# B Where does a quantum experiment *begin*?

Tags:
1. Aug 29, 2016

### Davor Magdic

Apologies if the question has been asked, I didn't see it in my search but maybe I missed it.

I was wondering if there is a formal definition of when/where a quantum experiment begins (as opposed to where it ends, i.e. with the collapse of the wave function), and whether it matters.

For example, with a double-slit experiment, we talk about firing "one electron at a time" towards the slit, and we say the experiment ends when we measure that the electron has hit a particular area of the screen. But it would seem that not just its path but also the presence of that electron is conditional, i.e. that prior to the measurement, the electron was in a superposition of states fired-and-flying-towards-the-slit and not-fired-yet. The electron comes from the electron gun which is being heated. From what I understand that means the electron in question was in a superposition of states jumped and not-jumped the barrier in the heated filament due to the flow of electrons making the electrical current in the filament. Those electrons themselves are presumably in a superposition of states of passing and not passing through the filament, and so on.

In other words it seems like prior to the measurement, it's not just the landing position of the electron on the screen that's in the superposition of states, but that, tracking backwards, everything else that makes the chain is fuzzy until a certain point (if it exists). I.e. if there is a such thing as the "rise" of the wave function, can we say that, assuming you are the experimenter, if your first observation is that your finger is pushing the "on" button, and your next observation is that you see is a quick flash on the screen, the theory doesn't tell you what happened in between? That seems somewhat counter-intuitive.

(As to whether this matters, my intuition is that the longer the parts of the chain from the end to the start we include in the observation, the more unique and less reproducible/repetitious that sequence is, and so less relevant for making predictions, but would appreciate hearing your thoughts.)

Thanks!

Last edited: Aug 29, 2016
2. Aug 29, 2016

### atyy

The start and the end are the same type of thing. Remember that the end is a start - that is the whole point of wave function collapse.

Last edited: Aug 29, 2016
3. Aug 30, 2016

### Demystifier

Quantum mechanics is not so much different from classical mechanics. Classical measurement ends with observation (which corresponds to quantum collapse), but where does the classical measurement begins? The beginning is not so well defined, but it is not really so much important. The point of measurement (either quantum or classical) is to make the observation.

4. Aug 30, 2016

### Davor Magdic

atyy, Demystifier, thank you for the replies. If the end is a start, and the point of measurement is to make an observation (i.e. sample the state of the system), does it not follow that measurements are continuously happening, in which case when does the collapse happen?

To put it this way, imagine you are pressing the "on" button on the electron gun and you're looking at the screen. There is a very small possibility that an electron fill fire right away and you see a flash, and say that doesn't happen. Since that was a measurement, which detected no interaction, I suppose it means that the probability wave of the entire system at the time of turning it on was collapsed to "filament-not-yet-heated-electron-not-yet-jumped-the-barrier"?

Let's say you keep looking at the screen and for several seconds nothing happens (as the filament is heating up), and finally you see a quick flash on the screen. It seems to follow that in all the moments when there was no flash, the system (battery + electron gun + screen) was in the collapsed state of "electron not jumped barrier" and then at one moment it was in the state "electrical current in the filament is strong, filament is heated, an electron has jumped the barrier, traveled to the screen and hit a phosphorus atom which emitted a photon that reached your eyes" (and so on).

To me this sounds like there was never room for the probability wave to not be collapsed? Or is this a way of looking at things that implies hidden variables?

5. Aug 30, 2016

### ZapperZ

Staff Emeritus
This is why that I wish that the school curriculum will let students play with basic stuff such an an electron gun tube.

First of all, let's get this out of the way. The old TV tube that we all had (before plasma, LED, LCD screens) all had electron guns. The electrons that are released were NEVER treated as quantum particles. They were treated as classical particles, and classical mechanics were perfectly valid in describing them. Why? Because the nature of how they are used, and what they are being used for do not require quantum mechanical picture (see, for example, the measurement of e/m in a classic Bainbridge tube setup).

What this means is that the electrons that come out of a thermionic gun, after they have been emitted, can easily be treated as classical particles. Heck, if you look at particle accelerators today, even there, they are treated as classical particles (see, for example, beam physics simulators code such as PARMELA). Also note that I don't have to use a thermionic gun. I can easily use a photoinjector gun. The source here is irrelevant as long as I can get a monochromatic electron beam (within my experimental limits).

What will make this a quantum mechanical experiment (i.e. quantum effects will come into play) is the setup that the electron beam will go through. A double-slit equivalent experiment will require that the electrons will have two equal probability paths that it can take, meaning the superposition occurs once it has entered this setup, giving it a superposition of paths.

{BTW, it is one of my pet peeve when someone claims that there is a superposition, without elaborating the property or observable that is in superposition. You have to indicate WHAT quantity that is in superposition. It is the position, the momentum, the spin, etc...? It is insufficient to simply say "the electrons are in a superposition" and left it at that.}

So if you really want to be picky and define the "start" of the quantum part of the experiment, then I'd say the entrance to the double paths.

