Talking theory on a forum is the most wastest of time ever. And the reason is trivial: you have no idea if it works in practice. Professional science is not meant as a revealer of truth, it is only meant as an empirical enterprise. It's validity goes only as far as experiments go. So if you are really obsessed about these things, go and do experiments. You will see instantly how your whole debate collapses instantly, because in practice F=ma will give you random results. For example, the mass that you will measure will be 1.525123541325312, the acceleration will be 52.45662436. And when you will multiply them, you will get 5345.2351235125132, which will contradict the theory by 0.0001%. The question is: what are you going to do ? Are you going to repeat the experiment at infinity in order to obtain the perfect result ? Or are you going to change at infinity the theory in order to match the result ? As such, you will realize that F=ma is just an empirical approximation. It says nothing about reality. As such, any theoretical debate on a forum is absurd. The point of science is to be a practical activity to produce technology. If you want theoretical debates, talk about consciousness, because only that is what exists and you have empirical access to it at all times, so any theoretical debates on a forum can be instantly compared to the empirical experience of consciousness and decide on the spot if they are good or not.
On Wednesday, 7 May 2025 at 06:53:17 UTC+3 Brent Meeker wrote: > > > On 5/6/2025 7:47 PM, Alan Grayson wrote: > > Maybe someone can explain this; if, say, the momentum operator always > returns an eigenvalue of the momentum of the system being measured, then > when used in the UP, how can there be an uncertainty in momentum to give a > statistical variance? TY, AG > > > You misunderstand what the HUP refers to. There is often confusion > between* preparing* a system in state, which is limited by the > uncertainty principle, and making a destructive measurement on the system > which can be more precise (but not more accurate) that the uncertainty > principle. In the literature the former, a preparation, is referred to as > an ideal measurement…but then the “ideal” gets dropped and people assume > that it applies to any measurement. Then there’s a confusion between > precision of single measurements and the scatter of measurements of the > same system state. > > Heisenberg’s uncertainty principle is commonly misinterpreted as saying > you cannot make a precise (i.e. to arbitrarily many decimal places) > measurement of both the x-axis momentum and the position along the x-axis > at the same time or on the same particle. This is untrue. It comes from > confusing the concept of preparing particles in a state and measuring the > state of a particle. Heisenberg actually contributed to this confusion > with his microscope thought experiment > > The theory only says you cannot prepare a particle so that it has precise > values of both momentum and position. The distinction is that you can > measure both x and p and get precise values, but when you repeat the > process with exactly the same preparation of the particle the measurement > will yield different values. So even though you measure precise values > there is no sense in which you can say the particle *had* those values > independent of the measurement. Your measurement has been precise, but not > accurate. And if you repeat the experiment many times, the scatter in the > measured values will satisfy the uncertainty principle. See Ballantine, > *“Quantum > Mechanics, A Modern Development”* pp 225–227 for more complete exposition. > > To illustrate, you can prepare particles so that their position has only a > small uncertainty and when you measure their position and momentum you will > get a scatter plot like the blue points below. > > > > Each point is a precise measurement of both momentum, *p*, and position, > *q*. But because the scatter in position is small the scatter in > momentum will be big - and the uncertainty principle will the satisfied. > The green points illustrate the complementary case in which the particles > have a small scatter in momentum, but a big scatter in position. The red > points illustrate an intermediate case, a preparation in which the momentum > and position scatters are similar. > > It might also mention that in practice, i.e. in the laboratory and in > colliders like the LHC, the error scatter due to instrument uncertainties > is usually much bigger than that due to the theoretical limit of the > Heisenberg uncertainty, So both position and momentum are measured and the > uncertainty in their value arises from instrument limitations, not from QM > > 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 everything-list+unsubscr...@googlegroups.com. To view this discussion visit https://groups.google.com/d/msgid/everything-list/db05aa35-2fb9-499a-810a-87f65076981dn%40googlegroups.com.
