I Uncertainty principle on macroscopic objects

[Kloo]

I recently came across the Heisenberg thought experiment involving a photon observed under a microscope. The photon’s position is completely localized through its interaction with the microscope’s lens. If I were to measure the lens's recoil—which is extremely small but measurable in this thought experiment—I could determine the photon’s momentum. However, due to the uncertainty principle, precisely measuring this recoil would make the lens’s position uncertain, causing the image of the photon to blur as the focal point shifts. Interestingly, the mass of the lens doesn’t matter, meaning this effect can apply to any macroscopic object.

This reminds me of Schrödinger's cat, where microscopic effects influence macroscopic objects. But does this really imply that the lens is in many possible locations simultaneously? Or does the momentum transfer have no significant effect on the lens’s position, leaving it stationary while only the image of the photon blurs?

 

[PeroK]

I recently came across the Heisenberg thought experiment involving a photon observed under a microscope.

Do you mean a electron?

 

[DaddyCool]

But does this really imply that the lens is in many possible locations simultaneously?

No. There is a lot of misunderstanding in the next paragraphs too.

 

[PeroK]

Or does the momentum transfer have no significant effect on the lens’s position, leaving it stationary while only the image of the photon blurs?

I'd make two general points.

First, QM is a competely non-classical description of nature. Whereas, you are thinking of QM as classical mechanics with a bit of uncertainty thrown in.

The uncertainty principle applies to macroscopic objects, but the uncertainty in position is unmeasurably small for something like a lens. You need to do the calculations. For example, if the position of a lens is uncertain to a hundred millionth of the width of a single atomic nucleus, how would you know? In fact, how do you even define the position of a lens beyond macroscopic limits of precision without identifying the exact position of every elementary particle that makes up the lens?

 

[Kloo]

I'd make two general points.

First, QM is a competely non-classical description of nature. Whereas, you are thinking of QM as classical mechanics with a bit of uncertainty thrown in.

The uncertainty principle applies to macroscopic objects, but the uncertainty in position is unmeasurably small for something like a lens. You need to do the calculations. For example, if the position of a lens is uncertain to a hundred millionth of the width of a single atomic nucleus, how would you know? In fact, how do you even define the position of a lens beyond macroscopic limits of precision without identifying the exact position of every elementary particle that makes up the lens?

I am not concerned with the actual realization of the experiment. In theory, I can make the momentum measurement more and more precise, and the lens' wavefunction in space coordinates spreads accordingly. But you don't seem alarmed by the uncertainty principle applying to macroscopic objects. I was shocked by this concept extending to macroscopic objects. In the end, this is but a thought experiment.

No. There is a lot of misunderstanding in the next paragraphs too.

I would like to know where my misunderstandings are; I am here to learn.

 

[PeroK]

In theory, I can make the momentum measurement more and more precise, and the lens' wavefunction in space coordinates spreads accordingly.

That's not the case. You cannot measure the position or momentum of a macroscopic object beyond a certain level without having to measure the momentum and position of its constituent molecules.

Suppose you want to measure an edge of the lens to arbitrary precision. This only works theoretically until your precision gets down to the molecular level. At that point, there is no longer a clear boundary between the "lens" and the air surrounding the lens. What you would see, if you could, would be lens molecules and air molecules bouncing around. This momentum no longer represents momentum of the lens as a rigid, unchanging macroscopic object, but as a measure of its internal heat.

If you try to go further, and measure the position of the edge of the lens to a millionth of an atom, then you are looking at empty space between molecules. Even theoretically, you cannot determine the position or momentum of a macroscopic object to arbitrary precision. I.e. beyond the point where it makes sense to consider the lens as a solid, continuous distribution of matter.

But you don't seem alarmed by the uncertainty principle applying to macroscopic objects.

If you do the maths you might understand.

I was shocked by this concept extending to macroscopic objects. In the end, this is but a thought experiment.

I would like to know where my misunderstandings are; I am here to learn.

The main point is that a macroscopic object (if you look closely enough) is a collection of a very large number of elementary particles. The uncertainties associated with QM are at a microscopic scale. They don't affect the macroscopic object as far as macroscopic properties are concerned.

 

[Kloo]

Suppose you want to measure an edge of the lens to arbitrary precision. This only works theoretically until your precision gets down to the molecular level. At that point, there is no longer a clear boundary between the "lens" and the air surrounding the lens. What you would see, if you could, would be lens molecules and air molecules bouncing around. This momentum no longer represents momentum of the lens as a rigid, unchanging macroscopic object, but as a measure of its internal heat.

If you try to go further, and measure the position of the edge of the lens to a millionth of an atom, then you are looking at empty space between molecules. Even theoretically, you cannot determine the position or momentum of a mecroscopic object to arbitrary precision.

This makes a lot of sense. I was carelessly assuming I could increase my precision "theoretically" without any limits.

Thank you for your explanation.

 

[Peter Morgan]

This makes a lot of sense. I was carelessly assuming I could increase my precision "theoretically" without any limits.

Thank you for your explanation.

I think @PeroK's account has to be added to, insofar as thermal noise is not the same as quantum noise.
kT, which determines the amplitude of the thermal noise, has units of energy, whereas ℏ, Planck's constant, has units of action. The difference can be understood in quantum thermofield dynamics, in which ℏ determines the amplitude of a Lorentz invariant noise, whereas thermal noise is not invariant under Lorentz boosts.
This difference of symmetry properties makes thermal noise and quantum noise fundamentally different in a field theory. If I want to discuss photons as something like classical objects (though I think much more in terms of only fields), I allow myself to think loosely in terms of Brownian motion: thermal noise of a background causes an object embedded within that background to be 'buffeted about' in a particular way, so I suppose that the details of how an object embedded within a background for which there is also a quantum noise will be different.
What is common to the Brownian motion caused by both thermal or quantum noise is that the trajectory is continuous but non-differentiable. Again loosely, we can only discuss the average of the momentum over some small region. Worked out in terms of what we choose to measure and in terms of generalized probability theory, this averaging process becomes the Heisenberg uncertainty principle, because there can be tradeoffs between position measurements and other, incompatible measurements.
To be clear, the basis of this reply is in published work in the physics literature (particularly Annals of Physics 2020, or the preprint on arXiv), but it is commonly said that there is no such thing as quantum noise or that quantum noise is irreducible in a way that thermal noise is not, so to that extent take care. We can say, however (or, at least, I say), that what is irreducible about quantum noise is ℏ, insofar as we have no way of changing ℏ as an amplitude of a Lorent invariant noise in small regions of space-time, whereas we do have ways of changing kT in small regions of space-time.