On Matter with Zero Rest Mass
Kevin Gibson
May 19, 2011
Introduction
The objective to this piece is to explore the topic of massless particles. What role do
they play? Why do they even exist? And in exploring this type of matter the nature of
matter interactions itself will be addressed.
The existence of zero mass particles
Consider two particles that interact with each other in a frame of reference S0 where
their paths intersect as shown below
#1'
#2'
#1
#2
fig. 1
Further imagine two events. Event e1 is associated with the transfer of energy E and
momentum p1 from particle 1. Event e2 is likewise associated with particle 2's transfer of
energy and momentum from particle 1. As a consequence of the situation as shown in
figure 1, these events must occur at the same time and place. But is there another
reference frame S in which these events do not occur at the same time? The answer can
be found by appealing to Einstein's special theory of relativity and in particular the
following2 3
2
2
2
2
2
2
2
 x 0 y 0 z0 −c⋅ t  = x  y  z −c⋅ t
2
(1)
As described above the events are concurrent events, so (1) must be zero. So if the
events are not simultaneous in S then the time between the events must be the distance
between the events divided by c. An elegant justification of this statement is that a
particle moving at speed c moves from one particle to another. This theory is consistent
with experimentation such as the photoelectric effect. This is depicted as figure 2 below.
#2'
#1'
X
#2
#1
fig. 2
The event e1 could now be described as the event where particle 1 gives off an
intermediate particle X and e2 when it is received by particle 2. What properties can be
deduced about this intermediate particle? According to quantum statistics and relativity
the energy and momentum of a particle obey the following
E=
2
E0

1−
2
(2a)
u2
c2
2
2
E =c ⋅∣p∣ E 0
(2b)
In order for the energy for the particle moving at c to not have an infinite energy the rest
energy E0 must be zero and
(3)
E=±c⋅∣
p∣
It can be further shown that a particle that absorbs or gives off a particle with zero rest
energy retains its own rest energy.
Frames of reference
Next suppose that a zero mass particle (ZMP) moves between particles traveling a
distance d in time ∆t and has energy E and momentum p. Further suppose that a 2nd
frame of reference moves along the direction of the ZMP at a speed of v. Using the
Lorentz transformation4 the above quantities would transfer into S' according to

