We
could not find any experiment that directly proves inertial mass increase,
though it has been inferred from some experiments. But there are alternative
explanations for those observations. Like other forces, we experience
mass through the effect it produces on others. This is the difference between
the body (dimension) and it’s mass. While energy creates temperature variation,
mass creates pressure variation. Both are related to the body. Inertial mass is
a mass parameter giving the inertial resistance to acceleration of the body as
determined by its momentum, when it is subjected to a force that is not due to
gravity. It is found by applying a known force to an unknown mass, measuring
the acceleration, and applying Newton's
Second Law, m = F/a. If the same body with the same mass is
displaced with application of different energy, its effect (a) would appear as
different in proportion to the applied force (F), i.e., with mass constant, F
varies with a. Thus, in principle, it need not be mass variation, but can
appear so due to energy variation.

Switching
over from Cyclotron to Synchrotron is not based on observational necessity, but
based on difference between relativistic and non-relativistic theories. They
are two different theories independent of each other. The variation factor γ
proposed in SR is a mathematical structure apparent to the observer and not
real to the physical structure being observed. This difference is generally not
recognized - mostly by the brane-world proponents. Unlike three dimensional
physical structures, mathematical
structures are two dimensional. The graph may represent space, but it is
not space itself. The drawings of a circle, a square, a vector or any other
physical representation, are similar abstractions. The circle represents only a
two dimensional cross section of a three dimensional sphere. The square
represents a surface of a cube. Without the cube or similar structure
(including the paper), it has no physical existence. An ellipse may represent
an orbit (a circle with a moving center), but it is not the dynamical orbit
itself. The vector is a fixed representation of velocity; it is not the
dynamical velocity itself, and so on.

The so-called
simplification or scaling up or down of the drawing does not make these
structures abstract. The basic abstraction is due to the fact that the
mathematics that is applied to solve physical problems actually applies to the
two dimensional diagram, and not to the three dimensional space. The numbers
are assigned to points on the piece of paper or in the Cartesian graph, and not
to points in space. If one assigns a number to a point in space, what one
really means is that it is at a certain distance from an arbitrarily chosen
origin. Thus, by assigning a number to a point in space, what one really does
is assign an origin, which is another point in space leading to circular logic.
The point in space can exist by itself as the equilibrium position of various
forces. But a point on a paper exists only with reference to the arbitrarily
assigned origin. If additional force is applied, the locus of the point in
space resolves into two equal but oppositely directed field lines. But the locus
of a point on a graph is always unidirectional and depicts distance – linear or
non-linear, but not force. Thus, a
physical structure is different from its mathematical representation. Hence, the
basic assumptions of all topologies, including symplectic topology, linear and
vector algebra and the tensor calculus, all representations of vector spaces,
whether they are abstract or physical, real or complex, composed of whatever
combination of scalars, vectors, quaternions, or tensors, and the current definition
of the point, line, and derivative are necessarily at least one dimension less
from physical space.

Perception
is related to physical structures. The field created by the content of our eye
interacts with similar fields created by other objects measuring those in the
process. They are not two dimensional like the impressions on a photographic
plate, but three dimensional like a mould, i.e., a shaped cavity that is
used to give a definite form to fluid or plastic material including radiation
that behave like fluids. Thus, we see three dimensional objects.
The photographic plate on the other hand represents the mathematical structure
in two dimensions. Thus, it is an abstraction, which is not physical.

While
there is no direct evidence of increase in inertial mass, there are many
experiments to conclusively show that the ratio of gravitational mass to
inertial mass is constant. Gravity is said to be an attractive force, i.e., the
force applied by one body brings the other body towards it, i.e., towards the
direction of the applied force. Inertia displaces the body in the direction
opposite to the direction of the applied force. Since both the displacements in
opposite directions are known to be equivalent, this implies that the concept
of inertial mass is only apparent like a mirage and can not be real.