Space Forum / Astronomy / September 2005

From Painius:

medium

It was because the perceived "void", the smooth, unrippled "nothingness"
paradoxically exhibits the properties of hyperpressurization, a fixed
value of c, and the ability to carry unlimited amplitudes of EM energy.
Yet we cannot "see" it; it resides below our sensorial and EM
resolution. Therefore its wavelengths _must_ be below the Planck limit,
the so-called "smallest length that has any meaning".
               Concomitantly, its energy states must rise per the maxim
that the shorter the wave the higher the energy. And that's totally
consistent with all observed effects of the SPED (like the high
propagation speed of light, no perceptible EM amplitude limit, and the
behavior of gravity which indicates a hyperpressurized state).
oc

Thank you, Bill... i did that moreso just to show the effect
upon the amount of energy if the "c" factor would change in
any way.  Fact is, cubing c, that is, using c³ in Einstein's
relativity equation is not mathematically valid.

I'm not all that good at math, but i do like to dick around
with it, sometimes.  So for the benefit of all gentle readers
who might feel the same way, let's play with it a bit...

Maybe it would help if we dug a little into the equation itself...

  E = mc²

Each letter is the initial of a word representing the concept it
stands for.  E is the initial letter of "energy" and m of "mass".
As for c, the speed of light in a vacuum, we know that it is
the initial letter of "celeritas", the Latin word meaning "speed".

This is not all, however.  For any equation to have meaning
in physical reality, there must be an understanding as to the
*units* being used.  It is meaningless to speak of a mass of
2.3, for instance.  It is necesary to say 2.3 grams or 2.3
pounds or 2.3 tons.  Just a mass of "2.3" alone is worthless.

Now, one can choose whatever units are convenient, of
course.  As a matter of convention, one system used in the
science of physics is to start with "grams" for mass,
"centimeters" for distance, and "seconds" for time.  Then
we can build up, as far as possible, other units out of
appropriate combinations of these three fundamental ones.

The m in Einstein's equation is expressed in grams,
abbreviated gm.  The c represents a speed, which is a
distance traveled in a certain amount of time.  Using the
fundamental units, this means the number of centimeters
traveled in a certain number of seconds.  The units of c are
therefore centimeters per second, or cm/sec.

(Notice that the "per" is represented by a fraction line. The
reason for this is that to get a speed represented in lowest
terms, that is, the number of centimeters traveled in *one*
second, we must divide the number of centimeters traveled
by the number of seconds of traveling.  If we travel 24
centimeters in 8 seconds, our speed is 24 centimeters ÷ 8
seconds, or 3 cm/sec.)

One of the elegant things about the equation is that c occurs
as its square.  If we multiply c by c, we get c².  However,
it is insufficient to multiply the numerical value of c by itself.
we must also multiply the *unit* of c by itself.

An example of this is like in measurements of land area.  If
we have a tract of land that's 60 feet by 60 feet, the area is
not just 60 X 60 = 3600 feet.  It is 60 feet X 60 feet, or
3600 *square* feet.

So when dealing with c² we must multiply cm/sec by cm/sec
and end with the units cm²/sec² (which can be read as
"centimeters squared per seconds squared").

Next, what unit do we use for E?  Einstein's equation itself
will tell us, if we remember to treat units as we treat any
other algebraic symbols.  Since E = mc², that means the unit
of E can be obtained by multiplying the unit of m by the unit
of c².  Since the unit of m is gm and that of c² is cm²/sec²,
the unit of E is gm X cm²/sec². Now in algebra we represent
a X b as ab, so we can run the multiplication sign out of the
unit of E and make it simply gm cm²/sec² (which we read as
"gram centimeter squared per second squared").

This works out really well, because long before Einstein
derived his equation it had been decided that the unit of
energy on the gram-centimeter-second basis had to be
gm cm²/sec².  Let's see why this should be...

First, we remember that the unit of speed is cm/sec.  But
what happens when an object changes speed?  Suppose
that at a given instant, an object is traveling at 1 cm/sec,
while a second later it is traveling at 2 cm/sec, and another
second later it's traveling at 3 cm/sec. It is, in other words,
"accelerating" (also from the Latin word "celeritas").

In the above case, the acceleration is 1 centimeter per
second every second, since each successive second it is
going 1 centimeter per second faster.  We might say that
the acceleration is 1 cm/sec per second.  Since we are
letting the word "per" be represented by a fraction mark,
this may be shown as 1 cm/sec/sec.

As we've already seen, we can treat the units by the same
manipulations used for algebraic symbols.  An expression
like a/b/b is equivalent to a/b ÷ b, which is in turn equivalent
to a/b X 1/b, which is in turn equivalent to a/b².  By the same
reasoning, 1 cm/sec/sec is equivalent to 1 cm/sec² and it is
cm/sec² that is therefore the unit of acceleration.

And now... "May the force be with us!" <g>

A "force" is defined, in Newtonian physics, as something that
will bring about an acceleration.  By Newton's First Law of
Motion any object in motion, left to itself, will travel at
constant speed in a constant direction forever.  A speed in a
particular direction is referred to as a "velocity", so we might
more simply say that an object in motion, left to itself, will
travel at constant velocity forever.  This velocity may well be
zero, so that Newton's First Law also says that an object at
rest, left to itself, will remain at rest forever.

