Physicists commonly use the model of
two-dimensional beings living on the surface of a balloon to explain why there
is no preferred center of their universe and why expansion seems the same from
any location in their universe. Since we
are higher-dimensional beings, it is clear that they can't observe the third
dimension from their viewpoint, but it is obvious to us from our viewpoint.

Let's look at the situation from the viewpoint
of a hypothetical postdoc, Dr. Artoo, who lives in this two-dimensional world. Physics has progressed to the point that it is
thought that there are more than just two dimensions. Over the epistemological objections that
everything in the universe must be measurable, the current theory is that the
extra dimension is curled up so tiny that it cannot yet be seen.

Dr. Artoo is disturbed by this theory, as he
learned from mathematics that dimensions have no size, but are just mutually orthogonal
directions in any multidimensional vector space. Therefore, he proposes a hypothetical
three-dimensional observer who can see the universe from that privileged
viewpoint. He supposed that if the real
universe were three-dimensional, say R3, then our inability to see
true reality would be like taking the partial derivative of R3 with
respect to our dimensionality, R2, or as a mathematician would put
it, ∂R3/∂R2. He submitted a paper on this, called A Change of Viewpoint Resolves the
Centerless Universe Problem, but it was rejected because of its
unsatisfactory metaphysics. After this,
he was ridiculed for his deism and could not publish or obtain a job in any
laboratory or university.

Dr. Artoo is disturbed by this theory, as he
learned from mathematics that dimensions have no size, but are just mutually orthogonal
directions in any multidimensional vector space. Therefore, he proposes a hypothetical
three-dimensional observer who can see the universe from that privileged
viewpoint. He supposed that if the real
universe were three-dimensional, say R3, then our inability to see
true reality would be like taking the partial derivative of R3 with
respect to our dimensionality, R2, or as a mathematician would put
it, ∂R3/∂R2. He submitted a paper on this, called A Change of Viewpoint Resolves the
Centerless Universe Problem, but it was rejected because of its
unsatisfactory metaphysics. After this,
he was ridiculed for his deism and could not publish or obtain a job in any
laboratory or university.

If we take this to its logical conclusions,
however, and look at the universe, not from the limited viewpoint of a
three-dimensional observer, say Dr. Arthree, but from the viewpoint of an
observer on the particles actually existing in the ten-space, say Dr. Arten, some
interesting conclusions become obvious.
It is well known, for example, that the proper speed of light is infinite.
A clock traveling with a photon is permanently stopped. It is Dr. Arthree, with his limited perspective,
who measures the speed of light to be a finite number, c. The speed of light is also predicted by Maxwell's
equations as a function of the parameters ε0 and μ0, but these
are measured by Dr. Arthree from his local viewpoint, and gives only the coordinate,
or improper, speed of light. We recall
that coordinate speed is the coordinate distance measured by the observer divided by the coordinate time of the observer. Proper
speed is the local proper distance divided by the local proper time. In the
case of the observer Dr. Arten, who is traveling with the photon, his local
proper time is always zero, so his proper speed is any distance divided by
zero, or as Dr. Arthree would call it, infinite.

From the viewpoint of the hypothetical Dr.
Arten, then, all problems with theoretical talk of non-locality, the EPR
paradox, quantum entanglement, Bell's Theorem, and unsatisfactory
action-at-a-distance claimed by Dr. Arthree, is as naïve as the cosmology of
Dr. Artoo observed from Dr. Arthree's perspective. No information can travel faster than light,
nor does it need to, as its speed is already infinite. It takes no time at all for a photon to
travel from one entangled particle to another, from one galaxy to another, or
from one eon to another. From this
viewpoint, all photons everywhere and everywhen are in instantaneous
communication.

One of my favorite physicists, Dr. A. Zee, writes
in his book “Fearful Symmetry”: “A central notion in mechanics, of course, is
that the velocity of a moving object is defined as the distance the object
traveled divided by the time elapsed. But which time? Should we use the
object’s proper time, or the time clocked by an observer watching the object go
by? Physicists betray their prejudices and call these two possible definitions
velocity and improper velocity, respectively. In everyday experiences, the
distinction is entirely negligible. For fast moving objects, however, the
proper and improper velocities can differ enormously. The photon provides the
most extreme example. Recall, the clock carried by a photon is stuck perpetually
at high noon. The proper time of the photon does not change. Thus, the proper
velocity of light is actually infinite. The improper velocity of light, in
contrast, is perfectly finite, equal to about 300,000 km per second.
Some laymen find one aspect of relativity particularly fascinating: the
existence of an ultimate speed limit imposed by the speed of light. Actually,
this speed limit refers to the improper velocity of light, not the proper.”