The Expanding Metric


It is proposed that our Universe is expanding according to a very specific geometry. Two geometrically related processes physically describe it; the expansion of observable space and the expansion of observable space along an unobserved dimension.

The mathematics for the geometry of the two expansion relationships are somewhat the same, but this thread will be discussing the geometry of the expansion of observable space.

This posting is an updated version of previous work in that it emphasizes the concepts of an Expanding metric, and a relative metric. The examples provided also help illustrate how the Principal of Conservation of Energy and Conservation of Momentum are the result of an expanding geometry. The examples also show how the effect of gravity is function of the Expanding Metric.

This topic summarizes the basic information I presented at a Gravity Conference at Caltech this past fall.

I would appreciate it if the discussions in this thread were somewhat limited to the geometry of the model, rather than peripheral issues. I do not mind a brief diversion, and I encourage such diversions it since side issues are usually the most interesting and they help focus my attention on important issues not yet explained, or resolved. I am desperately trying to keep the presentation of my Geometric Expansion Model somewhat coherent by dealing with one topic at a time.

Thank you for your consideration,
Snowflake

The metric

http://en.wikipedia.org/wiki/Metric_space
http://en.wikipedia.org/wiki/Metric_%28mathematics%29

A metric is simply the geometrical relationship of points in space and time.

Relative distance measure

Consider an imaginary cube in space. Each corner of the cube represents a point in spacetime. Every point imaginable on and within the cube also has a fixed relative distance to each other.

Relative temporal Measure
These points in the metric space are also separated by fixed intervals of time. This interval of time between points is physically revealed by the speed of light. For example, if two points in a cube were separated by 299,792,458 meters, the two points would be separated by an interval of time of one second.

Spacetime
The integration of time as a part of the structure of Space is fundamental. John Archibald Wheeler, one of the leading educators of Relativity, and collaborator of Albert Einstein, advocated the use of the term Spacetime to stress the integration of time with spatial relationships. His suggestion will be used. http://en.wikipedia.org/wiki/John_Archibald_Wheeler (Wheeler also created the term Worm hole, and black hole.)

Spacetime as a Volume
The imaginary cube also conveys a fundamental physical property of spacetime; its intrinsic nature is that of a volume measure.

Like a snowflake
The integration of space and time forms a kind of geometrical relationship that can be visualized as being like a snowflake. Just as a snowflake is defined by a geometrical relationship so to is spacetime. The physical interdependence of relative intervals of distance to relative measure of time is so fundamental that the speed of light is often expressed a one-unit measure of distance per one-unit measure of time. This “one to one” geometry along three orthogonal spatial dimensions describes a geometric structure. This conformance of spacetime to a geometric structure is analogous to the conformance of a snowflake to structure.


Continued

Snowflake

The Expanding Metric
Consider again the imaginary cube in spacetime. Now lets proportionally expand the cube and every point within the cube away from every point in the cube. This is an expanding metric. Its geometry of the expansion is not yet defined but that will come.

Relative spatial measures preserved
Imagine our expanding cube in space and it contains a pizza and a ruler. Everything in the expanding metric proportionally expands. Not just the spacetime within the expanding cube, but also the spacetime within every atom. If our imaginary cube doubled in size, our pizza doubled in size and our ruler doubled in size. All relative measures of distance have been preserved.

Model not Trivial – The effect of Gravity a function of Time
Some have suggested that such a proportional expansion of spacetime is trivial since everything would proportionally remain the same. (Wheeler writes this in the book called “Gravitation” by Misner Thorne and Wheeler) This is not the case. Density has become a function of time in this model and therefore the effect of gravity becomes a function of time. If the Earth were 1/2 its present size, with the same mass, the effect of gravity on the surface would increase 4 times. (The Nobel prize winner Paul Dirac believed that the effect of gravity would vary over measures of Cosmological time. He never derived a viable geometric model. I believe I have.)

Relative temporal measures must be preserved
If the distance between two points increases then it is logical to conclude that the interval of time between the two points within the metric has also increased. This creates a problem. The metric of spacetime defines a fundamental geometry to which everything in our Universe conforms. In order for the geometry of spacetime to be preserved, all spatially based measures of intervals of time would also have to proportionally expand the same proportional amount. It is easy enough to see that all measures of distance would be locally preserved since everything is proportionally expanded, but measures of time are more complicated.

