Why don't you guys go and actually perform the experiments that you hallucinate about here ? Let's see how you will manage when the results obtained diverge by 30% from your delirium here on the forum.
On Tuesday, 20 May 2025 at 08:13:19 UTC+3 Brent Meeker wrote: > > > On 5/19/2025 9:03 PM, Alan Grayson wrote: > > > > On Monday, May 19, 2025 at 9:55:36 PM UTC-6 Brent Meeker wrote: > > > > On 5/19/2025 8:39 PM, Alan Grayson wrote: > > > > On Monday, May 19, 2025 at 6:57:57 PM UTC-6 Brent Meeker wrote: > > > > On 5/19/2025 3:00 PM, Alan Grayson wrote: > > > > On Monday, May 19, 2025 at 12:22:29 AM UTC-6 Brent Meeker wrote: > > > > On 5/18/2025 9:58 PM, Alan Grayson wrote: > > > > On Sunday, May 18, 2025 at 4:16:26 PM UTC-6 Brent Meeker wrote: > > > > On 5/18/2025 10:02 AM, Alan Grayson wrote: > > > > On Tuesday, May 13, 2025 at 4:54:55 AM UTC-6 Alan Grayson wrote: > > On Monday, May 12, 2025 at 4:15:52 PM UTC-6 Brent Meeker wrote: > > > > On 5/12/2025 1:58 PM, Alan Grayson wrote: > > > > On Friday, May 9, 2025 at 10:40:42 PM UTC-6 Brent Meeker wrote: > > On 5/9/2025 7:08 PM, Alan Grayson wrote: > > *I can see that the measurement spreads due to instrument limitations are > usually immensely larger than the much smaller spreads accounted for by the > UP, but what causes these much smaller spreads? Is this a quantum effect? > AG* > > > Yes. Quantum evolution is unitary, i.e. the state vector just rotates in > a complex Hilbert space so that probability is preserved. Consequently the > infinitesimal time translation operator is U=1+e6/6t or in common notation > 1-i(e/h)H where H=ih6/6t and h is just conversion factor because we measure > energy in different units than inverse time. It's not mathematics, but an > empirical fact that h is a universal constant. > > Brent > > > *If one wants to prepare a system in some momentum state to be measured, > doesn't this imply a pre-measurement measurement, * > > Right, given that it's an ideal measurement. Most measurements don't > leave the system in the eigenstate that is the measurement result. An > ideal measurement is one that leaves the system in the state that the > measurement yielded. > > > *and the observable to be measured remains in that state on subsequent > measurements? * > > Only if they're ideal measurements of that same variable or of other > variables that commute with it. > > > *If so, how can the unitary operator, which just changes the state of the > system's wf, create the quantum spread? * > > You don't need a change in the wf to "create the quantum spread". Having > prepared in an eigenstate of A just measure some other variable B that > doesn't commute with A. In general A will be a superposition of other > variables, say A=xC+yD; that's just a change of coordinates. But the > system is not in an eigenstate of C or D. > > Brent > > > *Sorry, I really don't get it. Not at all! If we want to prepare a > particle with some momentum p, why would we measure it with some > non-commuting operator, and why would this, if done repeatedly, result in a > spread of momentum? And what has this to do with a unitary operator which > advances time? TY, AG * > > > > *Is the spread in momentum caused by an imprecision in preparing a > particle in some particular momentum? Generally speaking, how is that done? > TY, AG * > > *The HUP doesn't limit how precisely you can prepare a particle's > momentum. The HUP just says that the more precisely the momentum is > determined the less precisely defined will be the conjugate position. * > > > *I know. What I don't know is the cause of the spread. AG* > > > > > *See attached. Brent* > > > > *Your attachment shows how to establish the HUP, not why there is a spread > in momentum. Classically, energy and momentum are related by a simple > formula. So if one wants to prepare a system in some specific momentum, one > needs to control the energy of the particle. Presumably, this can never be > done precisely; hence we get the spread. Is this not a sufficient > explanation for the spread? AG* > > > *As far as the HUP is concerned the cause of spread in momentum is that > the spread in conjugate position must be finite, and vice versa. * > > > *Are all the momenta in the spread, eigenvalues of the momentum operato*r*? > AG* > > > > *Yes. But they have different probabilities of being found when measured. > Brent* > > > > *But if one always gets a spread, how can any particular momentum in the > spread be measured? AG * > > > > *You can't choose which value you get measuring a random variable. You > just measure momentum and you get a certain value. Then you repeat the > experiment and you get a different value. You repeat this a thousand times > and you can plot the distribution function of momenta and measure the > spread. Brent* > -- 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 visit https://groups.google.com/d/msgid/everything-list/5680e6d2-815f-49dc-bf78-e3292545693bn%40googlegroups.com.
