Cosmology – part 2
The Gunslinger and his Motorbike
An interesting analogy can be made
about the interactions between charged particles. It runs as follows...
A man sits atop a stationary motorcycle, pistol in hand, arm
outstretched and aiming forward. He fires a shot. Revving up his bike,
he then accelerates in pursuit of the bullet. After achieving a certain
velocity, he again takes aim along the same trajectory and fires a
second shot. What will happen?
Assume that both bullets are neither affected by gravity nor air
resistance. This allows them to move in perfectly horizontal lines at
constant velocities. The first bullet has a good head start. But the
second has the advantage of added initial velocity. At some point it
will catch up and strike the first from behind.
Now let’s modify the bullets a bit. We’ll say they can somehow overlap
and pass through each other. We’ll also say that when they overlap they
form a combined bullet of the same size but double the mass. In this
case the second bullet would merge into the first from behind and
temporarily form a combined bullet. It would then pass out the front of
the first bullet, leaving it trailing behind at lower velocity.
We’ll now add to the situation and say that as the motorcycle
accelerates, the biker fires a steady stream of bullets, all on the
same trajectory. Because of the steady acceleration, each bullet starts
out with a higher initial velocity than the one before it. That means
that each bullet will eventually catch up to and overtake the one
before it. In fact, each bullet will ultimately pass through and
overtake all bullets fired earlier on.
What the biker has could be described as ‘ghost bullets’ due to their
ability to pass through each other. But let’s limit this ghostly
property to interactions with other bullets and say that they strike
other objects the way normal bullets would.
When one of these bullets strikes a target it exerts force. The force
applied will be proportional to the bullet’s momentum, i.e. its
mass times velocity. So far so good. Now here is where it gets
interesting. When two bullets overlap they form a combined ‘super
bullet’. This super bullet has double the mass and hence (assuming the
same velocity for both bullets) double the momentum of a single
bullet. So if it hits a target it will apply twice the force.
Getting back to the motorcyclist, you may be wondering why he is
shooting in the first place. Well the reason is he’s a vandal and
trying to punch a hole in a metal road sign up ahead. The sign is too
thick to be punctured by a single bullet. And even if he stood firing
one after the other at the same spot he’d make no progress.
But it happens this vandal is also a part-time physicist and knows it’s
possible to overlap his special ghost-bullets for maximum effect. With
the right timing, he knows it should be possible to fire ten in a row
and get them all to overlap at the same point. If they overlap at the
point when they hit the sign, they’ll hit it with ten times the force
of a single bullet and punch a hole straight through.
The oddly accelerating particle
The story just told represents an
analogy for what might occur on a much smaller scale with charged
particles. Take an electron for example. We know it carries a charge
and emits a constant electric field. In an earlier chapter this
field was described as being analogous to a stream of tiny bullets.
These ‘bullets’ radiate from all directions at light speed. When they
strike another charged particle they impart a force.
We’ll start by assuming our electron is perfectly still and has been
that way for some time. We now take that electron and move it slowly to
the right. Referring back to our analogy, the electron is the gun and
its field is a stream of bullets moving to the right (the field
radiates in all directions of course but we’re only looking at the part
moving right). As the electron moves right it continues to radiate
‘field bullets’ and these will move right with an added velocity, just
like those fired by the biker after moving. Therefore, just like the
biker’s, the electron’s later bullets will at some point catch up with
its earlier ones.
The basic point here is that the field emitted by a moving electron
must eventually catch up with a field emitted from the same electron
when it was stationary earlier. It may take a long time and occur far
away, but it must happen.
So what will happen when the later and earlier field overlap? Not a
lot, other than there will be a temporary peak in the field strength at
that point. This means that if there is a charged particle at that
location it will feel (roughly) double the force. But other than that,
not a lot.
