"Science is the belief in the ignorance of
experts!" - Richard Feynman
Is it enough to say that mass and energy codify
information, or is there a more fundamental relationship?
Does the apparent existence of physical limits such as the
speed of light and the indivisibility of quarks suggest
value in an alternative description of physical phenomena?
Is information really a form of mass and energy, perhaps
the most fundamental form? Is the Holographic Paradigm
more than just a philosophical exercise?
The Twentieth Century will likely go down in the history of
science as the century of the discovery of limits. Our universe
has infinite volume, but finite diameter. There appears to be a
family of "smallest particles," indivisible and perhaps even
unobservable, the quarks. Heisenberg tells us that we can specify
position or momentum of a particle to arbitrary precision, but not
both. On a very small scale, various properties are not
continuous, but take on only certain "quantum" values, strictly
avoiding all other values. There are many other examples,
including what is perhaps the most important, the universal limit
to relative velocity, the speed of light.
Even information processing has important limits. Indeed, one
formulation of Relativity is based on the limits of our ability to
transfer information from one place to another. This leads to a
limit on computational power. There are only two ways to make a
computer go faster, build the same thing out of faster parts or do
more than one thing at a time. Both methods are ultimately
limited by our ability to signal between two points. The fastest
known way to do that is with light. When light is too slow, we
must move the two points closer together, leading to the limit on
computations per second, and to the interesting fact that "bigger"
computers must be physically smaller. In fact, my interest in
faster-than-light (FTL) travel has always centered around
computation: you give me FTL and I'll give you arbitrarily large
The Nature of Computation
What do computers do? This question is easy only at a superficial
level. They compute. But what is computation? At any given
instant, a computer maintains what is known as a "state."
Computation is a systematic progression from state to state. But
this notion is highly abstract. Ask any film maker who has ever
tried to show a computer in operation. Mostly we are shown
irrelevancies, such as blinking lights or spinning tape drives,
because the actual work that the computer is doing is very hard to
Computers manipulate information. We can describe in detail the
data given to a computer, the programs it executes, the algorithms
and mathematics that these programs implement, the various
hardware representations of programs and data, and the results or
output which the computer returns to us. In some sense this does
indeed describe what a computer is doing, but at the simplest
level, a computer is merely a large mass that consumes power.
It is not easy to understand what computers do, at least not in
the sense that we normally understand machines. A car consumes
power and produces motion. A computer consumes power and
produces...what? Perhaps consuming power and producing motion is
an apt analogy: can we envision a computer as a machine which
translates energy into movement in some abstract state space? Can
we usefully think of a computer "latching onto" some information
and "motoring" through a transformational highway?
A computer, then, is a machine which manipulates something called
information, requiring intricate mass arrangements and consuming
energy as it does so. Perhaps we should look more closely at the
relationship between mass, energy and information.
Mass and Energy as Data Structures
What is an electron? Physicists tell us that it is an elementary
particle with a certain mass, charge, spin, and so forth. There
are currently eight properties associated with an electron.
Anything which has these eight properties, and no (known) others,
is an electron. These "observable" properties all require
interactions with other things in order to be quantified. In
other words, these properties are "measured" by relating them to
properties of other objects, which are "measured" relative to the
electron or still other objects, and so forth. These properties
have no intrinsic values, only relative values.
In other words, an electron sounds a lot like a data structure.
If one thinks of these eight properties as eight "fields" in a
data record, and defines the values of each field relative to
values in other records, one has captured the nature of an
electron. If we write a program for this and run it in some
computer, have we created an electron? Of course not, because the
resulting program execution does not correctly interact with
"real" electrons. So maybe there is some kind of ninth property
needed which specifies a distinction between "real" electrons and
But the idea of an electron as a data structure is seductive. Is
it possible that the state of an electron is the same kind of
slippery concept as the state of a computer? Is it possible that
an even more fundamental relationship exists between information
and mass/energy than the simple one of mass/energy "coding"
There are many examples in nature which suggest an intimate
relationship between mass/energy and information. All electrons
apparently have the same charge, at least to our ability to
measure, which is quite good. This is easily explained, if the
charge of an electron is some kind of universal constant, perhaps
being accessed as needed by the computer running the simulation of
the universe. For that matter, quantization is easy to understand
if that simulator is using integer arithmetic. Even the limit of
the speed of light can be understood as a limit on the ability to
How's that last part again? Sorry, in order to understand this
state change limitation, we need a small digression into the world
of holograms and transform mathematics.
