What constitutes a measurement in physics?

[Yora]

In quantum physics, pretty much no term appears to mean what it normally means.

Everyone is talking about particle wave packages collapsing when the particle is measured. What is "measured"? It can't have anything to do with a scientist looking at the result, and it can't have anything to do with a machine designed to display the result to a scientist. So what is it?

[NichG]

Basically, any interaction with a macroscopic system that is not being explicitly modeled.

[shawnhcorey]

Measurement means that when one quantum interacts with another.

A common type of quantum detector is two plates in a vacuum that are heated until they are just below the temperature where electrons would spontaneously fly off. When a quantum hits one of them, energy is added to an electron that causes it to fly off and hit the other plate. This causes more electrons to fly off and hit the first plate. And so on until there is enough current for a sensitive circuit to detect.

Sometimes electrons do fly off on their own which creates a false measurement. This is called noise. By adjusting the temperature of the plates, this noise can be minimized.

[halfeye]

What is an observer is a similarly good question.

I want to hear about the experiment where grad students measure the resposes of undergraduates, who measure the responses of crows, which measure the responses of pigeons, which are measuring the responses of light through lenses or something.

[shawnhcorey]

What is an observer is a similarly good question.

An observer is any device that make a measurement (q.v.)

[NichG]

What is an observer is a similarly good question.

I want to hear about the experiment where grad students measure the resposes of undergraduates, who measure the responses of crows, which measure the responses of pigeons, which are measuring the responses of light through lenses or something.

The math doesn't really require an observer. Basically, the issue is that what you should really be solving for is the combined wavefunction of every particle and field that participates in a given experiment. But in practice for the kinds of systems you study in textbook QM, you can usually almost perfectly factorize out the wavefunction of a single electron, and just worry about that. The 'almost perfect' part is that at some point in any actual experiment, that electron or other thing you're solving for is going to have to interact with a detector. The idea of a measurement is then basically a way to marginalize over the part of the joint wavefunction associated with the detector's quantum state being entangled with the quantum state of the thing you're solving for. Rather than resolving that fully, you basically say 'okay, evaluate what the particle wavefunction looks like conditioned on the detector state being + and call that one branch (renormalizing the wavefunction to 1 net probability); then evaluate what the particle wavefunction looks like conditioned on the detector state being - and call that another branch (renormalizing the wavefunction to 1 net probability)'

That condition-and-renormalize-to-1 bit is wavefunction collapse. Even if the true quantum state of the joint wavefunction is a superposition between + and - states of the detector, since solutions are superposable, from 'within' the + state, the residual amplitude associated with - has no causal effect, and vice versa. So it works to continue from that point as if it were suddenly a pure state (but with which pure state being stochastically determined).

[Yora]

I believe to have heard somewhere that a particle interacting with another particle only makes it stop being in superposition in regard to that other particle. So if you have two protons, two neutrons, and two electrons in superposition, and they interact only with each other and nothing else, you get a helium atom that also is still in superposition in regard to the rest of the universe. And I think that was actually done in some lab.

In theory, you can have a complete cat that is in superposition, but in practice Schrödinger's Cat consists of so many particles that interact with all the particles of the air and the box it is in, that the wavefunction for all the particles in the cat collapses pretty much instantly. (I assume the cascade of collapsing wavefunctions propagates at the speed of light.)

But since we're already at it, I have a related question. Does a particle only exist in superposition after it is created and before it interacts with anything else, or can a particle revert to a state of superposition after it has interacted with something? I also heard that all protons in the universe existed since the big bang, which would conflict with that story about the helium atom in superposition. How would you even find a proton in superposition? When you try anything to tell one apart from one whose wavefunction has already collapsed, you cause its wavefunction to collapse.

[Anymage]

If a particle's waveform collapsing meant it was a point particle from that point on, you're right that we wouldn't have any uncollapsed particles left. As soon as you turn your back, they start acting all sneaky again.

And mind that this is just a layperson relating something he heard from a source that sounded like it understood the details better, but the big thing about interaction is that it means any time that specific information is required. All particle experiments on earth have happened within earth's gravitational field, and yet interacting with either the general gravitational field or the general electromagnetic field doesn't cause the waveform to collapse. If you had some way to tell whether the particle happened to interact with a graviton or an electron at a specific point, though, the universe would have to give a specific answer and the particle would have to have particle-like specificity.

