Do we measure the particle or the wavefunction?

[quantumfunction]

It seems to me that we don't measure a particle because a particle doesn't have an objective existence independent of the wave function or does it? The wave function in this case would have to be real because you can't have probability without the underlying possibility of a specific outcome being real. So if I roll a dice, I may get a 1-6 but I can only get a 1-6 because these are real possibilities.

If a particles wave function is spread out in a box, of course the particle itself isn't everywhere in the box but the wave function is which carries the possible outcomes that can occur. We also know the wave function can exist without a particle. It's just evolving according to Schrodinger's equation until somone or something decides to disturb it.

So isn't it wrong to say we measure a particles x and shouldn't we say that you can measure the wave function which produces a particle which carries a possible quantum state of the wave function? Where am I going wrong?

 

[PeterDonis]

isn't it wrong to say we measure a particles

Yes, we don't measure particles, we measure observables. See below.

shouldn't we say that you can measure the wave function

No, because measurements can only give you real numbers, and the wave function is not a real number. It's a function with complex values.

Mathematically, to make a measurement on a quantum system with a particular wave function, we apply an operator to the wave function that corresponds to the measurement. This gives us a set of real numbers that correspond to the probabilities of all the different possible measurement outcomes. One of those outcomes will be the actual measurement result.

 

[zonde]

Where am I going wrong?

You have to specify interpretation if you ask what's real in quantum mechanics.

 

[quantumfunction]

No, because measurements can only give you real numbers, and the wave function is not a real number. It's a function with complex values.

Isn't part of the wave function real?

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit which satisfies the equation i2 = −1. In this expression, a is the real part and b is the imaginary part of the complex number.

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

You said:

This gives us a set of real numbers that correspond to the probabilities of all the different possible measurement outcomes.

Doesn't these set of real numbers that correspond to probabilities of all different measurement outcomes, come from the wave function? If these probable states that can occur don't come from the wave function then where do they come from? When superposition occurs doesn't the wave function contain the information about each possible state the particle can be in?

It's like the dice. I can want to roll a 7 all day but it's not a possible outcome. So doesn't the wave function or something need to be real in order for these possible outcomes to be able to occur?

 

[quantumfunction]

You have to specify interpretation if you ask what's real in quantum mechanics.

It's not really an interpretation. It's Unamendeed Quantum Mechanics, so no collapse and no particles, just the wave function and all it's different versions exist from the electron to Schrodinger's cat.

 

[PeterDonis]

Isn't part of the wave function real?

Sure, every complex number has a real part. But that doesn't make the wave function as a whole real.

Doesn't these set of real numbers that correspond to probabilities of all different measurement outcomes, come from the wave function?

Not just from the wave function. The numbers come from applying an operator to the wave function.

When superposition occurs doesn't the wave function contain the information about each possible state the particle can be in?

"Each possible state" depends on the operator; the wave function itself doesn't tell you which states are "possible states" when you make a particular measurement.

doesn't the wave function or something need to be real in order for these possible outcomes to be able to occur?

"Real" is not a scientific term. If you want to say that the wave function must be "real" for this reason, that's just your choice of words; it says nothing about the physics. The physics is what I said above.

 

[zonde]

It's not really an interpretation. It's Unamendeed Quantum Mechanics,

Then setup of experiment is real. What else is real depends on interpretation.

 

[quantumfunction]

You said:

"Each possible state" depends on the operator; the wave function itself doesn't tell you which states are "possible states" when you make a particular measurement.

Wavefunction Properties

Image URL
http://hyperphysics.phy-astr.gsu.edu/hbase/imgmod2/wf2.gif

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/wvfun.html#c1

So the wave function contains measurable information. How can it not be real but contain measurable information. The wave function can transmit information without a particle as a medium.

The wave-function is real but nonphysical: A view from counterfactual quantum cryptography

Counterfactual quantum cryptography (CQC) is used here as a tool to assess the status of the quantum state: Is it real/ontic (an objective state of Nature) or epistemic (a state of the observer's knowledge)? In contrast to recent approaches to wave function ontology, that are based on realist models of quantum theory, here we recast the question as a problem of communication between a sender (Bob), who uses interaction-free measurements, and a receiver (Alice), who observes an interference pattern in a Mach-Zehnder set-up. An advantage of our approach is that it allows us to define the concept of "physical", apart from "real". In instances of counterfactual quantum communication, reality is ascribed to the interaction-freely measured wave function (ψ) because Alice deterministically infers Bob's measurement. On the other hand, ψ does not correspond to the physical transmission of a particle because it produced no detection on Bob's apparatus. We therefore conclude that the wave function in this case (and by extension, generally) is real, but not physical. Characteristically for classical phenomena, the reality and physicality of objects are equivalent, whereas for quantum phenomena, the former is strictly weaker. As a concrete application of this idea, the nonphysical reality of the wavefunction is shown to be the basic nonclassical phenomenon that underlies the security of CQC.

https://arxiv.org/abs/1311.7127

You said:

"Real" is not a scientific term. If you want to say that the wave function must be "real" for this reason, that's just your choice of words; it says nothing about the physics. The physics is what I said above.

