## Alternatives to Relativistic Mass
A simple particle accelerator (shown above) is constructed by placing two
electrically charged plates at either side of a vacuum tube. Inside the tube is a single
electron. Initially the plates are neutral and the electron is at rest. When a voltage is
applied to the plates this creates a uniform electrical field inside the tube. This field
then applies a force to the electron which causes it accelerate. The extent of
acceleration can be calculated using factors of mass, charge and voltage.
## Mass vs. ChargeAssuming that experimental evidence is correct in confirming a decrease in
acceleration as particles move towards light speed, might there be other ways of
explaining this phenomenon, other than by suggesting a mass increase? While it is true
that an increase in mass would certainly slow the rate of acceleration, it is also true
that a decrease in charge could achieve the same. In other words, suppose that as a
particle increased in speed, its electrical charge steadily decreased toward, and became
zero at light speed. In this situation, the amount of electrical force experienced by the
particle would decrease, and this would slow acceleration. The end result would be the
same – a light-speed limit.
## The Wind TunnelImagine a wind tunnel such as that shown below. It has fans at both ends to ensure a smooth flow of air at constant speed along its length. The fans are initially off. At one end of the tunnel is a marble. The marble sits in the cross-sectional centre of the tunnel so we’ll need to imagine that this is a zero gravity environment or that the marble is somehow magnetically suspended away from the tunnel walls. Now let’s turn on the fans. Very quickly the air in the tunnel
accelerates to a constant velocity as determined by the fan speed. This moving air applies
a force on the marble which then accelerates. Under the constant influence of this force
the marble moves increasingly faster along the tunnel.
## Speed DifferencingI submit therefore that the real reason for a particle’s slowdown
near light-speed has nothing to do with an increase in mass, and everything to do with a
decrease in force that results from a difference between field speed and particle speed.
Of course it is also possible that an increase in mass could be responsible for the same
result. But why invent a complicated reason to explain a phenomenon when a more plausible
explanation is available? Why the cube and not the square? There’s a subtle difference and the
reason will be explained in a later chapter about magnetism. For the sake of giving this a name I’ll call this the Electric Velocity Force Function (EVFF). If applied to a force equation it could look like this: Where F
is the ‘relativistic’ force.
## Interactions between opposite chargesThe above formula can be used when determining the interaction between
‘like’ charges; i.e. both negative or both positive. Now let’s consider
interactions between opposite charges. The sign in front of the velocity becomes positive, not because velocity has changed direction, but because the charges are opposite.
## A Velocity Dependent Coulomb’s LawNow let’s create a variation of Coulomb’s Law that takes into account particle velocities. Coulomb’s Law tells us the amount of electrical force that exists between two charged particles a given distance apart. The equation for this law is: Where q
are the charges of particles 1 and 2 respectively and _{2}r is the distance
between them.This formula is considered true for static charges. Next we’ll introduce what I’ll call the ‘Velocity Dependent Coulomb’s Law’ (VDCL) which allows for moving charges. Consider the below diagram that shows moving charges: The modified force equation for this situation becomes: Where v represent the velocities of particles 1 and 2
respectively and _{2}r is the distance between them. The term [q
refers to the sign of charge _{1}]q; i.e. for a positive charge
like a proton _{1}[q = +1 and for a negative charge like an
electron _{1}][q = -1. Likewise _{1}][q
is the sign of charge _{2}]q._{2}[Sidenote: To be precise, v is not the current velocity of
particle 1 but the velocity particle 1 had when it generated the field that has now
reached particle 2. This is a subtle distinction because there is a brief delay between
when particle 1 emits its field and when that field reaches particle 2; and the velocity
of particle 1 could change during that time. This will be covered later in more detail.]_{1}So why not just use the conventional LT instead of the EVFF? I discussed in an earlier chapter that the LT is based on questionable assumptions about time dilation that, even if true, shouldn’t apply to one-dimensional situations such as this. Of course it’s still possible that the regular LT may be the correct function. The above equation however does have some large benefits. If we assume it to be correct then a number of physical phenomena can be neatly explained including magnetism and static electricity as I will show in the following chapters.
## Examples with Same chargeBelow are some diagrams to better describe this. In each of these examples
particle 1 is at rest and particle 2’s velocity is given by v = _{2}v.First we have two positively charged particles at rest. Let’s say they are placed fixed distance apart and each experience an opposing force of 1 Newton (see below). Now we will repeat the above but this time they are moving away from each
other with a speed of According to the EVFF, So they experience an opposing force of 0.125 Newton; a large decrease
when compared to the static situation. The EVFF describes a positive velocity as moving away. So the velocity here is -1/2 and EVFF shows: So they experience an opposing force of 3.375 Newton. Here the force has greatly increased.
## Examples with Opposite chargeTake two identical but opposite charges, initially static and the same distance apart as in the above examples. They will each experience an attractive force of 1 Newton. Now we will repeat the above but this time they are moving away from each
other with a speed of The equation is the same as for similar charges but the force direction is different. According to the EVFF, So they experience an attractive force of 3.375 Newton; an increase when
compared to the static situation. Here both the velocity and the charge are negative and EVFF shows: So they experience an attractive force of 0.125 Newton. Here the force has decreased and this retards the rate of acceleration.
## ConclusionIt is possible to explain the decrease in acceleration of an object near light-speed without requiring a mass increase toward infinity as it approaches light-speed. One method is to say that the force of an electric field on a charged particle is proportional to the difference between field and object velocities. This is similar to the way fluid forces behave in classical mechanics. |

Copyright © 2010 Bernard Burchell, all rights reserved.