On Sun, Mar 15, 2009 at 11:06:42AM -0700, Brent Meeker wrote: > > Saibal Mitra wrote: > > If we consider measuring the spin of a particle, you could also say that the > > two possible outcomes just exist and thatthere are two possible future > > versions of me. There is no meaningful way to associate myself with either > > of the two outcomes. > > > > But then, precisely this implies that after a measurement and forgetting > > about the result will yield a version of me who is in a similar position as > > that earlier version of me who had yet to make the measurement. If one could > > perform measurements in a reversible way, this would be possible to > > experimentally confirm, as David Deutsch pointed out. You can start with a > > spin polarized in the x direction. Then you measure the z-component. There > > then exists a unitary transformation which leads to the observer forgetting > > about the outcome of the measurement and to the spin to be restored in the > > original state. The observer does remember having measured the z-component > > of the spin. > > > > Then, measuring the x-component again will yield "spin-up" with 100% > > probability, confirming that both branches in which the observer measured > > spin up and spin down have coherently recombined. This then proves that had > > the observer measured the z-component, the outcome would not be a priori > > determined, despite the observer having measured it earlier. So, both > > branches are real. But then this is true in general, also if the quantum > > state is of the form: > > > > |You>[|spin up>|rest of the world knows the spin is up> + |spin down>|rest > > of the world knows spin is down>] > > You're contemplating reversing three different things: > > 1) Your knowledge, by forgetting a measurement result. Something that's easy > to do. > > 2) The spin state of a particle. > > 3) The state of what the rest of the world knows. > > Because of the entanglement, I don't think you can, in general, reverse the > spin > state of the particle without reversing what is known about it by "the rest > of > the world". > If it was a known state (to someone) the particle can easily be put back in > that > state. But to do so for a general, unknown state, after a measurement would > require invoking time-reversal invariance of the state of whole universe (or > at > least all of it entangled with the particle spin via the measuring apparatus). > > Brent Meeker >
By contrast, I think this line of reasoning can be used to create an experiment that tests a couple of different versions of MWI. Consider a Stern-Gerlach experiment where a particle is prepared in the x+ state. Then measure the state of the particle's spin along the z-axis, but _do not_ record the result. Finally measure the spin along the x-axis. According to Saibal's interpretation (which accords with my own intuition), the result should be spin up (x+) always. According to the interpretation you're suggesting Brent (the decoherence of the environment to contain a memory of whether the spin was z+ or z- - which I think accords with David Deutch's intuition), the final result should be x+ or x- with 50% probability. It may be important to send the result of the intervening measurement to a memory store somewhere else that the experimenter does not look at. This should be a doable experiment, and in fact may already have been done. It is similar in some respects to a version of the two-slit experiment performed a couple of years ago that generated a spark of interest. -- ---------------------------------------------------------------------------- Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [email protected] Australia http://www.hpcoders.com.au ---------------------------------------------------------------------------- --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---