First consider a light clock. The time it takes for light to travel back and fourth between the ends of a light clock would define an interval of time. Expand the light clock and it is logical to conclude that the interval of time described by the light clock becomes greater.

Now consider some of the vast number of additional cyclical or predictable processes that can be used to measure intervals of time; Pendulums, oscillating crystals, oscillating springs, orbital periods, rotational rates of tops to planets, electronic resonating circuits, chemical reactions and biological processes, including life spans, are just a few examples of ways to measure intervals of time. All these measures of local time would all have to proportionally slowdown exactly the same amount as measured by the light clock in order for the local geometry of Spacetime to be preserved.

Relative metric and an Expanding metric
What are being proposed are two metrics; a relative metric that locally appears to be constant in its relationships of intervals of time and space, and an Expanding metric, which from an “Eye of God” perspective has Absolute measures of distance and time changing.

Terms
Absolute
The term “Absolute” is a measure of change as seen from an “Eye of God” perspective. For example, consider our imaginary expanding cube and we are outside of the expanding cube watching how it expands. Our measure or description of changes within the cube as seen from this absolute or “Eye of God” perspective would be an absolute measure of those changes.

Relative
The term “relative” is a measure of relationships within the expanding metric using rulers and clocks that are local and apart of the expanding metric.

Local
The term local refers to relationships that are based on clocks and rulers that are part of the expanding metric and that they are being used in close proximity to the objects being measured.

Global
The term Global refers to relationships that are either described by “fixed” clocks and “fixed” rulers that are outside of the expanding metric, or clocks and rulers that were once apart of the expanding metric but were set to be “fixed” in order to provide a means of comparison.

Relative time
Relative time is defined as the time interval between points

Absolute time
Absolute time is defined as the historical location of a point relative to the beginning of time. Absolute time will also be called Cosmic time or perhaps more meaningfully, Historical Time.

Two dimensions of time

Some may argue that Absolute time is not a separate dimensional measure since a simple scalar multiple of a relative measure of time could be used to describe our historical location in time. This is not true. Certain physical properties can only be described by absolute measures of time. Using a relative measure of time would not describe how some physical measures change. A two dimensional graphic example illustrates this, a physical property appears to be constant for all values of relative time, yet along absolute measures of time the physical properties are found to be changing. Both dimensions, or measures of time, are required in this model.

This issue has been discussed previously in this forum at Two dimensions of time describe the Universe

To be continued…
Snowflake

A Brief description of the geometry of the expansion of observable space.


S ==T^2

The geometry of the expanding metric is simple. The volume of the expanding metric “S” varies to the square of the Cosmic measure of time. Double the age of the Universe and the absolute volume increases 4 times. (The double equal sign “== “ represents a proportional relationship that is also a geometric relationship).

Based on this geometric expansion, absolute measures of Distance, Velocity and Acceleration within the Expanding metric can be derived.

Derivation
I have presented for discussion the derivation of the fundamental formulas in this forum a few years ago.

My (Discovered) Unified Field Theory
My (Discovered) Uniform Expansion Model – Applied

Those interested may want to review at least the first thread since I think the commentary and critiques of the derivation posed by members of this Forum were thoughtful and insightful. Those who have questions after reviewing the derivation of the fundamental formulas, please feel free to ask in this thread.

Ratios of Time
The result of the derivation is a set of scalar field equations that describe how the Expanding Metric Expands. I call these equations the Ratios of Time.

Ratios of Time Formulas
D1/D2 == (T1/T2)^2/3 Equation D, for Absolute distance
V2/V1 == (T1/T2)^1/3 Equation V, for Absolute velocity
A2/A1 == (T1/T2)^4/3 Equation A, for Absolute acceleration
E2/E1 == (T1/T2)^2/3 Equation E, for Absolute Energy

T∆1/T∆2 = T1/T2 Equation for intervals of time

te = To(1 + (ln(To/T1))) Equation te, for experiential times

To = Age of Universe

Notation
1. Terms beginning with a capitol letter refer to measures as seen from the “Eye of God” perspective, such as D,V,or A.
2. Terms beginning with lower case letters are relative measures, such as d, v or a.
3. The numbers “1” and “2” after a term respectively describes and earlier and later measure.
4. The double equal sign == can be initially consider to represent a proportional relationship but it actually defines a geometric relationship.
5. The term “o” after a designation letter refers to a present measure. For example, To is the present age of the Universe, Do is the present measure between two objects, etc.
6. te = experiential time, which is the cumulative measure of intervals of relative time.
7. All the following capitalized letters represent absolute measures of the following
D = Absolute Distance
V = Absolute Velocity
A = Absolute Acceleration
E = Absolute Energy
T = Absolute Time .

