From: Ron Kean (ronkean@juno.com)
Date: Fri Jul 16 1999 - 10:22:11 MDT
On Fri, 16 Jul 1999 09:56:10 +0100 Rob Harris Cen-IT
<Rob.Harris@bournemouth.gov.uk> writes:
[Ron]
The product of the uncertainties of position and momentum is
>at>> least Planck's constant.>> >> So the precise initial conditions
needed to make a prediction cannot >be>> obtained, given the uncertainty
principle.
>>
>>
>I see, in the most part. I just don't get the most juicy bit. How was
>Planck's constant arrived at and declared the limit of all detection
>and >computation, regardless of the system in question?
Good question. See below.
Why is tracking >the>momentum AND the position so difficult? Perhaps it
is not regardless >of the>system - are we talking specifically about
molecular/atomic
>interactions>here?
Good questions. See below.
>Also - is this (Planck's constant) an absolute upper tracking
>limit >(dubious),
Yes, it is the fundamental absolute limit of observation according to
today's physics, not just a technological limitation. But you are
welcome to regard it as dubious; skepticism is healthy. You are right to
want those who claim it is the limit to back up their claim with an
explanation.
>or does it concede that new, unknown technologies may
>provide the >key ?
No, it does not.
>Do you?
No, I do not.
What about SI's ?
I don't know.
>
>Cheers Ron, >Rob.
>
I have had discussions concerning Planck's constant with Keith Lynch,
physics expert. You might want to ask him for an explanation by email at
kfl@clark.net, as he is much more knowledgeable than me on this subject.
He has been quite helpful in answering physics questions, and he
maintains a large searchable archive of answers which he has given in the
past, which often makes it possible for him to answer questions without
much effort. If you do send him a question, please try to make it
specific, and please cc me as I would like to read the question and the
response. Some of the questions you have are the same as the ones I
had, so I have reproduced below an exchange which I had with kfl about
Planck's constant. Please excuse the fact that it sounds somewhat
dis-jointed; it was cut and pasted from several messages.
Ron Kean
************************************************************
> (Planck's constant is in units of joule-seconds.)
>ACTION is work times time. Measurable in kilogram meters squared per
>second, or newton meters seconds, or joule seconds.
'Action' is listed in the CRC Handbook, where it is indeed defined as
work times time. But I'm having trouble picturing what it is apart from
its abstract dimensionality and why the word 'action' is appropriate to
describe it. 'Impulse', for example, which is force times time, is much
easier to understand. But I find it confusing to imagine that one joule
acting or spread over one second is 1,000 times less 'action' than one
joule acting or spread over 1,000 seconds. Perhaps you could give an
illustative example of 'action' which shows why it is a useful concept.
Work and energy are both measured in joules. But is there any difference
between work and energy? Is not work in a strict sense mechanical energy
as opposed to any other kind of energy?
Planck's >constant>has these units. It's about 10^-23 joule seconds.
Action is always>quantized in some integer number of multiples of
Planck's constant.
Planck's constant h should be about 6.6 x 10^-34 joule seconds.
>
>There is a "natural" system of units in which Planck's constant, the
>speed of light, and Newton's gravitational constant are all given
>values of exactly 1. If you've ever heard of the "Planck mass,"
>"Planck distance," or "Planck time," those are the units of mass,
>distance, and time in that system.
>
Would that be the h or h-bar version of Planck's constant? Conceptually,
how would Planck's constant be measured?
> 'Action' is listed in the CRC Handbook, where it is indeed defined
> as work times time. But I'm having trouble picturing what it is
> apart from its abstract dimensionality and why the word 'action' is
> appropriate to describe it. 'Impulse', for example, which is force
> times time, is much easier to understand. But I find it confusing
> to imagine that one joule acting or spread over one second is 1,000
> times less 'action' than one joule acting or spread over 1,000
> seconds. Perhaps you could give an illustative example of 'action'
> which shows why it is a useful concept.
One answer is to regard action, not as energy times time, but as
energy divided by frequency. The energy of a photon (or any other
quantum particle) is always Planck's constant of action times its
frequency. So the action of a photon is always its energy divided by
its frequency, and is the same for all photons. And for every other
quantum particle, too, since action only comes in multiples of
Planck's constant.
Another answer is that action is important because every system acts
to minimize its action. For instance a photon, which has constant
energy, always takes a path of minimum time (Fermat's principle). And
a thrown baseball that starts at one point and ends at another point
and starts with a particular amount of energy always takes the path
between those points which minimizes its total action. Similarly with
planets in their orbits, and blades of grass bending in the wind.
