Impact of quantum effects on macro scale objects

[kibler]

Not long ago I was arguing with someone on the Internet (where everyone is wrong) about impact of quantum effects on macro scale objects.

Imagine ice-hockey table (one with almost no friction) with number of pucks on it. If you'll hit one of them it is safe to say that pucks' paths are very hard (if not impossible) to predict for long time because of very unfavorable propagation of errors.

Is it reasonable to claim that Heisenberg's principle is responsible for this prediction being impossible? Fact that position does not commute with momentum makes it impossible to know initial conditions with infinite precision. It implies that you can't predict whole process.

On the contrary I was taught that this principle has no sense when object sizes are orders of magnitude bigger that Planck's length (and hockey pucks surely are). I believe that in macro scale micro- effects average out to zero, and Newton equations are sufficient to describe any situation.

So, what do you think (know) about it?

 

[Disinterred]

Well it would seem that the Heisenberg principle does limit us if infinite precision of every particle path is what you are after. But nothing in physics has ever been predicted/measured to infinite precision.

That being said, on the macro scale the puck's position and velocity can be known at every instant with great accuracy( but not to infinite precision of course). It would be rather hard to analyze, but overall it would come down to collision analysis of 3D approximately cylindrical objects. That is my two cents.

 

[94JZA80]

Imagine ice-hockey table (one with almost no friction) with number of pucks on it. If you'll hit one of them it is safe to say that pucks' paths are very hard (if not impossible) to predict for long time because of very unfavorable propagation of errors.

the short answer is no, it is not the Uncertainty Principle at work here. while it may at first seem impossible to track the motions of several different pucks with any sort of accuracy, it most certainly can be done...especially with computer simulation. take the Milkyway@Home distributed computing project for instance - it simulates the motions of billions of particles (simulated stars mostly) affected by gravity and other influences to try and solve how our spiral galaxy came into existence and how it continues to exist today. if computer simulation can handle something that intense, then it can certainly handle simulating a hockey table full of pucks in motion.

there isn't anything on the macroscopic scale in this universe whose position and/or velocity we can't constantly monitor or measure simultaneously, provided it is within observing range. while its constituent subatomic particles' positions and velocities are described by a probability distribution, the puck itself is not. we can always see it - therefore we can always measure both its position and its velocity. the Uncertainty Principle is reserved for particles whose positions and velocities are described by probability distributions.

i agree with Disinterred's points.

 

[kibler]

And what about environment pucks are surrounded by (I'm talking here about real-life situation, so it would be air)? It is well described by fluid mechanics, but it is only macroscale approximation of low-level processes. Is it possible that "random" effects in gas pressure distribution would make it impossible to predict evolution of the pucks' positions?

Still, I'm not sure if these considerations have any sense, since it's impossible to measure initial position with infinite precision, so chaotic process will always diverge from predicted path...

 

[94JZA80]

And what about environment pucks are surrounded by (I'm talking here about real-life situation, so it would be air)? It is well described by fluid mechanics, but it is only macroscale approximation of low-level processes. Is it possible that "random" effects in gas pressure distribution would make it impossible to predict evolution of the pucks' positions?

Still, I'm not sure if these considerations have any sense, since it's impossible to measure initial position with infinite precision, so chaotic process will always diverge from predicted path...

i wouldn't say that adding another parameter to the experiment (such as the impact of the surrounding air) would make it impossible to predict the evolution of the pucks' paths. it would just make the simulation more complex. as Disinterred said previously, even on the macroscopic scale we can't measure these things with infinite precision, but that doesn't mean we can't take measurements with enough precision to give us a "good enough" approximation and call it a day. for instance, applications like machining combustion engine internals or lithography techniques used to etch transistors onto a silicon wafer (manufacturing CPUs) require very high precision. if we're able to make combustion engines and CPUs work properly despite the fact that we cannot manufacture parts with infinite precision, it stands to reason that our approximations of the current and future positions & velocities of all those hockey pucks are accurate enough to say with confidence that "puck #1 is here now, will be there in approx. 1 second, and will be moving with velocity v," and so on and so forth. sure, those values may not be infinitely accurate, but they describe the positions and velocities of those pucks with enough precision for real world application.

 

[Cleonis]

Imagine ice-hockey table (one with almost no friction) with number of pucks on it. If you'll hit one of them it is safe to say that pucks' paths are very hard (if not impossible) to predict for long time because of very unfavorable propagation of errors.

Is it reasonable to claim that Heisenberg's principle is responsible for this prediction being impossible?

Rephrasing the question:
If it would be possible to have a universe that is just classical physics, would it be possible to predict into the future indefinitely?

I think not. I think that in a purely classical universe there can be knife-edge situations. With knife-edge situations occurring from time to time I think infinite prediction is not possible.

The more precise current velocity and position are known, the longer the span of reliable prediction. Knife-edge situations shorten the span of prediction. In a classical universe you can keep pressing for more accurate knowledge of current velocity and position, increasing the span of prediction, but I don't think the problem of knife-edge situations occurring can be overcome completely.

 

[TopherC]

I think you're asking an interesting question!

Most physical scenarios, including motion of many pucks on a small ice hockey field like you're describing, are essentially non-linear and chaotic. So, as you said earlier, uncertainties at one point in time grow larger for predicting positions (and momenta) at future times. If it's a chaotic system, which this is, then all uncertainties grow at an approximately exponential rate as the system evolves. I say "approximately" here since there are several "knife's edge" kind of moments possible, so nearly-identical starting positions will diverge in their trajectories in an erratic, jumpy way. But still these differences in configuration space will tend to grow in a way that is recognizably exponential, most of the time, provided you start with small enough of a difference.

So even from a purely classical point of view, *any* limits of knowledge of the system will severely limit how long you can predict future motion.

As you pointed out, quantum mechanics can introduce fundamental uncertainties. One way is by the uncertainty principle, and another might be quantized and random interactions with air molecules, and the short-range interactions between the pucks. So you could ask the question: How long would it take on a frictionless table for these various fundamental QM uncertainties (pick one or two) to manifest themselves in a macroscopic way? The answer may be a very long time, such that no actual physical setup could have so little friction (and high restitution) to allow pucks to bounce around that long. Or perhaps it's a shorter time. I'd bet on the former, but I'm curious even so.

One might answer this by modeling the system, watching it from some starting points, and computing the differences in phase space over time. Fit these to an exponential and you'll have a Lyapunov exponent. This, divided by QM uncertainties expressed in that same phase space, will give the answer to "how long?"

This also might make a good (but difficult) Fermi problem! I've never seen anyone estimate a Lyapunov exponent by pure dimensional analysis. I wonder how close one could get?

 

[BruceW]

There's two issues with calculating the eventual position of the puck:
First is in classical physics, there is the issue of 'chaotic' dynamics. This is not so much of a problem here, but it is a problem, for example, when calculating the paths of two water molecules in a river. In the case of a puck, if the momentum has a particular error, then the error in the position of the puck at some later time will increase with time, because the puck is moving further and further from the estimated path.
Secondly, there's Heisenberg's uncertainty principle. So this says that you cannot predict both the momentum and position of a quantum particle exactly.
BUT the issue is about whether the puck can be considered a quantum particle.
This is a controversial issue.