the potential barrier. Discarding the concept of time doesn't solve the problem so much as it disregards all of physics altogether.

Unlikely, but I would say it is still possible. As such, though I would now agree that the most likely result is that a particle appearing outside a well is the same as the one that was in it, it cannot be definitely known. The possibility exists that it is a different particle.

Where did the original particle go, and where did this replacement particle come from?
It's possible, through some extremely lucky tunnelling event, for two electrons to conveniently swap position in a way that mimics normal tunnelling, but at the end of the day, it's still tunnelling.

Saying "particle" may be a semantic problem. Surely there must be some physical manifestation that creates the potential barrier. If not, then we have something interesting to talk about.

There's usually (but not always) a particle which creates the barrier, but, thus far, the barriers you've talked about have been the particles themselves.

If you would help me, we might get there. So far you've seemed unwilling to joust with the windmill of established physics. Maybe you are willing to do that, but if so, I haven't seen you express in what regard that would be.

Wave-particle duality. Never got on with that. It's particles all the way down.

 

[Resha Caner]

Wave-particle duality. Never got on with that. It's particles all the way down.

Bummer. Can't help you with that one. It was a strange thing to accept, but I'm at peace with that idea now.

I'm a very conceptual person, so I tend to do things backwards. I grasp the idea (or develop the idea) and then work backward to understand the math that supports it. It makes things quite disappointing as 9 times out of 10 the math later forces me to change or abandon said concept.

Anyway, philosophically I assign substance to the wave and mode to the particle. What's cool about that is our recent discussion on mass - which was a new thing for me, but it fits well with that conception.

I think that's something of a non sequitur. Everything you've said points to quantum tunnelling: particles existing as a blur of probability, with a non-zero chance of simply appearing outside their potential well. Not some sort of phantom clone particle, but the real deal.

Your classical example has yet to explain how particles can surmount the potential barrier. Discarding the concept of time doesn't solve the problem so much as it disregards all of physics altogether.

Shrug. If you prefer to think that for now. I'm not sure you understood what I meant by the comment. Quantum tunneling doesn't explain how either. It just says that it happens. That's why you get people trying "high jump" analogies and so forth (don't like that analogy BTW). All I really meant is that the math of the classical example could still be taken to demonstrate that some possibility for tunneling at the macro level exists, and that if our dear physicists of antiquity had not been tightly held within a certain paradigm, they might never have claimed what they did.

If it's supported by observation, how is it a 'very poor' model of reality? The preponderance of evidence should make it a very good model of reality, no?

It seems your objection is one of principle - your personal philosophy doesn't allow for QM - rather than any objective veracity of the model.

Before, the particle's in the well. After, it's not. If you do not believe in time, then no phenomenon has occurred - what, then, are you trying to explain?

I'm not really ready to explain, as this is a new thing for me. It will take some "time" to gel.

As a little anecdote to go with that, my philosophy has been frozen with Newton for years. I've just recently decided to remedy that and get a better handle on more recent philosophers, so I've started a book by Scruton. I'm only up to Spinoza so far, so I've got a long way to go. But, it was funny to read Scruton's take on Spinoza. It came off as: this guy seems really smart, but nobody can really understand what he was saying. He said he was a monist, but his writings seem very dualist.

Or how about this analogy: Did the sun rise this morning where you live? Well, no, that's not really an accurate description according to modern physics, but I bet you still use that phrase. It's a useful phrase that helps you communicate.

So, even if I say motion doesn't exist - that what we see is the extent of existence - and thereby, time doesn't exist ... Well, I'm still in that "fuzzy" stage, and "time" is still an easier way to convey many concepts - just as CM is still more practical for my engineering work than QM.

If space is not 3D, then what are we talking about when we think of height, width, and depth?

You should have quit while you were ahead ... but I've never been smart enough to do that either.

I never said you can't choose a Cartesian reference to describe the extent of a body. I said it would be misleading to think such a reference will appropriately describe motion for all systems.

