Hi Eppy
If by
"Why is the speed of light what it is (approx 300,000 km/s)"
you mean a) 'Why this numerical value'?
then short answer is : It is an accident of human cultural history,
influenced by the accident of the astronomical values of our planet
and solar system
(mass, size, rotation of Earth and its orbit around the sun).
b) If you strip away the cultural aspect and express the
value of c in so called Planck's units (an example of natural units)
then you get an interesting question which the famous British
astronomer and physicist (sir Arthur, 1882?1944), tried to solve and
failed.
c) If you look at it 'from the point of view of the
future', it is an open question in physics. Adherents of the
Anthropic principle believe (in a way) that this is 'the only
possible universe' consistent with data. In such a case, one of the
M-theories, may show that those 'only possible constants' can be
derived from geometry.
An example of such a constant would be the ratio of
the mass of the neutron to the mass of the electron (1038,..),
More generally - the spectrum of masses of elementary particles.
To derive that from theory, from geometry and group theory, is one
goal of string theories.
Note that this value does not depend on the units of measurement.
The ratio is dimensionless.
In more detail - the long answer which follows, will explain the
'natural units' which provide interesting 'dimensionless' values in a
more general way.
Another analogy, to complement (or fix) the previous analogy
-----------------
According to Chomsky, or at least according to his student Pinker,
http://pinker.wjh.harvard.edu/articles/media/1994_01_24_thenewrepublic.html
http://www.amazon.com/gp/product/0060976519/102-7446460-2049751?v=glance&n=283155
the principles of grammar are 'hardwired' into the human brain,
but each language fills those general principles with specific rules.
The analogy I used in
http://answers.google.com/answers/threadview?id=708533
can be complemented by adding this analogy with grammar:
Space-time geometry M4 implies the existence of a fundamental limit on speed,
whic we call c ,but it does not specify its value or name.
The name 'c' itself is not dictated by the rules of M4:
It comes from Latin word 'celerity':
"Speed or quickness=
celerity. Origin: Latin alacritas, from alacer, lively.... alacrity" )
Like the name, the specific value of c also has roots in the history
of human culture, and is not universal.
Philosophers recognize 'objective reality' (Kant's "Ding an such");
In physics we call that the 'invariant" (or covariant) reality.
There is also 'appearance of things', as revealed by observation
(by a given person, in a given location, having a given speed, or
frame of reference ...).
The invariant aspects of reality are called 'objects' and their
'appearance' in a given 'frame of reference' are called 'components'
of those objects (in the teminology of differential geometry:
http://www.amazon.com/gp/product/0486655822/102-7446460-2049751?v=glance&n=283155
Cosmologists assume that 'the laws of physics' are the same 'always
and everywhere.' This is obviously one of the most basic assumptions
behind our theories and postulates.
"The cosmological principle of isotropy and homogeneity, like other scientific
hypotheses, is testable by confrontation with data"
http://www.astro.umd.edu/~ostriker/ASTR340/lectures/lect6.ppt.pdf
The laws and data have to be expressed in covariant form, before they
can be applied to the universe at large.
a) Numerical values of physical constants which are not dimensionless
--------------------------------------
are not universal, not quite 'objective reality',
more an 'appearance of reality in a given culture':
The numerical value of the constant c is different in different units
c=299792.50 km/s = 161874.977 nautical miles/s
and units are a matter of convention, and convention depends on
accidents of culture/history.
So, a valid answer to your question could be:
The value 'c' today is what it is because a commission said so.
Indeed,
"The committee defined the speed of light in a vacuum to be exactly c
= 299 792 458 m/s.
For most calculations you should use c = 3.00 x E8 m/s."
http://hypertextbook.com/facts/2002/JohnnyAlicea2.shtml
The current definition of the meter:
The metre [French spelling], or meter [English spelling] (symbol: m)
is the SI base unit of length. It is defined as the length of the path
traveled by light in absolute vacuum during a time interval of
1/299,792,458 of a second.
http://www.onlineconversion.com/article_meter.htm
Of course, the SI commission selected the value to agree with the
previous one, which was
1) determined by measurements
(when the meter was still defined differently, originally based on
the size of Earth and the length of a yard)
2) calculated from magnetic permeability and electric permittivity of the vacuum
" Remember how we got the constant c: from Maxwell's equations"
http://www.fnal.gov/pub/inquiring/more/light/light_page10.html
But those values, too, depend on the choice of units, which is not arbitrary.
Its history belongs to the field of the 'humanities' and not the hard sciences.
So, while you might say my analogy with triangles and 180 degrees was
inaccurate and while I admit that all analogies have some
deficiencies, I may ask:
Where did the 180 = 1/2 of 360 come from?