Back to our biker vandal. His goal remember, was to punch a hole in a
road sign up ahead. He knew that to do this he needed to overlap
multiple bullets at once, and have them overlap at where they strike
the sign. He estimated ten bullets should do the trick. His first
attempt involved accelerating at a constant rate and firing at
half-second intervals. It was a failure. The bullets ricocheted off the
sign in an uncoordinated cacophony.
Examining high-speed footage from cameras placed along the roadside
(yes he brought them along), he noticed the bullets passed through and
overlapped each other at different points along the way. Not good. They
needed to overlap at the same point and where they hit the sign.
Realising that a fixed rate of acceleration was not going to do the
trick, he set to work figuring out what will. Eventually he came up
with a function describing an acceleration that increases as he
approaches the target. Switching his high-tech bike to auto pilot, and
entering the acceleration function into its on-board computer (nice
bike!), he set off in direction of the sign, firing a volley of shots.
Success! The bullets overlapped at the sign and punched right through.
Super-intense overlapping of fields
By now the analogy I’m working
toward should be obvious. So I’ll go ahead and ask: What would happen
if our electron accelerated like the biker above?
The electron ‘shoots’ a field rather than bullets. The speeds are
faster and the distances shorter. Yet the same principles apply. The
logical answer to this is that the accumulation of its field emissions
will overlap at a single point as this diagram shows.
Here the electron starts motionless
on the left and accelerates to the right. The blue dots show the
electron at fixed intervals. The red circles are field pulses, one
corresponding to each blue dot. The electron accelerates in such a
manner that these field circles steadily merge. Then at one brief
instant they all overlap and cause a large spike in the field strength.
The pulses then diverge and the spike is gone.
In reality of course, the electron doesn’t emit pulses but a constant
field stream. But the result is the same: a temporary spike in field
strength . If there was
nothing at the point where that spike occurred (no charged particle)
then nothing would occur. But what if there was, say, another electron
That second electron is akin to the road sign. In the case of the sign
the multiple overlap of bullets punched through it. Could the large
field spike cause similar damage to a target electron?
Probably not. The electron is light and not tied down. Most likely all
that will happen is that it will receive an almighty kick that
accelerates it to light speed in no time flat. So let’s change the
situation a bit. Say the target electron is sitting still while two
‘attack’ electrons accelerate toward it from left and right sides, as
Both attack electrons mirror each
other’s motion, i.e. they have the same starting position and
acceleration profile, just in reverse. The result is that two
field-spikes will hit the centre electron from the left and right
sides. So what effect might this have? Again, probably nothing much.
Since the spikes are coming from different directions, their forces are
opposite and should simply cancel.
But let’s change the situation slightly and say that the spikes hit the
electron on opposite sides as shown:
In this diagram the spike from the
left-approaching attack electron hits the right-hand side of the target
electron, and the spike from the right-approaching attack electron hits
the left side of the target.
The situation now is quite different. The middle electron feels two
opposing forces. Its left and right sides are being pulled in opposite
In the chapter on subatomic
particles we looked at the internals of charged particles and
there I suggested that a charged particle consisted of a mass-core
surrounded by a layer of charge, made of ‘charge substance’. I also
pointed out that the charge within a particle must be constantly
repelling itself, e.g. that the left and right hand sides of an
electron would push against each other, causing the electron to fly
apart. I then suggested that the mass-core within a particle provides a
binding force that holds the charge together.
Whether or not you accept this theory is unimportant. The point is, if
you agree that charged particles have a finite size then you would have
to agree that the charge within them must be in constant repulsion
against itself. And therefore, there must be some counter force holding
this charge together. This force must be quite strong because it is
able to confine the charge within a small volume. But... it
cannot be infinitely strong.
