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'[EE:] The speed of light has been varying again - '
2004\07\01@084506 by Russell McMahon

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Another round in the "has the fine structure constant (alpha) been varying"
and "if so, does it mean the speed of light has changed" debacle.

       http://www.newscientist.com/news/print.jsp?id=ns99996092

This time around they are using the results from the one time natural
nuclear reactor in Gabon to support rather than rebut the theory.

IF the fine structure constant has ever varied by even minute amounts (parts
in 10^8) then much of Physics is up for grabs.

What they don't cover except in passing in the article is that the speed of
light is not the only constant that may have varied to cause alpha to vary.
eg the value of 2 could have varied and caused the same result. Those who
think that the idea of 2 varying is ludicrous ain't seen nothing yet :-)


       Russell McMahon

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2004\07\01@113330 by Nate Duehr

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Russell McMahon wrote:

>What they don't cover except in passing in the article is that the speed of
>light is not the only constant that may have varied to cause alpha to vary.
>eg the value of 2 could have varied and caused the same result. Those who
>think that the idea of 2 varying is ludicrous ain't seen nothing yet :-)
>
>
2+2 = 5 for very large values of 2!  ;-)

Nate

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2004\07\01@142223 by Bob Barr

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On Fri, 2 Jul 2004 00:45:51 +1200, Russell McMahon wrote:

<snip>
>
>What they don't cover except in passing in the article is that the speed of
>light is not the only constant that may have varied to cause alpha to vary.
>eg the value of 2 could have varied and caused the same result. Those who
>think that the idea of 2 varying is ludicrous ain't seen nothing yet :-)
>

Any possibility that pi will ever get down to 3? That sure would make
trig a whole lot easier. :=)


Regards, Bob


P.S. And yes, I have heard of the legislature (somewhere in the U.S,
midwest) that tried to legally change the value of pi to 3.

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2004\07\01@153206 by Jason S

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> What they don't cover except in passing in the article is that the speed
of
> light is not the only constant that may have varied to cause alpha to
vary.
> eg the value of 2 could have varied and caused the same result. Those who
> think that the idea of 2 varying is ludicrous ain't seen nothing yet :-)

What definition of "2" do they use in Physics?

In Math, we used Peano's Axioms to define the numbers.  The only number that
is directly defined is "0", and "2" is inductively defined as the thing that
comes after the thing that comes after "0".

By this definition, "2" is nothing more than a label on a point on the
number line, so it can't vary.  If the number line shifts, the label we're
calling "2" should move to a different on the line to hold its same meaning.

Obviously this isn't what the Physicists are using to define "2", so I'm
curious what they are using that can vary.

Jason

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2004\07\02@065045 by Peter L. Peres

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>In Math, we used Peano's Axioms to define the numbers.  The only number
>that is directly defined is "0", and "2" is inductively defined as the
>thing that comes after the thing that comes after "0".

Oh. But Peano's axiom system (and any other according to G"odel's proof)
is not perfect. So defining 1 inductively as the thing that comes after 0
relies on the definition of integers. But as we discussed before on this
list 1.(9) is equal to 2 and thus 1.(9) is an integer since 2 is defined
as an integer. Therefore there 2 is the 4th integer on the number axis,
after 0.(9) which equals 1, 1 and 1.(9) which equals 2. No ? And if no,
then 1.(9) does not equal 2 or 2 is not an integer or equal does not
always mean equal, or the definition of the integer is up the same creek
the parallel axiom is ? ;-) Oh, and I'm not a math major (not even minor).

>By this definition, "2" is nothing more than a label on a point on the
>number line, so it can't vary.  If the number line shifts, the label
>we're calling "2" should move to a different on the line to hold its same
>meaning.

Is the line straight ? Does it cross itself due to a curved non-convex
space it is defined in (while you think it's as straight as the horizon
all the time) ? If it does not cross itself now, would it cross itself
when you're not looking due to a large mass passing nearby ? ;-)  (this is
preparation for the definition of 2 in physics)

>Obviously this isn't what the Physicists are using to define "2", so I'm
>curious what they are using that can vary.

2 would probably be the average of the number of electrons one can see in
an atom over 100,000 tests or so, while disregarding any measurements that
showed more or less than 2 electrons from those 100,000 ;-) ;-) (and I'm
not a physicist).

Peter

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2004\07\02@072649 by Wouter van Ooijen

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> Oh. But Peano's axiom system (and any other according to
> G"odel's proof) is not perfect.
> Oh, and I'm not a math major (not even minor).

That shows :)

According to Godel an axiom system is either
1) not that interesting because it can not self-reference
2) capable of undecideable stentences

I don't know what you mean by calling either class 'not perfect'.

Wouter van Ooijen

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2004\07\02@100417 by David VanHorn

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>
>Is the line straight ? Does it cross itself due to a curved non-convex
>space it is defined in (while you think it's as straight as the horizon
>all the time) ? If it does not cross itself now, would it cross itself
>when you're not looking due to a large mass passing nearby ? ;-)  (this is
>preparation for the definition of 2 in physics)

It's not in space or time, it's a mathematical construct.

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2004\07\02@173317 by Jason S

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From: "Peter L. Peres" <spam_OUTplpTakeThisOuTspamACTCOM.CO.IL>
Sent: Thursday, July 01, 2004 10:10 PM


> So defining 1 inductively as the thing that comes after 0
> relies on the definition of integers. But as we discussed before on this
> list 1.(9) is equal to 2 and thus 1.(9) is an integer since 2 is defined
> as an integer.

