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Uniform Expansion

The Uniform Expansion of Space-time

 by John M. Kulick     Updated May 10, 2004

Abstract

The following hypothetical model describes a uniform geometric expansion of space-time. Every atom, not just every galaxy, is the perceived center of an expanding universe. Since all rulers and timepieces are uniformly affected by the uniform expansion, based upon specific geometric relationships, no locally observed changes in any of the fundamental constants and conservation principles are measured with local rulers and timepieces. The establishment of an “Absolute” reference frame exempt from the uniform expansion results in additional dimensional measures of reality that allows the description of the uniform expansion. This expansion is only detectable when there is a historical separation of points in space-time. Relative and Absolute measures are directly associated with two unique dimensions of time, Relative and Absolute time. Relative time describes the time interval between two points, as described by the speed of light, thereby maintaining the locally observed principles of Special Relativity. Absolute time describes a point’s location historically from the beginning of time. Paul Dirac's belief that the "Gravitational Constant" would decrease with the passage of Cosmic Time, or Absolute time, is predicted since “absolute” density decreases with the expansion of space. Locally this change in the effect of gravity will be undetectable. Non-baryonic matter is not necessary in this model to preserve celestial stability. The expansion must conform to a specific geometric rate in order to preserve Atomic and Celestial stability. Newton’s Law’s of gravity are predicted. The dimensional relationship describing space-time and matter is the same, D^3/T^2.

Since this is a geometric model, the dimensional relationships can be "drawn".  It is recommended to first review the Figures illustrating the basic inter and extra dimensional relationships that are being proposed. The links on the upper left of this web page will go to the Figures.

Also, those who wish to post a response to the proposed work, please send an email.  (link to email found in list to the left or bottom of page.  Thank you).  

I Introduction

This hypothetical model describing the relationships between space and time is based on a simple idea; the geometrical expansion of space-time includes everything, even matter itself. Current, (2004) texts on astronomy stop the expansion of Space-time at the boundary of galaxies. Galaxies are assumed to be gravitationally bound, thereby exempting them from the expansion of space. There is good reason to avoid extending the expansion to include matter. Such an expansion initially seems unlikely, basic principles such as the conservation of energy, and momentum would appear to be violated. Not only that, but atomic and celestial stability would seem to be destroyed. A uniform expansion also results in apparently no possible way to even detect the expansion since it would include all the rulers necessary to measure the expansion. For now, it is hoped the reader will allow the conjecture long enough to see how the theoretical model addresses these issues.

There are some benefits to the proposed model, making it worth the struggle to consider someone else’s ideas.

1. The effect of gravity becomes a function of time, with the effect of gravity being greater in the past. Paul Dirac and George Gamow (Noble prize winners in physics) also believed gravity decreased with the passage of Cosmic Time but they never derived a viable model. *

2. The theoretical model proposed is conformant and predictive of Newton’s experimentally derived Laws of gravity.

3. The assumption for non-baryonic “dark matter” is not required to preserve celestial stability.

4. The “dark energy” driving the expansion of space conforms to a specific dynamic structure tied to our reality.

5. The model is mathematically simple, only basic algebra and introductory calculus is used to explain the geometric structure of an expanding space-time field.

6. A number of cosmological or astronomical anomalies can be resolved. These will be discussed in some detail in another paper.

7. The model lends itself as a means to unite cosmological physics with quantum physics since the proposed expansion occurs probabilistically at the quantum scale of observation. The result of space-time expanding a “quanta” at a time results in the quantum physics.

8. The model is consistent with the epistemological considerations associated with special relativity and general relativity in that the formulas proposed are described by dimensional relationships between distance and time.

9. The model implies that matter is a property described by dimensional relationships of distance and time, M = D^3/T^2. This will be shown to be consistent with the principle of Equivalence.

10. The model is philosophically appealing. All points in the Universe are at the perceived center of a uniform expansion.

* (George Gamow writes in his book “Thirty Years That Shook Physics” the following. “It was once suggested by Dirac that the Newton’s “constant of gravity” is not really a constant but a variable which decreased in inverse proportion to the age of the Universe. And he may very well be right!”. Dirac also published at least one paper on the topic).

There are a number of nagging questions that arise from stopping the expansion of space-time at the boundary of galaxies. Most of these questions have proposed theoretical answers that as of yet have to be conformed by observation.

1. Where is the energy that is driving the expansion coming from? (What and where is “Dark energy?)

2. Why is the rate of expansion apparently occurring at exactly the correct rate to be balanced between expansion and collapse? (Why is the universe “flat”?)

