Self-interference in double-slit experiments

[Carpe Physicum]

Perhaps we have to distinguish between "phenomena" and "properties of phenomena". If specifying a phenomena exactly requires describing all its properties, we are out of luck - yet we do it approximately all the time. For example, "my cat".

Maybe. My point was, it's not so simple as the holier-than-philosophers poster implied.

 

[vanhees71]

Like epicycles, right? ;)

Epicylces are no observation but a (by the way correct though not very efficient!) description of planetary motion.

 

[Carpe Physicum]

Epicylces are no observation but a (by the way correct though not very efficient!) description of planetary motion.

Epicycles are phenomenon observed in nature, just like orbits. Or so they thought. My point is, they were considered real in their time until it was realized they weren't. Same with circular orbits. Point being, they were considered real, and in a sense reproducable, albeit by "the creator" or the sun.

 

[Stephen Tashi]

Epicylces are no observation but a (by the way correct though not very efficient!) description of planetary motion.

The formalism of QM speaks of measurements and their association with linear operators. If the result of a "measurement" is single number, then how do we formalize "observations" that are more complicated - such as "The particle was detected at 3 points that lie in a straight line" or "the planet moves in an elliptical orbit"?

In a hand-wavy manner, I could say that "observations" are merely elaborate sets of measurements, each of whose result is a single number. However, can we handle the mathematical technicalities of assigning probabilities to observations? - meaning can we handle them by the standards of mathematics - measure theory as opposed to intuitive physical arguments.

 

[vanhees71]

"The particle was detected at 3 points that lie in a straight line". Where has this been ever observed. You observe particles as single point-like events in a detector (of course with always finite position resolution). "The planet moves in and elliptical orbit" is described with overwhelming accuracy by classical mechanics (and be it general relativistically if it comes to high accuracy). Why this is a good description is understandable from quantum statistics (particularly decoherence through interaction with the "environment").

Mathematics is the language we use to describe our observations and theories about them. In my opinion the relation between probabilities and observations is given by the usual frequentist interpretation, and that's how probabilistic predictions as those from QT are tested by observations. An important addition to "classical probability theory" (e.g., a la Kolmogorov) are the notions of information theory (a la Shannon and Jaynes).

 

[Stephen Tashi]

"The planet moves in and elliptical orbit" is described with overwhelming accuracy by classical mechanics (and be it general relativistically if it comes to high accuracy). Why this is a good description is understandable from quantum statistics (particularly decoherence through interaction with the "environment").

It is understandable in a hand-wavy way, but I was speaking of how to define "observations" of that sort in a precise mathematica formalism. Or is the elliptical orbit of a planet not an "observation"? You said epicycles are not "observations".

This is somewhat of a quibble about vocabulary, but it is an important one. If the formalism of QM is based on "measurements" and the result of a "measurement" is a single number, then what is the formalism for defining an "observation" ( or "result" or whatever we want to call it) that is more complicated that a single number?

One thought is that the single number produced by a "measurement" is interpreted as the coefficient of a particular vector and that vector can contain complicated information. However, in the example of the shape of the orbit of a planet, I don't see how to do this.

 

[PeterDonis]

is the elliptical orbit of a planet not an "observation"

No, it's not. The observations are the locations of planets on Earth's sky at particular times by Earth clocks. The elliptical orbits are theoretical constructions from the data. They are extremely useful theoretical constructions, but they're still theoretical constructions.

 

[Stephen Tashi]

The observations are the locations of planets on Earth's sky at particular times by Earth clocks. The elliptical orbits are theoretical constructions from the data.

How is the measurement of a location at a given time not, in practice, also theoretical construction based on the theory of how the detecting apparatus works?

I agree that we can think of an underlying "real" measurement whose result is inferred from data and how the detection process is performed. What I don't understand is the limitation on what such a measurement can represent. The typical examples of measurements are measurements of position and momentum - or things inferred from such measurements (e.g. spin-up = it was detected above as opposed to below). Is there a terminology for a set of such measurements taken at different times, possibly on different physical systems ? Or is there a way to define a "the wave function" in a generalized way so that a measurement performed on it gives a set of such measurements?

 

[PeterDonis]

How is the measurement of a location at a given time not, in practice, also theoretical construction based on the theory of how the detecting apparatus works?

