Observations
on the Hubble Expansion of the
Universe
Dr. Roy
Lisker
8 Liberty
Street
Middletown,
CT 06457 USA
(1) Ordinary
space is an indecomposable 3-dimensional
continuum.
All tangible objects must be
fully 3-dimensional, with positive volume.
Argument: when straight lines are defined
as the unforced paths of
particles or fields, the dynamic
structure is seen to be that of Euclidean geometry. Abstract mathematical
models can focus on 1 or 2 dimensional simplifications of the things we see around us, but any
object, body or entity encountered in daily life must have positive volume.
One can argue, successfully I believe,
that even electrons and
quanta must have volume, and
that the notion of a Òpoint particleÓ is once more an abstraction and not a
reality. This is because we accept the validity of the Hawking-Penrose postulate, which
states that nature cannot possess
naked, or unshielded singularities: a Òpoint electronÓ implies the ÒnakedÓ
presence of an infinite electromagnetic potential in real space. This postulate
is necessary to avoid a breakdown in customary notions of causality.
(2) Einstein showed that we actually live in
a full 4
dimensional space-time. What
is true of space must therefore also be true of space-time: even as one never
encounters real, tangible objects which are 2-dimensional slices without volume , or
1-dimensional curves, or pure dimensionless points, in the same way, all ÒobjectsÓ
in space-time must be fully
4-dimensional.
(3) This has important consequences for all of physics.
It
means that when one speaks
about static objects, like rocks and stars, one is always simplifying the
reality, which is that of 4-dimensional ÒeventsÓ happening in non-vanishing
intervals of time.
In particular it is absurd to speak of the Òexpansion of
spaceÓ.
Two
errors are committed by the use of this expression:
(a) To speak of the Òexpansion of spaceÓ
alone is to imply a separation
of
time from space, which is contrary
to the spirit of Relativity, in which time is a geometric dimension.
(b)
To speak of theÒexpansion of spaceÓ is also
an error in logic. Space
can
no more expand than time can move. These are dimensions , not magnitudes or quantities. Measured amounts of
change, or, as Aristotle observed, motion, are expressed in units of time.
The relative separations of objects are expressed in units of length, area and space.
(4) Because space-time must be treated as an indecomposable
unity, and because ÒspaceÓ
and ÒtimeÓ themselves can neither move nor expand, one must can therefore only talk about the Òexpansion
of some entity whose relative distances
and motions are changing in space-timeÓ.
That
space must be thought of as indecomposable, can be seen from the following
consideration: even though local spatial coordinates are designated by a
coordinate system x,y,z, yet the orientation of this system is arbitrary: I can
choose to have the z-axis point in the direction of the sun, or the moon, or
the center of the earth. This would not be possible if space were not an
indecomposable homogeneous unity.
In
the same way, oneÕs orientation in space-time is also arbitrary (up to the
speed of light). I can choose any object moving at constant velocity less than
light and designate it as the origin of my rest-frame. This shows that
space-time must also be considered an indecomposable unity, that, in
particular, all measurements of ÒeventsÓ must be 4-dimensional.
Otherwise
stated, there is no time ÔdirectionÕ
, independent of space. Even as the Òx-axisÓ can be freely chosen, so (within
the limits of Minkowshi space), the Òtime axisÓ can also be freely chosen.
(5) Granting that there is ÒsomethingÓ in space-time that is
expanding, how can one make sense out of the idea
that Òtime is expandingÓ or, more accurately, something is expanding in time? As explained above, time itself
does not move , any more than space expands: systems change over time, even
as lengths are distances between objects. Following more than a century of
discoveries in physics, one can say that these ÒsomethingsÓ are either particles (bosons), or fields (fermions), that is to say,
actualizations of energy.
(6) Therefore: a space-time object is the
set of all transformations
between
two ÒstableÓ (relatively motionless) states of a entity (system of fermions and
bosons) in 3-space. We
will use the word ÒeventsÓ to designate Òspace-time objectsÓ. This is very much
in the spirit of Relativity, which relates events to one another, rather than speaking of bodies in fixed
locations. The phrase ÒHubble expansion
of distances in spaceÓ, should
therefore be corrected to Òthe
Hubble expansion of events in space-timeÓ.
(7) We illustrate the need to look at the
expansion of
temporal quantities in
addition to the expansion of spatial measurements, by the following examples:
a. A change of reference frame from rest to one with relative velocity
ÒvÓ leads to changes in
coordinate measures by the constant of proportionality 
. The Lorentz contraction shrinks distances and slows down clocks. In the same way, a
universal expansion must expand distances and accelerate clocks.