Scalar field Equations

http://en.wikipedia.org/wiki/Scalar
http://en.wikipedia.org/wiki/Scalar_field_theory
http://en.wikipedia.org/wiki/Scalar_...eudoscience%29

The Ratios of Time formulas can be categorized as a set of Scalar Field relationships. A scalar number is simply a fixed value before a variable term, for example the number 2 is a scalar value for the variable x in the following expression, 2x. In the Geometric Expansion Model the scalar values are defined by function based on the Geometric Expansion of Spacetime. These scalar values multiply the physical measures associated with the Absolute measures of distance, velocity, and acceleration.

For example, at a historical location in time of T1, the absolute distance between two points is D1. At the historical location in time of T2, the absolute distance between two points is now D2. It is the Scalar function associated with absolute distance measures that describes the proportional change expected in these two distance measures over measures of Absolute time. The next posting will help illustrate the use of the above relationships.

Must preserve Relative Metric
It is important to stress that the Ratios of Time formulas describe properties of the Expanding Metric. In order for the model to be correct, the relative metric should show no variation in the measures of distance, velocity, acceleration or intervals of time. The structure of the relative metric has to be preserved. If all measures of relative distance maintain their relative proportional relationship then so must all spatially based measures of relative intervals of time maintain their proportional relationship.


Continued

Snowflake

Conservation of the relative Metric and Conservation Principals

The next two postings are illustrative examples of the dynamics of the Expanding Metric. The first set of examples will show how absolute intervals of distance and absolute intervals of time change in an expanding metric. The three examples provided will show that within a relative metric the same proportional change in measures of intervals of time are preserved. The examples will help illustrate that with in the relative metric the Principals of Conservation of Momentum and Conservation of Energy are preserved.

At first the relationships will appear to be simplistic since a vast number of functions could produce the same relationships. Please be patient, the equations are the result of a specific geometry and their uniqueness does not really become evident until accelerative relationships are added to the model, as illustrated in the next thread.

Problem 1. The Light Clock

Write the relationships that define how both the length of a Light clock, and the speed of light change in an expanding metric. Derive the interval of time described by a light clock in absolute measures.

Length of Light Clock in absolute measures
The length of a light clock, within the Absolute metric, increases in length according to the following relationship.

D1/D2 == (T1/T2)^ (2/3 )

Speed of light in Absolute Measures
The speed of light is a velocity that slows in the Absolute Metric according to the following relationship.

V2/V1 == (T1/T2)1/3

Absolute Interval of time
The absolute interval of time described by the motion of a photon within the absolute metric is the distance to be traveled divided by the velocity

T∆ = D/C

For the general case

T∆1/T∆2 = (D1/D2) / (V2/V1) = ( (T1/T2)^ (2/3 ) ) / ((T1/T2)1/3 ) = T1/T2

1/2 Example
What is the comparative change in the Absolute measures of Distance, Velocity and interval of time described by a light clock using a Historical Ratio of Time of T1/To = 1/2?

Absolute distance, T1/To = 1/2
Increase in absolute distance
D1/Do == (T1/To)^ (2/3 ) = (1/2)^ (2/3 ) = 0.63.

In the past the absolute distance between the ends of the light clock was 0.63 of its present measure.

Absolute velocity, speed of light, T1/To = 1/2

V2/V1 == (T1/T2)1/3 = 0.79

In the past the speed of light was 1.26 times faster

Absolute interval of time T1/To = 1/2
From an absolute perspective, what are the proportional changes in an interval of time describe by a light clock when the Universe was 1/2 its present age?

T∆1/T∆2 = T1/T2 = .5To /To = 1/2

When the Universe was 1/2 its present age, the interval of time described by the light clock in the absolute metric was 1/2 as much. The light clock was smaller and the speed of light was faster, and in this example the Light clock “Ticked” twice as fast.


Problem 2 – Linear Motion

The distance the object travels divided by the velocity describes an interval of time. The distance an object travels in an expanding metric increases and the velocity of the object decreases in an expanding metric when described in absolute terms. Derive a general expression describing how absolute intervals of time change for an object in motion within an expanding spacetime field.