Another answer is that whether action seems like a natural concept
depends almost entirely on how much you use the concept. A century or
two ago, energy seemed a very unintuitive concept. How can a piece of
coal, a voltaic battery, a charged capacitor, a twisted rubber band, a
spinning flywheel, and a waterfall have anything in common with each
other?
> Work and energy are both measured in joules. But is there any
> difference between work and energy? Is not work in a strict sense
> mechanical energy as opposed to any other kind of energy?
The distinction is mostly historical. What a piece of coal, a voltaic
battery, etc, had in common was they all had the ability to cause
a force to be exerted through a distance, i.e. to do work. Or at
least that's what seemed most important about energy when the main
applications were threshing grain, draining mines, hauling railroad
cars, and sawing wood.
If electricity had come first, perhaps energy would have been defined
as the ability to cause an electric current to flow against a voltage
for a period of time.
Whether work IS energy, or is something that energy can DO, is mostly
a matter of perspective.
>> Planck's constant has these units. It's about 10^-23 joule
>> seconds. Action is always quantized in some integer number of
>> multiples of Planck's constant.
> Planck's constant h should be about 6.6 x 10^-34 joule seconds.
Yes and no. There are two Planck's constants, which differ by a ratio
of 2 pi. The larger one is used with frequencies in Hz. The smaller
and more natural one (often called h-bar) is used for everything else,
including frequencies measured in radians per second, which is actually
a more natural unit.
>> There is a "natural" system of units ...
> Would that be the h or h-bar version of Planck's constant?
H bar.
> Conceptually, how would Planck's constant be measured?
The simplest way is via the photoelectric effect. Light of various
frequencies is shined on metal object in a vacuum. The voltage which
has to be applied to block the flow of current across the vacuum
to another identical metal object (which is kept in darkness) is
measured. Or rather the change in frequency is compared to the change
in voltage, so as to factor out the ionization energy of the metal.
It the voltage change for a particular frequency change is ten volts,
then the electrons are each given an extra ten electron volts of
energy by the extra energy associated with the higher frequency of
light.
Of course you then have to know how much energy an electron volt
really is. It's the same fraction of a coulomb volt (yet another
synonym for joule or watt second) that the electron charge is of
a coulomb of charge.
So it remains to measure the charge on the electron. This is done by
levitating tiny oil drops between two metal plates. Let them fall for
a while with the plates both grounded, so that they sort themselves by
size (since larger ones fall faster). Once you have a population of
oil drops that are the same size (and you can figure out what that
size is based on how fast they fall), apply a small voltage between
the plates. Observe that the oil drops are now falling, not at the
same rate, nor at a continuum of different rates, but at several
distinct rates which differ by a fixed amount of speed. Crank up the
voltage between the plates to the value where the drops that were
going the closest to the original speed (but not AT the original
speed) are stopped. Those are droplets with one unit of charge, i.e.
that have one too many electrons (or one too few, depending on the
polarity of the plates). The electrical force on them equals their
weight, which you know. You know the electrical field strength --
it's simply the voltage difference between the plates divided by the
distance between the plates. So it's easy to calculate what the
charge would have to be.
Finally, we need to know what frequency the light is. To do that,
we measure its wavelength, and divide the speed of light into that.
To measure its wavelength, send it through a pair of closely spaced
holes, and measure the line spacing of the resulting diffraction
pattern.
There are completely different ways of measuring Planck's constant.
They give the same answer, within the precision of the measurement.
To me, how we can know things is just as interesting as the things we
know. Especially when the numbers we learn are very small or very
large, and were learned a long time ago using primitive but ingenious
equipment.
For instance the speed of light, which was first measured in the
1600s, even though it's extremely fast, at least by 1600s standards.
Or the gravitational constant, which was first measured in the
1700s, by Cavendish who managed to detect and accurately measure the
incredibly tiny gravitational attraction between two cannonballs.
Or the half-life of particles which last less than a millionth of a
millionth of a millionth of a millionth of a second. Or the distance
to the edge of the observable universe.
-- Keith F. Lynch -- kfl@clark.net -- http://www.clark.net/pub/kfl/ ******************************************************* . . . . . . . ___________________________________________________________________ Get the Internet just the way you want it. Free software, free e-mail, and free Internet access for a month! Try Juno Web: http://dl.www.juno.com/dynoget/tagj.
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