The nature of uncertainty

[KipIngram]

Often I encounter materials online that motivate the mental picture of quantum uncertainty by describing it primarily as a measurement error.  "Electrons are small, so to "see" them we have to use light of very small wavelength.  But photons of such light have a lot of energy, and so necessarily disturb the momentum of the electron severely."  Etc.

I tend to find such descriptions very unsatisfying - they imply that the electron actually has both position and momentum, but that we are just unable to measure them both simultaneously because by making the measurements we disrupt the thing being observed.  When I think about it, I tend to think about it in terms of the wave description of the electron (or whatever) and the unavoidable truths of Fourier theory.  In other words, to describe an electron as having a well-defined position, we must use frequency components in the wave description that also describe a wide spectrum of possible momenta, and vice versa.  It just can't be dodged.

So my question is "Is there any sort of deep physical connection between these two ways of discussing uncertainty?"  Or is the first way I described above just in the weeds from the jump, because it still tries to describe the electron as a localized particle, regardless?

Thanks,

Kip

Edited November 22, 2017 by KipIngram
Just added a bit more detail.

[swansont]

1 hour ago, KipIngram said:

Often I encounter materials online that motivate the mental picture of quantum uncertainty by describing it primarily as a measurement error.  "Electrons are small, so to "see" them we have to use light of very small wavelength.  But photons of such light have a lot of energy, and so necessarily disturb the momentum of the electron severely."  Etc.

I tend to find such descriptions very unsatisfying - they imply that the electron actually has both position and momentum, but that we are just unable to measure them both simultaneously because by making the measurements we disrupt the thing being observed.  When I think about it, I tend to think about it in terms of the wave description of the electron (or whatever) and the unavoidable truths of Fourier theory.  In other words, to describe an electron as having a well-defined position, we must use frequency components in the wave description that also describe a wide spectrum of possible momenta, and vice versa.  It just can't be dodged.

So my question is "Is there any sort of deep physical connection between these two ways of discussing uncertainty?"  Or is the first way I described above just in the weeds from the jump, because it still tries to describe the electron as a localized particle, regardless?

Thanks,

Kip

Heisenberg Uncertainty is not measurement error. Even though Werner used that as an explanation, they are distinct things. Unconnected.

What this ties back to is the fact the conjugate variables are Fourier transforms of each other, as you note. There is an inherent uncertainty there. You can also look at the commutation relations. There is an uncertainty inherent in any variables whose operators don't commute.

[KipIngram]

Thanks, swansont.  I thought so - just wanted to make sure I wasn't totally overlooking something subtle.

[studiot]

I started this thread to discuss this question, amongst others.

 

The point is that Heisenberg uncertainty has the same roots as classical uncertainty I offered there.

Objects do not have zero size.

Even a one dimensional object stetches from point X₁ to point X₂.
So when you calculate a quantity that depends on X, what value do you take for X?

X₁  or X₂ or somewhere in between?

This and other matters concerning uncertainty are discussed in the thread I linked to.

[Dubbelosix]

The best way to view uncertainty, is as a limitation to how much information we can gain from any complimentary system.

 

Note also, that doesn't mean that a wave function has to be indeterministic. The evolution of a wave function can be of course entirely deterministic. So we must be careful when we think about the uncertainty as a measure of probability because even probability isn't fully understood, for the model we choose is very important.

[Shauno]

Hi Studiot,

On ‎22‎/‎11‎/‎2017 at 6:43 PM, studiot said:

The point is that Heisenberg uncertainty has the same roots as classical uncertainty

No, the nature of uncertainty in the Classical world and Quantum world are very different. For example, in the classical world, the simultaneous error can conceptually be reduced to zero. In the quantum world, it is just not  possible and it is a question of interpretation as to why. The  uncertainty in position after a measurement of momentum is totally different to the nature of uncertainty in position in Classical mechanics. In fact, Bell's inequality implies that the position no longer exist (undefined)

At the risk of being off topic..

On ‎22‎/‎11‎/‎2017 at 6:43 PM, studiot said:

Objects do not have zero size

There is no reason to think electrons or any other "fundamental" particle has any size, whatever that means. Perhaps  down at the Plank scale, but everything is speculative there.

Edited March 15, 2018 by Shauno

[studiot]

9 hours ago, Shauno said:

Hi Studiot,

No, the nature of uncertainty in the Classical world and Quantum world are very different. For example, in the classical world, the simultaneous error can conceptually be reduced to zero. In the quantum world, it is just not  possible and it is a question of interpretation as to why. The  uncertainty in position after a measurement of momentum is totally different to the nature of uncertainty in position in Classical mechanics. In fact, Bell's inequality implies that the position no longer exist (undefined)

.

Good morning, Shauno. thank you for your reply.

Please read swansont's reply above.

Fourier transforms, for instance, are used classically.

I think it is important to note that there is a difference between errors and uncertainty.

Uncertainty is inherent in the mathematics and cannot be avoided. Errors are more tractable by various operational and mathematical means.

