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Books and publications on the
interaction of systems in real time by A. C. Sturt |
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Mass in the Universal Inertial Field |
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A Revised Version by
A. C. Sturt |
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SUMMARY 1. The Inertial Field Model 2. Mathematics of
Transformation to Rectangular Hyperbola Form 3.
Evaluation of the Inertial Field Resistance R 4. The
Quantity of Energy Generated in the Inertial Resistance Field 6. The
Form of the Energy Generated in the Inertial Resistance Field 2. Mathematics of
Transformation to Rectangular Hyperbola Form 3.
Evaluation of the Inertial Field Resistance R 4. The
Quantity of Energy Generated in the Inertial Resistance Field 6. The
Form of the Energy Generated in the Inertial Resistance Field 2. Mathematics of
Transformation to Rectangular Hyperbola Form 3.
Evaluation of the Inertial Field Resistance R 4. The
Quantity of Energy Generated in the Inertial Resistance Field 6. The
Form of the Energy Generated in the Inertial Resistance Field |
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Summary
The analysis of a previous paper (1) pointed towards the
existence of a universal, isotropic inertial field which permeated all space
and resisted the acceleration of mass. This gave the appearance that mass
increased with velocity, whereas in fact it remains unchanged. This is in
contrast to the Special Theory of Relativity which predicts that mass
increases with velocity, with the consequence that the length of intervals of
time and space must also change. The present paper develops a methodology for evaluating
the resistance of such an inertial field to the acceleration of a particle of
mass. The inertial resistance is called R, and it is measured in
newtons. The value of R increases hyperbolically with the velocity of
the particle. The methodology involves transformation of the hyperbola to
rectangular form. The reciprocal of R then becomes a straight line
when plotted against velocity, and so it can be characterised by two points. The concept of a universal inertial field for mass fits
well with the new theory that light consists of rotating electromagnetic
dipoles (2). This theory requires that there should exist a medium of space
which is universal and isotropic, and accepts electromagnetic induction. The
model of inertial resistance to the movement of mass suggests that this too
may be a property of the same medium of space, one which applies to mass. The model allows calculation of the quantity of energy
generated in the inertial resistance field, and the increasing force required
to cause unit acceleration as the particle increases in velocity. The
magnitude of this force increases to infinity at a velocity which is equal to
the speed of light in vacuo. In this model the connection between the velocity of mass
and light is that the energy generated in the inertial field is in fact
electromagnetic. Light of increasing energy, and hence electromagnetic
frequency, is generated and radiated away as the particle accelerates. As the
particle approaches the speed of light, light energy is shed as fast as
energy is pumped in, and so the particle can go no faster. Hence the limiting
value for particle velocity of 3x108 ms-1, which is the
speed of light. It is shown that the model is compatible with the Law of
Conservation of Momentum. Tests are proposed to validate the model experimentally. The model raises the possibility that velocities
approaching the speed of light may also affect other phenomena such as
electric charge. A further possibility is that different phenomena may
interact under these conditions. The model may offer an explanation of the nature of
inertia. It could form the basis of a Universal model embracing all
phenomena.
In the inertial field model it is suggested that mass as a
quantity of matter stays constant in terms of the number and mass of atoms,
but that the increasing force required for acceleration results from
interaction with an inertial field as the velocity of light is approached. The nature of the interaction is such that the resistance
of the field to the acceleration of unit mass increases hyperbolically with
velocity. The limit of attainable velocity is reached at the asymptote of
resistance and velocity. The form chosen to model this is a rectangular
hyperbola in which the resistance tends to infinity at a definite value of
velocity, the speed of light. Other curves, such as the parabola or the
exponential increase indefinitely, so that there is no cut off value to give
a limiting velocity. The difficulty of relating to velocity is that it must
always be relative. Everything is moving: the Earth, the solar system, the
galaxy etc. There is no degree of freedom, no firm place from which to
measure. By contrast, acceleration is measurable from zero wherever there is
a stopwatch and a metre rule, because it is a local change of velocity. Hence
the prima facie attraction of acceleration as a phenomenon which can be
applied generally. However the analysis which resulted in the new theory of
light suggested that velocity must in fact always be relative to a general
phenomenon in the form of a medium of space, even if the relative value was
uncertain. On this basis a methodology for handling the uncertainty was
developed as follows. Zero velocity v0 is defined as the
position of rest measured at the point on Earth at which the standard of mass
is also defined. The velocity of light c is also measured from a
position of rest here on Earth i.e. it is measured relative to the standard v0.
The parameter c is called vlim here during the
analysis. Thus the hyperbolic function which relates inertial resistance to
velocity can be drawn as in Figure 1. The value of the inertial field resistance R at v0
is just above the asymptote, which itself has an uncertain value because it
is an indeterminate distance away back along the x-axis. If a constant force is applied to a particle at v0,
it produces an acceleration. However, as velocity increases, it produces less
acceleration, because of inertial resistance; velocity continues to increase,
but at a diminishing rate i.e. the acceleration which the force produces decreases. To maintain a uniform
acceleration, the applied force must increase by the factor R at every
stage. When force is removed, acceleration ceases and velocity continues at
the increased level. The implication is that when force is reapplied at the
higher level of velocity, an increased force with the appropriate value of R
will be required to produce unit acceleration.
By contrast, in the Newtonian world one unit of force
always produces one unit of acceleration, whatever the starting velocity. It
is this prediction which is seen to break down as the body approaches the
speed of light. The corollary is that bodies all over the Universe may
have velocities which are different from that of Earth i.e. they may have
velocities relative to v0 and values of R to match
according to the Earth’s framework of units. However, for each individual
body its own framework of units could be derived from its own rest mass on
the spot. The value of R may be calculated as follows. It is
a characteristic of the hyperbola that it can be converted to rectangular
form, the reciprocal of which is a straight line with a negative slope. Thus
a graph of 1/R as a function of velocity is a straight line which cuts
the x-axis at vlim, the limiting value for velocity.
If 1/R is zero at the limiting value of velocity, the corresponding
inertial field resistance R is infinite, which is what is required. Two points are sufficient to characterise the straight
line. This provides a means to evaluate R without the need to specify
the values at the indeterminate point. 2.
Mathematics of Transformation to Rectangular Hyperbola Form
The basis for this transformation is as follows. The
equation for a hyperbola is:
where a and b are the usual algebraic
constants. This transforms to a rectangular hyperbola with the formula:
where c in this case is the next algebraic constant
after a and b, and the new axes, which are at right angles to
each other, are the former asymptotes. Let z = 1/x, then:
which is a straight line with slope dy/dz. |
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methodology to
evaluate inertial resistance electromagnetic
connection of light with inertia of mass inertial field model rectangular hyperbola asymptotes relative velocity medium of space acceleration and
velocity relative to Earth evaluation of R rectangular hyperbola algebraic
transformation straight line slope |
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Copyright A. C. Sturt 27 September 2001 |
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Churinga
Publishing |