VISTAS
IN TIME I: THE PHYSICS Gerardus D. Bouw, Ph.D. Introduction This
paper was started back in 2002 and was originally entitled “Inconstant
Constants.” However, no matter how
exciting and stimulating its start, the original attempts quickly disintegrated
into boredom. This
paper focuses on the speed of light.
The universe appears to be immense.
We speak of billions of light years as if it really took billions of
years for the light to reach earth from the most distant objects observed. That such long travel times are not required
has been demonstrated numerous times by such luminaries as Parry Moon and Dominica
Spencer and John Byl. In 1956 Moon and
Spencer showed that the light from a 10-billion light-year distant galaxy could
reach earth in as little as 15.6 years.[1] About twenty years ago, Dr. John Byl reduced
that to less than ten years. Still,
many geocentrists and creationists think that the universe cannot possibly be
so large without making a liar of God in the physical realm. They assume that we know all things
perfectly—that the speed of light is sacrosanct—so that God would have to
invent a fictitious history of the universe in order to make it appear that
light took billions of years to reach earth whereas light could have traveled
only as far as 6,000 light years since the creation. To
address that concern, Barry Setterfield postulated that the speed of light was
much greater during the creation week.
Later he teamed with Lambert Dolphin to reassess and confirm his
conclusion that historic evidence shows a steady decline in the speed of light
until 1960. But therein lies the
problem with his theory. Why would the
speed of light stop decreasing in 1960?
It is too much of a coincidence to believe that we would detect the
decrease in the speed of light just after the time it stopped decreasing. It seems much more likely that our measuring
technology is much better than in prior decades. In 1982
the inflationary universe was introduced into the study of cosmology. According to that theory, for a brief
instant in time, the universe’s size inflated some thirty orders of magnitude[2]
while the speed of light was equally increased. The inflationary theory was first proposed some ten years earlier,
in 1972, but was ignored because it showed the entire universe to be at most
100,000 years old instead of the “scientifically acceptable” ten billion or
more. By moving the time of the
inflation back, closer to the universe’s origin, the billions of years
supposition was saved and the theory was rescued from obscurity. The inflationary
model demonstrated that a rapid stretching of space increases the speed of
light without affecting time. Prof.
James Hanson notes that modern science views time as the ultimate independent
variable.[3] The net effect is that the universe “ages”
even though the length of a second of time remains the same. In a sense, this is the four-dimensional
counterpart of the expanding universe.
The Big Bang is sometimes described as “an explosion of space instead of
an explosion in space.” Likewise,
inflation can be likened to an explosion of time instead of an explosion in
time. And that
brings us to the essence of this paper.
What happens if our units of measure, the inch, the second, the pound,
the kilogram, the meter, etc. changes over time? The question is related to how the wavelength of light and radio
waves changes as the universe expands.
Although the mathematics is algebra with a little bit of multivariate
calculus notation thrown in, it should never be forgotten that we are not
describing how things normally happen. Technical
Introduction The
analysis presented here is not to be thought of as an attempt to predict the
behavior of normal interactions in space and time. Nor is it an order-of-magnitude study (meaning the use of gross
approximations). This study deals with
fundamental units, namely, units of mass, length, and time. It describes what would happen to the speed
of light, say, if the first law of thermodynamics—also called Conservation
of Energy We
have all seen the formula < Remember that this is not the
same as The
changes in units for expression (1) relate as follows (∂ reads “change in” and d
as “the total change in”): d<E>=< In what follows, we shall drop
the unit notation unless it is necessary to the understanding. Doing so for the above statement gives: d ^{-2}
∂m + 2m l t^{
}^{-2} ∂l – 2m l^{ }^{2 }t^{ }^{-3} ∂t. Conservation of energy tells us
that the total change to the unit of energy d ^{-2}
∂m + 2m
l t^{ }^{-2} ∂l – 2m
l^{ }^{2 }t^{ }^{-3} ∂t = 0. (2) Physicists avoid this
complication by assuming the solution ∂ ^{2}):
Equation
(3) relates changes in the units of mass, length, and time under the constraint
that energy must be conserved. Thus an
increase in the centimeter (∂ Planck’s
Constant Considered Unit-wise Planck’s
Constant is usually denoted as < We can now write any change in
the unit of ( Subtracting
( ( From (3) we see that the rhs
(right hand side) is zero. It follows
then that after a bit of algebra and rearranging terms: ∂ Converting this to unit notation
for a moment we get: ∂< This is a particularly important
result because it says that any changes detected in
which says that any change
in the unit mass will be countered by
twice as large a change in the unit length.
