The uncertainty principle and the observer effect

[geordief]

I understand  that the uncertainty  principle is  "baked into" the world as we know it whereas the observer effect describes the practical impossibility of an actual sentient observer from  taking a simultaneous  measurement of an object with attributes  such as  position and momentum to  an idealised degree of complete accuracy 

 

What I am asking is how these two concepts relate to each other?

Is ,perhaps the UP a generalization  of the OE or is the OE a specific case of the UH (not  sure if those are equivalent definitions  or not)

 

I understand that  even Heisenberg  thought (at first?) that the he was describing an OE so I don't feel bad about myself  for having believed likewise for a very long time over the years..

 

So what is the relationship? Are they two separate  concepts or are they joined at the hip?

A quick google brought up  discussions in  a few philosophy forums  .I hope that is not where this topic actually  belongs 

[MigL]

I always thought the 'observer effect' was related to the fact that any observation is an interaction with the system being observed, and would necessarily 'alter' the observation by disturbing that system..
QM is, to borrow a thought from another thread, based on the fact that the quantum domain has no reality ( as we know it ) until we force it to, by making an observation ( interaction ).

The HUP is a more concrete effect, that dictates the accuracy to which we can know certain related observables, and is built into the mathematical formulation of a quantum system.
It is not dependant on our technical ability to measure accurately, nor is it based on whether we make a 'proxy' measurement or disturb the system with the measurement.

[geordief]

8 minutes ago, MigL said:

I always thought the 'observer effect' was related to the fact that any observation is an interaction with the system being observed, and would necessarily 'alter' the observation by disturbing that system..
QM is, to borrow a thought from another thread, based on the fact that the quantum domain has no reality ( as we know it ) until we force it to, by making an observation ( interaction ).

The HUP is a more concrete effect, that dictates the accuracy to which we can know certain related observables, and is built into the mathematical formulation of a quantum system.
It is not dependant on our technical ability to measure accurately, nor is it based on whether we make a 'proxy' measurement or disturb the system with the measurement.

So they are entirely  separate ? (I hope so because I am more interested in the HUP  than the OE at the moment)

 

In the HUP what is it that  makes ,eg position and momentum mutually dependent?

Or is it   self evident that they do and does the fact that they do share this  mutual dependency  mean that one  cannot know the one in isolation  from the other?

 

And so the position/momentum  state has to be described mathematically  in a "two dimensional"  way?

 

Are there other pairs of attributes that apply to other systems that behave the same way?

[MigL]

The Uncertainty Principle is a 'feature' of all wave-like systems.
Quantum Mechanics does not allow for simultaneusly accurate determination of conjugate variables, like position and momentum.
Time and energy are another pair that follow the HUP.

See here    Uncertainty principle - Wikipedia.
 

[swansont]

43 minutes ago, geordief said:

In the HUP what is it that  makes ,eg position and momentum mutually dependent?

They are conjugate variables. Each is a fourier transform of the other.

In QM it means the operators don’t commute, i.e. the order matters.

[geordief]

Thanks.I will have to do a little(a lot) more reading before I can ask any more questions. 

[exchemist]

9 hours ago, geordief said:

Thanks.I will have to do a little(a lot) more reading before I can ask any more questions. 

In simple terms, the key to the momentum:position thing is wave/particle duality. The momentum of a QM entity is inversely proportional to its wavelength (de Broglie's relation), i.e. proportional to frequency, while the probability of detecting the entity at a position is determined by (the square of the) amplitude of the wave. 

If you have a QM entity represented by a pure sine wave, it has only one frequency component, so its momentum is determined precisely. But a sine wave extends throughout space. So you have no idea where it is. Conversely, if you have a superimposed series of waves of different frequencies, with phases aligned to interfere constructively at one location, then, because of the frequency differences, as you move away from that spot they will start to interfere destructively. So then you have a situation where all the amplitude is in one location - the position is well-defined - .............but you have no idea anymore what the momentum is, because it is composed of lots of different frequencies and hence momenta.

This idea of adding waves of different frequencies to obtain various non-sinusoidal waveforms is familiar to radio and hi-fi engineers. It's not a QM idea. For instance the reason why you need good high frequency response, way above what you can hear, in an amplifier is to reproduce transients faithfully, because those require a complex mix of frequencies including very high frequency components. 

The special ingredient in QM is de Broglie's insight, associating momentum (p) with wavelength(λ) : λ=h/p .  (h is Planck's constant).

 

 

Edited October 12, 2022 by exchemist