The Uncertainty Principle

[deleteduser]

Ive been trying to understand what exactly it is, and from my perspective it is a principle that explains the more accurately you try to measure a particles position the less accurately you will be able to measure its speed.

Also that: '
the uncertainty of a particles position X the uncertainty of a particles speed X the uncertainty of a particles mass = a number always greater than planks constant.


So does this mean we cannot measure a particles position and velocity at one given time? But we know it will be greater than planks constant?


Also what is "a position of a particles" what references are used in determining the position?

[AdamL]

On the last question - the position of a particle is the location upon measurement. It's actualization.

[Silent A]

the uncertainty principle is:

uncertainty in momentum * uncertainty in position >= plank's constant > 0

It means you cannot know a particles exact position and exact momentum. The more you know about one, the less you must know about the other.

And strictly speaking, this isn't just an issue about measurement. At the fundamental level, the uncertainty princple says that the particle in question doesn't have an exact position or momentum.

[ChrisV]

I think there are pairs of properties other than position/momentum to which the uncertainty principle also applies. As originally stated though it is as given above.

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And strictly speaking, this isn't just an issue about measurement. At the fundamental level, the uncertainty princple says that the particle in question doesn't have an exact position or momentum.

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This is important. A lot of explanations imply that it is the act of measurement (for instance, bouncing a photon off a particle) which causes the uncertainty. But in fact the uncertainty is intrinsic to the particle itself; it really does not have a defined momentum or position. Another way to say this is the familiar statement that particles have wavelike characteristics.

[Silent A]

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I think there are pairs of properties other than position/momentum to which the uncertainty principle also applies. As originally stated though it is as given above.

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Another description is:

Uncertainty of energy * uncertainty of time >= plank's constant > 0

this actually implies that conservation of energy can be violated for small time periods. Or, at least, that's how it was taught to me in high school.

[Max Raker]

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I think there are pairs of properties other than position/momentum to which the uncertainty principle also applies.

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Yes, there are also energy time and one for different components of angular momentum.

[Neuge]

Nit time: It isn't exactly ">= Planck's constant" either. For all pairs of non-commutative operators, the product of the uncertainty in the measurement of their corresponding observables is >= a number proportional to Planck's constant. For the position/momentum and energy/time complementary pairs, the product of their uncertainty is actually >= h/4*pi.

[Neuge]

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I think there are pairs of properties other than position/momentum to which the uncertainty principle also applies.

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Yes, there are also energy time and one for different components of angular momentum.

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These are the most common, but the strict definition of complementary observables is "observables of two non-commutative quantum mechanical operators." I think there are others, but I can't remember any off the top of my head.

[Max Raker]

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I think there are pairs of properties other than position/momentum to which the uncertainty principle also applies.

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Yes, there are also energy time and one for different components of angular momentum.

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These are the most common, but the strict definition of complementary observables is "observables of two non-commutative quantum mechanical operators." I think there are others, but I can't remember any off the top of my head.

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The other common one is angular position and angular momentum in the same component. But you are right, any non commuting hermitian operators will have an uncertainity realation.

[PairTheBoard]

So particles are really non commuting hermitian operators?

PairTheBoard