The Holographic Paradigm (WILB85)
Think of a holographic transform as a relationship between two
representations of a dataset. We can never have access to THE
data, only to representations of data. In holography there is a
spatial representation, commonly called a "photograph," and a
phase representation, commonly called a "hologram." It is not the
commonly understood three dimensional aspects of holographic
transforms that we focus on here, but the relationships between
the two representations. Each pixel of the hologram is a unique
function of the entire photograph. That is, in order to compute
the value of a single pixel of a hologram, we must take into
account each and every pixel in the photographic representation.
Thus, each pixel of a hologram is a kind of "point of view,"
capturing something unique about the entire photograph.
Surprisingly, each pixel of the photograph is a unique function of
the entire hologram, and captures its own "point of view" about
the hologram. Each representation therefore contains "all the
data," and you can go back and forth between them.
Because of this local "point of view" aspect of holography, every
subset of either representation can be used to form the other
representation. Any subset smaller than the full set will
necessarily form the other representation degraded in some way,
but the degradation in the other representation will be global,
not local! In simple terms, you can tear a hologram in half, and
each half can generate the ENTIRE photograph uniformly degraded by
some kind of noise. Same for the photograph. Every part of each
representation contains information about the entire alternate
Karl Pribram and David Bohm (PRIB76), have suggested that the
brain functions as a holographic transformer between "reality" and
our mental representation of the world. They argue that if our
mental representation involves spatial dimensions, objects,
motions and so forth, then "reality," that is, the world on the
"other side" of the brain's holographic transform, must be a phase
space. If this is true, then we have described nature under the
hallucination that three dimensions and time exist "out there,"
when in fact they exist only in our minds.
Suppose the universe is more like a hologram than a photograph,
and it is our internal model which is more like a photograph. Let
us call the hologram the "phase domain," and the photograph the
"spatial domain." Consider the speed of light in this context.
The transmission of information from one point to another in the
spatial domain corresponds to the simultaneous modification of all
points in the phase domain. Each point in the phase domain is
"running" a grossly simplified representation of all of the
spatial domain, from a unique perspective. To represent any
change in the spatial domain, all points in the phase domain must
It is in this context that the statement was made that the limit
of the speed of light can be understood as a limit on the ability
to change state. If the universe is "really" a phase domain, then
the speed of light limitation is simply our perception of
limitations on the ability of the universe to change. Going
faster than the speed of light would amount to increasing the
local computational speed of the universe's phase domain.
It is not my purpose here to argue the merits of this perspective,
but to suggest value in re-examining (and possibly reformulating)
physics in this light, perhaps leading to an alternative and
potentially insightful understanding of some of the limits we have
encountered in physics, and to make one additional provocative
Is it possible that e=mc**2 is too limiting a conservation law?
Energy has been shown to be a "tenuous" form of matter;
conversely, matter is "dense" energy. Is it possible that the
same type of relationship exists between information and energy?
Specifically, is there some sense in which information or data
structures can be shown to be "tenuous" energy, while energy is
"dense" information? Is there a corresponding equation relating
information to energy? (i=ec**2 comes to mind, satisfying a human
need for symmetry, and leading to: i=ec**2=(mc**2)c**2=mc**4). If
so, then information must be considered in any formulation of the
laws of conservation of mass and energy.
Summary and Conclusions
Could it be that the relationships between information, energy and
mass we find everywhere are telling us something fundamental about
the universe? Are mass and energy really "programs" running in
some phase domain informational computer? Do we have it
backwards, and computers are simply a clumsy attempt to "latch
onto" the most tenuous form of matter, information?
I think it is likely that our discoveries of physical limits in
the universe this century are the harbingers of yet another
convulsive reorganization of science. What form it will take
remains to be seen, but it will undoubtedly require the
incorporation of information at a much more fundamental level than
is found today.
(PRIB76) K. Pribram and D. Bohm, Consciousness and the Brain, G. Globus, editor, 1976.
(WILB85) K. Wilber, editor, The Holographic Paradigm, New
Science Library, Shanbhala, 1985.