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an attempt to determine the position of a particle changes the determinabiity of the momentum of the particle (in some kind of inverse proportion) and vice versa

John Davies> asked the Naked Scientists: About the uncertainty principle (as distinct from the observer effect) - according to the principle, is it the case that a) an attempt to determine the position of a particle changes the determinabiity of the momentum of the particle (in some kind of inverse proportion) and vice versa, or b) there is in pre-existence a degree of determinability of a particle's position and momentum (in inverse proportion) which observation determines but does not change. or c) other? If you could answer this question for me, could you please render it comprehensible to a relative simpleton such as I? What do you think?

About the uncertainty principle (as distinct from the observer effect) - according to the principle, is it the case that a) an attempt to determine the position of a particle changes the determinabiity of the momentum of the particle (in some kind of inverse proportion) and vice versa, or b) there is in pre-existence a degree of determinability of a particle's position and momentum (in inverse proportion) which observation determines but does not change. or c) other? If you could answer this question for me, could you please render it comprehensible to a relative simpleton such as I? What do you think?

Particles are probability waves, and are described by mathematical relationships.

We can calculate, by measurement, certain properties regarding particles.

The change or uncertainty (Δ) of momentum (p) of a particle is described by Planck's constant (h) divided by the de Broglie wavelength ( λ ). So Δp = h/λThe change or uncertainty (Δ) in position (x) of a particle is simply its wavelength (λ). So Δx = λSo we can now substitute Δx above in the momentum equation where we had λ. So now Δp = h/Δx We can rewrite this is ΔpΔx = h.It was rewritten more precisely as ΔpΔx ≥ h/2π

Hi pmb,I understand the Uncertainty principle quite well, but thank you. What I provided was a simple derivation meant to explain it for the average person using math. It is not innacurate or wrong.

Furthermore, the term uncertainty is commonly used to describe the delta of position and momentum when explaining the Uncertainty Principle to the average person.

I can prove this if you like.

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I am not sure why this is so difficult for you to understand.

Hi pmb,The standard deviation reflects the spread or expected fluctuations in a series of measurements of an observable in a given state. This spread in QM is the uncertainty, which grows for one operator as the other shrinks. The standard deviation is commonly referred to as the "uncertainty" in this context. In fact, the standard deviation is what is describing the uncertainty. I am not sure why this is so difficult for you to understand.

The uncertainty principle for position and momentum (there are many other uncertainty relations) is a relationship between standard deviation of position measurements to the standard deviation of momentum measurements.

"The change ... (Δ)" is a wrong statement. That symbol does not stand for change. It refers to standard deviation.

I have never heard "standard deviation" applied to either the Dirac or Heisenberg treatments of probability densities. Nor is standard deviation used used to explain the hyperfine sprectum of Hydrogen.

The change or uncertainty (Δ) of momentum (p) of a particle is described by Planck's constant (h) divided by the de Broglie wavelength ( λ ). So Δp = h/λThe change or uncertainty (Δ) in position (x) of a particle is simply its wavelength (λ). So Δx = λSo we can now substitute Δx above in the momentum equation where we had λ. So now Δp = h/Δx We can rewrite this is ΔpΔx = h.

I would like to take a stab at this one as a layman. I'm adapting an analogy I've used before which is not perfect, but should prove useful.Imagine there's a two-bladed spinning propeller on an airplane. You want to determine the momentum and position of the propeller's blades, but the only technique you have available is to fire objects at it.First, fire a small bullet out of a gun at the propeller. It keeps spinning, barely affected by the bullet, but the bullet ricochets off the propeller. By performing measurements on the bullet after the ricochet, you could work out something about the propeller's speed, but you couldn't deduce much about which blade of the propeller caused the ricochet, or in other words, what position (location of both blades) the propeller was in when the collision occured.Now, try firing a large cannonball at the propeller. This knocks one of the blades clean off. You can tell exactly where that happened (which blade it happened to), but you can't determine how fast the propeller is spinning because it was destroyed in the collision and no longer spins.I'm trying to think of something in between those two extremes. Maybe a baseball-sized rock launched from a pitching machine. In that case, the rock would bounce off, so you could deduce something about the propeller's momentum from the rock's trajectory, but it was also large enough to damage the propeller so that it spins at a different rate now. So, you can determine less about the propeller's position from the rock than the cannonball, but also less about its momentum than with a bullet.Yes, I know this analogy has some serious problems. This is merely an illustration to help convey an idea.