In simpler terms, if the gram were to double, then the centimeter would
be reduced to a quarter of its current length.
(For now we beg the question as to how we could know that happened as
there would be no noticeable change.) Comparing
equation (4) with equation (1) shows us that < < If we replace the partial change
symbol, ∂ by the
uncertainty or error symbol, Δ we can rewrite (5) as: < Usually, physicists assume Δ< Δ< Converting back from unit
notation to regular notation, we can rewrite (7) in its regular form, Δ which is called the “Energy
Uncertainty Principle” or EUP for short.
It is somewhat related to the famous Heisenberg Uncertainty Principle
and we shall have much more to say about this mysterious expression in Part III
of our paper. For the time being, we
shall confine ourselves to the relationship between the expression (5) and the
inequality (8). The
classical, albeit erroneous interpretation of this form of the Energy
Uncertainty Principle says that no experiment can ever determine both energy
and time to any greater accuracy than half a Planck Constant. The Uncertainty Principle has to do with
uncertainties in experimental measurements, not in units. In (8) it is assumed that there is no change
in 2 In the parlance of physics, (8)
is local physics while (5) is universal.
Conclusion In
this first of three papers, we looked at the relationship between energy and
time. We started with the assumption of
conservation of energy: that energy can neither be created nor destroyed by
natural processes. Conservation of
energy is also known as the First Law of Thermodynamics. We next examined what would happen if the fundamental
units of length, mass, and time were changed under the constraint of the First
Law. Although we presented the units of
length as the gram, centimeter, and second, they could be any set of units,
even the Planck mass, Planck time, and Planck length. In
the course of the analysis, we derived a form of the Energy Uncertainty
Principle (9), which does not exactly correspond to the standard EUP (8)
because the latter is generally interpreted as statistical instead of
physical. However, cosmologists have
long recognized that the standard EUP cannot be interpreted statistically. The reason is that the standard uncertainty
principles require vectors or operators on the left-hand side of their
respective statements. Energy can be an
operator, [1] What Moon and Spencer did
was in the same vein as what we shall do in this paper. Moon and Spencer proposed a Riemanian [2] In mathematics, an order of magnitude is a factor of ten. Thus two orders of magnitude is a factor of 100 and thirty orders of magnitude is a one followed by thirty zeroes. [3] Independent variables are
quantities that drive the dependent variables.
Usually the dependent variable is found on the left hand side of an
equal sign while the independent ones are on the right side. Philosophically, treating time as the
ultimate independent variable means that scientists will have to look to time
to make their theories work. For instance,
those who do not like the Bible’s account of creation will look to time
(billions and billions of years) to account for the creation as a chance
event. Sometimes that appears as, “In
time we will discover how it ‘really’ happened.” For instance, 25 years ago I spoke with a biologist who thought
Joshua’s long day was a hallucination.
When I mentioned that Joshua’s long day was a long day for half the
world and a long night for the other half and that there was even an account of
a long sunset he was flustered. He had
assumed that all tales of a long day were of a long period of daylight
hallucinated by one man or a mass hallucination. All he could do was to blurt out, “Well, the study of
phenomenology is a just new science. In
time we’ll know how it happened.” In
other words, “I don’t want the Bible to be true, so I’ll put my hope in the
thought that in the future someone will come up with an explanation for such a
mass hallucination.” [4] This is probably the weakest
part of my argument. Even though the
conservation of energy is called a law, [5] Basically, |