WEBVTT
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This is College Physics Answers
with Shaun Dychko.
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We imagine that a virtual particle
with a mass of
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10 to the power 14 gigaelectron volts
per *c* squared exists
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and we want to know
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what maximum lifetime could this
virtual particle have
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and still be undetectable?
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If its lifetime is less than
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the minimum uncertainty in any measurement
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then it will be undetectable
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because its duration is less than the error
in the measurement.
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OK
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So we turn to the Heisenberg
uncertainty principle
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to figure out what is the lowest
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theoretical error possible
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in any measurement of the lifetime
of this particle.
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So we know that uncertainty in energy
times uncertainty in time
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is at a minimum Planck's constant
over 4*π*
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and we can solve that for time by dividing
both sides by the uncertainty in energy
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and we'll take the uncertainty
in energy to be
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the energy of the particle
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and so we'll figure out what that is by
multiplying its mass by *c* squared.
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So that's 10 to the 14 times 10 to the 9
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electron volts per *c* squared times
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this conversion from electron volts into
joules times *c* squared
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and we get 16020 joules
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is the mass energy of this particle.
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And so we substitute in Planck's
constant here
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and divide by this uncertainty in
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the energy of the particle
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times 4*π* and get the *Δt* then is
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3 times 10 to the minus 39 seconds.
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So the uncertainty is going to be
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in any measurement is going to be
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either this or more
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which means if the lifetime of the particle
is this or less
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then it will fly under the radar,
so to speak;
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it will have a lifetime that is less than
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the uncertainty in the measurement
and so it will be
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undetectable and that is the nature of
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virtual particles that they can violate
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these conservation laws that we have
for a duration
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that is less than theoretically detectable.