[gomipile]

In quantum physics, pretty much no term appears to mean what it normally means.

Everyone is talking about particle wave packages collapsing when the particle is measured. What is "measured"? It can't have anything to do with a scientist looking at the result, and it can't have anything to do with a machine designed to display the result to a scientist. So what is it?

Unfortunately, it's currently an "I know one when I see it" sort of thing in practice. With regards to fundamentals, the problem is still open: https://en.wikipedia.org/wiki/Measurement_problem

[NichG]

I believe to have heard somewhere that a particle interacting with another particle only makes it stop being in superposition in regard to that other particle. So if you have two protons, two neutrons, and two electrons in superposition, and they interact only with each other and nothing else, you get a helium atom that also is still in superposition in regard to the rest of the universe. And I think that was actually done in some lab.

In theory, you can have a complete cat that is in superposition, but in practice Schrödinger's Cat consists of so many particles that interact with all the particles of the air and the box it is in, that the wavefunction for all the particles in the cat collapses pretty much instantly. (I assume the cascade of collapsing wavefunctions propagates at the speed of light.)

But since we're already at it, I have a related question. Does a particle only exist in superposition after it is created and before it interacts with anything else, or can a particle revert to a state of superposition after it has interacted with something? I also heard that all protons in the universe existed since the big bang, which would conflict with that story about the helium atom in superposition. How would you even find a proton in superposition? When you try anything to tell one apart from one whose wavefunction has already collapsed, you cause its wavefunction to collapse.

Well, a couple of things. One is, thinking about things as being wave vs being particle as if that were two distinct states is wrong. Wave function collapse isn't a transformation from wave to particle.

If we're talking about particles in space, the wave function of one particle is psi(x,t). In classical physics, momentum would be an independent state variable, which would mean you should have psi(x,p,t), but in QM the momentum operator turns out to be related to x. Specifically, its 'i*hbar*d/dx'. If you make a wavefunction that is narrowly distributed in x, then the distribution of d/dx becomes wider and vice versa. So everything is always a wave, but can be concentrated more in position or more in momentum (but never both, because they are not actually independent quantities).

As far as superposition, it's a bit weird to talk about a particle being in superposition or not as a state function. Rather, there is one joint wavefunction for the entire universe, and the equation which determines that has the property that if X and Y are solutions, (aX+bY)/sqrt(a^2+b^2) is a solution for any scalars a and b. If X describes 'you' somewhere in it, it's impossible for 'you' to detect that you're mixed with Y because solutions add without interacting. We don't see quantum cats because the us in X that sees a living cat and the us in Y that sees a dead cat can't measure eachother's coefficients in the joint wavefunction, because our observation of the cat is entangled with the cat's state. The protocol prevents there from being amplitude in 'cat is dead but we measure alive' or 'we measure half-alive' or things like that.

However, if you can experimentally isolate part of this function where 'you' factorize out from the thing you are studying, then it's possible to see the effect of superposition in that sub-system. The easiest way to do this is to look at interference over multiple repetitions of the experiment and measure statistical quantities. That would like doing a bunch of 'double Schroedinger box experiments' with breeding pairs of cats and entangled decay products vs independent, then noticing that the statistics of how many kittens you end up with varies in each case.

[sktarq]

But since we're already at it, I have a related question. Does a particle only exist in superposition after it is created and before it interacts with anything else, or can a particle revert to a state of superposition after it has interacted with something? I also heard that all protons in the universe existed since the big bang, which would conflict with that story about the helium atom in superposition. How would you even find a proton in superposition? When you try anything to tell one apart from one whose wavefunction has already collapsed, you cause its wavefunction to collapse.

nah....An electron in valence shell (lets just be easy here for examples) can be observed via interaction...most common version of interaction is to hit it with a photon of some kind.

so you hit it and it drops out of superposition.

great...by the time the photon has moved basically at all that electron is once again spread out as a particle wave around the valence shell and by the time you detect the bounced photon you don't know where the electron "is" anymore....just where it was at the time the photon interacted with it.

[Radar]

I believe to have heard somewhere that a particle interacting with another particle only makes it stop being in superposition in regard to that other particle. So if you have two protons, two neutrons, and two electrons in superposition, and they interact only with each other and nothing else, you get a helium atom that also is still in superposition in regard to the rest of the universe. And I think that was actually done in some lab.