Like I said, 3D met its final death with me over the summer. This is a very complex thing to try to explain, but that death came from Hofstadter's book: Godel, Escher, and Bach. It was fascinating to read the section toward the end on the human brain because I've been mulling an idea of will for some time, but never had the proper framework in which to embed it. As he talked about the brain, he mentioned work by Brisson on how to represent complex structures in reduced form. For example, artists can draw on 2D paper and make it look 3D. So, there has always been a question about what is the minimum construction needed to represent higher dimension. In other words, is 3D necessary to represent 4D? Or, can it also be done with 2D? So, from there I read a collection edited by Brisson called Hypergraphics. Very cool stuff.

The other piece of the puzzle that I would need to mention is Non-Newtonian Calculus by Grossman and Katz.

So, after we take a deep breath, we can open Pandora's Box if you would like.

 

[Wiccan_Child]

Bummer. Can't help you with that one. It was a strange thing to accept, but I'm at peace with that idea now.

I'm a very conceptual person, so I tend to do things backwards. I grasp the idea (or develop the idea) and then work backward to understand the math that supports it. It makes things quite disappointing as 9 times out of 10 the math later forces me to change or abandon said concept.

Anyway, philosophically I assign substance to the wave and mode to the particle. What's cool about that is our recent discussion on mass - which was a new thing for me, but it fits well with that conception.

My objection to the 'wave' is that it seems to be nothing more than a mathematical simplification.

Shrug. If you prefer to think that for now. I'm not sure you understood what I meant by the comment. Quantum tunneling doesn't explain how either. It just says that it happens. That's why you get people trying "high jump" analogies and so forth (don't like that analogy BTW). All I really meant is that the math of the classical example could still be taken to demonstrate that some possibility for tunneling at the macro level exists, and that if our dear physicists of antiquity had not been tightly held within a certain paradigm, they might never have claimed what they did.

I disagree that classical mechanics can fully explain the phenomenon of quantum tunnelling, either conceptually or mathematically.

As for paradigm shifts, it's every scientist's dream to cause one. Academia is structured to reward those who challenge and refute the mainstream, rather than bolster it - peer review, for instance, works to strip papers of their errors, not pad out their strengths. No one's 'tightly bound', beyond their own reluctance.

I'm not really ready to explain, as this is a new thing for me. It will take some "time" to gel.

As a little anecdote to go with that, my philosophy has been frozen with Newton for years. I've just recently decided to remedy that and get a better handle on more recent philosophers, so I've started a book by Scruton. I'm only up to Spinoza so far, so I've got a long way to go. But, it was funny to read Scruton's take on Spinoza. It came off as: this guy seems really smart, but nobody can really understand what he was saying. He said he was a monist, but his writings seem very dualist.

Or how about this analogy: Did the sun rise this morning where you live? Well, no, that's not really an accurate description according to modern physics, but I bet you still use that phrase. It's a useful phrase that helps you communicate.

So, even if I say motion doesn't exist - that what we see is the extent of existence - and thereby, time doesn't exist ... Well, I'm still in that "fuzzy" stage, and "time" is still an easier way to convey many concepts - just as CM is still more practical for my engineering work than QM.

I disagree that 'time' is just a useful metaphor or literary device - to me, it's an actual thing across which change occurs. We are all very much aware of what time is, and I've never understood some people's fervent desire to show that time doesn't exist - it seems obvious, to me, that it does exist. You may as well try and prove there is no Moon.

You should have quit while you were ahead ... but I've never been smart enough to do that either.

I never said you can't choose a Cartesian reference to describe the extent of a body. I said it would be misleading to think such a reference will appropriately describe motion for all systems.

