Subject: QUANTUM-MIND Digest - 24 Dec 1999 to 28 Dec 1999 (#1999-124) Date: Wed, 29 Dec 1999 00:00:59 -0700 There are 12 messages totalling 1016 lines in this issue. Topics of the day: 1. [q-mind] Photon loss (reply to Thaheld) - Stan Klein 2. [q-mind] Relative decoherence - Tito Vecchi 3. [q-mind] The Super-Implicit Order (reply to Mutnick) - Chris Lofting 4. [q-mind] Another imagined separation between God and World (reply to Dy Douglas and Chris Lofting) - Tom Mandel 5. [q-mind] Gao Shan's Three examples for understanding quantum motion - John Cowley 6. [q-mind] Reply to G Stone and Chris Lofting on the hard problem - John Cowley 7. [q-mind] Experimental aspects (reply to Thaheld) - John Cowley 8. [q-mind] Protective measurement and quantum motion - Gao Shan 9. [q-mind] Reply to Lofting on OBE, NDE, RV & PLR - G Stone 10. [q-mind] Another imagined separation between God and World (reply to Dy) - Gorsky 11. [q-mind] New ideas please (reply to Cowley) - G Stone 12. [q-mind] Reductions and Choices (Make straight the path) - Peter Mutnick ============================================ Contributions distributed to this list are automatically archived at http://listserv.arizona.edu/lsv/www/quantum-mind.html ============================================== ---------------------------------------------------------------------- Date: Mon, 27 Dec 1999 23:31:03 -0700 From: Stuart Hameroff Subject: [q-mind] Protective measurement and quantum motion - Gao Shan Protective measurement and quantum motion Gao Shan Institute of Quantum Mechanics 11-10, NO.10 Building, YueTan XiJie DongLi, XiCheng District, Beijing 100045, P.R.China E-mail: gaoshan.iqm@263.net [Abstract] We show what protective measurement measures and reveals is just quantum (discontinuous) motion. [Protective measurement] Protective measurement[1][2] aims at measure the motion state of a single particle through repeatedly measuring it without destroying its state, in real experiment a small ensemble of similar particles may be required. By use of this kind of measurement, the motion state or wave function of the particle does not change appreciably when the measurement is being made on it, its clever way is to let the system undergo a suitable interaction so that it is in a non-degenerate eigenstate of the whole Hamiltonian, then the measurement is made adiabatically so that the motion state or wave function of the particle neither changes appreciably nor becomes entangled with the measurement device, this suitable interaction is called the protection. In the following, we will demonstrate how protective measurement can reveal the discontinuous motion of a single particle[3][4][5], which is described by the position measure density $\rho(x,t)$ and position measure fluid density $j(x,t)$, or the complex wave function $\psi(x,t)$, for simplicity but lose no generality, we only consider a particle in a discrete nondegenerate energy eigenstate $\psi(x)$ ( for this situation the protection is natural, we need no additional protective interaction, this example has been discussed by Aharonov et al, here we give its interpretation ), the interaction Hamiltonian for measuring the value of an observable $A_n$ in this state is:$H = g(t) P A_n $, which couples the system to a measuring device, with coordinate and momentum denoted respectively by $Q$ and $P$, where $A_n$ is the normalized projection operator on small regions $V_n$ having volume $v_n$, namely: $$A_n=\cases{ {1\over {v_n}},&if $x \in V_n$,\cr 0,&if $x \not\in V_n$.\cr} \eqno(3) $$ \noindent the time-dependent coupling $g(t)$ is normalized to $\int_{0}^{T} g(t) dt =1$, we let $g(t) = 1/T$ for most of the time $T$ and assume that $g(t)$ goes to zero gradually before and after the period $T$ to obtain an adiabatic process when $T \rightarrow \infty$, the initial state of the pointer is taken to be a Gaussian centered around zero, and the canonical conjugate $P$ is bounded and also a motion constant not only of the interaction Hamiltonian, but of the whole Hamiltonian. Now using this kind of protective measurement, the measurement of $A_n$ yields the result: $$\langle A_n \rangle = {1\over {v_n}} \int_{V_n} |\psi|^2 dv = |\psi_n|^2 $$ the result $ |\psi_n|^2 $ is just the average of the position measure density $\rho(x) = |\psi(x)|^2$ over the small region $V_n$, so when $v_n \rightarrow 0$ and after performing measurements in sufficiently many regions $V_n$ we can find the position measure density $\rho(x)$ of the discontinuous motion of the measured particle. Then we will measure the position measure current density $j(x)$ of the discontinuous motion, namely we need measure the value of an observable $B_n$ in this state, where $B_n ={1\over{2i}} (A_n\nabla + \nabla A_n)$, the measurement result will be $\langle B_n\rangle$, ant it is just the average value of the position measure fluid density $j(x) = {1\over{2i}} (\psi^* \nabla \psi - \psi \nabla \psi^* )$ in the region $V_n$, so when $v_n \rightarrow 0$ and after performing measurements in sufficiently many regions $V_n$, we can also find the position measure fluid density $j(x)$ of the discontinuous motion of the measured particle. Thus we have demonstrated that the discontinuous motion of a single particle, which is described by the position measure density $\rho(x)$ and position measure fluid density $j(x)$, or the complex wave function $\psi(x)$, can be revealed through the above protective measurement. [Standard impulse measurement] Certainly, the standard impulse measurement can also indirectly reveal the discontinuous motion of a single particle described by the wave function, its wrinkle lies in that we first prepare an ensemble of a large number of particles in the same discontinuous motion state, then measure every particle in the ensemble using this kind of measurement only one time, and we need not repeatedly measure the same particle, thus even if the motion state or wave function of a single particle will be destroyed after such measurement so that the following measurement will no longer reveal the real information about the original motion state, but all the individual measurement results about the ensemble can reveal the state of the ensemble, and also the discontinuous motion state of a single particle in the ensemble, since every particle in the ensemble is in the same discontinuous motion state. [1]Y.Aharonov, L.Vaidman, Phys.Lett. A178, 38 (1993) [2]Y.Aharonov, J.Anandan, and L.Vaidman, Phys.Rev.A. 47, 4616 (1993) [3]Gao Shan, e-print physics/9907001, (1999) [4]Gao Shan, e-print physics/9907002, (1999) [5]Gao Shan, Quantum-Mind Digest, 20 Dec 1999 (1999)