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I've recently started my journey in understanding the math of quantum mechanics and I've noticed a strange pattern. (I'm not saying that the popular interpretation of quantum physics is wrong or anything. I'm just genuinely curious about this aspect of it.)

All of the descriptions of experiments that I've seen are spoken about as if measuring a particle doesn't affect the particle. A lot of the conclusions regarding the interpretation of the experimental results seem to be based on the assumption that measurement doesn't affect particles.

But isn't it obviously the case the measurement always affects the particle?

A polarizer will always reorient the polarization of a photon (basically every light experiment involving polarization).

Beam splitters affect the photons going through them, each exiting beam having different properties created by and/or filtered by the splitter (basically every light experiment).

A magnetic field will reorient a particle that has something like magnetic poles (Stern-Gerlach experiment and such).

And so on...

That last one in particular bothers me, especially when someone says that an electron's spin is "always up" or "always down" and never in between, despite the fact that measuring it intuitively appears to force it to be up or down regardless of whether or not it was somewhere in between before being measured.

However, I've never seen any physicists talking about how measurement affects the particles being measured or its impact on interpretation. Every time I ask about it, I never get a clear answer (but then again, I've only had access to physics professors).

And it seems like acknowledging the intrusiveness of measurement makes the experimental results much more intuitive than my teachers and popular physics videos seem to claim. They say "that's weird", but assuming the measurement affects the particles makes it not seem weird at all.

Is there a reason that measurement is talked about as not being intrusive, despite the obvious instinct being that it is?

Have we been able to demonstrate that it isn't intrusive somehow? Or do we know that it's intrusive, but we don't know how so we don't talk about it? Or is it something else?


Note: I'm not asking about the Uncertainty Principle. I'm totally comfortable with the implications of wave-particle duality.

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    $\begingroup$ without attending the same classes you did, it's hard to answer this question. $\endgroup$ – niels nielsen Feb 4 at 3:05
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    $\begingroup$ The whole point of the Stern Gerlach experiment is the fact that measurement changes the state of the particle, so I'm not sure what the issue is here. Also I'm unsure as to how the uncertainty principal and wave-particle duality are the same thing. $\endgroup$ – Aaron Stevens Feb 4 at 3:50
  • $\begingroup$ @AaronStevens - The way Stern-Gerlach was explained to me was that it shows that an electron is always either spin up or spin down and can't be a spin in between, which doesn't make sense as a conclusion if the Stern-Gerlach experiment affects electron spin. As for the uncertainty principle, it naturally arises from the wave-particle nature of particles, because things like velocity and position cannot really be defined for waves the same way they are for classical particles. $\endgroup$ – Danegraphics Feb 4 at 5:09
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    $\begingroup$ Any reasonably complete treatment of spin that used Sten-Gerlach as a foil should have included a three stage SG. The one where you pick say the $y$-up beam from the first stage, measure it in $x$, and then pick the $x$-up beam to measure (again) in $y$ and find both states in the final beam. If you didn't get that (or it's moral equivalent) your education has not been complete. And of course, this makes explicit that the second stage has affected the state of the system established by the first stage. $\endgroup$ – dmckee Feb 4 at 5:21
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    $\begingroup$ As far as I know, you don't—as a practical matter you—do SG with electrons. The dipole-gradient force will be completely overwhelmed by the variation in the Lorentz force due to momentum distribution of the beam $\endgroup$ – dmckee Feb 4 at 5:27
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Classroom instruction in classical physics does address some of the items in your list. In particular the treatment of light passing through a polarizing medium is handled with two sub rules: (a) The emerging light takes on the polarization of the medium and (b) the intensity is reduced by the rule $I = I_0 \cos^2 \theta$ (or a suitable integration thereof). Not a hint there of the measurement not affecting the subject. Quite the opposite, in fact.

But for most cases in classical physics it is in principle possible to reduce the effect of the measurement to be smaller than dominant uncertainties in the problem (i.e. the time at which an apparatus passes some critical point can be measured with an IR photogate that introduces only trivial changes in the experimental conditions).

Practical instruction on making these kind of things work is one of the goals of the (often sadly neglected) laboratory component of physics instruction.

Quantum physics doesn't introduce the rule that the measurement affects the measured system (despite the many, many pop-sci treatment that either say that outright or give that impression). What is does is put bound on your ability to both make an accurate measurement and avoid significantly disturbing the system at the same time. No such bound is present in the theory of classical mechanics,1 though there are practical bounds which are often (usually!) more significant than the Uncertainty Principle.