Other than the limits of space and time, we know of no infinites in
nature. No infinite masses, velocities, charges, energies, and
certainly no infinite forces exist. Put another way, all physical
quantities that can be confined within a limited range of space or time
are observed to be finite. Therefore it seems reasonable to say that
this force holding the charge together, whatever it is, must also be
So here we have our hapless target electron stuck in the middle of two
‘attack’ electrons. It has just received a force on both sides, pulling
the sides away from each other. The spikes that delivered that force
are thousands, possibly millions, of times stronger than the force
between two adjacent electrons. Therefore, it seems reasonable to say
that at some point the force from these spikes will overpower whatever
it is that’s holding the charge together. As the saying goes: ‘something’s
At this point the target electron should be torn apart and its charge
scattered in opposite directions. Then what? Obviously we don’t know as
we’ve never observed anything like this. So here the discussion becomes
rather more speculative than before.
The Big Erasure
With no longer any binding force
holding it together, the charge substance that was previously attached
to the target electron scatters outward. How would it scatter? In the
chapter on faster
than light travel I described a situation in which a
collection of like-charged particles bunched close together and
released could accelerate to many times light-speed. This is
effectively what we have here. The charge-substance that made up the
electron is now free to move. It will accelerate to many times light
speed. Now it might be supposed that the acceleration will be infinite
because charge substance has no mass. But this will not be the case
because the substance will encounter weak electric fields from other
particles and from itself, and this will act to retard the acceleration
The charge spreads outward, reaching thousands of times light speed. As
it does so, it continues to radiate electric field. When this field
hits another charged particle, it does so at enormous speed and
therefore exerts enormous force. Just like the original target
electron, that charged particle is then shattered; its charge substance
likewise scattered and accelerated to immense speeds.
This process continues in an exponential cascading effect. More
particles break and expand, their ejecta breaking ever more particles.
Within a short time every particle in the entire universe is destroyed
and its charged scattered.
The space which used to occupy the physical universe is now filled with
charge-substance. In addition to this, the mass-substance that
originally held this charge together is also scattered because it no
longer has surrounding charge to hold it together. So now what? Does
the charge substance continue expanding? Well, perhaps not, because the
universe is now filled with charge-substance of both types: positive
and negative. And these two substances attract each other. Not only
that, the mass substance attracts both of them.
What we have now is a sort of ‘primordial soup’, made of scattered mass
and charge substance.
Being attractive, at this point the ‘soup’ begins to collapse in on
itself. Like a deflating balloon, it shrinks down into smaller and
smaller volumes. At some point the density of this soup increases to
the point where concentrations of mass-substance can condense into mass
cores with enough strength to attract quantum units of charge around
them and form new subatomic particles (see subatomic particles).
The particles initially form at random and different sized cores lead
to charged particles of differing mass. At this point, for some
unexplained reason, the particles begin to duplicate themselves. Once
one particle forms, it causes an identical one to form, leading to huge
numbers of similar particles. The reason for this duplication process
is unknown – but of course, this is a speculation designed to fit the
observation that our universe contains only a limited number of
Having formed, the particles then start arranging themselves according
to natural patterns such as nucleons and atoms. The formation of
particles into various groupings causes them to be rapidly scattered in
numerous directions. At this point a new universe is born.
A new kind of Big Bang
What I’ve just described sounds
somewhat similar to the big bang theory. And in part it is. However
there are some important distinctions. First, the explosion had a prior
cause, it didn’t just occur spontaneously and for no reason. Second,
the explosion was an expansion of matter, not an expansion of space.
Third, the event is repeatable. 
So the basic story is this: Our current universe is one in a long line
of universes, each of which self-destructed and reformed. The
triggering mechanism for destruction was due to the movement of charges
moving in opposite directions with a specific acceleration profile.
This would come about naturally due to the random movement of particles
throughout the universe. Getting the exact acceleration profile is an
extremely rare event and possibly happens only once in a trillion
years. But once it does happen and two such accelerating particles line
up with an appropriate target particle, that particle explodes and the
rest is history.
This is what a timeline of universe formation might look like:
The vertical axis is the size of the
universe and the horizontal one is time. As can be seen, each prior
universe grew slowly and collapsed suddenly and then a new one formed.