The actual experiment was even grander in scale.

nah....An electron in valence shell (lets just be easy here for examples) can be observed via interaction...most common version of interaction is to hit it with a photon of some kind.

so you hit it and it drops out of superposition.

great...by the time the photon has moved basically at all that electron is once again spread out as a particle wave around the valence shell and by the time you detect the bounced photon you don't know where the electron "is" anymore....just where it was at the time the photon interacted with it.

It is also useful to remember two more things:
1. A photon gives you a resolution around half of its wavelength without additional shenanigans.
2. Being hit by a photon is disurbing, since it is a collision with an object of significant momentum - proportionally higher for shorter wavelengths.

If you would would use single photons with short enough wavelengths to discern where the electron is with resolution better then the size of an atom, you would most likely send the poor electron flying in a random direction or the photon would not detect anything, since it did not hit at all. There are however nifty statistical methods of recovering probability density of electronic states in atoms.

[Telok]

At a meta level physics is a system of interactions. A measurement is the act of extracting information from that system. The issue with quantum physics is that our means of extracting information are large and clumsy compared to what we're measuring.

As an example if you have a pot of water and want to know the temperature, you stick a thermometer in and take a reading. Your reading isn't exactly true thiough, you're actually determining the temperature of the water minus the heat required to warm the thermometer. If you've got 10 L of water and a 10 mg thermometer you can probably ignore the difference, it's usually going to be less than the variance in accuracy anyways.

The issue at the quantum scale is that we relatively have a couple mL of water and the measuring tool relatively masses several tons. The act of measuring changes what you're measuring so drastically that the information may be useless. In fact you may end up changing what you want to measure before you measure it and you may not be able to tell if that happened.

[shawnhcorey]

At a meta level physics is a system of interactions. A measurement is the act of extracting information from that system. The issue with quantum physics is that our means of extracting information are large and clumsy compared to what we're measuring.

No, a measurement must be made at the quantum level. The only difference between a quantum measurement and a macro measurement is that macro measurements involve a very large number of quanta.

There is no extraction of information. QM tells us that to make a measurement is to change the system. Any measurement influences the system it is measuring. The measurement becomes part of the system.

[NichG]

It's not that our measurements are clumsy, or even the often stated 'any measurement changes what it measures' - those are both just as true of classical systems.

It's a deeper issue. QM shows us that things we believed to be independent properties of things when we talk in terms of their expectation values are actually not - and cannot be - independent when we talk about distributions (well, wavefunctions) over them.

The case of spins is cleaner than position/momentum. Spins are mathematical objects described by normalized vectors pointing to the surface of a sphere or set of concentric spheres. This makes it seem as though we could talk independently about their x, y, and z components in a cartesian representation. But, at the same time, spins are quantized: on every axis, the spin is always in a mixture of + and - states. This means that the xyz representation is over complete - it looks like there are more numbers needed to fully describe it than in reality.

So when we measure or describe the x component, we find to our surprise that we have some amplitude associated with +x and some with -x, but nothing that indicates something being on y or z. When we subsequently query y, maybe classically expecting 0, of course we can't get zero: we get some amplitude for +y and some amplitude for -y.

These are consistent with mathematical manipulations of the wavefunction over spin, but not consistent with the idea that a spin is 'actually' an xyz triple.

In general, for two operators, the overlap between them is described by their commutator. For operators that commute, there is no fundamental reason from QM at least that they could not be perfectly and simultaneously measured. Position and spin, for example.

[ChrisDemilich]

I will explain this in pretty simple layman's terms.

To observe/measure something, that thing needs to be interacted with. To see something you need light to hit that object and bounce to your eye. An X-ray requires radiation to bounce off solid matter. An ultrasound requires sound waves to bounce off and be recorded.

In quantum (very small) systems, a single radioactive particle, or a single photon of light can alter the natural state of the system. So a quantum system that is not being observed, is not being bombarded with particles/waves/energy that could change how it behaves.

As soon as you introduce any artificially introduced particles/waves/energy for the purpose of measurement, then the quantum system is likely to react differently based on that stimuli.

[Max_Killjoy]

Just don't confuse this for the froofy "observation creates reality" and "you can't look at something without changing it, even at the human scale" nonsense that sometimes gets mistakenly derived from this by certain types skimming the descriptions.