7. to the quantum measurement problem:
Four types of approach
to the quantum measurement problem:
1. Ignoring the problem
2. Taking the measurement postulate literally
3. Assuming further basic principles
4. No collapse approaches

8. Extreme form: the world just works like this
1. Ignoring the problem
Perhaps the most common view consists in giving up the search for a representation of microscopic reality
"Shut up and calculate"
Extreme form: the world just works like this
There is no deeper reason why the calculus works

9. 2. Taking the measurement postulate literally
Two different types of time evolution:
ordinary, governed by the Schrödinger equation (general)
special, collapse of the state vector (measurement)
Difficulties: what counts as a measurement?
Why should it be special?
What defines a measuring apparatus?
"Classical"? "Macroscopic"?
No physical criterion for collapse
Awkward idea two different sorts of dynamics at basic level

11. Only well defined way to take the formalism literally:
measurement involves the observer's CONSCIOUSNESS
(London & Bauer, 1939, Wigner, 1961)
Purely physical systems are governed by the Schrödinger equation
Collapse involves a non-physical cause
Difficulties: a macroscopic object
can be in a superposition of different macroscopic states
until a conscious being looks at it
Schrödinger's cat
The universe before the appearance of conscious beings
The notion of collapse sits uneasily with the rest of physics
(instantaneous, temporally asymmetric, nonlocal)

14. 3. Invoking further basic principles
General processes are still governed by the Schrödinger equation, but collapse is derived from new basic principles
GRW interpretation (Ghirardi, Rimini & Weber, 1986)
Particles described by clouds of probability, but they spontaneously collapse to a localized position every seconds
Difficulties: spontaneous collapse is an ad hoc hypothesis,
privileges the position representation

15. Hidden variables: Einstein's favorite Bohm's theory, 1952
Definite position and trajectories governed by the "pilot wave" or "quantum potential"
Difficulties: it radically abandons locality,
the quantum potential here is determined by the wave function on far away galaxies
Both Bohm and GRW privilege position over momentum, breaking the symmetry of quantum dynamics

16. David Bohm

18. 4. No collapse approaches
The world is really in a superposition of states at all levels, micro and macro
Schrödinger’s cat is really alive and dead at the same time
Why don’t we realize this?
What distinguishes a superposition from the corresponding "collapsed version" (i.e., from the corresponding set of "classical alternatives")?

20. E.g., what is the difference between a set of balls in the superposed state and a set of balls 50% of which are outside the box and 50% are inside the box?
A single observation wouldn't be able to distinguish these two situations, but the statistics of a number of observations would distinguish them

21. the ball is outside (0) or inside (1) the box
Let us consider a set of identical systems characterized by two properties:
the ball is outside (0) or inside (1) the box
the ball is light (L) or heavy (H)
What is the probability of finding a heavy ball?
Say p(H, 0) is the probability of finding the ball is heavy if I know that it is out of the box and
p(H, 1) is the probability of finding the ball is heavy if I know the ball is in the box.

22. Then in the classical alternative case: p(H) = p(H, 0) + p(H, 1)
In the superposed state there is a further term allowing for the possibility that the ball is inside and outside the box at the same time:
p(H) = p(H, 0) + p(H, 1) + p(H, 0, 1)
p(H, 0, 1)
is called "interference term"
The reason behind the name is clear if we refer back to the two slit experiment

23. We’ll look at three answers:
In the no collapse approach the quantum measurement problem consists essentially in the question: why does the interference term appear not to be there?
We’ll look at three answers:
- because the universe splits into many worlds (Everett)
- because of the macroscopic nature of the apparatus (decoherence)
- because of the existence of a trace or recording of the measurement (persistence of information)

24. Everett's many worlds interpretation (1957)
Takes the state vector of the whole universe as objectively real
Replaces the notion of collapse with that of branching
Each of the various possible outcomes of a quantum measurement exists in a separate universe
E.g. I measure the spin of a particle along a certain direction and I find “up”
In a parallel universe there is another copy of myself performing the measurement and finding spin “down”
All that could possibly happen (according to quantum physics) happens in some universe

27. Hugh Everett III proposed his theory when still a graduate student
Abandoned physics after completing his Ph.D.
Difficulties:
Occam’s razor?
Entia non sunt multiplicanda praeter necessitatem
(Entities must not be multiplied beyond necessity)
The “weight” of various worlds

28. Decoherence (Zeh, 1970)
The interference term in the superposition of two macroscopic states decays rapidly in time.
With a typical measuring apparatus containing something like 1023 particles the decay time is much shorter than the time required for a macroscopic observation.
Furthermore the measuring apparatus is not isolated: it becomes entangled with the laboratory environment and eventually with the whole universe.
Therefore, even though the interference term never exactly vanishes, it is in practice unobservable

29. Persistence of information (Sabbadini, 2005)
The interference term vanishes exactly when there is some kind of trace or recording of the outcome of the measurement process.
Trace can be anything macroscopic, e.g. the position of the pointer.
But it can also be something microscopic whose state is not further investigated,
e.g. quantum beats, quantum eraser
The interference term must be taken into account only when an observation is carried out that destroys all information about the previous measurement

34. Embodiment
What are the philosophical implications of the persistence of information approach?
Classical physics is the world seen through the eye of God. It is assumed to correspond to objective reality, to things as they really are.
Quantum physics is the world seen through the eyes of an embodied observer. Perception corresponds to an event happening in the body, to a trace being formed in the body. We are only aware through these traces. But the existence of a trace erases the interference terms and therefore makes the superposition equivalent to a classical alternative. That is why the world appears classical to us.

35. What image of the world arises from this?
First there is consciousness, without which there is nothing. Why consciousness is there, why there is something instead of nothing?
Impossible question, we are on the very edge of language!
What we do know is that experience is ordered, that it is structured. A fundamental structure of experience is what we call matter. And a center piece within this fundamental structure is our body.
Physics is a map of the “matter-structure” of experience.

36. We can live AS IF the world consisted of solid matter.
While in classical physics the map was assumed to represent something objectively existing out there, in quantum physics it merely represents the structure of experience, which can no longer be conceived as an external reality.
Nevertheless, the representation of the world as “objectively existing out there” is still practically adequate for the vast majority of our experiences (all, except those skilfully contrived to reveal the secrets of the microscopic world).
We can live AS IF the world consisted of solid matter.

37. I would propose the opposite point of view:
Some neuroscientists speak of consciousness as an “emergent property” of matter
I would propose the opposite point of view:
matter is an emergent property of consciousness!
Yet consciousness is embodied,
the world is experienced through a body and each experience leaves a trace in the body
The circle of existence:
CONSCIOUSNESS > MATTER > BODY > CONSCIOUSNESS

38. CONSCIOUSNESS
BODY
MATTER