Number (of moles) is one of the fundamental quantities and is a  good example of something that is inherently certain, but still prone to the possibility of error.

 

The next bit is not off topic because it is linked to uncertainty.

 

9 hours ago, Shauno said:

There is no reason to think electrons or any other "fundamental" particle has any size, whatever that means. Perhaps  down at the Plank scale, but everything is speculative there.

 

I don't see how this relates to the full text of the comment in my post and the mathematical procedure  was referring to.

Edited March 15, 2018 by studiot

[swansont]

22 minutes ago, studiot said:

Please read swansont's reply above.

Fourier transforms, for instance, are used classically.

But in classical physics, the momentum is not the Fourier transform of the position. The quantum uncertainties are irrelevant, because the classical measurements tend to have uncertainties larger than hbar.

[studiot]

5 minutes ago, swansont said:

But in classical physics, the momentum is not the Fourier transform of the position. The quantum uncertainties are irrelevant, because the classical measurements tend to have uncertainties larger than hbar.

I didn't say it was, I said FT s are used in classical Physics.

Your point I was indicating is that uncertainty is inherent in the maths, not the measurement.

It is there whether a measurement is made or not.

 

Please note I edited my previous post whilst you were posting yours.

 

Edited March 15, 2018 by studiot

[swansont]

1 hour ago, studiot said:

I didn't say it was, I said FT s are used in classical Physics.

Your point I was indicating is that uncertainty is inherent in the maths, not the measurement.

It is there whether a measurement is made or not.

But there's no inherent classical uncertainty, and the inherent quantum uncertainty only appears when you try to measure two non-commuting variables.

It's not apparent to me that because FTs are used classically has any relevance here. Looking at something in the e.g. frequency domain v time domain doesn't have the same uncertainty implications as it does in QM.

 

[studiot]

14 minutes ago, swansont said:

But there's no inherent classical uncertainty, and the inherent quantum uncertainty only appears when you try to measure two non-commuting variables.

It's not apparent to me that because FTs are used classically has any relevance here. Looking at something in the e.g. frequency domain v time domain doesn't have the same uncertainty implications as it does in QM.

 

 

Uncertainty manifests itself in many ways, the exact details varying with the circumstances.

Rather than argue over uses of FT, here is a clear cut classical example of uncertainty which also clearly demonstrates the difference between errors and uncertainty.

 

A concrete beam spans between two walls and carrier further structure above it.

Strength and deflection calculations involve the self weight of the beam, the exact span distance, the further loads imposed by the structure and so on.

None of these are certain and modern practice uses what is known as partial safety factors to accomodate these variations or uncertainties.

However it is also possible to make errors either in the measurements or the calculations which assume perfection in that respect.

 

[swansont]

8 minutes ago, studiot said:

 

Uncertainty manifests itself in many ways, the exact details varying with the circumstances.

Rather than argue over uses of FT, here is a clear cut classical example of uncertainty which also clearly demonstrates the difference between errors and uncertainty.

 

A concrete beam spans between two walls and carrier further structure above it.

Strength and deflection calculations involve the self weight of the beam, the exact span distance, the further loads imposed by the structure and so on.

None of these are certain and modern practice uses what is known as partial safety factors to accomodate these variations or uncertainties.

However it is also possible to make errors either in the measurements or the calculations which assume perfection in that respect.

 

But these are limits to measurement or fabrication precision, not anything inherent to classical physics. Unlike quantum physics.

[puppypower]

One explanation for uncertainty is connected to the electron and protons of atoms are not in the same reference. The reason is electrons move at a fraction of the speed of light and protons do not. There is a slight Special Relativity affect. Time and space and are not the same in both references.

The affect would be similar to the twin paradox, where the moving twin; electron, ages faster and the stationary twin; protons and neutrons age slower. There is an  uncertainty in space and time, that advances in time. Picture of the two teens were wired by nerves and one twin ages faster. The brains are not on the sam page. 

If we could assume the reference of the electron, instead of the proton=lab, we would see uncertainty in the proton, but not in the electron. I am not sure how to run this experiment, but it should work. 

In photography, there is an affect analogous to the uncertainty principle. This is called motion blur; below. Motion blur occurs  when the shutter speed of the camera is slower than the action speed. Since the photo freezes time, the difference in motion with t=K, shows up as uncertainty in distance. We get the impression of motion, using only distance. Our brain interprets time; motion, even with time stopped. Our measurements are accurate, but they stop time in our reference; shutter, but not in the electron reference. 

In the picture below, we can determine the position of the bird's head but we can't tell his momentum from the head. The birds looks stopped. We can tell his legs are in motion, and thereby infer momentum, but we can't tell the position of the legs, to the uncertainty caused by the motion blur. It has to do with time stopped in the photo, and two references causing a lingering time potential; different aging speeds. 

 

[/img]

 

 

Edited March 15, 2018 by puppypower

[swansont]

3 hours ago, puppypower said:

In photography, there is an affect analogous to the uncertainty principle. This is called motion blur; below. 

This is nonsense, and I've see this before...