Absolute distance
The absolute distance between points in an expanding spacetime field varies according to the following ratio.

D1/D2 == (T1/T2)^ (2/3 )

Absolute Velocity
The velocity of the object would diminish in absolute measures by the following ratio.

V2/V1 == (T1/T2)^1/3

Absolute Interval of Time
The ratio of the interval of distance traveled divided by the ratio of the velocity that the distance interval is transversed, yields a comparison of the Absolute interval of time to travel the interval of absolute distance.

(D1/D2) / (V2/V1) == T∆1/T∆2 = T1/T2

1/2 Example problem

(Note it is assumed that the interval of distance traveled is small compared to the scale of the Universe).

Absolute distance
When the Universe was 1/2 its present age, the distance between points in the expanding metric was

D1/Do == (T1/To)^ (2/3 ) = (1/2)^ (2/3 ) = 0.63.

Absolute Velocity
When the Universe was 1/2 its present age an objects motion would have been greater in the past..

V2/V1 == (T1/T2)1/3 = 0.79
In the past the speed of light was 1.26 times faster

Interval of time

The interval of time defined by the free moving object traveling an absolute interval of distance in an expanding spacetime field when the Universe was 1/2 its present age is…

T∆1/T∆2 = T1/T2 = 1/2

When the Universe was 1/2 its present age it took the object 1/2 the time to travel between two points in the absolute metric, compared to present measures.



Problem 3 - Angular Momentum
Derive the relationship that defines how absolute intervals of time change in an absolute Metric for a spinning object.

The solution for this example is identical to the Linear Motion example. The distance the spinning object must move or rotate would be defined by the expansion of the Metric, and the velocity of the particles on the spinning object would decrease according to the same expanding metric expression.

T∆1/T∆2 = T1/T2 = .5To /To = 1/2

1/2 Sample
When the universe was 1/2 its present age, the spinning object would have spun two times as fast.

Conservation of Momentum is Geometrically based
From the “Eye of God” perspective” there is a change in the measures of intervals of time in the light clock and for objects in motion, be it in a linear motion or in rotation. However, from a local perspective there would be no noticeable change in distance, velocity or associated measures of intervals of time. This consistency is the result of geometry. The proposed Expanding Metric geometrically predicts the principal of Conservation of Momentum and Conservation of Energy.



Continued

Snowflake

Second set of examples - Acceleration and Gravity

The Ratios of Time formulas include the prediction as to how measures of Absolute Acceleration are to change within the Expanding Metric. The following examples will show that cyclic processes that are dependant upon acceleration will still produce the same proportional variation in the measures of time within the relative metric. The temporal and spatial relationships within the relative metric will be preserved.

These examples will also show that the change in acceleration established in the Absolute Metric corresponds to an accelerative effect that conforms to the inverse square law of Newton’s Law of Gravity. The proposed theoretical model produces the Empirical or observationally derived Newton’s Law of Gravity.

General Relativity
Those familiar with General Relativity should not rush to judgment and dismiss the model. General Relativity would still be accurate within local or relative reference frames. The structure of the relative metric is still preserved. The proposed model would also resolve some issues or ambiguities created by applying General Relativity on a Global scale.

Problem 4 - A Pendulum
Derive the predicted variation in the Absolute Length of the Pendulum, the change in the scalar or Absolute acceleration the pendulum experiences and the Absolute Interval of time associated with a Pendulum.

The period of a pendulum is described by
Period = 2 π x (l/g)^(1/2) (for small angles of swing)
l = length of pendulum, D used in following formulas
g = accelerative field pendulum is experiencing

The change in the length of the Pendulum in absolute measures is described by…

D2/D1 = (T2 /T1) ^ (2/3)

The change in the scalar value of the absolute acceleration as derived by the Geometric Expansion Model is ..
A2/A1 = (T1/T2) ^ (4/3)

Substituting these values for the period of the pendulum at T1 and T2 to describe intervals of time results in:

T∆2/T∆1= ((D2/D1)/ (A2/A1)) ^ (1/2) =
( (T2 /T1)^(2/3) / (T1/T2)^(4/3) )^(1/2) = T2/T1

T∆1/T∆2 = T1/T2 (Note that the general case is the same as established in the Velocity examples).

