Hypothetical: Local uncertainty neutralizer

[OmegaGuy]

This might be a stupid question, but suppose for a second that someone developed a device that would effect a spherical area of, let's say, 100 meters in radius. In this area, the Uncertainty Principle and other quantum weirdness would cease to exist, and subatomic particles and energy would behave according to newtonian/relativistic mechanics.

What would be the effect of this?

[kheegster]

Newtonian mechanics breaks down at small scales, by which we mean that it doesn't apply as a viable description of physics, which is why there is a need for a different theory to describe matter at such scales.

What you're basically saying is to suspend all physics within this bubble.

[Nieztchean Uber-Amoeba]

A bubble of weird pseudo-vacuum implausibility as Newtonian physics break down at the smallest levels and everything gets messy.

[Surlethe]

Umm, since electrons are now treated as point particles instead of waves, don't all the atoms within this 100 m radius collapse, releasing all that electromagnetic potential in a huge explosion?

[SyntaxVorlon]

Newtonian physics doesn't break down at the quantum level, it still exists, but in the statistics. If such a device were even remotely plausible it would probably have dire effects on the states of atoms.

The uncertainty principle comes from how we find the expectation values for particles. The math is a bit heady but:

stdev o(A) = SQRT(SUM(Ai - <A>)^2/(n-1))

That is standard deviation is the square root of the sum of all the values minus the average value squared divided by the number of values minus 1.

In QM to find this we would integrate the wavefunction PSI* and PSI (* denotes complex conjugates[all the imaginary terms switch signs]) with the operator for a value to find its expectation value, what we commonly call the average. The standard deviation comes out when we use (A[op] - <A>) in our equation.

It is from here that we are able to define the uncertainty principle as

o(x)o(p)>= h*pi

In the situation you describe

o(x)o(p)>= 0

So the all measured positions and momenta may fall precisely on their expectation values. In this situation all particles would gain distinct position, which means...hell I can't even imagine that situation. All our experiences rely on the fact that everything blurs into itself. The color of your skin cells is reliant on small batches of color within each and every one, but seen up close they really don't look a whole lot different one to the other.

All of physics fails, is my conclusion. Quantum effects fail, so all newtonian effects which are their blurred average fail to a much greater degree. Chemistry, Nuclear binding, everything, kaput. The effect would instantaneously convert a region of space into its component energy and then release it since what ever causes the effect would be destroyed along with it.

This could probably cause a star to go nova, or a black hole.

[Kuroneko]

Well, as a formal mathematical process, fields can in principle be 'dequantized'; it's just typically done in the opposite direction (e.g., deform the corresponding algebra of operators ala Weyl). Additionally, it's unclear what sort of 'sanity check' one should enforce. For example, a pointlike proton and electron in a hydrogen atom would quickly collapse into one other, releasing an infinite amount of radiation. Perhaps a better approach might be to limit their radii to what would physically make the most sense (classical electron radius). The dequantized QCD field should be qualitatively similar to electromagnetism--U(1) is subsgroup of SU(3), so in principle these "classical chromodynamics" should be capable of anything electromagnetism does, but I'm not willing to speculate on further specifics without alcohol.

[SyntaxVorlon]

Well, as a formal mathematical process, fields can in principle be 'dequantized'; it's just typically done in the opposite direction (e.g., deform the corresponding algebra of operators ala Weyl). Additionally, it's unclear what sort of 'sanity check' one should enforce. For example, a pointlike proton and electron in a hydrogen atom would quickly collapse into one other, releasing an infinite amount of radiation. Perhaps a better approach might be to limit their radii to what would physically make the most sense (classical electron radius). The dequantized QCD field should be qualitatively similar to electromagnetism--U(1) is subsgroup of SU(3), so in principle these "classical chromodynamics" should be capable of anything electromagnetism does, but I'm not willing to speculate on further specifics without alcohol.

Wouldn't removing one of the major bases for the underpinnings of all quantum physics change all of physics and not simply drop everything into a classical state(which is just saying the best we can do just playing around with averages).

I would say that it probably would involve the first reaction you mentioned.

So I amend my previous position. This device of yours is what we call an instant naked singularity.

[OmegaGuy]

So, basically, any one of a number of rather unpleasant things would happen.

