Is the Heisenberg Uncertainty Principle a result of measurement inadequacies?

[DesertFox]

TL;DR Summary

What is the evidence for the claim "The Heisenberg Uncertainty Principle is not a result of inadequacies in the measuring instruments/technique"?

Quantum mechanics is the most successful theory in physics nowadays. The property of non-commuting operators results in a general uncertainty principle of which the Heisenberg Uncertainty Principle is a special case. Non-commuting quantities happily account for things like the two-slits experiment and the Heisenberg Uncertainty Principle pops out of the theory as natural consequence.

Also, the Heisenberg Uncertainty Principle can be considered as a mathematical conclusion, which emerges from the physical hypothesis of Hilbert space and operators on it. So, of course, no measurement is taken in the mathematical derivation of the the Heisenberg Uncertainty Principle.

That being said, what is the evidence for the claim "The Heisenberg Uncertainty Principle is not a result of inadequacies in the measuring instruments/technique"?

Or, is it merely a (well-argued) conjecture (taken for granted: 1) the axioms of quantum mechanics and 2) the fact that quantum mechanics is the most successful theory in physics nowadays and nobody has falsified it)?

 

[Motore]

Wikipedia:

Historically, the uncertainty principle has been confused[8][9] with a related effect in physics, called the observer effect, which notes that measurements of certain systems cannot be made without affecting the system, that is, without changing something in a system. Heisenberg utilized such an observer effect at the quantum level (see below) as a physical "explanation" of quantum uncertainty.[10] It has since become clearer, however, that the uncertainty principle is inherent in the properties of all wave-like systems,[11] and that it arises in quantum mechanics simply due to the matter wave nature of all quantum objects. Thus, the uncertainty principle actually states a fundamental property of quantum systems and is not a statement about the observational success of current technology.[12]

So the HUP has nothing to do with measurements.

Have a look at this video:

 

[DesertFox]

Wikipedia:

So the HUP has nothing to do with measurements.

Have a look at this video:

I have read the wikipedia article. And I have already watched the video.

Nobody questions the the following claim: "Thus, the uncertainty principle actually states a fundamental property of quantum systems and is not a statement about the observational success of current technology".

Now, the question is: what is the evidence for the claim "The Heisenberg Uncertainty Principle is not a result of inadequacies in the measuring instruments/technique"? Is it merely a (well-argued) conjecture (taken for granted: 1) the axioms of quantum mechanics and 2) the fact that quantum mechanics is the most successful theory in physics nowadays and nobody has falsified it)?

 

[vanhees71]

It is always good to keep in mind that the quantum state is a description of the result of a "preparation procedure", i.e., it describes the statistical properties of the outcome of measurements on the system when prepared in this state. The Heisenberg uncertainty principle for position and momentum of a particle, $\Delta x \Delta p \geq \hbar/2$ thus says nothing about the accuracy of measuring momenta or positions but it tells you that if you prepare the particle with a pretty accurately defied position, then its momentum is necessarily pretty large and vice versa.

That's also very intuitive: The preparation of the particle has nothing to do with the accuracy of a measurement, which is a property of the measurement device and not the system measured.

Another more complicated issue is the unavoidable perturbation of a system by measurement, which follows directly from the "atomistic structure" of matter. E.g., if you want to measure the electric field of a static macroscopic charge distribution you can use the concept of test charge, i.e., you can make the test charge much smaller than the charge making the electric field, such that you can neglect the perturbation of the field due to using a this test charge to measure it. If, however, you try to measure the electrostatic field of a single electron, that's not possible anymore, because your test charge also must be at least one elementary charge, i.e., as large as the electron's charge.

This is, however, not described by the standard uncertainty relation between observables but is a much more complicated issue.

 

[DesertFox]

It is always good to keep in mind that the quantum state is a description of the result of a "preparation procedure", i.e., it describes the statistical properties of the outcome of measurements on the system when prepared in this state. The Heisenberg uncertainty principle for position and momentum of a particle, $\Delta x \Delta p \geq \hbar/2$ thus says nothing about the accuracy of measuring momenta or positions but it tells you that if you prepare the particle with a pretty accurately defied position, then its momentum is necessarily pretty large and vice versa.

That's also very intuitive: The preparation of the particle has nothing to do with the accuracy of a measurement, which is a property of the measurement device and not the system measured.

Another more complicated issue is the unavoidable perturbation of a system by measurement, which follows directly from the "atomistic structure" of matter. E.g., if you want to measure the electric field of a static macroscopic charge distribution you can use the concept of test charge, i.e., you can make the test charge much smaller than the charge making the electric field, such that you can neglect the perturbation of the field due to using a this test charge to measure it. If, however, you try to measure the electrostatic field of a single electron, that's not possible anymore, because your test charge also must be at least one elementary charge, i.e., as large as the electron's charge.

