The most fundamental equation in mechanics , derived on the basis of absolute truths (derivation shown below), makes it really inevitable to recognize the fundamental discrepancy hampering clasical physics, deeply penetrating it and causing the unnecessary appearance of the physically deformed view of nature brought about by quantum mechanics. Here, the word is about the fundamental misunderstanding in classical mechanics of the concept of motion.
Thus, if the three laws of Newton are called laws of motion, then Newton's second and third laws being in fact laws of rest are in contradiction with Newton's first law, which requires an uncompensated force to be applied to the free body if it is to change its state of rest or uniform rectilinear motion.
Indeed, Newton's second law ,
which is an expression of Newton's third law, especially if it's written
to reflect the fact that the force
invokes a compensating equal in magnitude but opposite in direction
inertial counterforce .
The application of such force
on the body cannot change the state of the body as required by Newton's
first law and invoke motion. Force
only causes matching
Now, if conservation of energy is in effect, as physics
accepts, then, .
In other words, if conservation of energy is to be
obeyed then the body must be at rest.
The Most Fundamental Equation in
After the obviously necessary abandonment
of quantum mechanics, the comporting of classical mechanics with the scientific
method and its further development along the road of truth and reason
must begin with recognizing the imprtance of an equation, elevated by
this author as the most fundamental equation of mechanics when treating
a free body under the action of a constant force.
Thus, it's an absolute truth that velocity
Also, it's an absolute truth that acceleration
From these two definitions we can express
dt in two ways
Now, these two expressions being equal,
allows us to write
or, reordering it
which may also be written as
Now, we can integrate both sides of this
factoring out of the integral the constant
acceleration a as well as the constant one half. From where we get
Finally, we have
This equalion of a parabola, has come
about from absolute truths of physics. Therefore, the connection between
the velocity v, acceleration a and the position x is set in stone and
is also an absolute truth. We now can plot it and see what conclusions
we can get from it.
It is seen from the above that the graph of
as a function of square root of x is only an idealized plot, which
considers that acceleration is valid for any velocity, no matter how high.
However, as seen, as the velocity gets higher, the constant acceleration
becomes less and less significant and for some high velocities it becomes
so small in comparison that it can be neglected. In other words, the velocity
attains a constant value, reaching the clasical velocity limit.
When one looks at the above-shown graph of ,
one may wonder how is the velocity reaching a plateau. A parabola, such
as the one shown, doesn't have an asymptote. This is one of these moments
when we should remember that mathematics is only a helping tool in physics.
It's the physical reality which determine the conclusions. Thus, in this
case we should come to realize that numerically, when the velocities become
very high, they dwarf the constant acceleration. Therefore, acceleration
can be neglected and, therefore, force loses meaning. This can be seen
immediately from the complete expression of Newton's second law:
where the negligible acceleration makes the first
term after the equality disappear. The second term after the equality,
being equal to the first term (following from the most fundamental equation
of mechanics), is also negligible. Therefore, the whole expression for
the real force vanishes. Force has no meaning at high velocitites attained
when a free body initally at rest is acted upon by a constant force.
we see that none of the terms on the right side of
the equality can be neglected -- firstly, because the second term contains
the ever increasing positive value of velocity, squared at that. Secondly,
because the first term after the equality sign is equal (following from
the most fundamental equation of mechanics) to the non-neglectable second
This way of expressing energy conceals the origin
of the motion causing the displacement and only states that had there
been such displacement of the mass m, it would have required energy equal
to the product of the mass and the displacement itself. So, again, we
must consider the physical meaning of what was derived mathematically.