Uncertainty Principle in Classical Physics

[albroun]

I have often seen it stated that the Uncertainty Principle (UP) is a unique feature of Quantum Physics, but surely it applies classically too?

For example, if someone throws a ball across a room, and I take a photo with a shutter speed of 1 second, the resultant photo will tell me a lot about the ball's momentum but little about its position at the time the picture was taken. If I increase the shutter speed to 1/1000 second, the photo will tell me a lot about the ball's position at the time the picture was taken, but little about the momentum. So there seems to be a position-momentum uncertainty relation here in the classical world. What is so unique about Quantum Physics in this respect?

I gather that Planck's constant comes in somewhere, but being totally non-mathematical, and no background in physics, I am non the wiser! Perhaps someone can explain to me why the UP is unique to the quantum world - or is it??

 

[G01]

The uncertainty principle is not a statement about the accuracy of our measurement devices. Even in the case where we possesses a measuring device of arbitrary precision, the uncertainty in our measured values of, say, an electrons position and momentum will still be limited by the Heisenberg uncertainty principle.

In other words, we are not prevented from knowing an electrons definite position and momentum because of experimental limitations. Instead, an electron, or any quantum particle, is an object that does not have both a definite position and a definite momentum.

Uncertainty principles appear for wave phenomena, so you do see them in classical physics relating to waves. For instance, when working with modelocked lasers that produce short pulses of laser light, you cannot have a pulse that is both limited in time and limited in frequency. i.e. The shorter your laser pulse, the more frequencies ("colors") it contains. As another example, a similar uncertainty principle appears in signal processing (look up the "Gabor limit").

So, the Heisenberg uncertainty principle is a statement of the wave nature of quantum particles.

 

[jfy4]

I have often seen it stated that the Uncertainty Principle (UP) is a unique feature of Quantum Physics, but surely it applies classically too?

For example, if someone throws a ball across a room, and I take a photo with a shutter speed of 1 second, the resultant photo will tell me a lot about the ball's momentum but little about its position at the time the picture was taken. If I increase the shutter speed to 1/1000 second, the photo will tell me a lot about the ball's position at the time the picture was taken, but little about the momentum. So there seems to be a position-momentum uncertainty relation here in the classical world. What is so unique about Quantum Physics in this respect?

I gather that Planck's constant comes in somewhere, but being totally non-mathematical, and no background in physics, I am non the wiser! Perhaps someone can explain to me why the UP is unique to the quantum world - or is it??

That is an intriguing analogy. The uncertainty principle is related to the effect of measurement (interaction) on the physical dynamical variable being measured. This is the idea that to view an electron's position accurately you would need a high energy photon which would give you a bad measurement of the electron's momentum, while a low energy photon would give you a good measurement of momentum but a high uncertainty of position. While your camera analogy I think is a good idea at perhaps heuristically teaching about the uncertainty principle. the light in the room that arrives at the camera from the ball did very little to disturb the position and momentum of the ball, which is what the uncertainty relation reveals.

See also http://en.wikipedia.org/wiki/Uncertainty_principle" .

 

[albroun]

... we are not prevented from knowing an electrons definite position and momentum because of experimental limitations. Instead, an electron, or any quantum particle, is an object that does not have both a definite position and a definite momentum.

I have seen it argued another way and I think this was suggested by Heisenberg himself. There is a fundamental experimental limitation because the high energy needed to probe quantum phenomena interferes with the measured system - gives a kick to the particles.

At the time Heisenberg was writing, the philosophy of Logical Positivism was very popular. This stated that anything that could not be verified empirically was meaningless. Because, experimentally, a particle's position and momentum could not be simultaneously verified, it was therefore assumed that to say it had a definite position and momentum was meaningless. However, the Logical Positivist underpinning of this support for the UP is highly controversial among philosophers - infact Logical Positivism is widely regarded as self-contradictory because the verification principle cannot itself be verified.

So is there a sense in which a quantum particle not having both a definite position and a definite momentum, can still stand independently of the rather questionable philosophical foundation of Logical Postivism?

And secondly is there any sense in which the UP is unique to quantum systems, or does the UP actually apply to any system - such as my example of photographing a ball in motion?

 

[Matterwave]

Heisenberg originally thought about what his principle meant through the mechanism that you describe. However that thought process is a little antiquated and does not lead to the actual derivation of his principle. The HUP is derived from essentially wave mechanics.

