the problem with cats lessons in quantum collapse

hair balls, litter boxes, decapitated birds Schroedingers Cat & Wigners Friend the parts of collapse contributions of decoherence the remaining options (choose your weirdness)

hair balls, litter boxes, decapitated birds Schroedingers Cat & Wigners Friend the parts of collapse contributions of decoherence the remaining options (choose your weirdness)

Blaylock - UMass seminar 3/4/11 1

The problem with catslessons in quantum collapse


Shroedinger’s Cat

Until the box is opened and examined by the researcher, the cat is in a super-position of being alive and dead.

with apologies to Berk Breathed

The Measurement Problem I


Wigner’s FriendWhen and how does collapse occur?

WignerWigner’s friend

Wigner’s press agent

The Measurement Problem II


Collapse is nonlocal

This is a very particular, very restricted form of nonlocality. We still can’t make anything travel faster than the speed of light, or send a signal faster than the speed of light. Collapse is no use for intergalactic telephone calls.

Collapse changes a wave function that is spread out over a region to a wave function that is localized in one spot. This is a nonlocal process!

Rather like voodoo.


Collapse is not Lorentz invariant

Consider two photons produced in an entangled state:

Convention says when Alice measures one photon, both collapse simultaneously.

From Bob’s perspective in his relativistic space ship, Alice’s photon collapses after the other photon.

In what reference frame is the collapse simultaneous, and why that frame?

A single complete collapse can only be specified by an arbitrary rule.


Not Even Wrong

Wolfgang Pauli, when shown the paper of a colleague, once said:

“Not only is that not right, it’s not even wrong!”

The idea of collapse was an ill-defined ad hoc addition to the (very well defined) evolution described by the Schroedinger equation.


three parts to “collapse”

Disappearance of interference

The rules of probability change from those of a superposition to those of a mixture.

Choice of a basis

Only certain observations are possible (e.g. alive or dead); combinations of those observations are not.

Choice of a single outcome (a.k.a. projection)

Only one outcome is observed; the superposition has projected out a single component.


decoherence

Not really a new idea. Just a way of understanding how QM describes interactions between system and environment.

Accomplishments of decoherence:

•Explains disappearance of interference

•Explains choice of basis

A quantum system is never isolated in practice. It interacts with its environment, evolving into something that behaves like an incoherent mixture of states.


Double slitIn an undisturbed single-electron double slit experiment two electron waves combine destructively in the center of the screen, giving minimum probability of detecting an electron at that location.

electron gun

phosphor screen

mask with 2 slits


Scattering shift

If the wave has shifted by half a wavelength, there will be maximum probability of detecting an electron in the center of the screen.

What if a photon hits the electron on its way to the screen? The interaction will change the direction and the momentum of the electron.

originalnew

n.b. If the frequency has changed, the interference pattern will change as a function of time.


Scattering uncertaintyThere are many possibilities for where the interaction takes place, and what momentum is transferred. Many possibilities for interaction form many superposing interference patterns.

If the photon is low energy and doesn’t disturb the electron too much, the interference pattern is smeared out just a bit. If the interaction is energetic enough, the pattern is completely smeared (an apparent mixture).

originalnew


The Essence of DecoherenceConsider a system in a superposition of two possibilities (complete basis):

Let it interact with an environment that has a large number of degrees of freedom:

the phases of ai, bj tend to cancel

In the probability, the interference terms tend to zero; a superposition is turned into an approximate mixture.

n.b. Localized states are common because interactions often depend on direction and distance.

Blaylock - UMass seminar 3/4/11

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Quantum DarwinismFor a system that is frequently ‘measured’, the persistent states are (usually*) the eigenstates of the interaction Hamiltonian.

Interaction with the environment will not change eigenstates of the interaction. These states are stable and persistent. Written in terms of these states, the wave function has no 12 or 21 cross terms, and the mathematics of the previous page is valid. Looked at from any other basis, the system does not evolve into an apparent mixture.

*Assuming the self-Hamiltonian is negligible or absent. But if the difference in energy eigenstates is large compared to typical interaction energies, the persistent states are energy eigenstates, since these are the states that are time independent. (see esp. Zurek 99)

… unless the environment is watching Blaylock - UMass seminar 3/4/11 14

Quantum Zeno Effect

Shining the light through six 1 cm dishes of syrup (each rotating the light by 15o) followed by six polarizing filters, allows 66% of the light to get through.

If we shine green polarized light through 6 cm of corn syrup, we get 90o rotation. No light gets through.

The initial polarization evolves to something else…


ProjectionProjection must be:

• nonlinear (linear evolution cannot evolve a superposition into a single outcome)

• random and irreversible (there is no info in the wave function to choose a particular outcome)

• gradual – fast but not all at once (otherwise microsystems would sometimes collapse too early, macro systems too late).

An isolated cat is in a superposition of two possibilities until he is observed. Then very quickly, …


potential solutions

Sweep it under the rug

shut up and calculate

Specify the projection

dynamical collapse

Get rid of the projection

multiple realities: Many Worlds

one (nonlocal) reality: Hidden Variable Theory


Dynamical Collapse1. Each elementary component of the system is subjected at

random times to spontaneous localizations (“hittings”). These hittings are mathematically represented by multiplying the wave function by a localized Gaussian.

2. The hittings occur at locations given by the standard quantum probability (wave function amplitude squared).

3. The time of the hits follows a random Poisson distribution.

Toy model: Ghirardi Rimini Weber (GRW) 1986

It has been an important proof of principle to show that one can choose a Gaussian spatial width (~10−7 m) and a Poisson time frequency (~108 yr) that is consistent with both micro and macro experience (i.e. micro states don’t collapse too fast and macro states collapse fast enough.)

DC Observations


GRW and offshoots are focused on spatial collapse (is this all that’s needed?).

GRW is not Lorentz invariant, but Roderich Tumulka claims to have a relativistic version for non-interacting particles.

Even these models do not provide complete projection in the sense of a single outcome. Alternatives still exist in tails of Gaussian distributions.

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Everettian Many Worlds

Everett says even without projection, the experience of the MWI observer agrees with that of the orthodox ‘external observer’.

Suppose an experimenter measures a spin. Moreover, repeated measurements of

the same spin will yield identical results. It looks as if the particle spin has ‘collapsed’to a single outcome.

Two possibilities result (two branches).

Blaylock - UMass seminar 3/4/11


MW ObservationsMW adds nothing beyond the unitary evolution of QM.

It can be formulated as a local realist interpretation (taking the wave function to be the fundamental entity).

There is great controversy over whether it explains the Born rule. Everett defined probability in terms of sequences of measurement results seen by observers along different branches, and claimed that the “relativefrequencies” of different possible sequences is governed by the same amplitudes as in orthodox QM. But if all branches exist*, what does it mean to say that one branch is more probable than another? A rich literature surrounds this question, including many papers that claim MW is more appropriate for explaining probability than conventional QM (see esp. Deutsch 99, Wallace 03, Zurek 05).

*n.b. the same question could be applied to GRW collapse!


Bohmian QM(a.k.a. the de Broglie-Bohm interpretation of QM)

A system of particles is described (only) in part by the wave function. The description is completed by the specification of the positions of the particles.

Evolution of the system is determined by the Schroedinger equation for the wave function, and by a guide equation for the positions qk.

Since the velocities depend on a wave function that samples all space, this is an explicitly non-local theory (as it must be to be consistent with Bell experiments).

Also (irreparably?) non-relativistic. Bohmian trajectories for the 2-slit experiment.


Cat in a Box

There’s no comfortable solution.

But it’s time to admit there’s a problem.

the problem with cats lessons in quantum collapse

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