1 Mind you, exactly the same kind of bound is present in wave optics.2 Alas, many introductory treatments don't point out the places where this shows up, even when doing the wave physics. That is, they neglect to mention that the Rayleigh Criterion and the single-slit diffraction patterns are exactly the same physics that shows up in the HUP.

2 And it is due to the nature of waves. No surprise—then—that you get an uncertainty principle in the Schrödinger formulation of QM; the interesting part is that it shows up in all the formulations.

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  • $\begingroup$ I don't quite understand the point you are making with that last paragraph. Are you saying that measurement affects are taught? What does that mean for why it is or isn't taught? $\endgroup$ – Danegraphics Feb 4 at 3:11
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    $\begingroup$ I don't agree with your last paragraph regarding the effects of measurement. One of the postulates of quantum mechanics is that a measurement of an observable on a quantum system will indeed change the quantum state -- ie., by collapsing the quantum state into an eigenstate of the measured observable. Would you not say that in such a case the measurement affects the system? $\endgroup$ – Harry Levine Feb 4 at 4:10
  • $\begingroup$ @HarryLevine You seem to have missed my point: measurement affects the system in classical mechanics, too. It always has. Quantum mechanics simply did not introduce that idea. The difference is that for many classical system you can (theoretically) always reduce the disturbance to an acceptable scale. QM didn't even introduce the idea of systems for which you can't arbitrarily reduce the disturbance and still get good measurements because that exists in classical optics too. What QM did do is make the precision/disturbance trade-off ubiquitous: all quantum systems have it. $\endgroup$ – dmckee Feb 4 at 5:04
  • $\begingroup$ I'm still not quite understanding what you're saying. Are you sayin that QM wasn't the first to introduce the idea of measurement affecting the thing being measured? And regardless, how does that answer my question? $\endgroup$ – Danegraphics Feb 4 at 5:12
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    $\begingroup$ My answer is that my experience—as a student and as a teacher—simply does not agree with your assertion that the subject is taught without the idea. It has always been there. $\endgroup$ – dmckee Feb 4 at 5:21
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I can't address the state of education at your institution, but the effect of measurement on the state of a system has been a central theme in physics for well over a century.

In classical physics, one defines the gravitational or electric field using an arbitrarily small "test particle". That is, one imagines that the ratio of charges or masses can be made large enough so that any measurement effect can be neglected. This is not possible is quantum mechanics, as the Heisenberg uncertainty principle (HUP) makes clear. Note that Planck's constant $h$ which appears in HUP first arises in statistical mechanics, where the measurement effect is discussed in great detail. See for example Gallavotti's "Statistical Mechanics: a short treatise".

What is important to understand about quantum mechanics in particular is that the result of an experiment is always either

A) the state is destroyed: eg. an electron is captured by CCD device or reacts on a photographic film.

or

B) the state "collapses" i.e. becomes the measured Eigenstate.

The Stern-Gerlach experiment is an example of B on a simple system. You are entirely correct to say that the device forces the particle to become either spin-up or spin-down along whichever axis (perpendicular to the direction of motion) you orient it.

The observations of the experiment are that

1) The particle has intrinsic angular momentum 2) It's value upon measurement is quantized: the measured component in the chosen direction is always $\pm\sqrt{1/3}$ its magnitude. 3) Any information about its prior orientation along any perpendicular axis is destroyed by the measurement process.

In short, you are entirely correct to say that the measurement affects the results. However the precise way it affects the results is completely and fundamentally different than the way it does this in the classical case, in which 2 and 3 do not hold.

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There is an extensive literature on the quantum mechanics of measurement and measurement devices. In this literature the measurement device, the measured system, the environment and the coupling between them are modeled. See, for example, this paper and the references therein:

https://arxiv.org/abs/1412.5206

These interactions prevent interference between different eigenstates of the measured observables. Those eigenstates are still present unless you modify quantum mechanical equations of motion to include a collapse to just one state. Unmodified quantum mechanics implies the existence of multiple versions of all the objects you see around you: this is commonly called the many worlds interpretation of quantum mechanics (MWI) (the symbols in the pdf for this paper don't render properly on chrome but they do render properly in pdf viewers such as adobe or preview):

https://arxiv.org/abs/quant-ph/0104033

For reasons that are not very clear there is a taboo against talking about the MWI, which results in people fudging discussions of measurement.

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