The HUP actually says that if you prepared many systems identically (say, 2000), and you measured the position of half the systems (1000 of them) and the momentums of the other half of the systems (the other 1000), you would get a standard deviation in your measurements for position and momentum that, when multiplied together, is greater than hbar/2 no matter how accurate each individual measurement was.

Note that this statement is now subject to the law of large numbers, though. You could "by luck" get the product of the standard deviations to be lower than hbar/2 (e.g. if you only had prepared 4 systems), but as the number of trials increase, the closer you get to the real standard deviation.

 

[albroun]

... you would get a standard deviation in your measurements for position and momentum that, when multiplied together, is greater than hbar/2

Sorry - for the mathematically ignorant, is there a way of expressing what the above means in practical / real terms or by way of an analogy?

 

[Matterwave]

Well, when you make many many measurements of position (of identically prepared particles), and you plot those measurements on a histogram (a graph where you plot the number of measurements you got to within some bin, you can look it up on wikipedia if you don't know what it is), you will see that that histogram has some width to it (not EVERY measurement is within the same bin - at least not if you use reasonably sized bins). You do the same for momentum and you will see again that there is some width to it. The standard deviation is a measurement of this "width". If you multiply the two "widths" together, you will get a number that is greater than hbar/2.

 

[G01]

So is there a sense in which a quantum particle not having both a definite position and a definite momentum, can still stand independently of the rather questionable philosophical foundation of Logical Postivism?

I don't know enough about Logical Positivism to effectively comment on the issue.

I gave examples above of classical wave phenomena that exhibit uncertainty principles. Can the explanation of these phenomena stand independently of logical positivism? I think so. So, what's the problem with quantum systems that have a wave nature also obeying uncertainty principles?

And secondly is there any sense in which the UP is unique to quantum systems, or does the UP actually apply to any system - such as my example of photographing a ball in motion?

Heisenberg Uncertainty does not apply to your ball-camera system. Decoherence effects have washed out all quantum effects at this large scale.

 

[albroun]

There seem to be two kinds of uncertainty - epistemological (what we can know about something) and ontological (what is intrinsically so regardless of what we can know about it). Logical Positivism states that the two are the same - that anything unverifiable empirically is intrinsically meaningless and therefore cannot exist. (This is also related to the idea that an observer must be involved for something to exist).

The issue in physics seems to be - are quantum phenomena ontologically indeterminate (intrinsically so) or merely epistemologically indeterminable (not inherently uncertain, just that we can never know)?

 

[Matterwave]

That question is a philosophical one which depends on the certain interpretation of QM. However, Heisenberg's Uncertainty principle is NOT the limit created by measurement techniques.

 

[ThomasT]

albroun, the salient feature of the Heisenberg uncertainty relations is the assumption of the existence of a fundamental and irreducible quantum of action (usually expressed in joule.seconds). The quantum uncertainty relations are thus different from classical uncertainty relations in that the limiting quantity, Planck's Constant, h, is assumed to be an unalterable fact of nature, and not merely a current limitation on measurement accuracy.

That's all there is to it. Wrt quantum phenomena, the product of the statistical spreads, the deltas, of large numbers of two thusly related measurements such as position and momentum is presumably limited by an absolute of nature, whereas wrt thusly related classical or macroscopic measurements the limiting quantity is determined by the capabilities of the measuring instruments.

Now, does the fundamental quantum hypothesis imply that nature is evolving indeterminately? Or that there are entities that we refer to as electrons, photons, etc. propagating between emitters and detectors about which we can say, independent of instrumental behavior, that these entities have no definite positions and momenta? If so, then what exactly does that mean?

 

[Suwailem]

I appreciate the helpful discussions in this forum. I am only a hobbyist, but it seems that we can still have a kind of uncertainty at the classical level if we look at entropy. This uncertainty is related to time and energy. As I understand it, it states (roughly) that the higher the precision of energy, the less precise we are on the time it takes to reach that energy level.

If higher precision means that particles or components of a macro-system are organized in a very specific way, then we know that, left to its own, it might take the system a longer time to reach this specific configuration, and hence we will be less precise on the exact time needed. By definition, the more a configuration is precisely described, the less likely the system by random movements, may reach that configuration. So there seems to be a trade-off between time and energy at the classical level, which might be analogous to that of the time-energy trade-off at the quantum level.

This might be a silly idea, but it looks to me, as a layman, somehow intuitive.