Can measurement impulses be cancelled out in quantum uncertainty?

[hypnagogue]

The other day I was standing in front of a nice looking patch of nature and I decided to take a photo using the digital camera in my cell phone. On my first attempt, the photo came out blurry because the act of my pressing the button to take the photo moved the cell phone ever so slightly as it was taking the picture. It struck me that this was sort of similar to quantum uncertainty and measurement-- the scene before me appeared as a blur of positions due to the impulse imparted by my 'measurement.' Of course, the solution to my blurring problem was relatively simple-- I just had to hold the other side of the cell phone in place to prevent the cell phone from moving as a result of my pressing a button on it, and the picture came out fine this time.

I know this is not how QM works, but I would appreciate some elucidation on why the following scenario, as motivated by my camera example, would not work.

Suppose we shoot a proton straight out from a source in the y direction. Orthogonal to the direction of the proton and equidistant from the source on either side, we set up an array of measurement devices. Each device on one side has a 'twin' on the other side with the same x coordinate. For each pair of twins, both twins are set up to fire a single photon orthogonal to the direction of the source at the same moment in time. Now if we time it just right (perhaps we need some bit of luck to do this), as the proton speeds from the source it will be struck by an array of photons orthoganl to its path, such that the impulse imparted by a photon on one side is canceled out by the impulse imparted by the photon striking it on the other side at the same point in time. For instance, if we use a '.' to represent a photon, an 'o' to represent the proton, and an arrow to represent the impulse imparted by the photons, then the path of the proton will look something like this:

t0: .-->o<--.
t1: .-->o<--.

And so on. So the usual explanation for measurement uncertainty-- ie the impulse imparted by the measuring agent will change the position or path of the measured thing-- does not seem to apply here, since such measurement impulses are canceled out here for each separate measurement. So it would seem in turn that we could measure both the position and velocity of the proton just fine with our series of measurements.

Again, I'm not trying to challenge the established physics, just trying to get a better understanding by being shown the flaws in my thought experiment. I realize, for instance, that I am using a faulty sort of 'billiard ball' conception in my setup, but is there any way to show how the thought experiment is wrong without already presuming uncertainty principles in the explanation (which would sort of amount to begging the question)?

 

[ZapperZ]

Suppose we shoot a proton straight out from a source in the y direction. Orthogonal to the direction of the proton and equidistant from the source on either side, we set up an array of measurement devices. Each device on one side has a 'twin' on the other side with the same x coordinate. For each pair of twins, both twins are set up to fire a single photon orthogonal to the direction of the source at the same moment in time. Now if we time it just right (perhaps we need some bit of luck to do this), as the proton speeds from the source it will be struck by an array of photons orthoganl to its path, such that the impulse imparted by a photon on one side is canceled out by the impulse imparted by the photon striking it on the other side at the same point in time. For instance, if we use a '.' to represent a photon, an 'o' to represent the proton, and an arrow to represent the impulse imparted by the photons, then the path of the proton will look something like this:

t0: .-->o<--.
t1: .-->o<--.

And so on. So the usual explanation for measurement uncertainty-- ie the impulse imparted by the measuring agent will change the position or path of the measured thing-- does not seem to apply here, since such measurement impulses are canceled out here for each separate measurement. So it would seem in turn that we could measure both the position and velocity of the proton just fine with our series of measurements.

It's a good thought experiment, but you missed one important assumption that you made in this one - that you implicitly assumed that you know both the position and momentum of your photons with equal accuracy. Take note that if you confined your photon to move along the x-direction, it means that $$\Delta y$$ (the uncertainty in the position along the y-direction) is very small. However, the HUP will kick in and tells you that $$\Delta p_{y}$$ will be large. It means that you have no ability to determine your photons transverse momentum from one shot to the next as it hits your proton. This, btw, is why you see a diffraction pattern when light passes through a thin slit.

Thus, the photon that you are using itself has an uncertainty built into its own property.

Zz.

 

[Hydr0matic]

-> ZapperZ

...but is there any way to show how the thought experiment is wrong without already presuming uncertainty principles in the explanation ...

 

[ZapperZ]

-> ZapperZ

Thanks for pointing that out. I read that the first time and didn't think twice about it since these things are so interconnected.

My response to that "criteria" is that:

(i) one can always do the experiment and

(ii) the HUP isn't something that is put in by hand. Rather it is the OUTCOME or consequences of the QM formulation. So if you already buy the "photon" idea, and you know how to generate monochromatic single photons moving in a particular direction, and that you know how to create protons on demand and its motion, etc, etc.. then you have implicitly used several aspects of QM. Thus, the HUP is already within the setup.

But then again, maybe this is not what is being asked for...

Zz.

 

[hypnagogue]

Thanks for your reply ZapperZ. It appears to me then that we should take uncertainty principles to be a fundamental property of quantum systems (which I suppose has already been elucidated for example by Bell). But doesn't this imply that the typical explanation for uncertainty (or at least, one I have seen used a lot)-- ie that uncertainty arises as a result of the physical effects of measuring agents on the measured thing, like a photon knocking around the particle it collides with to perform the measurement-- is inadequate? It gives the impression that uncertainty arises as a result of physical interactions, when in fact it should be taken to be a fundamental property of the agents involved in those interactions in the first place.

 

[selfAdjoint]

Thanks for your reply ZapperZ. It appears to me then that we should take uncertainty principles to be a fundamental property of quantum systems (which I suppose has already been elucidated for example by Bell). But doesn't this imply that the typical explanation for uncertainty (or at least, one I have seen used a lot)-- ie that uncertainty arises as a result of the physical effects of measuring agents on the measured thing, like a photon knocking around the particle it collides with to perform the measurement-- is inadequate? It gives the impression that uncertainty arises as a result of physical interactions, when in fact it should be taken to be a fundamental property of the agents involved in those interactions in the first place.

You're absolutely right. That explanation is really inadequate, and is one of the first things you are encouraged to forget when you take a serious course in quantum mechanics.