3. Where is all this “dark matter”? What is dark matter?

4. How can some stars appear to be older than the universe?

5. How can evenly dispersed ionized gas clump into massive structures since the “big bang” spreads everything apart?

6. If gravitational collapse of material in space formed planets with metal cores, shouldn’t the sun also have a metal core?

7. Since our sun looks like so many other stars in the universe, do most of the other stars have iron cores? If so where did all the iron come from?

8. There is evidence our sun blew up 5 billion years ago, (Based upon evidence discovered by of Professor O.K. Manuel (http://www.microsoft.com/isapi/redir.dll?prd=ie&pver=6&ar=msnhome ). This seems preposterous since a supernova would destroy an entire planetary system, yet ours exists. How can this contradiction be resolved?

9. Why is the image size of radio galaxies non-conformit to theoretical predictions?

10. How can quasars put out so much energy in such a small region of space?

11. If a massive black hole is in the center of all galaxies, how does a galaxy evolve without consuming itself? How is the balance between existence and self-destruction maintained?

12. How can Mars with such a low surface gravity ever have an atmosphere that was dense enough to form rain clouds?

13. Why was the rate of growth and energy output of dinosaurs so much greater than the living organisms of today?

14. It is predicted that an object traveling at the speed of light does not change since time “stands still” for the moving object. How can the wavelength of a photon increase while traveling through space?

15. If one gram of mass were converted to light energy, sent off into space and reflected back, and then converted to back to mass, there would not be one gram of material left. What happened to conservation of Mass?

16. If one gram of electrons were sent off at 99.9999 percent of the speed of light and returned, would there be a similar loss of mass? Where did the electrons go?

17. Isn’t it inconsistent to state that the expansion of space-time results in a loss of energy outside of galaxies, but not within galaxies?

18. Why does light behave as a wave and a particle?

19. Since all points in space-time are separated by an interval of time, it is impossible for all points in space-time to agree on a simultaneous event. This in conflict the observation associated with the “big bang” in that all points in space-time would agree on the same simultaneous event associated with the beginning of the universe.

20. How does the transition between a singularity to an expanding space-time field occur? How does it create different properties such as charge or gravitational relationships?

21. Why is it that thousands of the best minds in physics, including Einstein himself, working for the last 50 plus years, have not been able to unite the fundamental forces into a comprehensive and consistent model?

22. Why is the speed of light the speed of light? Why is Plank’s constant the value it is? Should these and other fundamental constant’s that describe reality conform to some overall physical structure?

All the above questions have had proposed answers, but the issues remain. The field is ripe for conjecture.

Geometric model


II Basic Concepts and Definitions

 

The Uniform Expansion of Space-time results in Absolute and Relative measures

 

If the expansion of space were truly uniform, meaning that it includes matter, then there would be no way to locally measure the change since the rulers used to measure the expansion would also expand proportionally.  It is possible to imagine this kind of expansion if a frame of reference exempt of the expansion is established.  Two measures of distance are therefore required to describe a uniform expansion; a

Relative measure of distance in which rulers expand with the expansion of space, and an Absolute measure of distance that is exempt from the expansion of space.  These two measures of distance are shown in Figure 1.

 

Gravity is the Answer

 

Before going too far in the development of this theory there is an important question to answer: If everything remains proportionally the same with a uniform expansion, why assume that such an expansion exists since everything remains the same?  Actually, everything does not remain the same.  The effect of gravity, according to the model, is described by absolute measures, not relative measures.  For example, if the Earth were to proportionally expand to twice it’s size, the surface gravity would be reduced by a quarter ((1/2R)^2).  While the relative size has remained constant, the effect of gravity has not. 

 

The rate that the effect of gravity changes over time is very slow, measured as a function of the Age of the Universe itself.  Any decrease in the effect of gravity even over the course of a few thousand years is negligible, as will be shown later in this paper.  If objects are viewed very far away, meaning that they are also observed in the past, then it should be possible to observe the increased effect of gravity.   Objects should appear to be rotating too fast to maintain celestial stability.  Later, this proposed effect will be used to reduce the amount of non-baryonic matter required for celestial stability.

 

Gravity and General Relativity

 

It is hoped for a bit of grace from the reader familiar with general relativity.  Any model that proposes to alter how gravity is to be understood, runs face first into the principles established by general relativity. Even suggesting any change to the effect of Gravity without utilizing the techniques in general relativity is extremely risky for any theoretician. The interaction of curved space and its mathematical description associated with mass have established a form of truth that is impossible to deny.  This proposed model does allow the curvature of space, and for those who need to maintain the relationships of general relativity can do so. The effect of gravity becomes variable because the degree of the curvature of space-time is changing.   It is the change in curvature with the passage of cosmic time that results in the change in the effect of gravity.  Those who are inclined to dismiss any theory relating to gravity because the first mathematical tool used was not 4 dimensional Tensor Analysis should be patient.  Those familiar with relativity will find a common ground with the proposed theory in that specific relationships between distance and time are being proposed. At the very least, the fact that the proposed model establishes Kepler’s and Newton’s Laws means that the relationships proposed are curious. 

