Observations on  the Hubble Expansion of the Universe

 

Dr. Roy Lisker

8 Liberty Street

Middletown, CT 06457 USA

rlisker@yahoo.com

www.fermentmagazine.org

 

(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

rlisker@yahoo.com

www.fermentmagazine.org