(8) For events to happen there must be the
introduction
or removal of energy, and
energy is the ÒsubstanceÓ of fields .
(9) Combining all these considerations , we
claim that the
Òexpansion of (measurements
of events in) timeÓ, which must (given the unity of the 4-continuum) accompany
the Òexpansion of (measurements of events in) spaceÓ is made apparent to us
through the augmentation of a quantity of
energy. The natural candidate for this is Dark Energy .
(10) Where there is no matter, no energy, and
no fields, one
cannot speak of the existence
of space. Perhaps such regions should be described as Voids . Space exists between
objects, as Leibniz argues .
Even if
one wants to contest this view, one
has to agree that to speak of the Òexpansion of the spaceÓ within such a void
region, is utterly meaningless: for ÔspaceÕ can no more expand on its own, than
time somehow develop its own motion!
(11) This leads us to the following
hypothesis: that what is
called the ÒHubble expansion
of spaceÓ is best interpreted as
the intrusion or conquest of an encompassing 4+2 (4 spatial, 2 temporal)
dimensional Void by a 3+1
dimensional universal field. The most
natural candidate for that is the gravitational field. The argument for a second time dimension will be given below.
(12) The employment of this hypothesis allows
one to create a more
effective understanding of
the construction generally employed in popularizations of cosmology, namely :
our universe exists on the surface of a 3-dimensional balloon
( the 3-sphere surface of a 4-ball) that expands equally in all directions.
The
best theoretical framework for this picture (a somewhat abstract
ÔpictureÕ, admittedly) is to
think of our universe as being embedded in a 4-Void, which is being reclaimed, in an second time dimension t , by the expansion of a space-time field ,
whose spatial component is on the 3-sphere surface of a 4-ball. Even as the
fields of our 3-dimensional universe expand into the Void, so the time t,
measured by the trajectorieas of photons, expands into a void time t . The
equation of this surface is looks something like:
ÒuÓ is the added dimension
of the surrounding Void into which the
matter/gravitation field
of our universe is expanding. The dimension u is directed orthogonally away
from our ordinary 3-space. R is the
radius of that expansion, and t is the ÒtimeÓ in which the
expansion of both space Sand time t, are
occurring. Once again, time, whether local or cosmic, cannot move or
expand, which is why we hypothesis a second
time dimension t in which the universal
expansion is occurring. (There is no reason of course why this metric should be
Euclidean)
(13) Let us try to make more robust the claim
that 4 spatial
dimensions (x,y,z,u) , and
two time dimensions (t and t )
are needed to describe the space/time/matter universe that we live in. The two temporal dimensions are:
a. The time t in which radiation, or light
rays move
about. One cannot speak of this as either
ÒexpandingÓ or ÒdecreasingÓ as it is fixed by the condition r(t)/t < c, for
any material particle, and by r(t) =ct for radiation.
b. The time dimension t in
which the universal
expansion occurs , that is,
the encroachment of the fields of the 3+1-sphere 3 of space, one of time) onto
the 4 +2 (4 of space, two of time) Void.One can imagine that ordinary
time t is expanding into void time
t .
To date no upper limit has been
found for the speed of this expansion, but I suspect that there must be one:
ÒinfinityÓ is a concept of mathematics, not of physics.
(14) Since gravity appears to be the only
force that one finds in
either dark matter or dark energy, it is erroneous to speak of
gravity, or gravity waves, as travelling at the speed of light. Here is the
argument:
It is observed and claimed that
dark matter and dark energy are
everywhere present throughout
the universe. As our 3-universe expands , at exponentially increasing speeds, (the
expansion must be exponential to avoid being nullified by a change of reference
frame) over larger surface areas in the 4-void, the dark matter and dark energy
fields automatically and instantaneously enter into new enlarged 3-spherical surfaces . The
speed of gravitational radiation must therefore be pegged to the expansion of
the universe. Indeed, these ÒnewÓ regions are actually expansions of these fields
, given that to talk of the expansion of pure space is as absurd as to assert
that time moves.
Since, at the present time, we are recording redshifts much larger than
1, it follows that the universal gravitational field is also expanding at
speeds greater than light. Thus there is, at present, no known limit to the
speed at which gravity travels across the expanding space-time universe.
Roy Lisker
October 19,2012
www.fermentmagazine.org