 

Two distinct measures of Reality 

 

Two unique ways to measure reality are being established.  One is based upon “Relative” measures of distance and time; the other is based upon “Absolute” measures of distance and time.  Both measures must agree on the same description of realty. But before developing the basic formulas describing the expansion a few concepts and definitions are in order.

 

 

Notation

 

Relative measures will symbolically be represented by lower case letters, and Absolute measures will be represented by upper case numbers.  For example V = absolute velocity, v = relative velocity.

 

Dimensions

 

Dimensions are measures of change.  If change can be described, and quantified, a dimensional measure is established.  There are a lot of ways things change, so there are innumerable dimensions.  In this paper the dimensional measures of change will be the three spatial dimensions and two temporal dimensions.   These dimensions are fundamental, or unique.  They are also interdependent, forming a geometrical model. 

 

Describing Unobserved dimensions

 

A requirement of this theory is to establish relationships based upon unobserved dimensional relationships.  In Figure 1, the “absolute” distance is an unobserved dimension.

  

Local measures of distance are constant

 

Notice in figure 1 all relative measures of distance and time remain the same.  This means that if the Earth doubled in Size, and all the rulers proportionally doubled in size, all locally observed measures of distance would remain the same. No relative change in distance or relative time is observed.  It is only form this hypothetical “Absolute” frame of reference that the doubling in size can be measured. 

 

Establishing a “ruler”

 

Measuring the expansion based on an Absolute frame of reference requires a relative measure of distance to be first “fixed” at a particular time during the expansion.  Figure 1 illustrated the absolute expansion of the object to be 1 2/3’s times greater, based upon a “assumed ruler” established earlier.  This assumed measure is based upon a relative measure of distance established at a particular point in time, which can then be used as a ruler to describe the expansion.  This process of establishing a ruler at a particular time is an important part of the model.

 

Absolute Time

 

An interval of time has to pass for the hypothetical expansion to occur.  Recording the historical location of a point is necessary to describe the proposed hypothetical expansion.

 

The method of establishing the historical or temporal location used in this paper, is to assume that all historical events can be located in relation to the beginning of time.  It is common to call this kind of historical description of events from the “Big Bang” or


 

moment of creation, as Cosmic or Cosmological Time.  Since the historical location of a point is intimately tied to dimensional measures associated with what is called in this paper as Absolute measures of Distance, Absolute measures of Velocity, and Absolute measures of Acceleration, this historical measure of time is also called Absolute time.

 

Relative time, another dimension of time

 

This hypothetical model also proposes that there are two unique dimensions of time, Absolute and Relative. Relative time describes the locally observed interval of time between points, as determined by the speed of light in a “vacuum”. If it takes 1 second for light to travel between two points in space, the measure of Relative time between the two points is 1 second, and will always be measured to be 1 second, despite the absolute expansion of space.  The relative speed of light is constant.  This preserves the all the relationships of Special Relativity.

 

A separate discussion on the two dimensions of time will be made in more detail later in this work, but some fundamental properties are described now.

What is Physics?

Physics is the mathematical description of nature; the mathematical description of nature, on it’s simplest terms, is the description of the location of a point.  Three spatial dimensions demarcate a point’s relationship from another point.  Special Relativity integrates a temporal distance between two points.  These 4 dimensions are not enough to describe the location of a point.  All points in space-time also have a unique location in history.  Not only is it necessary to describe the location of a point in space time by it’s spatial dimensions, and the time interval between points, it is also necessary to demarcate where the point is located historically.

Orthogonal dimensions of time

 

The presented hypothetical model asserts that Absolute time is unique, and orthogonal to relative time. Figure 2 shows two objects separated from each other by an interval of time which are also historically located. The perpendicular relationship of absolute time and relative time is required in this model.

 

Uniformity of Physical Relationships – Uniform “Rules”

 

Another basic assumption, or constraint on the hypothetical model is that the physics that describes the relationships between points in space-time must be consistent or uniform in their application.  For example, the relationship that describes gravitational effects must map point for point in both the absolute and relative reference frame. If the hypothetical model is valid, the set of “rules” that describe dynamic structure in the absolute reference frame, must also result in a set of points that match, map, or correspond to what is observed in the relative reference frame.  If Celestial and atomic stability is preserved in relative measures, they must be preserved for absolute measures.