1/2 Example
Just as in the previous examples, the length of a pendulum would be .63 that of the length of the pendulum today and the pendulum would tick twice as fast in the past.

Proportional measures of relative distance and intervals of time are preserved.

Problem 5 – Inverse square variation

Recalculate the Pendulum problem but instead of utilizing the predicted scalar field variation for absolute acceleration, use the variation in centroidal distance measure and Newton’s empirically derived law of Gravity.

The effect of gravity predicted by Newton’s empirically derived law of gravity would vary to the inverse square of the centroidal distances. The proportional change in the gravitational effect due to the change in absolute distance measure is

(D2/D1)^2 = g1/g2

where D2 and D1 describe the change in absolute distance and g1/g2 describes the proportional change in the effect of gravity, if the inverse square law were to be applied to the effect of gravity and that gravity is an effect defined by the Expanding metric.

The change in length of the Pendulum is proportional to…
D2/D1 = (T2 /T1) ^ (2/3)

The corresponding change in the effect of gravity due to the change in absolute distance between the centroid of the Earth, and the centroid of the Pendulum over measures of absolute time is proportional to …

(D2/D1)^2 = g1/g2 = (T2 /T1) ^ (4/3)

The period of a pendulum varies by
Period = 2 π x (l/g)^(1/2)

The corresponding proportional difference in period is determined by the change in the length of the pendulum and the change in the effect of gravity, based on the variation in the centroidal distance (which is based on the assumption that Newtons inverse square law is valid), results in

T∆2/T∆1 = (D2/D1)/(g2/g1))^(1/2) = ( (T2 /T1)^(2/3) / (T1/T2)^(4/3) )^(1/2) = T2/T1

Problem 6 – Orbital Motion
Derive the change in orbital period of an object in absolute measures based on the absolute distance measure and absolute velocity measure varying according to the proposed scalar field relationships for velocity and distance.

D1/D2 = (T1/T2)^(2/3)
V2/V1 = (T1/T2)^(1/3)
T∆2=D2/V2, T∆1 =D1/V1
T∆1/T∆2 = (T1/T2)^(2/3) /(T2/T1)^(1/3) = T1/T2

T∆1/T∆2 = T1/T2

Problem 7 - Orbital Motion
Rework the above Orbital period calculation but base it on the assumption that Kepler’s law is valid and the distance measures change as proposed in the Expanding Metric.

T^2 == D^3 (Kepler’s third Law, == means proportional to, and period = T and D = diameter of orbit).

Torbital period == D^(3/2)
T∆1/T∆2 = (D1/D2)^(3/2)

T∆1/T∆2 = ((T1/T2)^(2/3))^(3/2) = T1/T2

(General relativity note
Those who are familiar with General Relativity may feel that some error is made here since there is a processional effect that alters the period of elliptical orbiting objects. It is important to stress that General Relativity is based on measures within the relative metric, not the Absolute expanding metric being developed.)

Problem 8 - Orbital Motion
Show that the necessary balance between centrifugal and gravitational force is maintained by equating the (M1 x v^2)/R = (G x M2 x M2 )/R^2 terms. Assume the property of mass is constant and gravitational constant is constant in the Expanding Metric.

This problem is left to the reader.

Summary

Energy
The perseverance of the relative measures of intervals of time is equivalent to stating that the relative energy of systems and the relative momentum of systems is locally preserved. The conservation of energy and conservation of Momentum Principals are a direct result of an Expanding Metric

Gravity

The relative metric is preserved within the proposed Expanding Metric. The accelerative scalar field relationships predicted within the Expanding metric produces or is compatible with the Inverse square law associated with the effect of Gravity. The effect of gravity is the predicted result of the Geometric Expansion of Spacetime.


Continued

Snowflake

Issues with model

I thought I’d mention a few problems or issues with the model as presented.


1. The model produces no Cosmological Red shift. The electrostatic field relationships around an atom would be denser in the past, therefore in the past when an electron drops from one energy level to another, the energy content of the departing photon would be greater. This extra energy imparted to the photon would be diminished by the expansion of spacetime. As it turns out, the extra energy a photon starts off with is exactly countered by the energy lost while the photon travels through the expanding spacetime field, thereby producing no Cosmological Red Shift.

2. Expansion within atom. The expansion of spacetime as presented so far has not addressed how this expansion would occur within the atom, nor the physical effects of an incremental expansion within the atom. (Hints of the physical process responsible for Electrodynamics and some of the probabilistic properties of Quantum the physics).