Zz.

6. Aug 30, 2016

### atyy

In the standard interpretation, observation is subjective. Some examples:

http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.115.250401
"During the analysis, if the recorded trace crosses a voltage level fixed at around 75% of the expected pulse height from an 810 nm photon, then it is considered to be a detection event. This level was chosen to eliminate with near certainty lower-energy blackbody photons. The time that the trace crosses a level set at around 20% of the expected pulse height is used to timestamp the detection event. We consider the detection event to be complete and the outcome fixed by this point.

7. Aug 30, 2016

### Demystifier

Typically, for larger objects the collapses happen more often. For macroscopic objects, it looks practically continuous.

8. Aug 30, 2016

### vanhees71

If anything is objective, it's observation, at least that's what good experimentalists do their entire life! If an experiment is not objective, it means that nobody else can independently verify its results, and that's to be taken as a sign that it is not a valid experiment in the sense of natural sciences!

I also don't understand, why you think that the quoted text below the link says that observation is subjective. To the contrary it gives clear objective definitions of what's measured in terms of objectively observable "detection events".

9. Aug 30, 2016

### vanhees71

I agree with what you are saying, but one should also emphasize that the classical behavior of electrons (or other charged particles) in setups from good old cathod ray tubes to modern acccelerators is very well in agreement with quantum theory. Why we see a "cathod ray" and not a smeared cloud when a charged particle is going through a gas or a cloud chamber was understood as early as 1929 by Mott's famous paper on the subject:

https://en.wikipedia.org/wiki/Mott_problem

Of course, I disagree with the formulation in terms of "collapse", but that's another story...

10. Aug 30, 2016

### Davor Magdic

I assumed that the electron is in the superposition of positions -- one being the filament is heated enough that the electron has jumped the barrier, and the other that the electron is still in the filament. I.e. I assumed that the electron leaving the filament is a quantum phenomenon and there is no deterministic time when that happens -- at one point the electron is in the filament, at another it's outside, unknowable when exactly. (I don't know if that is true but sounded like it from the description of thermionic emission.)

But if we choose to take the electron jumping the barrier as the start of the quantum part of the experiment, can we not go back to the quantum process that precedes it and so on?

Perhaps changing the definition of where the experiment begins changes the definition of the probability wave we are observing (the larger the chain, the more complex the function, and less calculable I assume).

11. Aug 30, 2016

### ZapperZ

Staff Emeritus
This is extremely puzzling.

1. Thermionic process is described accurately via the Richardson-Duschman model. Can you tell me where is this "superposition of position" here?

2. Why would the electron that never left the material even matter? In other words, why would the process of creating these electrons affect your double-slit experiment? This, you never explain.

If I say that I can give you single electrons, once every 5 seconds on average, with an energy of 2 keV, and an energy spread of 10 eV FWHM, are you telling me that you cannot adequately perform the electron double-slit experiment without knowing how the electrons were created? Are you saying that even if you get electrons with these characteristics, that your experiment will change if the electrons came from thermionic emission, photoemission, field emission, pair production, atomic ionization, etc... etc? Really?

Zz.

12. Aug 30, 2016

### Davor Magdic

I was under impression that if we are considering an electron escaping the metal we only talk about a probability of that happening under certain conditions, and probability implies a superposition of states, does it not? I do not understand the model in detail but several articles mention the thermionic emission as semi-classical i.e. needing quantum mechanics for complete description.

I had mentioned the double slit as an example of a setup, but it seems that even a no-slit experiment -- electrons firing from the gun hitting the phosphorus screen -- is also a quantum experiment, in that we cannot tell precisely what happens and when but only talk about probabilities, and so can be used as an illustration for what I'm trying to understand.

My question is essentially those single electrons, what happens -- how does it change the equations -- if we try to look into where they came from, and how far back we can go doing that, rather then assuming their existence and properties as a starting condition. I do not quite know what I'm trying to achieve with it, but was curious. Logically it follows that by moving the starting conditions further down the chain (towards the "beginning") the probability function gets more and more complex and less usable but maybe not, i.e. naively speaking maybe some complexities cancel each other out? Again my question is what happens if we apply the model to "earlier" starting conditions in the chain, and is there a "beginning".

13. Aug 30, 2016

### ZapperZ

Staff Emeritus
What "equations"? What "model"?

Zz.

14. Aug 31, 2016

### Stephen Tashi

To be clear about the requirement, is it true that we can have a situation of two "equal probability paths" without having a situation that is modeled by a superposition of states? For example, there could be a device that detects an electron and uses a random number generator to decide whether to send it down one path or the other.