I think real is a scientific term. I don't know any Scientist who wouldn't say the effects of Gravity isn't Real. We don't know if it's a fundamental force, an emergent property or if it comes from the entropy of entanglement but we do know it's a real effect.

 

[PeterDonis]

How can it not be real but contain measurable information.

If you want to say that "real" means "contains measurable information", then that's your choice of words.

I thin real is a scientific term.

You can certainly choose to use "real" to mean something scientific. But saying something is "real" doesn't tell you what that scientific something is; different scientists use it to refer to different things. If I say "applying an operator to a wave function gives a set of real numbers which tell the probabilities of the possible measurement results", that is a definite scientific statement with testable content; saying "and that means the wave function is real" adds no new information, it's just a label you choose to put on it.

 

[quantumfunction]

If you want to say that "real" means "contains measurable information", then that's your choice of words.
You can certainly choose to use "real" to mean something scientific. But saying something is "real" doesn't tell you what that scientific something is; different scientists use it to refer to different things. If I say "applying an operator to a wave function gives a set of real numbers which tell the probabilities of the possible measurement results", that is a definite scientific statement with testable content; saying "and that means the wave function is real" adds no new information, it's just a label you choose to put on it.

I didn't say the wave function was real in a vacuum. I said the wave function is real because of x,y and z. You can't debate the conclusion without the x, y and z that led to the conclusion.

The wave function contains all measurable information and establishes the probability distribution in three dimensions.

This is my point, the information has to be real in order for there to be possible outcomes. I can want to roll a 7 until I'm blue in the face but if the only possible outcomes that are real are 1,2,3,4,5 and 6 then I can't roll a 7. So the wave function contains real information about possible outcomes. I don't think you need anything but a wave function that contains this real information and no collapse or particles that mucks things up.

 

[rubi]

The wave function is just an improved version of a probability distribution. A probability distribution just stores the information about what is going to happen, but it doesn't itself "physically exist". It can nevertheless be objective. Here's an example: The probability distribution of a die is $p(n)=\frac{1}{6}$. This distribution just tells you how often you would expect $n$ if you throw a die a large number of times. The number $\frac{1}{6}$ doesn't have a "physical existence", but it is objective, since it best describes the experiment of throwing a die a large number of times. The situation is exactly analogous for the wave function. It's a just a specification of probability distributions. The difference between classical and quantum mechanics is that classical mechanics is deterministic and all probability distributions can in principle be derived from an underlying theory about things that physically exist. In quantum mechanics however, the world is not deterministic and there is a genuine element of randomness, so the best description you can have is a probability distribution. These probability distributions still just describe the relative frequencies of outcomes and they are still objective, since only one probability distribution will match the observed relative frequencies. But also, they still don't "exist physically", just like the probability distribution for a die doesn't "exist pysically".

(Disclaimer, so I don't have to bother with interpretations: Some people prefer alternative interpretations.)

 

[PeterDonis]

I didn't say the wave function was real in a vacuum. I said the wave function is real because of x,y and z.

Exactly. And for different situations, "real" will refer to a different x, y, and z. So why even use the term "real" at all? Why not just talk about the specific x, y, and z, since those are what contain the actual physics?

the wave function contains real information about possible outcomes.

The wave function plus an operator contains information about possible outcomes. But without an operator, the wave function itself does not.

This fact is obscured in many sources because they always write down the wave function in a particular basis (for example, the position basis or the momentum basis). But choosing a basis is equivalent to picking an operator and applying it to the wave function. So when you talk about a wave function written in a particular basis, you are not just talking about the wave function; you are talking about the wave function plus the operator that defines that basis. And all the information about possible outcomes which you read off from the wave function written in that basis is really information from the wave function plus the operator.

To really understand what it means to have just the wave function without choosing a basis, the Dirac bra-ket notation is much better. In this notation, the term "state vector" is usually used, not "wave function", to make it clear that we are talking about a vector in an abstract space (called Hilbert space) that can be defined and manipulated mathematically without choosing any particular basis.

 

[A. Neumaier]

a particle doesn't have an objective existence independent of the wave function

It's rather the other way around. A wave function has no objective existence, whereas particles exist at least under certain conditions. For example, a single proton is a very real particle. We measure properties of single particles or collective properties of multi-particle systems.