I did not say "location" unqualified. I said specifically "location on Earth's sky". If you want to say that a sextant, for example, requires a "theoretical construction" in order to explain how it gives you the location of an object on Earth's sky, I can't stop you, but it's certainly not the same kind of "theoretical construction" that is required to obtain an elliptical orbit about the Sun for a planet based on many, many observations of locations of the planet and the Sun on Earth's sky.

What I don't understand is the limitation on what such a measurement can represent.

I don't understand what kind of limitation you are talking about.

 

[Stephen Tashi]

I don't understand what kind of limitation you are talking about.

For example, in arguments about the interpretations of QM, some people have no hesitation in talking about kets that represent complicated phenomena such as "| alive cat>". Can such examples be taken seriously? Can we have a ket "| elliptical orbit>" ?

 

[PeterDonis]

in arguments about the interpretations of QM, some people have no hesitation in talking about kets that represent complicated phenomena such as "| alive cat>". Can such examples be taken seriously?

If we assume that everything can be described as a quantum system, then certainly a cat can be. So how seriously you take kets like |alive cat> depends on how seriously you take the assumption that everything can be described as a quantum system. Which in turn depends on which interpretation of QM you favor. Experimentally we have no prospect of, for example, putting cats through double slit experiments and measuring the interference, if any, any time soon; this illustrates why the QM interpretation debate is still alive and kicking after a century.

 

[vanhees71]

As you seem to imply by these questions, I don't think that $|\text{alive cat} \rangle$ makes any sense. A cat is a very complicated many-body system, and to associate a pure state to it (which in principle of course is theoretically possible) is impossible for all practical purposes, and it's almost always unnecessary to describe the cat. Rather you can try to describe it classically, i.e., to start you can take one fixed point in the cat and describe the cat thus as a "point particle" as in Newtonian mechanics, and this is already enough information to know where the cat (roughly!) is located. You can put, e.g., a GPS on the cat and follow its trajectory as a function of time. This is a perfectly adequate description to learn how the cat wanders around. Of course, you can also ask much more complicated questions, e.g., how a cat jumps down from a tree and always lands on its feet. That will be a much more involved description, but it will still consist of some "rough" parameters in terms of classical coordinates.

From a quantum point of view you describe the cat in a very "coarse grained" way, choosing the relevant observables depending on what you want to describe (e.g., a vet will not be interested in the trajectory of the cat but rather its temperature and other parameters to determine the cat's "state", e.g., whether it's "dead" or "alive", but also this will never need a complete microscopic description of the entire cat in terms of a pure state). Formally this is described by a statistical operator, which is not representing a pure state, i.e., it represents only the (supposed to be) relevant information about the cat for a given level or aspect of description, and that's the key for understanding "the emergence of a classical world". The coarse-grained macroscopic quantities of classical physics, depicting some relevant aspect at a given level of description, are averages over very many microscopic degrees of freedom, which are ignored based on the belief that these microscopic details are not relevant on the level of description chosen to describe the specific aspect of the cat's state that is of interest for the aspect you want to investigate about the cat.

The "weirdness of QT" mostly is due to the popularized description rather than QT itself. QT forces us to rethink about our view of the world which is trained by everyday experience with macroscopic objects, of which usually only a very coarse-grained view is relevant to predict their behavior at a level sufficient to deal with them in everyday life. It's no surprise that the world looks completely differently on a microscopic level where you resolve certain aspects of matter down to the most elementary constituents (or what we think these elementary constituents are at a given level of description).

If you look at the history of our natural-science knowledge about matter, in physics there are two ways of investigations about the world. The one is to figure out the tinier and tinier building blocks of matter, starting from condensed matter, extracting molecules, atoms, stripping of the electrons, finding the nucleus, splitting it into protons and neutrons and finally finding out that these themselves consist of quarks or quarks and gluons, which according to todays knowledge seem to be the fundamental building blocks of all matter (together with the electrons forming the neutral atoms, molecules and matter around us). This is roughly what a high-energy particle physicist does. Then s/he takes these supposed to be elementary building blocks and through scattering experiments and sophisticated theories investigates their interactions in all possible details.