v
c
d ′=d⋅
v
1
c
1−

(4a)
v
c
 t ′= t⋅
v
1
c


1−
v
c
E ′=E⋅
v
1
c
1−
(4b)
(4c)
v
c
p ′=p⋅
v
1
c
1−
(4d)
It would seem, according to (4a), that as v → c the S' frame becomes S0. However there
are some complications. First, as can be seen above when v → c the ZMP energy and
momentum vanish. The problem with this is that in the S frame it makes sense to have a
particle transferring energy and momentum between the particles while in S0 no energy
or momentum is transferred and so the existence of an intermediate particle makes no
sense.
A second complication arises when we view the ZMP as having a fixed momentum and
energy. We can model the ZMP thus within experimental accuracy so long as the
uncertainty principle for position and momentum is not violated.
ℏ
(5)
 x min⋅ pmin =
2
As the speed of S' (relative to S) increases the intermediate particle's momentum gets
smaller as stated above, consequently the minimal range of position must increase.
However while this is happening the distance between particles is being contracted. So
there must be some frame SQ moving at a speed of vQ where (5) is violated.
So consider the transfer of a ZMP between particle #1 (left) and #2 (right) in fig. 3
according to frame S' moves at different speeds relative to S.
1. v < vQ: For this observer the σx in the ZMP position is smaller than the separation
distance. So there is no difficulty in envisioning a ZMP moving from the 1st to the 2nd
particle in a non-quantum mechanical sense as depicted in figure 3 below.
.
fig. 3
2. v = vQ: In this frame the target particle is contained within the statistical distribution
of the ZMP position of the ZMP as shown in figure 4. The idea of the ZMP moving
between particles as depicted in #1 becomes blurry.
fig. 4
3. v > vQ: Now the destination particle is well confined within the ZMP packet. In fact
such an observer could describe the particles are being contained within an orbital of
the ZMP. In this frame the two particles can be considered to be colliding ala figure 1
with the intermediate particle acting as the medium through which the collision acts.
In this way the ZMP intertwines the two particles.
It is interesting to note that different statements can be made about the behavior of this
particle depending simply on the particular frame of reference. Since all these frames of
reference are of equal validity there must be a common way to view this process that fits
all the above descriptions.
Particles interacting via ZMPs
To explore the above query consider two large blocks separated by a large distance as
shown below. Further suppose that the atoms of either block interact by some
intermediate particle X.
X
X
fig. 5
If the atoms are close enough together than the collisions can be consider to to act via
the particle X orbitals per case #2 or #3 above. But what of the X particles going
between the blocks? If the sizes and distances are large enough then such processes can
be described in case #1 above. However there can be some other observer for whom the
the process can still be described according to the first. And since these frames of
reference must be just as valid then this interactions must be describable by any of these
cases. It then appears that the only difference between the frames of reference is the time
delay between when energy and momentum is sent away and received. In other words
case #1 can be considered as an asynchronous collision between particles. But regardless
of the frame of reference the ZMP fulfills the same role.
When matter collides
There are some remaining implications to be explored regarding what is meant by a
collision between objects. The customary interpretation comes from our everyday
world, that is objects make physical contact then are pushed into a different trajectory.
Now collisions involve the exchange of a ZMP particle, either at as short or long range.
Thus we have an image where the process depicted back in figure 2 is constantly being
played out. Of course a natural question that must arise is where does these ZMPs come
from? Answering this question might shed light on the nature of matter itself. It is
ironic that this piece began with a customary interpretation of what it means to collide,
only to conclude that such a view is overly simplistic in that it omits an intermediate gobetween.
Bell's Theorem and local realism
Lastly consider Bell's theorem. It has been demonstrated that particles adhere to a
process termed quantum entanglement5 in which the properties of quantum objects can
be influenced by other objects independent of distance. This entanglement has been
demonstrated in what has come to be known as the Bell test experiments.
How then does all the above tie into this? The existence of ZMPs in the above
discussion became necessary in the process of describing collisions in the light of
special relativity. However, what if not all interactions can be considered as a variant on
a collision? For such a case a ZMP need not be incorporated into the physical process,
eliminating the arguments above and allowing for instantaneous interactions.
Moreover, it has been shown6 that energy is no longer an intrinsic quality of matter, but
rather a field quality related to the statistical state of matter. Matter itself follows some
elements of non-local behavior within the bounds of the statistical distribution, involving
energy. Therefore if no energy is being transferred during a process, then there is no
need for a ZMP and processes can occur instantaneously.
Conclusion
There are manifold options by which matter interacts with matter. Some options are
non-local in nature while others require a particle of zero rest mass as a mediator. The
latter reaction can occur from the very short to the very long range. All this comes from
the nature of matter as it participates in the universe at large.
Works Cited
1. Kevin Gibson A new statistical view for elementary matter (unpublished)
http://www.mesacc.edu/~kevinlg/i256/A_new_statistic.pdf
2. Kevin Gibson Space and Time (unpublished)
http://www.mesacc.edu/~kevinlg/i256/Relativity.pdf
3. http://en.wikipedia.org/wiki/Spacetime
4. Paul A. Tipler and Ralph A. Llewellyn Modern Physics 4th ed. p. 21 – 24
5. http://en.wikipedia.org/wiki/Quantum_entanglement
6. Kevin Gibson Lessons from the Klein-Gordon Equation (unpublished)
www.mesacc.edu/~kevinlg/i256/Lessons_KG.pdf
Contact information
[email protected]
[email protected]
www.mesacc.edu/~kevinlg/i256