Re: [asa] planck for the layman?

Merv -

That's basically it but it's important to emphasize that it's not just the
warping of space & time that produces this this result. According the
general relativity, that happens on all scales. It's the combination of
that effect with quantum mechanical uncertainty that's critical. Thus the
limitation is due to the warping of space & time "by the presence of the
measuring device" - as you say - AND to the fact that increased precision of
the measuring device results, via the uncertainty principle, in even greater
warping. (Or, more accurately, to increased uncertainty in warping.)

It's perhaps worth pointing out that this result follows from very basic
concepts of general relativity and quantum theory, the equivalence principle
(i.e., equivalence of gravitational & intertial mass which leads to the
gravitational redshift & effect on clocks) and the uncertainty principle.
This means, OTOH, that it doesn't require the full machinery of those
theories - nothing need be said about Einstein's field equations or
Schroedinger's wave equation. OTOH, a genuine scientific revolution (& not
just an extension or tweaking of either GRT or QM) would be needed in order
to overturn this result.

Shalom
George
http://home.roadrunner.com/~scitheologyglm

----- Original Message -----
From: "Merv Bitikofer" <mrb22667@kansas.net>
To: "George Murphy" <GMURPHY10@neo.rr.com>; "asa" <asa@calvin.edu>
Sent: Wednesday, April 08, 2009 8:13 AM
Subject: Re: [asa] planck for the layman?

> Thanks, George --this was helpful to correct my misunderstanding of this.
> If I read you (or Planck) correctly below, it would be more correct to say
> that the "linear thinking" that we apply so well to our Macro world breaks
> down even for time and space in the [extreme] micro-world --but that is
> not the same as proving some discrete "smallest increment of space." &
> in any case, no mechanical thing could make any meaningful measurements in
> that scale since time & space itself (at that precision) would be warped
> by the presence of the mechanical measuring device. If any of this is
> still glaringly wrong, your further patience and correction is
> appreciated. It still feels like a trip down the rabbit-hole, but at
> least I can have my continuous space-time back for the moment!
>
> --Merv
>
>
>
> George Murphy wrote:
>> Merv -
>>
>> Actually Planck himself, in the paper in which he introduced "his"
>> constant h, pointed out that it, together with the speed of light c and
>> gravitational constant G, defined a natural system of length, time & mass
>> units:
>>
>> L = sqrt(hG/c^3) ~ 10^-33 cm, T = L/c ~ 10^-43sec , M = Lc^2/G ~
>> 10^-5gm.
>>
>> (h there is Planck's h over 2*pi.) But this is simply dimensional
>> analysis & doesn't mean that you can't actually have lengths or times
>> smaller than L & T. The best way to show that clearly is as follows.
>> (This follows a paper of mine in American Journal of Physics 42, 1974,
>> p.958.)
>>
>> The quantum mechanical uncertainty principle says measurement of a time
>> interval t will be related to the uncertainty in the energy of the system
>> DE by t*DE > h .
>> In addition, the gravitational field of the clock will, according to
>> general relativity, influence the rate at which the clock runs. The
>> fractional change in an interval t in the vicinity of the clock will be
>> on the order of dt/t ~ gravitational potential/c^2 ~ G[M + DE/c^2]/Lc^2,
>> where M is the clock's mass, L its linear dimension, and the uncertainty
>> in energy gives an uncertainty in mass according to Einstein's formula.
>>
>> Now in order for the clock to measure an interval t its parts must be
>> able to communicate with one another within that time, so L < ct. Thus
>> dt/t >
>> G[M + DE/c^2]/c^3 > GDE/c^5 . But since DE > h/t we have dt > Gh/tc^5.
>> The measurement is of no value unless dt < t - i.e., unless t >
>> sgrt(hG/c^5), the Planck time defined above.
>>
>> This does not mean, however, that space-time is quantized in the sense
>> that there are "atoms" of space & time. That may be the case but all
>> this argument shows is that the the concepts of length & time intervals
>> lose their meaning below the Planck scale. There are reasons to think
>> that space-time is still continuous, but it is not a metric space below
>> this scale.
>>
>> Shalom
>> George
>> http://home.roadrunner.com/~scitheologyglm
>>
>> ----- Original Message ----- From: <mrb22667@kansas.net>
>> To: "asa" <asa@calvin.edu>
>> Sent: Tuesday, April 07, 2009 5:14 PM
>> Subject: [asa] planck for the layman?
>>
>>
>>>
>>> I'm needing help understanding some of the apparent ramifications that
>>> come from
>>> Planck's constant ... such as: somehow a quantized packet of energy
>>> leads to a
>>> "smallest packet" of space? --and of time as well? I think I remember
>>> this from
>>> a previous ASA discussion, but didn't understand it at the time & still
>>> don't now.
>>>
>>> Does this effectively cap our logarithmic romp towards smaller things in
>>> much
>>> the same way as Einstein's still expanding space caps the "think-big"
>>> end?
>>> If there is a good book on Planck for the layman, let me know.
>>>
>>> --Merv
>>> (It's enough to give a Euclidean-minded geometry teacher a headache.)
>
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Received on Wed Apr 8 08:37:04 2009