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The statement "Uncertainty principle is valid for macroscopic objects" is (empirically) unfalsifiable: no macroscopic measurement is going to detect.

Yet, the majority of scientists insist that UP is valid at macroscopic level...

Qmechanic
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Pavel Borisov
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2 Answers2

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I agree with the general premise of your argument; it is unprovable by today's standards. However, saying "empirically unfalsifiable" is false in my opinion. This is because with the development of more sophisticated technology, the accuracy of the instruments would increase. Eventually, we could have advanced enough technology to measure these differences, so it's difficult to generalise like this.

Additionally, scientists insist on this because theoretically it is true, and so there is no reason to doubt such a statement.

Umar10A
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  • So, these scientists stick to a sort of "Absence of evidence is not evidence of absence" line of thought... – Pavel Borisov Jul 17 '22 at 10:32
  • Not really. Their arguments aren't arbitrary, they're based on theoretical facts. For example, we haven't lived for billions of years, but we know for a fact that the universe's age is ~14 billion years. We know it, and not just assume it, because of the overwhelming evidence, and not just due to a lack of a better explanation. – Umar10A Jul 17 '22 at 10:39
  • We don't have "overwhelming evidence" for the single statement "UP is valid at microscopic level". The overwhelming evidence is about quantum theory as a whole... So, in my opinion, the universe-age-analogy is not relevant here... – Pavel Borisov Jul 17 '22 at 10:50
  • Also, trying to establish the UP for, lets say, a car would require defining and monitoring the precise set of particles that constitute the car to a level of detail that even theoretically may make no sense. It's not a time-independent set of particles the way a specific molecule is. That seems to me to be more than a technical challenge and definetely more than incapabality of today's standards. – Pavel Borisov Jul 17 '22 at 10:53
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    To be honest, I think in the case of a car, you can measure its momentum (mass and velocity) pretty accurately, and so the uncertainty in its position would simply be: ℏ/(2*p), and thus be very, very small. I don't understand why you think we need to analyse all of its individual particles... – Umar10A Jul 17 '22 at 11:09
  • If we are to establish (not just roughly approximate "for all practical purposes") UP for a car, we have to analyse all of the particles. – Pavel Borisov Jul 17 '22 at 11:34
  • I think approximating the car to its center of mass (as we usually do) is what we would do in this case. – Umar10A Jul 21 '22 at 07:42
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The uncertainty principle at the quantum level

In its most basic form, the uncertainty principle states that you cannot simultaneously determine the position and momentum of a particle with arbitrarily high precision.

You state:

The statement "Uncertainty principle is valid for macroscopic objects" is (empirically) unfalsifiable:

Because it is the algebraic results from the definition above applied to a macroscopic object,

Take any object larger than the dimensions commensurate to h_bar.

The position and momentum of any imaginable moving car will be represented by its center of mass point, and if you go to the trouble to measure them you will see that the instrumental errors are huge with respect to the quantum mechanical uncertainty of delta(x)delta(p).

The HUP is a principle , principles are extra axioms imposed on theories, this to the quantum mechanics theory, to connect observations and measurements and have good predictions. After the theory of quantum mechanics became the mainstream one, the HUP can be derived from the theory as it is now.

So what is there to falsify?

anna v
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  • Does the HUP apply to a car at rest? Lets consider a car left at the parking lot. We know the position of the car... But what about the velocity (momentum)? Any elaborations on the question... I wil be very thankful! – Pavel Borisov Jul 17 '22 at 17:13
  • "The HUP is a principle , principles are extra axioms imposed on theories, this to the quantum mechanics theory". I don't understand what you mean by "extra" axiom; there is not such concept in modern logics. If we consider the HUP as an axiom, there's nothing to falsify, of course. However, such logical manuever creates space for a LOT of interpretation problems. I am not sure if we can undisputedly regard HUP as an axiom. It's highly problematic. To put it mildly. – Pavel Borisov Jul 17 '22 at 17:53
  • @PavelBorisov see my answers here https://physics.stackexchange.com/questions/352511/why-do-the-laws-of-quantum-mechanics-not-allow-to-put-a-pile-of-fermions-all-at/352529#352529 , https://physics.stackexchange.com/questions/678476/the-underlying-cause-of-the-heisenberg-uncertainty-theory/678527#678527 , https://physics.stackexchange.com/questions/439193/where-does-the-principle-of-equal-a-priori-probabilities-come-from-in-statistica/439208#439208 ,https://physics.stackexchange.com/questions/113092/why-does-a-system-try-to-minimize-potential-energy/113095#113095 – anna v Jul 17 '22 at 18:13
  • As I say the axiomatic supposition of the HUP was valid before quantum mechanics became a theory. Now the HUP can be derived using quantum mechanics. – anna v Jul 17 '22 at 18:14
  • "Now the HUP can be derived using quantum mechanics." That's my point. Technically, UP can be derived within quantum theory. However, "the HUP is valid for macroscopic objects" is an unfalsifiable statement par excellence. – Pavel Borisov Jul 17 '22 at 18:22