3. Fundamental Particles http://en.wikipedia.org/wiki/Fundamental_particles Fundamental particles, establish relationships that are somewhat contact like, or are relationships described by acting according to rules, as opposed to the volumetric relationships observed with atoms or with gravitational relationships. The ratios of time formulas are based on the properties of a volume of spacetime. There therefore appears to be a boundary issue with respect to the metric expansion. Also, a number of fundamental properties, such as spin, have not been explained as being a result of the expansion of spacetime.

4. Fission . Fission based Nuclear reactions can provide a means to describe intervals of time by decay times, such as the physical measure called a half-life. Since the relationships within the nucleus of the atom are not entirely spatial but contact like in their relationship to each other, the applicability of the above relationships would have to be modified for reactions occurring within the nucleus. As fundamental particles group there is a transition to volumetric based relationships that has not been addressed. http://en.wikipedia.org/wiki/Liquid_drop_model

5. Matter and Spacetime interaction. The physical connection between spacetime and matter has not been explained. How would an expanding spacetime field impart an effect on mass causing it to experience a force like effect? (Or from a General Relativistic perspective, given that the curvature of spacetime tells matter how to move and matter tells spacetime how to curve, how is the physical connection between curved spacetime and matter established?)

6. Scale. The Ratios of time formulas are expressed as a ratio. So far as presented, they do not establish a fixed measure at a particular time based on a physical property based on process. For example, the speed of light is proposed to vary over measures of time, but why is the speed of light the speed of light in the first place? Why not have the present speed of light twice as fast as it is now?


Snowflake

Predictions and Verification of the model

There are several physical predictions the proposed Expanding Metric would impose on nature. While locally all relative measures of time would be preserved, historically this would not be the case. The further in the past dynamic relationships are observed, the “Clock Rates” for these dynamic relationships would be faster. Stars would evolve faster. Also, the effect of gravity becomes a function of time, so less mass would be necessary to from a star. Type 1a supernovas would also be smaller and dimmer than presently thought, this effect alone could resolve the issue of dark energy. Allowing the effect of gravity to vary radially from the core of a galaxy outwards due to the expansion of spacetime would eliminate the necessity for dark Matter within galaxies. By allowing the historical relationship between galaxies to define the gravitational relationships, the additional necessity for even more dark matter associated with galaxies would be eliminated.

A list of some of the observational evidence indicating that gravity was greater in the past was posted on
Dirac, Gravity and observational confirmation


End of the Dark Ages
The proposed theory is predicting the observed properties of the Universe without supermassive black holes, without dark energy and without dark matter. Is this the end of the Dark Ages for Astronomy?

In the end, the model that produces the simplest and most beautiful description of nature will be the one that is right.

SnowflakeUniverse

Does this mean that you have abandoned the other, still open, ATM threads you started, with similar (or related) contents?

Is your model based on your own special version of metric expansion, or built on top of the mainstream version? Because as I understand it, in the mainstream version, objects are NOT expanding. The spacing between atoms, molecules, etc. are the result of balance between a myriad of forces. This balance does not change under metric expansion, so even as the universe expands, objects inside are not actually expanding along with it. To use your analogy, while the cube expands, the pizza and ruler do not expand. As such, object densities do NOT change, and the effect of gravity is NOT a function of time.

Please address this, as it currently appears that your model is built on top of a fatally flawed understanding of metric expansion.

To come at it from a different angle, if objects DO expand at the same rate as the universe, then why does the universe appear so vast to us? We should have expanded right along with it! If everything expands at the same rate as the universe, wouldn't the universe be filled to the brim with ultra-sized particles and atoms?

__________________
"It's over you head now. Time to get some professional help." - My fortune cookie from lunch

Ned Wright's Cosmology Tutorial

Usenet Physics FAQ

Hi Code Slinger

You asked
“Is your model based on your own special version of metric expansion, or built on top of the mainstream version?”

It my own special version, although John Hunter and Jon Masreliez have also derived a similar expansion of the relative metric based on relative measures of time.

In a paper at the American Physics Conference I transformed my model to relative measures and the expressed geometry becomes the same.



You also stated,
“Please address this, as it currently appears that your model is built on top of a fatally flawed understanding of metric expansion.”