In Peano's axiom system, only integers exist.  There is no such thing as
non-integer rationals or reals.  1.(9) would not be in that system.  But in
a larger system that does support rationals, 1.(9) IS 2.  It's not an other
integer that equals 2.

In fact, Peano's axioms do cover this case.  One of the axioms is "two
numbers of which the successors are equal are themselves equal".  Since
S(1.(9)) = 3 = S(2) we know 1.(9) = 2.

Jason

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2004\07\03@123303 by Peter L. Peres

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> It's not in space or time, it's a mathematical construct.

As long as it's pure math, fine. But one day you'll want to apply it in
the real world, and rely on its abstract mathematical proof too, for large
numbers. Murphy will be watching you.

Peter

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2004\07\03@135227 by Wouter van Ooijen

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> > It's not in space or time, it's a mathematical construct.
>
> As long as it's pure math, fine. But one day you'll want to
> apply it in the real world, and rely on its abstract
> mathematical proof too, for large
> numbers. Murphy will be watching you.

An abstract mathematical proof will hold for large numbers too. Nothing
'real world' about large numbers, they are mathematical constructs, lust
like 0 and its smaller successors.

If on the other hand you are applying a mathematical theorem to real
world situation you are doing an applied science (physics, or
chemsistry, or whatever). If that fails it's the applied science that
fails, because mathematics itself does not imply any real-world
consequences, so it can't be falsified by a real-world observation.

Wouter van Ooijen

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2004\07\03@140305 by D. Jay Newman

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> An abstract mathematical proof will hold for large numbers too. Nothing
> 'real world' about large numbers, they are mathematical constructs, lust
> like 0 and its smaller successors.

Agreed.

The "numbers" that are connected to the real world are those "constants"
that are based on measurable quantites. These can change.

For example, pi is the ratio of the circumference of a circle to its
diameter. If the ratio changes, then pi changes. I find it difficult
to guess how it could change, but...

Other examples are "Plank's Constant" and "Avagodro's Number". The values
of these are taken from the physical world.
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2004\07\03@142420 by Wouter van Ooijen

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> The "numbers" that are connected to the real world are those
> "constants" that are based on measurable quantites. These can change.
>
> For example, pi is the ratio of the circumference of a circle to its
> diameter. If the ratio changes, then pi changes. I find it difficult
> to guess how it could change, but...

Nothing measurable about pi. A circle is a mathematical construct,
circumference and diameter too.

> Other examples are "Plank's Constant" and "Avagodro's
> Number". The values of these are taken from the physical world.

Plank's constant is indeed something from the real world, something that
can be measured. I am not so sure about Avogadro's constant, IIRC it is
simply defined and other things follow from it, but I am not sure about
this.


Wouter van Ooijen

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2004\07\03@150649 by Denny Esterline

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> Plank's constant is indeed something from the real world, something that
> can be measured. I am not so sure about Avogadro's constant, IIRC it is
> simply defined and other things follow from it, but I am not sure about
> this.
>
>
> Wouter van Ooijen
>

As I understand it, Avogadro's number is defined as the number of atoms of
an element necessary to have a mass in grams equal to it's atomic weight.
For practical use that works out to be 6.022 x 10^23, also known as one
mole. (i.e. 6.022 x 10^23 atoms of oxygen weigh 15.999 grams)

The concept of a 'mole' was being used long before they could
experimentally define the quantity that it's based on.

-Denny

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2004\07\03@171227 by Jason S

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Close.  Avogadro's number is the number of atoms of Carbon-12 requried to
have a mass of exactly 12 grams.  For other elements/isotopes, the number
would be slightly different.  There is energy stored in the atomic bonds in
the nuculus, and this affects the mass of the atom according to E=mc^2.  For
example,a Helium-4 nuculus contains 2 protons and 2 neutrons, but it's mass
is slightly lighter than the sum of the 4 particles because some energy is
emitted when the particles are combined so the mass equivalence of this
energy is lost.

The reason oxygen will show up on your periodic table with an atomic weight
of 15.999 is because it's a weighted average of all the isotopes of oxygen
in the proportions they appear on Earth.  If you take a sample of oxygen, it
will have all the isotopes present in these relative quantities, so when you
go to measure it, you'll be measuring across the weighted average.

Jason

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2004\07\04@071214 by Jake Anderson

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tid bit
avagadro's number used to be 16 grams of oxygen ;->


{Quote hidden}

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2004\07\04@072911 by Jake Anderson

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simple way to visualise it.
ok on a flat piece of paper draw a circle with a compass.
measure the perimiter and circumfrernce
now cut the hole out of the paper
put the paper over a ball and draw a circle on the ball so it has the same
perimiter
now measusre the circumference from the high point of the ball over the
surface to the circle. if you base the calculation of Pi on that you wind up
with a different number.

now instead of paper we have the universe.
if the universe is curved in some fundamental way, Pi will be different.
(assuming your measurement devices dont bend too ;->)
now when it gets real weird is rather than having a spherical curve, have a
cylindrical one let that warp your mind a little

> {Original Message removed}

2004\07\04@073533 by Wouter van Ooijen

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> if you base the calculation of Pi on that you wind up
> with a different number.

True, but in that case it is not pi that has changed, but the
applicability of flat mathematics/geometry to your real world that has
been falsified. Flat matematics/geometry itself is still irrefutably
correct.

Wouter van Ooijen

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