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What really happens upon quantum measurement? [needs revision]. Art Hobson Prof Emeritus of Physics University of Arkansas. R eferences are more fully listed in my Phys Rev A paper. ABSTRACT.
Prof Emeritus of Physics
University of Arkansas
References are more fully listed in my Phys Rev A paper
Measurement causes the measured quantum system to entangle non-locally with the measurement apparatus. Quantum theory, and non-local two-photon interferometry experiments, show that the locally observed states of both subsystems are mixtures of their eigenstates, while the unitarily-evolving composite global state, which can be accessed only by comparing after-the-fact records from the two local subsystems, evolves as a coherent superposition of correlations rather than of subsystem eigenstates. Thus, nature violates the eigenvalue-eigenstate link: Entanglement causes the subsystems to exhibit mixed state outcomes (such as a dead-or-alive Schroedinger’s cat, rather than dead-and-alive), but the subsystems do not actually collapse into the corresponding eigenstates. Instead, the subsystems remain entangled.
I. What’s the problem?
II. An enlightening experiment.
III. A proposed solution
• Assume A has states |ready>, |a1>, |a2> ∊ HA
--“ideal non-disturbing meas.”
• Linearity of the Schrodinger evolution implies
|ready>|𝜓>S→ α|a1>|s1> + β|a2>|s2>
• Note that the meas process entangles S and A.
• Thus the correlations between S and A are non-local (Gisin 1991). This turns out to be crucial.
appears to describe a macro superposition of SA
with superposed states |a1>|s1> & |a2>|s2>.
• Ex: If A is Schrodinger’s cat, and S is a radioactive nucleus that kills the cat if it decays, then MS appears to be a superposition of dead & alive. But that’s absurd.
• Where’s the collapse, to |a1>|s1> or |a2>|s2>?
• Such a collapse would be non-linear, contradicting the linear Sch. eq.
• Most experts think the problem is solvable only by altering the quantum fundamentals.
• When SA is in the MS, neither S nor A issuperposed. E.g. S cannot be described by a state of the form γ|s1>+δ|s2>. Proof: see Phys Rev A paper.
• So cat is not predicted to be dead & alive.
• This mistake results from neglect of the non-local connection between S and A. Entangled states are nonlocal (Gisin 1991).
• Exactly what is superposed in the MS? What interferes?
--It’s not your ordinary superposition!
A source sends entangled photon pairs through two Mach-Zehnder interferometers:
photons, A & S.
The exp, which used beam splitters, variable phase shifters, and photon detectors, is equivalent to the following 2-photon double slit exp:
With no entanglement, this would be two 2-slit exps:
states (|a1>+|a2>)/√2 and (|s1>+|s2>)/√2.
Interference fringes at both screens.
With entanglement, the photons are in the MS
|𝚿> = (|a1>|s1> + |a2>|s2> )/√2.
Each photon “measures” the other!
The RTO exp is a probe of the MS …with variable phases!
ρS= (|s1> <s1| + |s2> <s2|) / 2
ρA = (|a1> <a1| + |a2> <a2|) / 2.
These are notcoherent superpositions.
y-x is proportional to
the difference of the
two phases 𝝋A - 𝝋S.
Schrodinger evolution is “unitary.”
• When coincidences of entangled pairs
are detected at A’s and S’s screens: coincidence rate ∝cos(𝝋A - 𝝋S) = cos(y-x).
𝝋A-𝝋S=0, 2π, 4π
If the phase difference is 𝝋A-𝝋S= 0, 2π, …, A and S are correlated: ai occurs iffsi occurs.
When 𝝋A-𝝋S=π, 3π, 5π, ..., A and S are anti-
corr: ai occurs iffsi does not occur.
When 𝝋A-𝝋S=π/2, 3π/2, 5π/2, …, A and S are not at all correlated.
This is an interference of correlations between states, rather than the usual single-photon interference of states.
…that the results are truly non-local: Cannot be explained by “prior causes” or by “causal communication.”
If S’s phase shifter changes, the outcomes on A’s (and
S’s) screen are instantly (i.e. faster than light) altered.
Aspect (1982) tested these predictions (but with photon polarizations): The results confirmed violation of Bell’s
≠ and the observed changes showed up at the distant station sooner than a lightbeam could have gotten there.
ρS= (|s1> <s1| + |s2> <s2|) / 2,
ρA= (|a1> <a1| + |a2> <a2|) / 2.
• But the non-local, or global, correlations between A and S must be described by the coherent MS
|𝚿> = α|a1>|s1> + β|a2>|s2>.
• ρS and ρA are local states observed separately at S or A.
• |𝚿> is the global state, observable only by gathering info from both S and A.
• S and A are non-locally connected.
In fact Ballentine 1987 and Eberhard 1989 show that quantum probabilities do just what’s needed: When A alters φA, only the correlations change—the statistics of the outcomes at S don’t change. RTO exp confirms this.
• ρS = (|s1> <s1| + |s2> <s2|) / 2 and
ρA = (|a1> <a1| + |a2> <a2|) / 2
describe what is observed at S and at A. Schrodinger’s cat will be either dead or alive, not both.
• Nevertheless, S & A are actually “in” the global state. They retain a “coherent correlation” not described by ρS & ρA.
• This sounds like a contradiction, but it is not. Instead, the eigenfunction-eigenvalue rule is broken: S exhibits the value s1 or s2, but it’s not in the state |s1> or |s2>. Similarly for A.
•This resolves the problem(while disproving the standard eigenfunction-eigenvalue connection).
• RTO separates the problem of outcomes from the problem of irreversibiity.
• The MS describes S & A after they are emitted from the source but before either photon impacts its screen.
• The MS is still reversible, in principle.
• Upon impact, the coherence of the MStransfers to the environment (the screens) as described by Zurek 1981.
• This leaves S & A in mixtures ρS & ρA--definite outcomes
that are now irreversible i.e. macroscopic & permanent.
• This locks in specific outcomes.