Whether or not my expanding metric is flawed or not has yet to be proven. As far as I am concerned the present “Limited Expansion Model” , (LEM) that is assumed by the Mainstream is wrong.


You also asked
If objects DO expand at the same rate as the universe, then why does the universe appear so vast to us? We should have expanded right along with it!

Proportional measures would remain the same, if the Universe starts off as vast, it stays vast.

More specially.
Imagine a galaxy 1 billion light years away. It is the same size as our galaxy, which means that 1 billon years ago both galaxies were proportionally smaller. As the image of the distant galaxy travels through the expanding spacetime field, the image is expanded. When the light from the distant galaxy reaches us, our galaxy has proportionally expanded thereby maintaining the same proportional relationship.

Snowflake

I see, thank you for clearing that up.

I will leave it to others more knowledgeable than I to critique your special version of metric expansion.

__________________
"It's over you head now. Time to get some professional help." - My fortune cookie from lunch

Ned Wright's Cosmology Tutorial

Usenet Physics FAQ

Hi Nereid
You asked
Does this mean that you have abandoned the other, still open, ATM threads you started, with similar (or related) contents?

No,

I am responding to the questions brought out in the other threads.

All I trying to due is discuss one issue or topic at a time.

I was asked to provide empirical relationships

In order to do that, I have to have equations.

If I am to use equations, I have the responsibility to explain the foundation for those equations.

If you wish to discuss the proposed geometry in this thread, then please do.


Thank you
Snowflake

[QUOTE=snowflakeuniverse;1197804]The metric

http://en.wikipedia.org/wiki/Metric_space
http://en.wikipedia.org/wiki/Metric_%28mathematics%29

or simply just distance between the two points . without time involved at all




yet without time each corner still represents as you say a fixed distance



true

yes and no

only if we want to know how long it takes to get there or to understand how long a certain action > reaction between objects takes place

but in no way does time have any physical consequence to this reaction

time is used to understand the reaction between simple and multiple actions by objects and the consequences of . nothing less and nothing more

You said,

…in no way does time have any physical consequence to this reaction

time is used to understand the reaction between simple and multiple actions by objects and the consequences of . nothing less and nothing more

I think from your comments you do not believe in a geometric description of nature based on measures of distance and time, or perhaps more accuratiy, you do not believe that time is a fundamental part of the sturcutre of space.

Is that right?

Snowflake

exactly

Hi North

Time is an integral part of nature.

I suspect that there is nothing I can do to convince you of the geometry because you are already convinced that time is not a part of the structure. Your ideas are clearly out of the mainstream, and your mind is made up.

I also suspect that there will be nothing I can do to convince the “mainstream” that the proper geometry of spacetime must include two dimensions of time. Their mind is already made up.

I hope that my suspensions are wrong. It would be a shame to have a significant advancement in theoretical physics pass by unrealized because everyone’s mind is already made up.

Snowflake

time is not really an integral part of Nature

but time is an integral part of our ( Humanity ) Nature to understand movement behaviour between objects . this is Natural and there is nothing wrong with this use of time to do just that , to understand why the movement took place in the first place . the mathematical construct of time was developed to do just that and it works for the most part just fine

the thing is that , between objects , time is not a concern , since time is a geometric or mathematical concept , created because we want to understand why objects and energy do what they do . whether from interaction between themselves or by themselves . and it is because of the mathematical concept of time which leads us too look deeper into the reasons why , such and such happens or not etc . but this does make time an intertwining fabric of why such and such happens or not

in actual fact , that between the interaction of the objects themselves and energy , the only things that stimulate the consequence(s) is the fundamental Nature of the objects themselves , such as spin , magnetic-fields , electronics , electrons , protons , neutrons etc. and the fundamental particles that they themselves are made

look if one takes a mathematical point of view of the physical Universe then the mathematics must be shown to depict a real physical property of the Universe . time does not do this . time has NO physical influence on any physical object or property of a said object.

time is a tool used by us to understand deeper than perhaps had we not had the mathematical concept of time


I can't speak for the mainstream

that is yet to be seen

Does this idea produce a particular value for H₀ (the present-day Hubble constant), from first principles? or is it something you have to put in by hand? or something else??

How, if at all, is (Special Relativity) time dilation modified, in this idea?

Is there some effect comparable to (or even the same as!) the Sachs-Wolfe effect under this idea?