It comes from the same human history:
In 'the olden times' the Sumerians based their counting and accounting on the
(rather inaccurate ) notion that year (a full circle) has 360 days ...
http://it.stlawu.edu/~dmelvill/mesomath/sumerian.html
That notion also influenced the definition of our
'second' = 1/60 x 60 of an hour
our 'first' subdivision was 1/60 of an hour.
one hour = 1/2 * 1/12 of a day
where 12 *60 = 360 (an influence of Moon = month gave us 12) etc
So, both the sum of the angles in E2 geometry and the value of c
depend on choices of the Old Sumerians, based on 'special numbers 12, 6, and 36.
If we express the sum of angles of a triangle in natural units,
then 180 degrees becomes pi/2 radians
http://braznet.com/david/physics/richard/rotation.htm
Value if pi=3.141 ,,, which is 180 degrees in natural units
can be measured on a plane (=E2 geometry) and can also be derived
mathematically, from geometry.
http://www-xray.ast.cam.ac.uk/~jgraham/hypo/h10/pi_1.htm
Now back to your question:
Can we transform 'fundamental physical constants' into a form which
can be derived from geometry, like pi?
Perhaps, if we express their values in natural units.
b) Natural units describe physical reality, rather then cultural artifacts
-------------
Under the
SEARCH TERM: natural units
you will find a specific example: Planck's units
Those are units from which the accidents of history in selecting particular
'units of measure' have been eliminated.
http://www.superstringtheory.com/unitsa.html
Just as the French eliminated 'a foot of King so-and-so' from
definitions of units of length, 20 century physicists eliminated
accidents of our planetary parameters by selecting units in which the
values of some units are 1:
c=1, h=1, e=1 (atomic units).
http://en.wikipedia.org/wiki/Planck_units
In those units, other constants have values which do not depend on
accidents of history. These other constants contain a value of c
implicitly (Like in dimensionless ratios,the units of measure are
cancelled).
An example is 'alpha = fine structure constant.
The great physicist, Sir Arthur Eddington
http://www.infoplease.com/ce6/people/A0816736.html
http://scienceworld.wolfram.com/biography/Eddington.html
spent lot of time speculating about why this constant has a particular value:
This biographer says:
"Eddington was arrogant, and in his later years, cooked up
pseudo-scientific "proofs" on "physical" grounds that the
fine structure constantwas exactly 1/136.
When experiments yielded a more accurate value, Eddington produced
another proof "proving" that it is exactly 1/137"
That earned him the 'mocking nickname' "Sir Arthur plus one".
That whole line of inquiry fell into disrepute and is now called
'physical numerology'. Today's views are quite different.
http://physics.nist.gov/cuu/Constants/alpha.html
Current value is 1/alpha= 137.035 999 11
http://physics.nist.gov/cgi-bin/cuu/Value?alphinv
Of course, the numerology lives on:
http://milan.milanovic.org/math/english/alpha/alpha.html
In spite of many successes, some physicists today are skeptical about
efforts to 'calculate' the masses and other values of elementary
particles just from geometry, like pi. They consider it as fruitless
as Sir Arthur's pursuit. Some would include the whole M theory in
that.
To soften that radical view, let's remind ourselves that what this
biographer called 'pseudo-scientific and arrogant' was a 'bold and
controversial' hypothesis in those days.
Eddington's reasoning may be resurrected in connection with what is
called Lem's cosmological hypothesis, somewhere in
http://answers.google.com/answers/threadview?id=441149
if the Eddington number (which we still do not know experimentally)
turns out to be close to his value
of 136 * 2^256.
So, in conclusion. and as a summary and for amusement - a peek into the future:
------------------------------------
On some planet in 'a galaxy far far away' there may be a
civilization, advanced enough to determine
the speed of light. The speed would be 'same' as what we measure
here, on Earth. But, in their physics (based on their units --
with time based on their year and day,
and size based on size of their planet)
it would have a different numerical value.
This will be one day a testable statement and so it is a scientific hypothesis
I will call it "Hedgie's cosmological conjecture of the Alien's value of c"
Hypothesis says: their value of c will be like our 'c'
but in expressed in 'their units' [ times n, n being a small number 3
4 or 5 ..most likely 4]
Why 4? Well, originally, unit of length proposed by French scientists
was 4 of today's meters
(making the circumference of Earth E7 of original meters.) That was considered
to impractical and so it was cut down by factor of four, to make it 'human size'.
Therefore, we allow for a small integer, which depends on surface
gravity of the planet) to enter the numerical
value they will use for their value of c (the aliens will about two
(alien meters) tall, of course :-)
Rating appreciated - and thank you for your kind words. Hedgie |