Like I said, 3D met its final death with me over the summer. This is a very complex thing to try to explain, but that death came from Hofstadter's book: Godel, Escher, and Bach. It was fascinating to read the section toward the end on the human brain because I've been mulling an idea of will for some time, but never had the proper framework in which to embed it. As he talked about the brain, he mentioned work by Brisson on how to represent complex structures in reduced form. For example, artists can draw on 2D paper and make it look 3D. So, there has always been a question about what is the minimum construction needed to represent higher dimension. In other words, is 3D necessary to represent 4D? Or, can it also be done with 2D? So, from there I read a collection edited by Brisson called Hypergraphics. Very cool stuff.

The other piece of the puzzle that I would need to mention is Non-Newtonian Calculus by Grossman and Katz.

So, after we take a deep breath, we can open Pandora's Box if you would like.

Be my guest. I'm interested in seeing where this rabbit hole goes

(and, if nothing else, my 'Ask a Physicist' thread is still closed! )

 

[Resha Caner]

My objection to the 'wave' is that it seems to be nothing more than a mathematical simplification.

That doesn't bother me. As we've discussed before, I'm not looking for science to discover truth or reality. To me it's all a model.

I disagree that classical mechanics can fully explain the phenomenon of quantum tunnelling, either conceptually or mathematically.

Do you know of Paul Marmet? Speaking of people on the fringe ...

As for paradigm shifts, it's every scientist's dream to cause one. Academia is structured to reward those who challenge and refute the mainstream, rather than bolster it - peer review, for instance, works to strip papers of their errors, not pad out their strengths. No one's 'tightly bound', beyond their own reluctance.

Actually, a study of scientific history and philosophy usually yields the opposite conclusion - that scientific institutions work to maintain the status quo. That's why Marmet, Smolin, and others ran off to Canada. Everbody wants to have Einstein once he's established, but not when he's a nutty patent clerk.

Be my guest. I'm interested in seeing where this rabbit hole goes

Then I suppose we should start with a few definitions.

"Dimension" in the context you're thinking of it is probably better called "coordinate." A coordinate, then, is one of the set of numbers used to describe the location of a point. Note that this is not the same as the set of numbers needed to define the orientation of a body. But, by specifying the minimum set of coordinates for a point, one specifies the space that contains it. A point (speaking in Euclidean terms) has 0 coordinates. A line has 1, a plane 2, and a space 3. One can, of course, imagine going on forever to a "hyperspace" with 4 and so forth. But, most would agree that the universe equates to a space of 3 coordinates.

Defining location further requires defining an "origin," which is the point to which all other points will be referenced. Within a rigid body, the center of mass is usually selected as the origin. Regardless, once the origin is selected, if Cartesian coordinates are chosen, it actually takes 6 coordinates to define the orientation of the body (3 translational and 3 rotational). Interestingly enough, this is not the minimum. The minimum set of coordinates is 4, which is to specify a vector length and 3 Euler angles.

Regardless, from that definition, "dimension" is defined as the minimum set of attributes needed to define a body. My college text on dynamics lists 5 dimensions: length, force, charge, temperature, and time. This minimum set depends upon which attributes one is trying to describe, so there isn't really a fixed set. The intent of "dimension" is that they be independent of each other. If one takes F = m*a as a first principle, then one has to choose 2 of the 3 as independent "dimensions", and the 3rd is dependent. That is the essence of a dimensional analysis (I can't tell you how many times a young engineer has worked a problem using units of Newtons, seconds, and millimeters ).

For our purposes, I think we only need to discuss the dimensions of length and time. So, the next question becomes: what is time? One second is the time that elapses during 9,192,631,770 cycles of the radiation produced by the transition between two levels of the cesium 133 atom. That is the "measure" of time, but what is "time?" Can it be separated from its measure? Not really, except to say that time is the reference used to describe motion.

... Pause for comments

 

[Maxwell511]

It is for quantum tunneling that I don't believe the result. The "barrier" in tunneling is something physical. Why must we assume it is the original particle that tunnels? What has always troubled me is that all the "tunneling" explanations require extra energy. And physicists do this "presto, chango, wave the wand and the particle appears on the other side of the barrier". I've always tried to reserve the possibility that there is something I don't understand, but my that seems like crap.