As soon as a force, which may be gravitational,
electromagnetic, mechanical, or anything, is applied to the
object, its velocity is changed.  This means that its speed of
travel or its direction of travel (or both) is changed.

The quantity of force applied to an object is measured by the
amount of acceleration induced, and also by the mass of the
object, since the force applied to a massive object produces
less acceleration than the same force applied to a light object.
(We can check this for ourselves by kicking a beach ball with
all our might and watching it accelerate from rest to a good
speed in a very short time.  Next we kick a cannon ball with
all our might and OUCH!!!  We observe--while hopping
around in agony--what an unimpressive acceleration we have
imparted to the cannon ball.)

To express this observed fact, we can use the expression,
"Force equals mass times acceleration" or, to abbreviate,
f = ma.  Since the unit of mass is gm and the unit of
acceleration is cm/sec², the unit of force is the product of the
two or gm cm/sec².

Physicists grow tired of muttering "gram centimeter per
second squared" every other minute, so they invented a single
syllable to represent that phrase.  The syllable is "dyne", from
the Greek *dynamics* meaning "power".

So the expressions are the same, 1 dyne = 1 gm cm/sec².
Dyne is just a breathsaver and can be defined as follows:  A
dyne is that amount of force which will impose upon a mass
of one gram an acceleration of one centimeter per second
squared.

Sokay... next, there arises the problem of "work".  Work as
defined by science is not what we do to bring home the bacon.
To the astrophysicist, "work" is simply the motion of a body
against a resting force.  To lift an object against the force of
gravity is work.  To pull a bar of iron away against the pull of
a magnet is work.  To drive a nail into the wood against the
resistance of friction is work, and so on.

The amount of work depends on the size of the resisting force
and the distance moved against it.  This can be expressed by
saying, "Work equals force times distance," or by abbreviation,
w = fd.

The unit of distance is cm and the unit of force is dyne.  So the
unit of work is dyne cm.  Again, scientists invented an easy
one-syllable word to express "dyne centimeters", and the new
word is the vulgar sounding "erg" (did somebody burp?), from
the Greek *ergon*, meaning "work".

An erg is defined as the unit of work, and 1 erg is the amount
of work performed by moving an object one cm against the
resisting force of one dyne.

Lest we forget that this is all based on the gram-centimeter-
second system, bring to mind the fact that a dyne is equivalent
to a gm cm/sec².  This means that the unit of work is cm times
gm cm/sec² (distance times force), and this works out to
gm cm²/sec².  In other words, 1 erg is the work done by
imposing upon a mass of 1 gm an acceleration of 1 cm/sec²
over a distance of 1 cm.

It was discovered well over a century ago that work and
energy are equivalent, so that the units for one will serve as the
units for the other.  So the erg is also the unit of energy on the
gram-centimeter-second basis.

Now shall we get back to Einstein's equation?  There the units
of E worked out to gm cm²/sec², and that is equivalent to ergs.
Those are the units we expect for energy, and it's no coincidence.
If the equation had worked out to give any other units for energy,
Einstein would have sharpened his pencil and started over again,
knowing he had made a mistake.

If we de-elegance the equation E = mc² by getting rid of the c²,
we get...

  E = mcc

...and if we do this to the equation E = mc³, we then get...

  E = mccc

...so cubing c just makes the = (equal) sign go away.  We are
obligated to do the same thing to both sides of the equation,
aren't we?  If we multiply one side by c, then we must do the
exact same thing to the other side to be able to keep the equal
sign as valid.  Sorry, but this makes the equation E = mc³ not
valid and, more importantly, not an expression of physical
reality.

And yet, while we must continue to stick with Einstein's most
elegant and valid expression E = mc², it may be a little easier
to see what a tremendous difference it makes if the speed of
light actually *can* be increased by one or two orders of
magnitude.

As you say, Bill, this expresses the enormous energy density
of space, so we would have to replace the m with an s to try
and begin to find true validity to the equation.  So we have...

  E = sc³

Now all we need is a math/astrophysics wizard to tell us
what would be the best units to use for the space/SPED
factor which would keep the equal sign valid.

Perhaps the first thing to look at would be the acceleration.
We know that if speed increases we have an acceleration.
And the unit for this is cm/sec².  So what if the acceleration
increases?  If in the first instant our speed is 1 cm/sec, then
a second later it is 2 cm/sec, then another second later our
speed is 4 cm/sec, after one more second we're going 7
cm/sec.  In the first second we accelerated 1 cm/sec. Then
in the next second we accelerated 2 cm/sec.  And in the
third second we acclerated 3 more cm/sec.  Would it be
correct to say that the acceleration is accelerating at a rate
of 1 cm/sec³?

Lately we may have read about the accelerated acceleration
of the Universe.  Perhaps we need a simpler name for the
term "accelerating acceleration"?

happy days and...
  starry starry nights!

PS -- credit for most of this post goes to the guy in the
pome...

It reminds me of the infinity reflections of barbershop mirrors.  As
much as it smacks of Zeno's Paradox, i still like the idea.  I'd wager
few others will, though.

So maybe quantum theory is doing with nonlocality what all of us
used to do with light?  Until the Ole Rømer measurement, almost
everybody thought that light traveled instantaneously from one place
to another. Maybe nonlocality isn't instantaneous, but just *appears*
to be so?  Maybe it's only "functionally" instantaneous? <g>

happy days and...
  starry starry nights!