Observation Techniques: Brian Green's NOVA Show & Quantum Physics

[elassoto]

After watching Brian Green's show on NOVA last night. I was left with a big question that one of you may be able to answer.

Brian ended the show by saying that one of the biggest problems that physicists were trying to answer these day is why quantum physics works at a very small scale, but the rules don't seem to apply at a normal or macro scale.

This leads me to believe that there is a problem with how they are measuring quantum mechanics. That is, when they are measuring at a very small scale they are increasing the probablistic nature of quantum mechanics. The are in fact reducing time and space to such a small aperture, that they are losing accuracy, and therefore increasing the probablistic nature of the measurement.

It seems like there needs to be more dimensionality to their measurement to decrease the probablistic nature of what they are seeing. This dimensionality can be either space or time. IE, measurement over time, or measurement over space (movement?).

Does anyone have any input on this?

 

[cbetanco]

No, the probabalistic nature of quantum mechanics is not a problem with our measurements, its a direct result of the theory. The reason we can't measure, say, both the momentum and position of a particle is not because our instruments are not sensitive enough, but because the position operator [itex]X[/itex] and the momentum operator [itex]P[/itex] satisfy the following commutation relation [itex][X,P]=XP-PX=i\hbar[/itex], which just means you cannot find a basis in which both operators are simultaneously diagonal. Also, another postulate of the theory is that if the state of the system is [itex]\psi[/itex], and you wish to measure some observable value, let's say the energy E, then the possible values you can measure would be [itex]E_1, E_2, E_3, ...[/itex] with probability [itex]<\psi_{E_1}∣\psi>[/itex]², [itex]<\psi_{E_2}∣\psi>[/itex] ², [itex]< \psi_{E_3} ∣ \psi >[/itex] ², ... respectively, where [itex]\psi_{E_N}[/itex] is the Nth eigenvector of the operator representing the things you wish to measure. So the probability comes from the theory, not our ability to measure things

 

[elassoto]

Thank you for that excellent answer.

 

[Zarqon]

No, the probabalistic nature of quantum mechanics is not a problem with our measurements, its a direct result of the theory. The reason we can't measure, say, both the momentum and position of a particle is not because our instruments are not sensitive enough, but because the position operator [itex]X[/itex] and the momentum operator [itex]P[/itex] satisfy the following commutation relation [itex][X,P]=XP-PX=i\hbar[/itex], which just means you cannot find a basis in which both operators are simultaneously diagonal. Also, another postulate of the theory is that if the state of the system is [itex]\psi[/itex], and you wish to measure some observable value, let's say the energy E, then the possible values you can measure would be [itex]E_1, E_2, E_3, ...[/itex] with probability [itex]<\psi_{E_1}∣\psi>[/itex]², [itex]<\psi_{E_2}∣\psi>[/itex] ², [itex]< \psi_{E_3} ∣ \psi >[/itex] ², ... respectively, where [itex]\psi_{E_N}[/itex] is the Nth eigenvector of the operator representing the things you wish to measure. So the probability comes from the theory, not our ability to measure things

Even though I agree with your main point, I just want to say that you should be careful about saying that an experimental outcome is a "direct result of the theory", because a theory is just a description of reality, it cannot be the cause of anything!

For example, the measurement postulate is just that, a postulate, that is formulated because we have observed experiments that could otherwise not be explained. Since it itself is a direct consequence of measurements, it would be a circular reasoning to say that it's causing or explaining experimental outcomes.

What the theory does allow us to do however, is to "purify" the experimental results by finding common ground explanations for a large set of experiments performed on different systems, using different equipment. Since all these experiments yield similar results, we draw the conclusion that the quantum effects do not arise from our equipment, or any limitations on them, but from nature itself.

 

[cbetanco]

I completely agree with you, Zarqon. Of course our formulation of quantum mechanics arose out of the need to explain certain experimental results. But I think elassoto was worried that all of our uncertainties in QM might be just a result of our poor measuring apparatus. What I was trying to drive home was that even if you had a perfect measuring device, and could take an ideal measurement without any added uncertainties coming from the measurement procedure, the theory of QM still is inherently probabilistic, and also predicts that certain observables (like momentum and position) cannot be known simultaneously with exact certainty.

I would have to say it would be pretty amazing if we developed QM before we ever had any experimental observations that something was wrong classical mechanics. So of course the postulates of the theory are based on measurements, but now that we have the theory, it can predict future measurements, and the predictions are inherently probabilistic.