How (if at all) does gravitational (wave) radiation differ, in this idea, from that which follows in GR?

To what extent is it appropriate to ask how well this idea matches relevant astronomical observations, in this thread?

Hi Nereid
You asked,
1. Does this idea produce a particular value for H0 (the present-day Hubble constant), from first principles? or is it something you have to put in by hand? or something else?
2. How, if at all, is (Special Relativity) time dilation modified, in this idea?
3. Is there some effect comparable to (or even the same as!) the Sachs-Wolfe effect under this idea?
4. How (if at all) does gravitational (wave) radiation differ, in this idea, from that which follows in GR?
5. To what extent is it appropriate to ask how well this idea matches relevant astronomical observations, in this thread?

Ho and fundamental measures, age of Universe

Ho, the observed rate of expansion based on Cosmological Red Shift and the associated distance measures, is a result of the expansion of spacetime along the unobserved dimension in this model.. Technically Ho is not a part of the proposed expanding metric, which is the expansion of observable space.

However, since the geometry is similar, Ho is a directly associated with the age of the Universe. Since the geometry is flat, with no dark energy or no dark matter, the age of the Universe is To = 2/3 1/Ho, which probably is a familiar expression to you.

Actually there is another geometrical relationship that I have also used to describe the extra dimensional relationship between the expanding metric of observable space along an unobserved metric. In this geometry the age of the Universe is, To =((square root 2) /3 ) x 1/Ho.

At first glance this proposed young absolute age to the universe seems unrealistic since the two possible ages are either about 9, or 7 billion years old, assuming a measured Ho of 71 km/s per million parsecs.

This young age to the Universe is based on Absolute Measures of time, not relative. The cumulative measure of relative time, or experiential time, is greater than the absolute or historical location measures of time.

A number of issues also have to be addressed by asserting that the Universe is this young.

Special relativity
Special relativity, at least in terms of application is unaffected on a local level. See the previous discussion about the Lorentz factor. It is actually more complicated but until the expansion along the unobserved dimension is integrated with the expansion of observable space, any explanation will appear contrived.

Sachs-Wolfe effect
The Sachs-Wolfe effect is a predicted red shift variation in the Cosmic Background Temperature due to the gravitational red shift caused by dense of clusters of matter in the early universe. The overall effect would be expected in the proposed model. I made a separate posting about the background temperature that illustrated that the formation of the Cosmic Microwave Radiation would still be produced with the same general relationship to the matter existing in the early universe.

There are a few differences that should be mentioned. The Age of the Universe is less in this model, which would tend to make the size of the expected zones of temperatures variations to be smaller than the 10-degree measures of fluctuations presently observed. Initially this would seem to invalidate the model. However in the model proposed the universe starts off with an initial proportional separation between galaxies, This offset is proportionally preserved and it therefore increases the separation measures if the background temperature variations.

Gravitational waves
Gravitational waves, or a variation in the density of spacetime would still exist within the model. A fundamental difference is that while locally general relativity is valid, the metric used by general relativity is expanded or compressed depending on the historical location the gravitating masses are located.

Observational evidence
It is hoped that some will review the derived formulas and see that local relationships are preserved in the expanding metric. Remember Wheeler said such an expansion was trivial, I have shown it is not, Clock rates slow with the expansion of spacetime, and the effect of gravity diminishes with the expansion of spacetime.

While local measures are proportionally preserved, the model predicts that in the past clock rates would be faster, and the effect of gravity would be greater. These predictions should be born out by cosmological observation.

I was asked to provide empirical evidence of the validity of the proposed Uniform or Geometric Expansion of Spacetime. In order to do that I have to provide for review the relationships that will be used to produce the requested empirical verifications.

Worrisome
What worries me somewhat is the lack of verification or acknowledgement by anyone of the rather remarkable way the proposed relationships integrate together. All I used was basic geometry, calculus and algebra. A good High school student can follow the development of the model.

Any application of these relationships to real physical parameters will certainly be more involved. If what is already presented is not acknowledged as being essentially correct, what hope is there of providing any kind of convincing verification of the model using empirically based boundary conditions?

Snowflake

To what extent are UHECR (ultra-high energy cosmic rays) a potential test of your ATM idea?

In their own frame, they will have travelled for only milliseconds from source to Earth; in our frame, they travelled for millions, possibly billions, of years. Thus they would seem to be physical samples of the much different, distant universe ...