It
has always been difficult to consider the nature of time
because it is difficult to define it in terms of other quantities
which are readily understood. There seems always to be a problem with
one or more of the other quantities because they are also time
dependent, and a circular discussion which leads nowhere ensues
through the mathematics.
There is a way around this
circularity by using a different SI unit of measure for acceleration.
The measure most common is metres per second per second, m/s2
in most physics texts. There is another measure available to
consider, from a previous paper by this author :-
From
Newton's second law of motion, that is F = ma, then mathematically a
= F/m from which SI units a
evidently has units of measure Newtons per Kilogram ( F newtons
divided by m kilograms).
Acceleration can be measured in N/kg in addition to the more commonly
used m/sec2
.
An
alternative unit of measure for acceleration also offers another set
of Newtonian equations. They represent an alternative approach to
calculating quantities seen in Newtonian physics.
For
example, given the alternative measures for acceleration N
kg
-1
= ms-2,
then mathematically s-2
= N kg-1
m-1,
therefore s2
= kg m N
-1
and s = √
(kg.m / N) which
in English says that time equals the square root of (mass times
length divided by force).
This
is as difficult as the maths gets and the equation for time is
t
= √
( m r / F ).
The
SI unit of measure for time
from this equation is ( kg.m / N )½
.
None of these quantities involve the use of time in their definition
in SI units of measure, hence the circularity mentioned above is no
longer a problem. If these SI units are converted to space-time units
the result is t,
confirming their validity. (For
those with a mathematical mind, in S-T units √
kg.m/N equals ( t3/s3
x s / t/s2)½
= t .)
Looking
at this equation for time, if it is assumed that the element r/F
remains constant for the moment, then time varies as the square root
of the mass, or t
= √
m.k
where k is the constant r/F.
Albert
Einstein has already proven to the satisfaction of most scientists
that mass is a form of energy. It then follows that so it is the case
with time because of its direct relationship to mass as outlined
above. Einstein's Theory of Special Relativity does allow for a
variability in both time and mass within the supporting mathematics,
relating velocity referenced to the speed of light. That is
consistent with the factor r/F, r (distance) divided by F (force)
which, from the above equation for time, is the other factor relevant
to the variation of time when mass is constant.
If
it is assumed that time t = 0 means that time has stopped and t = 1
means that time passes as we perceive it, as a measure of the Earth's
orbit, then to change time to a point somewhere above 0 would mean a
change of mass as the square root of the time change. If mass
equaled 0 so would time, and if mass were at its natural value both
would equal 1. The ability to alter mass would theoretically relate
as outlined by the above equation to the ability to change time. The
mathematics might state the above as Δt
= (Δm.k)½.
( delta, Δ,
means 'a change of ') So for example, if a mass were changed from 1
kg to ½
kg, then the associated time change would equal t
= (½.k)½
or 0.707√
k (slower time); or if mass were doubled from 1 kg to 2 kg then t =
(2.k)½
or 1.414√
k (faster time). The above equation for time does not allow for a
negative value for t.
The square root of a negative number is, in mathematics, called an
imaginary number - which suggests that time does not run in reverse,
at least in our part of the universe. That is consistent with
observation.
In
summary, time could theoretically be altered in two ways, one as
outlined by Special Relativity relating to the velocity of an
observer compared with the speed of light, and the other by changing
the observer's mass. Mathematically both amount to the same thing,
the two are connected indirectly by the maths of Special Relativity
Theory, but are connected directly by the equation for time, t = √
(mr/F).
