Heisenberg's Uncertainty Principle: Exploring Possibilities

[smithnya]

Hello everyone. This is my first post, but I enjoy reading all the forums.

I have a simple question that I thought about recently:
Would Heisenberg's Uncertainty Principle still hold up if we could somehow observe a particle without the aid of instruments? I know it is entirely hypothetical, and more of a little fun thought experiment to muse over, and I just needed your opinion. Thanks in advance.

 

[gamma5772]

In the orthodox interpretation of quantum mechanics, the answer is yes, the uncertainty principle will still hold. The uncertainty principle is a statement that the wavefunction of a particle cannot be simultaneously localized in both position and momentum -- this has nothing to do with measurements. (Strictly speaking, we have made assumptions about what it means to measure something without an instrument...)

Put more coarsely -- and in fact, incorrect in some unimportant details -- a function cannot simultaneously be $e^{ikx}$ (state of definite momentum) and a delta function (state of definite position).

There do, however, exist interpretations of quantum mechanics in which particles have definite position and momentum, such as Bohmian mechanics. Somewhat counter-intuitively, Bohmian mechanics and the orthodox interpretation give identical predictions for experiments.

Maybe the best conclusion to draw is that the question doesn't really make sense.

 

[davidj89]

well how do you define an instrument? Your eyes sure are, which see photons bouncing off of things (such as particles) and thus effect the particles. I think the idea of "observing" something without any kind of instrument would be an interesting problem.

 

[smithnya]

well how do you define an instrument? Your eyes sure are, which see photons bouncing off of things (such as particles) and thus effect the particles. I think the idea of "observing" something without any kind of instrument would be an interesting problem.

I see what you mean. I never thought about it that way, but I still wonder if the uncertainty principle is tied to our limitations to observe and if that could change in time and with more advanced instrumentation. Although I can't imagine how/

 

[gamma5772]

The uncertainty principle is NOT tied to our abilities to observe.

The uncertainty principle is
$$\sigma_x \sigma_p \geq \hbar / 2.$$
What this says is if you have an bunch of identically prepared states of a particle, and you go through and measure the momentum of half of them, and the position of the other half, you will get a distribution for both quantities. Even if your measuring device is perfect, you will still get distributions -- granted, you will know the distribution very well, but you won't change it's shape.

$\sigma_x$ is the standard deviation of the distribution in position and $\sigma_p$ is the standard deviation of the distribution in momentum. Thus, the uncertainty principle implies that both distributions cannot be arbitrarily sharply peaked -- if one is sharply peaked, the other must be broad. Of course it is possible that both are broad because it is an inequality rather than an equality.

This much is experimentally verifiable, and hence doesn't depend on the interpretation of quantum mechanics. The orthodox interpretation of quantum mechanics, in fact, asserts that a particle does not even have definite position and momentum. The Bohmian interpretation of quantum mechanics, on the other hand, DOES assert that particles have definite position and momentum. Both interpretations give rise to the same predictions about the outcomes of experiments. Therefore, whether or not a particle has a definite position and momentum that "god" could measure is not an experimental question.

Finally, it is worth noting that the uncertainty relation is not a postulate of quantum mechanics -- it is derived from the postulates of quantum mechanics. Hence, it's not really coherent to ask "What if we could change the uncertainty relation?" because to change the uncertainty relation, you'd have to throw out quantum mechanics.

 

[Mannix99]

Orthodox QM is all about measuring. Therefore your question doesn't have any sense in the framework of the Copenhagen interpretation. It doesn't recognize the existence of proprieties such as the momentum or the position that exist independently (it's an interpretation that is not realist). In other words, in the orthodox QM your particle doesn't exist, it's momentum doesn't exist, unless it's being measured. The measure create the particle, the position, the spin, the momentum, etc...

 

[smithnya]

Thank you. I understand a bit more now. I always thought that that the uncertainty principle was tied to our ability to observe or to our technological limitations, but your post helped me understand.

 

[DrChinese]

Thank you. I understand a bit more now. I always thought that that the uncertainty principle was tied to our ability to observe or to our technological limitations, but your post helped me understand.

Welcome to PhysicsForums, smithnya!

These examples may help to see what you are understanding.

1. Commuting observables on any particle are NOT limited by the principle. An example would be momentum and spin. So it must not be the measurement itself that leads to the limitation.

2. A pair of entangled particles (say electrons called Alice and Bob) will obey the uncertainty principle. If you measure the x spin on Alice and the y spin on Bob (which are non-commuting and therefore subject to the principle), you do not know the y spin on Alice and x spin on Bob - these will be completely uncertain. So even though you have 2 particles which can each yield information about the other, you cannot beat the principle by learning some from each of the particles.

 

[Naty1]

Here is an interesting, brief and understandable physical interpretation of wave uncertainty, thanks to Louis DeBroglie:

http://en.wikipedia.org/wiki/Heisenberg_uncertainty_principle#Matter_wave_interpretation

("compression" and "sine waves added together" mentioned in the Wiki discussion, which locate a particle is constructive wave inteference; elswhere the particle waves intefere destructively...they largely cancel...that's everywhere else the particle is not...)