Note that each universe had a different lifespan, depending on when the
catastrophic ending event occurred. Our current universe might be 100
billion years old (13.7 seems too short for extensive galaxy
formation). Its end date is not known but could be 10 times that.
Where did all the anti-matter go?
One of science’s perplexing
mysteries is the large imbalance between matter and antimatter. For
example there are huge numbers of electrons, but almost no positrons.
And there are huge numbers of protons but almost no anti-protons. As
far as we know, the only difference between matter and anti-matter is
the sign on their charge. Everything else is the same. If you could
replace all matter particles in the universe with their antimatter
equivalents, and vice versa, everything could continue functioning
normally. Therefore, given that they are equivalent, why should one
type outnumber the other?
In an earlier chapter on particle
physics I talked about how positrons and electrons could
overlap to form neutral composite particles (called poseltrons). It
might be tempting to think therefore that that accounts for the missing
antimatter. Unfortunately it can’t because this process removes equal
numbers of matter and antimatter particles from view.
Fortunately there may be a simpler explanation at hand. What if the
universe does contain equal amounts of matter and antimatter substance
but we don’t see both at once because they repel each other? In the
chapter on gravity we
looked at how the orbital motion of quarks inside protons and neutrons
could cause additional attractive and repulsive forces that would not
be predicted by applying Coulomb’s law alone. In there I showed that a
proton combined with a single stationary electron would exert a net
attraction on a negative charge and a net repulsion on a positive
charge. That means a proton+electron combination would attract an
electron but repel a positron.
I also showed
that a proton+electron combination would repel an antiproton+positron
combination. Based on these situations it appears that the most common
forms of matter and antimatter will repel each other gravitationally.
So here’s the scenario. In the early stages of the universe, equal
amounts of antimatter and matter were created. In fact, matter and
antimatter particles possibly formed simultaneously, as
positive/negative pairs. The matter formed itself into proton+electron
combinations (hydrogen molecules) and the anti-matter formed into
anti-hydrogen molecules. The matter and antimatter repelled each other
gravitationally into different parts of the universe. The only
antimatter left behind was a few grains that got bound in with the
matter. We just happen to live in a region dominated by matter. The
antimatter will be far away now. Entire galaxy clusters will be made of
antiatoms: positrons orbiting nuclei made of antiprotons and
antineutrons. These galaxies will also contain the odd electron here
and there but mostly bound up as poseltrons. Perhaps we can also see
these galaxies from earth but they look the same as galaxies made of
Another mystery has to do with the
size of the universe. As pointed out in Part
1, our universe is likely to be physically finite, but
surrounded by an infinite sized space. This is all well and good but it
does raise a somewhat metaphysical question. In Part 1 we also looked
at probability, and there I pointed out that an event with non-zero
probability must reoccur at some point. And given an infinite amount of
time, the event must reoccur an infinite number of times. Based on this
I concluded that if there was such a thing as a big-bang, then it
should reoccur on a regular basis.
When we talk about probability we are usually talking in terms of time,
as in: what is the likelihood of an event occurring during a given time
interval? But we could also talk about probability in terms of space.
For example: what is the likelihood of finding an object in a given
region. In this case the question will be: what is the likelihood of
finding our universe within a given region (volume) of space?
To answer this we need to divide the volume of the physical universe by
all available space. The universe is extremely large but still finite.
When you divide the finite volume of the universe by an infinite volume
of space you get zero. What this tells us is that the probability of
finding the universe within any randomly chosen region of space is
zero. Now that’s a problem because it’s effectively saying that the
universe doesn’t exist. If the universe is physically finite in size,
then, in comparison to an infinitely sized surrounding space, its size
is zero and essentially non-existent.
Except of course, the universe does exist. No
doubt many would object that this is just playing mathematical
word-games. Nonetheless it can’t be denied that the size of a finite
universe, large though it is, is zero in comparison to the space
surrounding it. And zero size is essentially non-existence.