Why must it tunnel? What if the "particle" were an electron and the "barrier" were 3 electrons? Then wouldn't the impact of electron 1 on the barrier dislodge electron 4 on the opposite side? Sure, some particle appears on the other side of the barrier, but its not the original particle. And it seems to me that explanation doesn't require the particle to escape the well. It doesn't require any "presto chango" of mysterious energy hiding in the quantum uncertainty.

Now, an example that lines up electrons isn't very realistic. So, I've been thinking of taking on something more realistic, but the math is likely to bury me. I've been thinking of trying my explanation with something like the simple example of tunneling given in Razavy's book, but I haven't gotten there yet.

You hit a very important nail on the head here and it is the reason why it is believed that it is the original particle and not a particle that is "knock" out.

Potential energy barriers can/mostly exist with mulitple layers of particles. Now say that you have a "thick" wall of neutrons at which you throw another neutron. The thrown neutron will hit a first neutron in the wall which will hit a second neutron behind it and so on. It creates a sound wave, in the wall, that will eventually knock the last neutron out on the other side of the wall. In classical mechanics to obey the conservation of energy the sound wave front must travel at most the speed of the original particle that hit the wall therefore the speed at which a particle would seem to tunnel is proportional to the velocity of the particle. This is not experimentally the case. Quantum tunnelling happens much faster, and I believe a consistant speed, than classical physics would allow under you hypothesis.

As an example of an experiment on the timing of QM see this (PDF). In that one a photon tunnels through a barrier apparently faster than the speed of light.

 

[Targ]

I keep wanting to sing a Katy Perry song every time I see this thread.

YouTube - Hot N' Cold - Katy Perry (With Lyrics)

 

[Resha Caner]

OK, those weren't the comments I was expecting, but I guess we've wandered far from the OP ... as is typical. Maybe, as is also typical, interest waned before I was done talking. Regardless, I'll add a bit more to what I said in post #72 to see if that breathes life back into this.

I ended with a comment on time. The final point was to indicate that the measure of time is arbitrary (i.e. basing it on cesium) in that it could be scaled to any consistent motion without any real loss of information. (Note that in another thread I was poking at whether this means time didn't exist in the first moments because there was nothing consistent to use as a reference) That is true of any measure, but I think time (as science uses it) has an additional arbitrary element that no one seems to see. Even further, the discussion on tunneling makes me wonder if time is even redundant (though I haven't nailed that down yet). Before getting to that, though, we need to talk about dimension (or coordinate).

As I hinted at, defining a set of coordinates as a minimum set defines something about space. What I realized a long time ago, however, was that there are other implicit assumptions that go with it. For example, in highschool I wondered why the minimum number of sides for a closed figure was 3 (the triangle). Why couldn't there be a "biangle" or a "monoangle"? I set out to try to develop a geometry for that. What I realized was that there was an implicit assumption in Euclidean geometry about the nature of space. It could be expressed several different ways, but I formulated that an additional assumption was needed about the curvature of a line (with the Euclidean assumption being that the curvature was infinite). At the time I didn't have the math skills to carry the idea to completion, but I have since found the necessary math.

As a simple example, consider a line with finite and constant curvature. It is, therefore, a circle. If one point on the circle is defined as the origin, we can specify a dimension of length along the line. Movement in that "space" is 1D, but in Cartesian space it would be called 2D. In fractal geometry it would be given yet a different dimension (based on the ability of the circle to fill a plane). "Dimension," then, becomes a bit arbitrary.

My position is that what science is really seeking is Ockham's Razor - the parsimonius solution. I would also contend then, that for circular motion, the parsimonius solution is to call it 1D. To accept that, in my mind, makes "space" a mere convenience - a choice of model that best suits the problem.