Thanks, believe it or not, this was actually helpful.

[Surlethe]

So, basically, any one of a number of rather unpleasant things would happen.

Thanks, believe it or not, this was actually helpful.

Your civilization had better be uber-advanced to be playing around with bombs created this way.

[Lancer]

Wouldn't it be drastically simpler to simply throw some antimatter around if you're at the level of technology to fundamentally break physics in such a fashion?

[drachefly]

There's another catch - if something inside the bubble hits the side of the bubble, then its state is abruptly reinterpreted - its position wavefunction is a dirac delta function, so it has infinite momentum in every direction.

[SyntaxVorlon]

There's another catch - if something inside the bubble hits the side of the bubble, then its state is abruptly reinterpreted - its position wavefunction is a dirac delta function, so it has infinite momentum in every direction.

Fuck I hadn't thought of that. Those dirac deltas will bite you in the ass.

[OmegaGuy]

Actually it's for a story I'm writing when an ordinary guy suddenly gets godlike power, and he doesn't really understand how to use it correctly, so he keeps accidentally destroying the universe and such.

[Surlethe]

There's another catch - if something inside the bubble hits the side of the bubble, then its state is abruptly reinterpreted - its position wavefunction is a dirac delta function, so it has infinite momentum in every direction.

So if so much as one particle hits the edge of the bubble, everything outside the bubble gets destroyed?

[Kuroneko]

Wouldn't removing one of the major bases for the underpinnings of all quantum physics change all of physics and not simply drop everything into a classical state(which is just saying the best we can do just playing around with averages).

The position that this whole scenario is physically meaningless, as the 'underpinnings' of physics are removed, is certainly a defensible one, but if we are to make any sort of rationalization of it at all, we would need some way to associate classical systems with quantum ones. Fortunately, quantization already does this for us, albeit in reverse order. Unfortunately, I don't know whether there always exists a unique classical system that generates it (up to physical equivalence; I know this would not be mathematically unique even in the same framework).

There's another catch - if something inside the bubble hits the side of the bubble, then its state is abruptly reinterpreted - its position wavefunction is a dirac delta function, so it has infinite momentum in every direction.

That's true, but it's also misleading, as subsequent comments demonstrate. If the position wavefunction is the dirac delta, then the momentum wavefunction is completely nonlocalized in the momentum space. This can be interpreted as a sum of waves of all momenta, but it's not the same thing as having infinite momentum.

So if so much as one particle hits the edge of the bubble, everything outside the bubble gets destroyed?

Possibly, but at the worst it means that the momenta of the incoming particles would not have a well-defined second moment once they enter the bubble. That's not something that necessarily makes it completly meaningless or infinite; the Cauchy distribution, i.e., the distribution of the ratio of two normal variates, is a good example of that.

[drachefly]

There's another catch - if something inside the bubble hits the side of the bubble, then its state is abruptly reinterpreted - its position wavefunction is a dirac delta function, so it has infinite momentum in every direction.

That's true, but it's also misleading, as subsequent comments demonstrate. If the position wavefunction is the dirac delta, then the momentum wavefunction is completely nonlocalized in the momentum space. This can be interpreted as a sum of waves of all momenta, but it's not the same thing as having infinite momentum.

Okay, not strictly infinite. Wavelength must be more than the planck length. That's awfully big, though.

But it seems that's not the nature of your objection; but I can't figure out what it is. If it's a superposition of all those momentum states, then if you measure the momentum, it's got a chance to have those momenta.

And to get a dirac delta, you need the distribution to be even all the way out to the planck length (components lower than that would clean up the delta function more than makes sense due to granularity of space).

If you take the expectation value of the kinetic energy of this particle, it's going to be huge.

So if so much as one particle hits the edge of the bubble, everything outside the bubble gets destroyed?

No, as soon as one particle hits the edge of the bubble from the inside, it goes flying off at a random momentum selected from the range of physically sensible momenta. While in principle it does radiate outwards in all directions, entanglement with local objects makes it seem like it only went one direction.

Possibly, but at the worst it means that the momenta of the incoming particles would not have a well-defined second moment once they enter the bubble.

The details of how particles would enter depend on implementation details that haven't been given.

[Kuroneko]

Okay, not strictly infinite. Wavelength must be more than the planck length. That's awfully big, though. But it seems that's not the nature of your objection; but I can't figure out what it is.