The other way is in some sense the opposite: It tries to reconstruct from the understanding of the fundamental building blocks and their interactions, the composite objects forming the everyday matter around us. This research reaches over almost all subdisciplines of physics, from condensed-matter physics over nuclear physics to astrophysics and cosmology. This rough subdisciplines roughly depict also the different levels of description, i.e., which constituents can be taken as fundamental and described as the effective microscopic degrees of freedom to describe the observed macroscopic behavior (e.g., for a solid-state physicist the fundamentale consituents are atoms, for a nuclear physicist the protons and neutrons, etc.). The usual description then leads to other effective degrees of freedom, socalled quasiparticles and to layers of effective classical and semi-classical models (e.g., in condensed matter physics Boltzmann or Boltzmann-Uehling-Uhlenbeck equations, which is already a semiclassical description which can be derived from relativistic or non-relativistic many-body QFT via coarse-graining techiques, then further down to fluid dynamical descriptions assuming local thermal equilibrium).

 

[A. Neumaier]

everything can be described as a quantum system, then certainly a cat can be. So how seriously you take kets like |alive cat> depends on how seriously you take the assumption that everything can be described as a quantum system.

No, but on how seriously you take the assumption that everything can be described as a quantum system in a pure state. Nobody in real applications describes a macroscopic quantum system by a pure state - it is always described as a mixed state.

Note that the concept of superposition of mixed states does not make sense - thus the problem disappears.

 

[Stephen Tashi]

As you seem to imply by these questions, I don't think that $|\text{alive cat} \rangle$ makes any sense.

...

to associate a pure state to it (which in principle of course is theoretically possible) is impossible for all practical purposes,

To understand why defining "alive cat" is impossible for practical purposes, I'd have to understand how it would be theoretically defined! Are definitions like this going to be controversial matters of interpretation?

One interpretation of a "pure state" is that it is a result of some measurement process on the system that satisfies the property that it we repeat the measurement without letting the system "evolve" then we always get the same result. As I understand this (as a basis for a definition) the measurement may be a complicated data set, not just a single number, or it might be a single "bit" (0 or 1) that is the output of a complicated algorithm applied to a complicated set of data.

One theoretical challenge to defining "the cat is alive" as a pure state is that such property involves processes that take place in time - e.g. the cat's heart is beating. Can the definition of the state "alive cat" be formulated in way that does not involve considering data taken over an interval of time during which the system (the cat) is "evolving"?

I can imagine a cat in a box as a system of classical particles and imagine a super-veterinarian who pass judgement on any joint state of these particles (at a given time) and tell me whether they represent a live cat or a dead cat. Let's say the super-veterinarian can judge whether a (static) configuration of particles is such that a live cats bodily processes are proceeding properly. The super-veterinarian doesn't make the mistake of defining a dead cat that comes back to life. Judgements about the current state of the particles only classify the state as "dead cat" when the system will continue to evolve only to other configurations classifed as "deat cat".

That's the best I can do to define the state of "alive cat" in a classical model. I don't see how that translates to a QM model of particles.

 

[vanhees71]

It's not impossible to define "alive cat". Usually it's pretty obvious if a cat is alive ;-)). It's in my opinion only pointless and impossible to think you can describe such a very rough statement about "an object" by a pure quantum state.

 

[zonde]

To understand why defining "alive cat" is impossible for practical purposes, I'd have to understand how it would be theoretically defined! Are definitions like this going to be controversial matters of interpretation?

Well, if you take "alive" as quantum property then defining "alive cat" as pure state is not possible even theoretically. The starting point for pure state is ensemble of identical particles. Say electrons are all indistinguishable. Cats on the other hand are very, very distinguishable. QM certainly does not say that you can describe by single state vector an ensemble of distinguishable systems.
Alternatively you could specify (and clone) certain cat down to all the particles and their configurations, but then this specification will already determine if particular cat is alive.

 

[Stephen Tashi]

Well, if you take "alive" as quantum property then defining "alive cat" as pure state is not possible even theoretically.The starting point for pure state is ensemble of identical particles. Say electrons are all indistinguishable. Cats on the other hand are very, very distinguishable. QM certainly does not say that you can describe by single state vector an ensemble of distinguishable systems.

Then what's going on in the thread https://www.physicsforums.com/threads/quantum-theory-nature-paper-18-sept.955748/ ?
There we have coins and laboratories. Does that discussion avoid the assumption that such things have pure states?

 

[zonde]

Then what's going on in the thread https://www.physicsforums.com/threads/quantum-theory-nature-paper-18-sept.955748/ ?
There we have coins and laboratories. Does that discussion avoid the assumption that such things have pure states?

I would say no, it does not avoid that assumption. But I tried to think of that thought experiment replacing macroscopic objects with microscopic or simply doing the math part. I don't know about the others participating in that discussion.