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Books and publications on the interaction of systems in real time by A. C. Sturt
Economics, politics, science, archaeology. Page uploaded 25 November 2004

 



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Mass in the Universal Inertial Field


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A Revised Version

by A. C. Sturt

 

 

 

 

 

 

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

5. The Partition of Forces

6. The Form of the Energy Generated in the Inertial Resistance Field

7. Conservation of Momentum

8. A Universal Model







 












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

5. The Partition of Forces

6. The Form of the Energy Generated in the Inertial Resistance Field

7. Conservation of Momentum

8. A Universal Model

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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

5. The Partition of Forces

6. The Form of the Energy Generated in the Inertial Resistance Field

7. Conservation of Momentum

8. A Universal Model

 

 

 

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.

 

 

  1. The Inertial Field Model

 

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.

 

 

 


 




isotropic inertial field



 

 

 

methodology to evaluate inertial resistance


consistent with new theory of light




energy


 

electromagnetic connection of light with inertia of mass



tests

 


 

 

 

 

 

 

 

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

 

Copyright A. C. Sturt 27 September 2001

continued on Page 2

 

 

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