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The question may seem stupid but I have heard from doubtful sources that the Heisenberg uncertainty principle results from the observer effect. I don't understand however how this works and i'm now confused on the semantics of both terms and if they have any links between them.

From my understanding the uncertainty principle comes from the wave nature of particles which limits the precision we can have between position and movement.

And the observer effect was the collapse of the probability wave function of a particle when it is observed to appear like a particle.

EDIT : Is Heisenberg's uncertainty principle due to the wave function collapse ?

mael Delaunay
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  • So the observer effect was Heisenberg’s interpretation of the uncertainty principle, but it’s more fundamental than that. It’s actually a result of Fourier transforms. I’d start by studying those. :) – moboDawn_φ Jan 14 '22 at 19:40
  • @moboDawn_φ Thanks for the answer, I think I understand how for any wave there is a similar property for a more imaged example precision between the frequency and position in time of sound, but when i was told about this link i think was that the act of observing the postion would change its state making the speed "less" measurable. However how i understand it the act of observing doesn't change anything for the position and movement and this uncertainty comes from the wave function itself. Pls correct me if i'm wrong – mael Delaunay Jan 14 '22 at 19:48
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    @moboDawn_φ The Fourier transform is a good way to understand the uncertainty principle in some cases, but not all. Consider a spin 1/2 system. There's uncertainty between various axes of the spin, but there's no Fourier transform in sight there. – DanielSank Jan 14 '22 at 19:49
  • @maelDelaunay In the end, what you're probably going to find out is that the "observer effect" and "intrinsic uncertainty in the wave function" are intimately related concepts and that one cannot really exist without the other. – DanielSank Jan 14 '22 at 19:50
  • @DanielSank "are intimately related concepts and that one cannot really exist without the other" I'd greatly appreciate if you could develop or give any direction to further understand or answer my question. – mael Delaunay Jan 14 '22 at 19:54
  • Bounded systems obey the uncertainty principle and only allow certain values for their energy states, typically discrete states. If measurement were the cause, you'd get a range of measurements outside the discrete spectrum. – R. Romero Jan 15 '22 at 07:07

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The "observer effect" as you put it can be thought of as the plain fact that in Quantum Mechanics observations do not commute. This is a physical fact that has many different interpretations (Copenhagen, Many Worlds, etc.) but it is a starting point for our Theory of Quantum Mechanics.

So before any discussion of waves, Fourier Transforms or even physical situations let us consider observations in Quantum Mechanics generally by some operators that do not necessarily commute. That is to say $[A,B]=AB-BA \neq 0$

We find using basic algebra:

$$\sigma_A \sigma_B = \frac{1}{2}\Big|\big\langle [A,B] \big\rangle\Big|$$

If you're interested in the derivation see here: https://www.youtube.com/watch?v=qgkWUuqoSVM

We see that the uncertainty product between two observables is directly proportional to the absolute value of the expected value of their commutator; and so observables which do not commute MUST posses an uncertainty relation; weather that observable is position, energy, spin, whatever.

And so yes the "observer effect" which is the physical fact that observations do not commute in Quantum Mechanics implies uncertainty relations.

xXx_69_SWAG_69_xXx
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  • But isn't the Heisenberg uncertainty principle a consequence of the wave nature of quantum particles, so is this uncertainty and the uncertainty due to the non commutative nature of certain observations the "same". – mael Delaunay Jan 14 '22 at 20:18
  • The fact that observables do not commute is why we have quantum mechanics to begin with. It's a lot more fundamental than the "observer effect" which results when a quantum system interacts with a measurement device. The uncertainty principle and the observer effect are separate concepts within quantum theory, but are still results of quantum theory. – joseph h Jan 14 '22 at 20:25
  • "And so yes the "observer effect" which is the physical fact that observations do not commute" are you sure that's what the OP meant with the phase "observer effect"? – DanielSank Jan 14 '22 at 20:37
  • @DanielSank I think the example of "observer effect" that i was told about was the wave function collapse. – mael Delaunay Jan 14 '22 at 20:59
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The “observer effect” results from the interaction of a quantum system with a measurement device (though the term observer seems to imply that you need a conscious person for this effect, which is not true and sometimes causes confusion). The uncertainty principle is more fundamental and results from the fact that certain quantum measurements cannot be made simultaneously, or equivalently, certain quantum observables do not commute, most famously, position and momentum. Thus it is inaccurate to say that the Heisenberg uncertainty principle results from the observer effect. They are both results of quantum theory that are related via the theory instead one being the result of another.

The HUP is perhaps the most fundamental result of quantum theory.

joseph h
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  • "though the term observer seems to imply that you need a conscious person for this effect, which is not true and sometimes causes confusion" I challenge you to explain wave function collapse without a conscious mind. You can write math for how a sub-part of a quantum system decoheres when it interacts with another sub-part (i.e. the reduced density matrix loses coherence), but I cannot imagine how to even talk about observation without consciousness, whatever "consciousness" even means. – DanielSank Jan 14 '22 at 21:58
  • A conscious observer seems to imply that every quantum process that is happening/happened throughout the entire universe is/was being observed. Unless you are going to invoke a deity, then of course this is not what’s happening. – joseph h Jan 14 '22 at 22:47
  • Instead, insisting on mentioning a conscious observer is admitting that there is simply no sense in pretending that we can describe Nature in any way beyond our own experience of it. In fact, statements about Nature as it exists apart from observation are literally non-scientific in that they are not falsifiable. – DanielSank Jan 15 '22 at 00:24