uncertainty
RTF: Heisenberg Uncertainty Principle
If several identical copies of a system in a given state are prepared, measurements of position and momentum will vary according to known probability distribution; this is the fundamental postulate of quantum mechanics. We could measure the standard deviation Δx of the position measurements and the standard deviation Δp of the momentum measurements. Then we will find that
ΔxΔp>=h/2
where is Planck's constant (h) divided by 2pi. (In some treatments, the "uncertainty" of a variable is taken to be the smallest width of a range which contains 50% of the values, which, in the case of normal distributed variable, leads to a larger lower bound of h/2π for the product of the uncertainties.) Note that this inequality allows for several possibilities: the state could be such that x can be measured with high precision, but then p will only approximately be known, or conversely p could be sharply defined while x cannot be precisely determined. In yet other states, both x and p can be measured with "reasonable" (but not arbitrarily high) precision.
In everyday life, we don't observe these uncertainties because the value of h is extremely small.
QED.
N.B. some physcis, crappings omitted
If several identical copies of a system in a given state are prepared, measurements of position and momentum will vary according to known probability distribution; this is the fundamental postulate of quantum mechanics. We could measure the standard deviation Δx of the position measurements and the standard deviation Δp of the momentum measurements. Then we will find that
ΔxΔp>=h/2
where is Planck's constant (h) divided by 2pi. (In some treatments, the "uncertainty" of a variable is taken to be the smallest width of a range which contains 50% of the values, which, in the case of normal distributed variable, leads to a larger lower bound of h/2π for the product of the uncertainties.) Note that this inequality allows for several possibilities: the state could be such that x can be measured with high precision, but then p will only approximately be known, or conversely p could be sharply defined while x cannot be precisely determined. In yet other states, both x and p can be measured with "reasonable" (but not arbitrarily high) precision.
In everyday life, we don't observe these uncertainties because the value of h is extremely small.
QED.
N.B. some physcis, crappings omitted
posted by qed at 10:06 AM
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