I was prompted to ask this question after reading Hedgie-GA's most
informative answer the recent question 'Speed of light, why not?'

I have now read all the referenced material, and have gained a high
level overview of most areas from duality to 10 dimensional string
theory. However, there no no reference to the question that I am most
interested in. Thus this question:

Why is the speed of light what it is (approx 300,000 km/s) and not
(say) 10 x slower or 10x faster?

I understand Hedgie's analogy of the three angles of a triangle always
adding up  to 180 degrees, and I understand the mass/time boundary of
c dictated by e=mc2

However, I can't intellectually 'see' 300,000 km/s as being a boundary
in the same way as I can 180 degrees.

I would appreciate a high level (non mathematical) explanation of the
current understanding of why the speed of light boundary is what it is
and not another arbitary 'relative velocity' (either slower or
faster).

If this isn't known, that is fine - please explain the current thinking.

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

Comprehensive and no less than 19 good references! 

What takes the cake is to get a personal "Hedgie's cosmological
conjecture of the Alien's value of c" out of a $10 question;
outstanding value!

Now that is a very interesting question. The short answer is: no one
knows why the speed of light "c" has the particular value of 3x10^8
m/s. Your question can be generalized to "Why do any of the
fundamental constants of nature, like the speed of light, the
gravitational constant, and the charge of the electron have their
particular values?"

We need to get one thing sorted out first. The speed of light depends
on the units we use to measure length and time. Our units like meters
and seconds are completely arbitrary, chosen for odd historical
reasons like the Babylonian's fascination with the number 60 and the
rotation period of the Earth. In theoretical physics, one recognizes
that c is just the conversion factor between our units for distance
and time. To make the equations simpler and get to the heart of the
matter, theorists commonly use a set of units in which c is equal to
one, so E=mc^2 becomes E=m (Energy equals mass). This can be done with
other units and constants as well.

The goal of theoretical physics then becomes explaining and predicting
all dimensionless ratios (that is, all pure numbers with no units on
them). Your question about c is then replaced by questions like this:
why is a particular combination of fundamental constants called the
"fine structure constant" equal to approximately 1/137? This constant
is just the square of the charge of the electron divided by the
product of the speed of light and Planck's constant. It is a pure
number in any system of units and thus does not depend on arbitrary
choices like measuring distance in multiples of some King's foot size.
Other questions you could ask include things like: 1) why is the ratio
of the electron's mass to the proton's mass about 1/1800, 2) why is
the gravitational force between two protons ~10^40 times smaller than
the electromagnetic force, etc.

Again, the answer is that we do not know and it is a major goal of
physics to predict all these things. One possible answer is something
I personally detest but many others like called the "Anthropic
Principle". It notes that the existence of intelligent life depends in
detail on the physical constants and on the fact that slight changes
in any of these dimensionless ratios would render life as we know it
impossible. Thus, among the infinite possibilities for a universe, it
should be no surprise that we live in one in which intelligent life
can exist and, "Voila" that explains the values of the fundamental
constants.

Your question is very timely, since this week John Barrow just won the
Templeton Prize of $1.4 M dollars for his work including the
formulation of the Anthropic Principle. Who says mixing science and
religion does not pay?

http://www.templetonprize.org/bios.html

An even better answer is that "why" isn't a question addressed by
science, it is a question for religion or philosophy.

Physics is about what IS.

who says mixing science and religion doesn't pay?

All the people over the centuries who were tortured by various religions for
trying to promote science, anyone with a disease that could probably
be cured by stem cell research, anyone who caught AIDS because a
government thought it was "against god" to tell people about condoms,
etc., etc., etc.

Science often answers the question "Why?" Why is the sky blue? Why is
the hydrogen atom stable? The answers are given in terms of something
simpler and more fundamental. At the bottom, you are left with
questions that may be beyond our ability to answer and in the realm of
philosophy. It is certainly my hope that a more fundamental theory
will explain the fine structure constant, the masses of the quarks (in
dimensionless units), etc. This won't answer all the questions, like
why do quantum field theories explain so much of our universe, but I
hope they will provide the answer to Eppy's question without invoking
voodoo like the Anthropic principle.

Thanks very much Kottekoe, if you were a reasearcher I would have
asked you to post as an answer.

So, to paraphrase what you said, my question is not much different
from asking why pi=3.1415926535... c is really a conversion factor and
only has context in the world of realtivity when considered from a 4
dimensional space/time perspective. However, because the concept of
velocity is embedded in our thinking so much in an (apparently)
non-relativistic way, we intellectually tend to consider it one
dimensionally, without boundary.

A couple more quick comments. I note from a paper
http://www.btinternet.com/~ugah174/ on the fine structure constant
that you refer to that it also incorporates pi. Fascinating..

I remember about 20 years reading an article by Isaac Asimov on the
development of our knowledge of the speed of light. He mentioned that
that the number being within 1% of 300,000 km/s was no co-incidence,
as the early metric definitions had the same variables, and should
have equaled exactly 300,000 km/s but the speed of light was fined
tuned after the metric units were agreed.

Eppy, thanks for your kind words. I agree that alpha is in many ways
to physics what pi is to mathematics, but there are major differences.
We can use mathematics to calculate the value of pi in any number of
consistent ways. In physics, we have no theory whatever to explain the
value of alpha. I had never heard of James Gilson's work that is
described at the URL you gave, but I am very skeptical. My immediate
impression was that it sounds like the kind of numerology that
Eddington used almost 100 years ago when he claimed that 1/alpha was
an integer equal to 1^2+6^2+10^2. I just did a Google search for
Gilson and found a nice article on the Fine Structure Constant on
Wikipedia, which mentions Gilson's work, also relating it to
Eddington's numerology.

With regard to c being within 1% of 3x10^8 m/s, this is pure
coincidence. If Asimov really wrote what you said, he was really off
base. The meter was originally defined so that the distance from the
pole to the equator was 10,000 km. The second was defined so that a
solar day has 24x60x60 seconds. All these things are entirely
arbitrary and have nothing whatever to do with the speed of light.
Perhaps Asimov was talking about the modern definition of the second
and meter, which are made in such a way that the speed of light is now
defined exactly to be:

299 792 458 m/s

The meter used to be the length of a platinum iridium bar carefully
maintained in Paris. Now it's definition is more prosaic. According to
the web site of the National Institute of Standards and Technology:

The meter is the length of the path travelled by light in vacuum
during a time interval of 1/299 792 458 of a second.

The appearance of that strange number with six digits is to make the
new definition agree closely with the historical one. It is still just
a coincidence that it is so close to 1/300 000 000.

Thank you kottekoe-ga for the thoughtful and enlightening (no pun)
contributions you make to Google Answers.

Richard, Thanks. I enjoy your answers also, like the recent ones about
evolution and the number of dead people.