15. Aug 31, 2016

### vanhees71

Again, you have to specify what you mean by "superposition of states" here. You have to specify which states you superimpose. In case of a pure state you just specify a ray in Hilbert space, and that's it. It doesn't matter in which basis you express it. E.g., if the state is represented by an arbitrary normalized member of the ray $|\psi \rangle$ you can express it as superposition of any basis states you like. If you want to calculate the probatility to measure a certain value $a$ of the observable $A$, where $a$ is necessarily in the spectrum of the representing operator $\hat{a}$, and $|a,\beta \rangle$ is a set of orthonormalized (generalized) eigenvectors of $\hat{A}$ with eigenvalue $a$, then the probability to find $a$ when measuring $A$ is
$$P(a|\psi)=\sum_{\beta} \left | \langle a,\beta|\psi \rangle \right|^2.$$
That's it. There's no need for superposition. Here the choice of the right basis is dictated by what observable you measure.

16. Aug 31, 2016

### Stephen Tashi

In the case of an experiment, you have to do something practical so their has to be some physical procedures that implement the process of specifying a ray in Hilbert space etc. It seems to me that the original post is asking when it is valid to analyze the outcome of an experiment by approximating the initial conditions as completely known.

In the case of classical physics it is clear that if you achieve some initial state (e.g. an object initially at rest at the top of an incline plane) then the further progress of the experiment is determined by the information in the initial state (e.g. it doesn't matter whether you put the object at the top of the inclined plane with a winch or with a forklift.). I suppose a similar principle applies to a QM model of an experiment if we consider Quantum states. So the question seems to boil down to asking when we can use macroscopically observable processes (e.g. I set the voltage reading to 1230 volts) to create initial quantum states that are approximately "known".

17. Sep 1, 2016

### atyy

Yes, if you keep looking at the system, you will cause the wave function to continually collapse.

Collapsing a wave function is one way of beginning a quantum experiment. I don't have time to describe it, but attaching a time to an observation, and hence a time to collapse is often carried out in Bell tests, in which observations have to be time stamped. Another place to look is Fig. 3 and 4 of https://arxiv.org/abs/1604.08020 where they use a "heralding event" to mark the time at which an experiment begins.

18. Sep 1, 2016

### Demystifier

Yes, you often emphasize this, so this must me important for you. But formulation with collapse cannot be experimentally distinguished from the formulation without collapse, so it is a matter of interpretation. On the other hand, you also often emphasize that interpretation is not relevant for physics. So if the question of collapse is not relevant for physics, then what is it relevant for?

19. Sep 1, 2016

### vanhees71

Collapse is contradicing very basic principles of (relativistic) physics, the locality of interactions and causality, and it's not observable, as you say yourself. So why should I keep this unnecessary assumption as part of any interpretation?

20. Sep 1, 2016

### Demystifier

21. Sep 1, 2016

### vanhees71

Do you mean your question: "So if the question of collapse is not relevant for physics, then what is it relevant for?" Then I answered it. I try once more: First of all the collapse assumption is relevant to physics because it violates basic principles of relativistic physics. 2nd it's (thus fortunately!) irrelevant to physics, because it's never observed and never necessary to be invoked to apply quantum theory to the analysis of real-world observations/experiments, while the very foundations of relativistic QFT (locality of interactions) is a very successful assumption. So in my opinion there is no collapse and there must be no collapse since its assumption just makes the physical (!) interpretation inconsistent with its very foundations. So it's a contradiction within the entire framework of (relativistic) QT and thus shouldn't be postulated to begin with.

22. Sep 1, 2016

### Demystifier

So basically, you are saying that collapse is both relevant and irrelevant to physics. Don't you see that as a contradiction? Aren't you using double standards for "being relevant to physics"?

23. Sep 1, 2016

### vanhees71

No, I guess I just don't express my opinion clearly enough. Let me try again: I think the postulate of collapse is contradicting the fundamental postulates of relativistic QFT (locality of interactions, (micro-)causality). At the same time it's not needed to apply QT to real-world observations. That's why I just don't postulate it to begin with. In this sense it's irrelevant to physics. At the same time it's not just a matter of interpretation, but it's even worse, because postulating it makes the theory inconsistent in itself. So it must not be postulated (and fortunately it also doesn't need to be postualted).

24. Sep 1, 2016

### Demystifier

I still don't get it.

Let me compare it with gauge ghosts. They have a wrong connection between spin and statistics, so they contradict relativistic QFT. Fortunately they are not observable, so they do not really contradict relativistic QFT. But everything can also be computed without them, so it is not necessary to introduce them. Yet, many physicists find physics easier when they use them.

Aren't gauge ghosts similar to collapse? By what general criteria are gauge ghosts acceptable and collapse not? After all, they are both just a tool for thinking about nature (neither of them is physically "real"), and the point of theoretical physics is to give us useful tools for thinking about nature.

Last edited: Sep 1, 2016
25. Sep 1, 2016

### Demystifier

In addition, the collapse does not need to be postulated. It can be invented as a thinking tool, compatible with minimal ensemble interpretation and standard rules for conditional probability. In this sense it can be derived from QM, or even from relativistic QFT, in a minimal ensemble interpretation.

The only interpretational aspect of collapse is talking about whether it is real or just a tool. But as long as you merely use it as a tool, and don't talk or think about it's possible reality, there is nothing controversial or interpretational about collapse. As a tool, the collapse is neither more nor less physical than gauge ghosts.