I'm not actually objecting to anything you've said there; I said it was true. I was simply correcting an apparent misconception that other posters had in interpretating your statement.

If it's a superposition of all those momentum states, then if you measure the momentum, it's got a chance to have those momenta.

Right--that's all it means. Others have apparently taken this to mean that it has infinite momentum, however.

And to get a dirac delta, you need the distribution to be even all the way out to the planck length (components lower than that would clean up the delta function more than makes sense due to granularity of space).

It's not at all clear what role would any such considerations have here, since the system is turns to be explicitly classical.

The details of how particles would enter depend on implementation details that haven't been given.

That statement used nothing more than the assumption that the position wavefunction should become infinitely localized, which is what was talked about, and for its observables to be some value permitted by the wavefunction after its turns classical, which you have also assumed. What's the problem?

[SyntaxVorlon]

The position that this whole scenario is physically meaningless, as the 'underpinnings' of physics are removed, is certainly a defensible one, but if we are to make any sort of rationalization of it at all, we would need some way to associate classical systems with quantum ones. Fortunately, quantization already does this for us, albeit in reverse order. Unfortunately, I don't know whether there always exists a unique classical system that generates it (up to physical equivalence; I know this would not be mathematically unique even in the same framework).

That makes sense.

I think though that under a new quantum system where this is taken into account something should be kept in mind:

o(x)o(p) >= 0 = ( 1/(2i) [xhat, phat]) and that means:

[xhat, phat] = 2i

This means that the momentum or position or both operators are entirely different, meaning that classical physics must be entirely re-imagined because classical mechanics depends on the blurring of QM into the background. And since <x> and <p> form the backbone of the interface between QM and CM, we get a whole new classical mechanics.

It may be possible for a system like this to be created, but it would be excedingly difficult to represent. We would probably lose conservation of energy and momentum in the process, so the effect of edge particles gaining arbitrary momentum is just the tip of the iceburg.

[Kuroneko]

In a classical system, the position and momentum operators would commute, [x,p] = 0. If they did not, the system would not be classical by definition. Perhaps you're thinking of the Poisson bracket.

[drachefly]

And to get a dirac delta, you need the distribution to be even all the way out to the planck length (components lower than that would clean up the delta function more than makes sense due to granularity of space).

It's not at all clear what role would any such considerations have here, since the system is turns to be explicitly classical.

I was talking about outside the bubble, where quantum mechanics persist.

[Master of Cards]

Wouldn't it be drastically simpler to simply throw some antimatter around if you're at the level of technology to fundamentally break physics in such a fashion?

He's talking about a Little Doctor amlost without the speard effect and it works on all matter

[Kuroneko]

I was talking about outside the bubble, where quantum mechanics persist.

And yet you've assumed that this effect is caused by the bubble, i.e., by the whatever dequantization process the bubble represents. I don't disagree with assuming this--on the contrary, some sort of assumption along these lines is necessary for this scenario to have any meaning, and that one is the most reasonable guess unless more detailed information is given. But you simply can't have it both ways by disclaiming any mechanism at all and at the same time making a prediction at how the particle would behave upon encountering the bubble.

[SyntaxVorlon]

In a classical system, the position and momentum operators would commute, [x,p] = 0. If they did not, the system would not be classical by definition. Perhaps you're thinking of the Poisson bracket.

Whoops, you're right I was solving for uncertaintly>=1 not 0. In the case I put up x and p do commute, so you are right. My mistake.

[drachefly]

But you simply can't have it both ways by disclaiming any mechanism at all and at the same time making a prediction at how the particle would behave upon encountering the bubble.

I have not made a prediction for how a particle would behave upon encountering the bubble. I made a prediction for how a particle would behave upon leaving the bubble.

Unless there is some boundary layer on which the particles undergo a smooth transition from one ruleset to another, that provides an initial condition - a dirac delta function - and we know the rules (quantum mechanics).

[Kuroneko]

Ah. My apologies. It does seem to be physically reasonable to have the quantization/dequantization as mirrored processes, but of course it's not a given and not mathematically justifiable. ed-If we allow that sort of generality, it's not then even a given that the particle will have a dirac delta position wavefunction when leaving the bubble either.