 

Geometric Structure – Interdependence of dimensions

 

One of the results of the uniformity of physical relationships is that dimensional relationships become interdependent, resulting in the formation of a geometric structure.  For example, the three dimensional relationships between points in space conform to the geometric structure described by the Pythagorean theorem.  The three spatial dimensions while being unique, are interdependent. 

 

This geometric description of dimensional interdependence becomes dynamic when time is included.  The dynamic structure of space-time is in part, described by the Principals of Special Relativity, which also utilizes the geometric structure based upon the Pythagorean theorem.  Spatial coordinates become separated by relative measures of time, defined by the speed of light. The conformance of celestial bodies to an orbit also describes a dynamic geometric structure of space-time.

 

Uniqueness and Fundamental Dimensions

 

There are many ways to describe the properties associated with a point in space-time. The least, and most concise expressions that describe the properties of a point form Fundamental Dimensional measures.  Each of these Fundamental dimensional measures are unique, meaning that each dimensional relationship is required to completely describe properties of a point.

 

Fields and Reference Frames

 

A field can be viewed as a matrix of points in space-time. A frame of reference allows the description of points in space-time.

 

A system

 

A system is anything that is enclosed within a bounding surface.

 

Congruence

 

While normally congruence is associated with similar measures of two independent objects, in this work it’s meaning is somewhat different.  A set of points in space-time are congruent if two geometrically described and unique frames of reference simultaneously describe the same set of points.  See figure 3.

 

Flatland universe

 

One way to visualize the relationship of an unobserved dimensional relationship with three-dimensional space is to reduce the number of spatial dimensions from three to two, and then allow the removed spatial dimension to represent the unobserved dimension.

 

Two forms of motion or expansion and concepts of uniformly expanding universe

 

Figure 4 illustrates several concepts important to the proposed model.

1.            First there is the idea that a set of congruent points can be defined by a specific dynamic interaction of geometric relationships.  These congruent points can represent observed reality; in this case a Flatland universe.

2.            Reality can include or be described by unobserved dimensional relationships.

3.            The expansion is a uniform expansion; proportional measures remain the same.  This is illustrated in Figure 5.

4.            Not only is there a motion associated with the uniform expansion of Flatland, there is also a motion associated with motion of Flatland itself along the unobserved dimension, which is indicated by the velocity of the Plane in Figure 3.  This idea will be developed in more detail in the section called “expanding the expansion”.

 

Detecting a uniform expansion within a Flatland Universe

 

If the uniform expansion of a Flatland universe were to be detected, there would have to be some relationship that could be associated with the expansion that could be measured.  There are a few possibilities to consider.

1.            The implication that the expansion is the result of a dynamic interaction with some kind of locally unobserved relationship allows the opportunity to consider looking at relationships that involve motion. 

2.            If the flatland universe were moving in an unobserved dimension, there is the possibility for establishing “intrinsic” properties to objects in Flatland.  Intrinsic properties would be measurable characteristics observed in Flatland that would have no locally observed or explained reason for the observed properties. An example of an intrinsic property could be the mass of an object.  Einstein used “intrinsic” properties to explain the energy “intrinsic” to matter. 

3.            If the motion in the unobserved dimension were orthogonal to the Flatland universe, the observed “intrinsic” rules or properties found in Flatland would be uniformly experienced by everyone at the same point in Absolute time. 

4.            If there is a delay in observing events across the Flatland universe, then there is the possibility to observe “intrinsic” properties of objects in the past.  If “intrinsic” properties are changing slowly over time then observation of objects very far away should be perceived as behaving differently than those locally observed.  If mass were involved, the effect of gravity could be seen as changing over time.

5.            If the physical properties of a Flatland universe were intimately tied to motion in an unobserved dimensional relationship, then such a physical interrelationship could provide an appealing completeness or unification to the Flatland universe. For example, if there was some geometric relationship between motion in the unobserved dimension and Flatland universe’s observed speed of light, it would result in a physical explanation as to why the speed of light is the speed of light.

6.            If motion in an unobserved dimension affected light, a Doppler effect may be induced. 

 

Intrinsic properties

A physical description of an object’s characteristics defines an objects “intrinsic” properties.  The intrinsic properties may be determined locally between two points found in the present or local frame of reference, or the intrinsic properties may be the result of an association with the unobserved dimensional measures described by historical measures of time.  Figure 6.

Intrinsic Relationships

Intrinsic relationships are a result of the dynamic “rules” that the proposed uniform expansion imposes on points in space-time.  These intrinsic rules from a basis for unifying the dynamic structure of space-time.

