On Saturday, October 26, 2019 at 10:07:07 PM UTC-5, Brent wrote: > > > > On 10/26/2019 7:09 PM, Alan Grayson wrote: > > Maybe this will work as a definition of "interference". Imagine an > > electron impinges on a screen in a double slit experiment, and at a > > particular location on the screen, called "the Event", through either > > of two slits. Suppose it has a probability amplitude of phi1 through > > slit1. Now imagine another electron, at a later time, impinging on a > > screen with probability amplitude of phi2 for the same event, but > > through slit2. If phi1 and phi2 represent different amplitudes or > > paths for the same Event, we must imagine the waves "interfering" even > > though they are not simultaneous, and the probability of that event > > with two possible paths, is the absolute value squared of the sum of > > phi1 and phi2. AG > > In a Young's slit experiment the particles interfere with themselves. > The interference pattern appears even if the electrons are sent one per > hour. That's what makes it strange, since it violates the classical > "logic" that a thing cannot be two different places at the same time. > > Brent >
"the particles interfere with themselves" One can write that (English) expression above, and many do, but others *Hilbert Spaces from Path Integrals* https://arxiv.org/abs/1002.0589 It is shown that a Hilbert space can be constructed for a quantum system starting from a framework in which histories are fundamental. The Decoherence Functional provides the inner product on this "History Hilbert space". It is also shown that the History Hilbert space is the standard Hilbert space in the case of non-relativistic quantum mechanics. might write instead "a particle's histories interfere". It may not sound like a distinction to some, but to others it may. @philipthrift -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/3f5d946b-0d57-4e74-846b-1cce890077a5%40googlegroups.com.
