Conference rusure::math

    Re .0:
    
    No.  The speed of light, as measured in natural units, is 1.  This is a
    consequence of the fact that time _is_ space, literally.  What one
    person observes as purely distance another person might observe as
    partly distance and partly duration -- their point of view is "rotated"
    in four-dimensional space-time.
    
    
    				-- edp

    the resone i asked, is that i was reading a magazine where apparantly
    speed of light in empty space keeps having some digits added to it on 
    the right of decimal point , (better measurments methods).
    the value 180,000 miles per second is only aproximate. excat value
    of C seems to keep improving.
    i understand that C is independent of the speed of the observer.
    
    

    Measured in miles per second, c is probably irrational.

    Until recently the speed of light was (except in the "natural" system
    of measurement used by relativicists) an irrational number.  It is
    now a rational number.

    The reason for the former is that the probability of any value being a
    rational value, unless constrained somehow to so being, is zero.

    The reason for the latter is that c was, farily recently, given an
    exact value (this sounds screwy, like declaring pi to be exactly 3,
    but it isn't).  The "second" is now defined so as to make the speed of
    light that exact value.  The decimal points in the "legislated" value
    of c were designed so that the length of the second in the newly
    defined units were indistinguishable with the technology of that time
    from the "old" second.  Now, more accurate measurements of the travel
    time of a photon over some distance refines our knowledge of the
    "second" rather than of the speed of light.  To put it another way,
    it used to be that "length" and "time" were fundamental quantities
    in the various systems of measurement, while the value of c was derived
    -- now, however, length and the speed of light are fundamental and
    units of time are derived.  In that regard, we are now using a scaled
    natural system of measurements.

					Topher

        I thought it was c and the second that were fixed, with
        technological advances "refining our knowledge of" the
        meter.
        
        Dan
        

RE: .6 (Dan)

    Could be, but that's not what I remember.  Let's see if anyone can find
    a current reference.

					    Topher

        I'll try the DECWET::PHYSICS conference tomorrow.
        
        Dan

    since we are taking kind'a physic here, i'd like to point a very
    good TV series currently showing on public TV, called 'astronommers' , it is
    of 6 series. tonite was first one on channell 11. 

    It might be more useful to look at dimensionless quantities that
    arise in physics, such as the fine structure constant.

    My feeling is that if such constants are really irrational or
    transcendental and not knowable in terms of some simpler
    form (such as being an eigenvalue of some kind) that
    it would require knowing "everything" about physics to know them
    to full precision.

    - Jim

	From DECWET::PHYSICS 120.2:
        
>>                            -< exact speed of light >-
>> -----------------------------------------------------------------------------
>>     Just to put a current fact in this topic.
>>     
>>     In 1983, the meter was defined as the distance light travels in a
>>     vacuum in one second divided by 299,792,458.  That makes c =
>>     299,792,458 m/s EXACTLY. I don't think this number is likely to change
>>     in my lifetime.
        
        Later replies discuss how the second is defined.
        
        Dan

.10>    It might be more useful to look at dimensionless quantities that
>    arise in physics, such as the fine structure constant.

alpha = 1/137.036 = fine structure constant

beta = 1840 = mass of neutron / mass of electron

e^2/G*mp*me = 10^39 = ratio of electromagnetic to gravitational force


Eddington once did a lot of work with these.  For example, when the experimental
value of 1/alpha was 136, this was shown to be the number of terms in a 16
dimensional tensor:

	(16^2-16)/2 + 16 = 136

When the experimental value became 137, unity was added to the expression above.
When it became 137.04, the game was abandoned.

        re .-1,
        
>> beta = 1840 = mass of neutron / mass of electron
        
        I once read that the ratio of the rest mass of a proton
        to the rest mass of an electron was equal to 6 * pi^5
        (i.e., the known (as of then) digits of the ratio
        matched the initial digits of 6 * pi^5).
        
        Dan

Looks like the value of Pi has changed since then. :-)

        No, the number quoted from a previous reply was the ratio
        for a neutron; the 6 pi^5 figure was for a proton.
        
        According to VAX LISP, 6 pi^5 is 1836.118..., and
        that was said to be within the bounds known for the
        proton/electron rest mass ratio.
        
        Dan

    Its interesting to compare this problem with the discussion in
    Feynman's QED about the theoretical calculation of the magmetic moment
    fo the electron. It is based on an increasing complex look at higher
    order coupling between electrons and photons. The number is based on
    summing probability amplitudes, so the result would not be based on a
    ratio of integers in any easy way. It may be the case that "C" will
    also evolve out of similar calculations and therefore would probably
    not be ratiol.

.16>    summing probability amplitudes, so the result would not be based on a
>    ratio of integers in any easy way. 

I don't think this follows.  I can do (and occasionally to my embarrassment,
have done) some fairly complex calculations and ended up with integer solutions.
It is logically possible that all these amplitudes will sum to something which
could be expressed much more simply.

Personally, I think this is possible, but very unlikely.  The only reason I have
for thinking that is that so many people have played with these numbers and
this theory.  If there were a simple answer, somebody would have stumbled across 
it.