For every relative measure there is a absolute measure

A flatland universe is shown in Figure 1 has a relative measure that also corresponds to an absolute measure.  This means that any particular time, a relative distance, d, correlates to an absolute distance D measure.  (note upper case and case).

Orthogonal Velocity

Since an absolute distance D, can be correlated to a relative distance d, which are both functions of orthogonal dimensions of time, this results in a “surprising” orthogonal velocity relationship.  This idea is expressed in the following two Figures, 7,8.

Whenever an absolute measure is correlated and matched to a relative distance measure, and the velocity between the two points is determined based upon absolute functions of time describing the distance between the two points, the velocity will be observed to be described by a perpendicular relationship relative to the distance between the two points.  This is a result of the orthogonal relationship Absolute measures of time has to relative distance measures.

Direction of Absolute Velocity vector

The distance between two points describes a line.  A velocity perpendicular to a point on that line can have any direction confined to a perpendicular plane to the line.  This possible 360-degree orientation becomes fixed to one direction if there is an existing velocity.  This restraint is necessary to maintain a consistent physical model, an object with a momentum in one direction will continue in that same direction unless “forced” to change over time.

 

Direction of Acceleration vector

 

If the derivative of the Absolute velocity is taken with respect to absolute time to establish the acceleration associated with the two points, there will be another 90 turn in the associated vector, since absolute time is orthogonal.  The net result is that the acceleration between two points will again be in line or parallel to the distance between the two points.  If a flatland example is used, the acceleration associated between two points due to motion in the unobserved dimension will result in acceleration that is intrinsic to the two points.  

 

Describing a physical model

 

It is important that a physical model corresponds to what so far must seem to be somewhat arbitrary rules, particularly regarding the proposed “perpendicular” direction of the velocity and acceleration vectors associated with a point.  Describing a meaningful physical model is challenging since it requires visualizing several relationships based upon an unobserved dimension. A number of drawings are included in this work in an effort to illustrate the relationships.   There are a number of aspects to this proposed uniform expansion that will be developed and it is hoped that by the end of this theoretical development, a somewhat comprehensive description of these inter-dimensional relationships is realized. 

 

Physical explanation of orthogonal velocity change, intrinsic relationships

 

One way to make visualize the proposed orthogonal change in velocity is to represent a region of space-time as an expanding balloon.  A balloon that expands due to a loss of surface tension will loose energy and the atoms in the balloon will move slower.  Similarly a region of space-time expanding based upon relationships associated with an “unobserved” dimension would impose a similar loss of energy. While for a balloon the loss of energy is associated with the expansion of the balloon causing a reduction in the velocity of the atoms hitting the side of the expanding balloon and then sharing that loss with all the atoms in the balloon, this energy loss for an expanding space-time field is the result of the elastic like expansion of space-time itself.  If the dimensional measure describing the expansion is the unobserved dimension that is orthogonal to three-dimensional space, there will be a change in the observed “intrinsic” properties, which in this case are associated with the velocity of regions of space-time. All systems are uniformly affected within an expanding space-time field.

Changing Velocity – mapping to a relative or absolute distance measure

 

How the velocity between two points changes with respect to absolute time will be developed shortly, but there are a couple concepts that should be expressed.  In this model there are two changes in velocity that can be associated with Absolute time.  If an absolute distance is mapped to a relative distance between two points, the change in velocity predicted by relationships based upon absolute time will be perpendicular to the distance measures between the two points and this change in velocity will be mapped to the congruent set of points forming our reality. The change in velocity will be based upon the observed “intrinsic” velocity observed locally, which was established at a particular moment in history to allow the creation of a “ruler”. All objects in an expanding space-time field separated by a relative distance will experience the same proportional change. Any region of space will experience the same proportional loss of energy for every system within the enclosed region of space-time.

On the other hand; if the single absolute distance of an object or point is mapped to an Absolute measure of distance (not relative), the change in velocity predicted by the relationships based upon absolute time will be perpendicular to all the locally observed distance measures and this velocity will appear to be a uniform motion away from the single point.  See Figure 10.  This will be explained in more detail in the Cosmological Red shift section of this work called “Expanding the Expansion”. 

 

 

 



|Welcome| |Geometry of Model| |Figures 1-5| |Figures 6-10| |Figures 11-15| |Figures 16-20| |Figures 21-25| |Figures 26-30| |Preserving Laws of Physics| |2 dimensions of Time| |Integration of Time| |Expanding Expansion| |Age of the Universe| |Unifying Structure| |AccelerationDeceleration| |Expansion theories by others| |Other| |Expansion of space graph| |Other| |1a super novas and z|