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Pullin et al have an article addressing the question
what is theoretically the most accurate clock one can build
to measure intervals of time less than a certain [tex]\inline T_{max}[/tex]
If the clock must be able to time intervals as long as, for example,
[tex]\inline T_{max}[/tex] = 1 billion years
then how finely can such a clock discriminate
what is the smallest [tex]\inline\delta T[/tex] difference in duration that it
can detect?
initially they employ an argument of Salecker and Wigner
and they proceed to observe that to make the Wigner clock distinguish more finely one needs to make it more massive, but not increase the size, and so
if one tries to make the clock more and more accurate eventually it will collapse and become a black hole, which is after all very good because that is the best kind of clock anyway
It is a fine argument and you should probably read it in the original
Pullin et al paper
http://arxiv.org/hep-th/0406260
now if the clock has to last a billion years then it must be a black hole that will not go and evaporate sooner than that, so this lowerbounds the mass and upperbounds the ringing vibration frequency and lowerbounds the [tex]\inline\delta T[/tex]
so the discrimination of the clock is bounded by the lifetime duration of the clock.
In fact the formula for the best possible clock is very sweet.
[tex]\inline\delta T[/tex] is simply going as the cube root of [tex]\inline T_{max}[/tex]
this is in natural units, understandably, so a billion years is 5.855E59
So if we want to know how fine time differences we can discriminate we just take the cube root of that number and get 8.366E19
this is an incredibly short interval of time. what a wonderful clock!
After all a second is 1.855E43
so this [tex]\inline\delta T[/tex] that the clock can distinguish is over 20 orders of magnitude briefer than a second. It is E19 and the second is E43.
-------------
I decided I would get a really long-lasting Pullin clock, one that will last for 100 billion years
so [tex]\inline T_{max}[/tex] is 5.855E61
then the discrimination or "tick" of the clock is 3.88E20
this is still over 20 orders of magnitude smaller than a second
--------------
obviously these people are making very good clocks so I thought I should advise everyone about it
http://arxiv.org/hep-th/0406260
the paper is actually by Rodolfo Gambini, Rafael Porto, Jorge Pullin
but Pullin is the name I recognize because he edits the American Physical Society newsletter on gravity and quantum gravity and such. So I call it Pullin et al, for short
what is theoretically the most accurate clock one can build
to measure intervals of time less than a certain [tex]\inline T_{max}[/tex]
If the clock must be able to time intervals as long as, for example,
[tex]\inline T_{max}[/tex] = 1 billion years
then how finely can such a clock discriminate
what is the smallest [tex]\inline\delta T[/tex] difference in duration that it
can detect?
initially they employ an argument of Salecker and Wigner
and they proceed to observe that to make the Wigner clock distinguish more finely one needs to make it more massive, but not increase the size, and so
if one tries to make the clock more and more accurate eventually it will collapse and become a black hole, which is after all very good because that is the best kind of clock anyway
It is a fine argument and you should probably read it in the original
Pullin et al paper
http://arxiv.org/hep-th/0406260
now if the clock has to last a billion years then it must be a black hole that will not go and evaporate sooner than that, so this lowerbounds the mass and upperbounds the ringing vibration frequency and lowerbounds the [tex]\inline\delta T[/tex]
so the discrimination of the clock is bounded by the lifetime duration of the clock.
In fact the formula for the best possible clock is very sweet.
[tex]\inline\delta T[/tex] is simply going as the cube root of [tex]\inline T_{max}[/tex]
this is in natural units, understandably, so a billion years is 5.855E59
So if we want to know how fine time differences we can discriminate we just take the cube root of that number and get 8.366E19
this is an incredibly short interval of time. what a wonderful clock!
After all a second is 1.855E43
so this [tex]\inline\delta T[/tex] that the clock can distinguish is over 20 orders of magnitude briefer than a second. It is E19 and the second is E43.
-------------
I decided I would get a really long-lasting Pullin clock, one that will last for 100 billion years
so [tex]\inline T_{max}[/tex] is 5.855E61
then the discrimination or "tick" of the clock is 3.88E20
this is still over 20 orders of magnitude smaller than a second
--------------
obviously these people are making very good clocks so I thought I should advise everyone about it
http://arxiv.org/hep-th/0406260
the paper is actually by Rodolfo Gambini, Rafael Porto, Jorge Pullin
but Pullin is the name I recognize because he edits the American Physical Society newsletter on gravity and quantum gravity and such. So I call it Pullin et al, for short
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