This is, however, not described by the standard uncertainty relation between observables but is a much more complicated issue.

The undisputed facts that 1) the HUP says nothing about the accuracy of measuring and 2) the preparation has nothing to do with the measurement accuracy are not an evidence for the claim "The Heisenberg Uncertainty Principle is not a result of inadequacies in the measuring instruments/technique", neither are evidence for the opposite claim. So, the question remains untouched.

 

[Motore]

[Mentors' note: A possibly irrelevant link to a stack exchange dscussion has been removed]

As the HUP has nothing to do with measurements (at least is not defined with observables) the claim itself doesn't make much sense.
What more is there to say?

 

[DesertFox]

[Mentors' note: A possibly irrelevant link to a stack exchange dscussion has been removed]

As the HUP has nothing to do with measurements (at least is not defined with observables) the claim itself doesn't make much sense.
What more is there to say?

What makes/does not make sense (to you) is completely irrelevant to the question. It is not even clear what you mean by "to make much sense".

Here it is a statement: "Even with perfect instruments and technique, the uncertainty is inherent in the nature of things". Source: http://hyperphysics.phy-astr.gsu.edu/hbase/uncer.html

Nobody claims that the statement is incorrect.

However, the question is: How do we know that? What is the evidence for the claim "The Heisenberg Uncertainty Principle is not a result of inadequacies in the measuring instruments/technique"?

Or, is it merely a (well-argued) conjecture (taken for granted: 1) the axioms of quantum mechanics and 2) the fact that quantum mechanics is the most successful theory in physics nowadays and nobody has falsified it)?

 

[vanhees71]

As I wrote above, it's evident from pure logics that the uncertainty relations have nothing to do with the precision of measurements but with the possibility of which states you can prepare. For the space-momentum uncertainty relation it simply says that if you have the particle localized in a small region of space, the momentum is quite undetermined. If to the contrary you prepare a particle with a very precisely determined momentum, it's not well localized.

However, there is no fundamental limit on the accuracy to measure either the position or momentum of a particle, no matter in which state it has been prepared for the measurement.

That's indeed just a logical consequence of the standard postulates and the minimal interpretation (i.e., the interpretation which makes statements about the physics only).

 

[Nugatory]

That being said, what is the evidence for the claim "The Heisenberg Uncertainty Principle is not a result of inadequacies in the measuring instruments/technique"?

We look at the derivation of the uncertainty principle and see that the inadequacy doesn't enter into that derivation.

This fact is sufficient to establish the truth of the proposition "The HUP is not a result of inadequacies in measuring instruments". (Of course that proposition can be true even if the quantum mechanics upon which its derivation is based is not correct - but in the absence of any remotely plausible alternative theory there is little point in spending time on that possibility).

 

[DesertFox]

We look at the derivation of the uncertainty principle and see that the inadequacy doesn't enter into that derivation.

No measurement is taken in the mathematical derivation of the the Heisenberg Uncertainty Principle. However, that does not necessarily infers the conclusion "The HUP is not a result of inadequacies in measuring instruments".

There is an equally valid logical possibility that (even if no measurement is taken in the mathematical derivation of the the HUP) the HUP nevertheless is result of the measurement inadequacies.

but in the absence of any remotely plausible alternative theory there is little point in spending time on that possibility).

That is a sort of "absence of evidence is evidence of absence" line of thought, which is not pretty convincing.

 

[DesertFox]

That's indeed just a logical consequence of the standard postulates

That is just a logical possibility from the standard posturates.

As you already pointed out, the Heisenberg Uncertainty Principle says nothing about the accuracy of measuring. However, that does not inevitably necessitate the claim "the uncertainty relations have nothing to do with the precision of measurements".

IN SUMMA: Pure logics cannot be "evidence" for the claim "The Heisenberg Uncertainty Principle is not a result of inadequacies in the measuring instruments/technique".

So, what is the evidence for that claim? Or, is it merely a (well-argued) conjecture (taken for granted: 1) the axioms of quantum mechanics and 2) the fact that quantum mechanics is the most successful theory in physics nowadays and nobody has falsified it)?

 

[Nugatory]

No measurement is taken in the mathematical derivation of the the Heisenberg Uncertainty Principle. However, that does not necessarily infers the conclusion "The HUP is not a result of inadequacies in measuring instruments".

The HUP is a mathematical theorem derived from mathematical axioms. That mathematical derivation is the only argument for its correctness - if measurement inadequacy does not enter into that derivation there is no way in which it can be involved.

That is a sort of "absence of evidence is evidence of absence" line of thought, which is not pretty convincing.

Well, that’s how empirical science works. I find the proposition “there is not a five-ton bull elephant in my kitchen pantry” to be quite convincing even though it is supported only by the absence of evidence.

 

[berkeman]

Thread closed temporarily for Moderation...

 

[Doc Al]

IN SUMMA: This thread will remain closed.