Solving this conundrum does seem to require that there be more than one
universe. In fact it requires that an infinite number of universes be
spread throughout space. Why so? Well, since our universe exists in
this region of space, that means it has a non-zero probability of being
there. This means there is a non-zero probability of another universe
existing elsewhere. Given enough space then, we can guarantee that
another universe will be found in it. And given an infinite volume of
space, we can guarantee an infinite number of universes.
These universes will be located very far from ours. They will be in
different stages of growth. The particles they contain will have been
randomly generated and self-duplicated at the start of each universes’
growth. Therefore they will be different from ours, in terms of mass,
although each will have the same quantum of charge. Occasionally some
of these particles will be accelerated to super light speeds, like
those mentioned in the faster than
light chapter. Since they are moving much faster than the
light coming from that universe, it’s possible that these will cross
over into other universes, such as ours. These particles may then
account for some of the very rare particles found on earth.
In each of these universes the basic physical laws will be the same:
they will each have the same speed of light and the same integer unit
of charge. But due to differing masses of common basic
particles, other ‘physics laws’ will be different. For
example Plank’s constant and Newton’s gravitational constant will have
different values. In fact the phenomena of gravity may not
be present at all, or at least not in a form familiar to us.
This is because atomic nuclei, which allow such a thing as gravity (see
gravity), might not
exist in all universes. And without atomic nuclei the concept
of Plank’s constant would also have no meaning.
Further interesting premises stem from this. In some
universes, such as ours, the subatomic particles will allow for the
formation of complex molecular structures like carbon-based DNA and
this will allow life to exist. In other universes (probably
most) the formation of complex molecular structures will not be
possible, meaning that life forms will be unable to exist there.
This possibility of multiple
universes leads us back to the earlier mystery of Olbers’
paradox. If there are infinitely many universes shouldn’t their light
eventually reach us and fully illuminate the night sky?
Coulomb’s law tells us that the electric field generated by a charged
particle extends to infinity. As it travels, this field spreads out
spherically and becomes weaker – much like an expanding balloon whose
skin becomes thinner. To reach unlimited distances requires this field
become infinitely weak but without becoming zero. Is that possible?
When we look at a nearby star, the light we see comes from the activity
of the electrons on its surface. That means the field from individual
electrons has travelled several light years at least. The field
strength from a single electron over that distance would be extremely
small. For distant galaxies the strength becomes far smaller again.
To make matters worse, the field from a single electron comes from the
charged region within it. This means that each tiny part within that
region is generating a field that spreads over a sphere of billions of
light-years radius, and without becoming zero.
Is it possible for the electric field from individual electrons, or
from parts within them, to become thin without limit? In some ways this
seems difficult to fathom because quantities like mass and charge seem
to have non-zero limits. Yet the fact that we can see distant galaxies
means the field their electrons generated did reach here.
Well perhaps there is a limit on how thin a field can get before
ceasing to exist. And perhaps the reason we see distant galaxies is
that the field from numerous emissions combines and this is allows it
to cross large distances.
What I’m suggesting is that the field from a single electron can travel
only a certain distance before becoming too thin and cutting out
completely. Whereas the combined field from two electrons can travel
double that distance. In this way we are able to receive light from
distant galaxy clusters because the combined strength of many fields
enables it to reach earth.
But in the case of other universes, the gap between them is too great
due to all matter from the previous universe being removed during the
‘big erasure’. Thus their light becomes too thinly stretched and
disappears before it can make it to a neighbouring universe.
acceleration needed produce a simultaneous overlap of fields from a
charged particle is a = c2/(d-c
t), where d is the initial
distance from the target. This makes the velocity function v
= c log[d/(d-c
t)], and the distance function x
= c t-(d-c
t)]. The strength of the final overlapping pulse will
depend on how far away the starting point is.
 This idea is
also similar to a theory called Quasi Steady-State Cosmology (QSSC) [by
Hoyle, Burbidge and Narlikar, 1993], except it doesn’t require gravity
for the collapse stage. http://casswww.ucsd.edu/personal/gburbidge.html