 

[quantumfunction]

The wave function is just an improved version of a probability distribution. A probability distribution just stores the information about what is going to happen, but it doesn't itself "physically exist". It can nevertheless be objective. Here's an example: The probability distribution of a die is $p(n)=\frac{1}{6}$. This distribution just tells you how often you would expect $n$ if you throw a die a large number of times. The number $\frac{1}{6}$ doesn't have a "physical existence", but it is objective, since it best describes the experiment of throwing a die a large number of times. The situation is exactly analogous for the wave function. It's a just a specification of probability distributions. The difference between classical and quantum mechanics is that classical mechanics is deterministic and all probability distributions can in principle be derived from an underlying theory about things that physically exist. In quantum mechanics however, the world is not deterministic and there is a genuine element of randomness, so the best description you can have is a probability distribution. These probability distributions still just describe the relative frequencies of outcomes and they are still objective, since only one probability distribution will match the observed relative frequencies. But also, they still don't "exist physically", just like the probability distribution for a die doesn't "exist pysically".

(Disclaimer, so I don't have to bother with interpretations: Some people prefer alternative interpretations.)

Where did this probability distribution come from if the wave function isn't the underlying reality that contains all measurable information about the system. You can't have a probability distribution without the possible outcomes being real. So in this case, the wave function is like the dice that contains all measurable information that can occur. The dice contain the numbers 1-6 and the wave function contains all measurable information.

 

[quantumfunction]

It's rather the other way around. A wave function has no objective existence, whereas particles exist at least under certain conditions. For example, a single proton is a very real particle. We measure properties of single particles or collective properties of multi-particle systems.

There's no need for particles. Waves are enough to explain particle like properties. Here's 2 good papers on this.

There are no particles, there are only fields

Quantum foundations are still unsettled, with mixed effects on science and society. By now it should be possible to obtain consensus on at least one issue: Are the fundamental constituents fields or particles? As this paper shows, experiment and theory imply unbounded fields, not bounded particles, are fundamental. This is especially clear for relativistic systems, implying it's also true of non-relativistic systems. Particles are epiphenomena arising from fields. Thus the Schroedinger field is a space-filling physical field whose value at any spatial point is the probability amplitude for an interaction to occur at that point. The field for an electron is the electron; each electron extends over both slits in the 2-slit experiment and spreads over the entire pattern; and quantum physics is about interactions of microscopic systems with the macroscopic world rather than just about measurements. It's important to clarify this issue because textbooks still teach a particles- and measurement-oriented interpretation that contributes to bewilderment among students and pseudoscience among the public. This article reviews classical and quantum fields, the 2-slit experiment, rigorous theorems showing particles are inconsistent with relativistic quantum theory, and several phenomena showing particles are incompatible with quantum field theories..

https://arxiv.org/ftp/arxiv/papers/1204/1204.4616.pdf

No Evidence for Particles

There are a number of experiments and observations that appear to argue for the existence of particles, including the photoelectric and Compton effects, exposure of only one film grain by a spread-out photon wave function, and particle-like trajectories in bubble chambers. It can be shown, however, that all the particle-like phenomena can be explained by using properties of the wave functions/state vectors alone. Thus there is no evidence for particles. Wave-particle duality arises because the wave functions alone have both wave-like and particle-like properties. Further the results of the Bell-Aspect experiment and other experiments on entangled systems, which seem to imply peculiar properties for particles if they exist, are easily and naturally understood if reality consists of the state vectors alone. The linear equation-Hilbert space structure for the state vectors, by itself, can explain every mystery in quantum mechanics except the origin of the probability law.

https://arxiv.org/ftp/arxiv/papers/0807/0807.3930.pdf

Like I said, all you need is the wave function to describe particle like properties.

 

[Nugatory]

So if I roll a dice, I may get a 1-6 but I can only get a 1-6 because these are real possibilities.

It's not at all clear what you mean by a "real possibility", but if you mean "has a non-zero probability" then this statement is correct.

However, you wouldn't claim that this means that the axioms of probability theory are real solid tangible things that we can measure, nor that the abstract probability space that contains abstract elements corresponding to the six possible outcomes is real. It just means that these mathematical abstractions can be used to make useful calculations, including that the outcome of rolling a die modeled by these abstractions will always be 1, 2, 3, 4, 5, or 6.

The situation is similar with the mathematical formalism of quantum mechanics. We have an abstract mathematical object (called a "wave function" for historical reasons) in an equally abstract infinite-dimensional Hilbert space, and if we perform certain abstract mathematical manipulations on this object we will get results that match the results of measurements quite well. That doesn't mean that we're measuring the wave function, it means that we're using the wave function to calculate the results of measurements performed on the system it describes (and yes, that system may be a single particle).

So... If we are looking for a B-level answer to the question in the thread title, it will be, consistent with @PeterDonis's and
@A. Neumaier's posts above: We measure observables of the quantum system, which may but need not be a single particle. We don't measure the wave function; it's just a piece of math that we use to calculate the likelihood of various measurement results.

There are many subtleties here, but unfortunately none of them can be discussed effectively in a B-level thread, so this thread is closed. As always, anyone can a PM any mentor to ask that it be reopened of there is more to say at this level.