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Old 02-June-2006, 03:13 AM
snowflakeuniverse snowflakeuniverse is offline
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Default Critiques of Presentation of Uniform Expansion Theory

Critiques of Presentation of Uniform Expansion Theory

Every couple of years I have the opportunity to present my Uniform Expansion Theory to a group of Advance Placement High school physics students, many of who will receive college credit for the course. These are smart kids.

Historically, I have been able to convince the students that the model makes sense and they have always signed a statement that others with more expertise in the field should review the model. This year I will be forwarding their request to the American Astronomical Society in an effort to convince the organization to allow me to present an oral paper for the January Meeting.

(Specifically, the paper I wish to present will show that based on the Uniform Expansion Model, the correlation of the brightness of type 1a supernovas verses the cosmological red shift corresponds to a “flat” universe. There is no dark energy required for the model, nor is there any need for dark matter. Since the model predicts that the effect of gravity is greater in the past, it would take less mass to reach the Chandrasekhar limiting pressure, which would mean that the supernovas should be smaller by a predictable amount, and therefore dimmer by a predictable amount. Once this effect is accounted for, and mapped to the red shift predicted by the model, the rate of expansion conforms to being “flat”, meaning that there is no dark energy needed. )

In the interest of truth, I thought that this year I would also post on this forum what I taught, thereby allowing a more diverse critique of the model. If I was teaching something wrong, someone within this forum could show the error. (Someday, someone with authority, and more importantly, someone with courage, will acknowledge that what I am teaching is right, and it is the presently taught model that is wrong, but at this site I know I can depend upon critiques).

As I am still in the process of organizing the presentation, it will be a couple of days before I can post it to this site. It may seem a bit premature to begin this thread without the theoretical presentation, but I wanted the link to this site to be available to the students in the material I am providing them tomorrow. The presentation will be on Tuesday June 6.

Thanks

John M. Kulick
AKA Snowflake
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Old 02-June-2006, 04:55 AM
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Quote:
Originally Posted by snowflakeuniverse
Critiques of Presentation of Uniform Expansion Theory

Every couple of years I have the opportunity to present my Uniform Expansion Theory to a group of Advance Placement High school physics students, many of who will receive college credit for the course. These are smart kids.

Historically, I have been able to convince the students that the model makes sense and they have always signed a statement that others with more expertise in the field should review the model. This year I will be forwarding their request to the American Astronomical Society in an effort to convince the organization to allow me to present an oral paper for the January Meeting.
We've been over this before. High school students, gifted or not, even undergraduates, are not the audience that matters. The AAS will not be any more impressed with your petition signed by high-schoolers than I am. Which is not impressed.
Quote:
Originally Posted by snowflakeuniverse
(Specifically, the paper I wish to present will show [Snip!] In the interest of truth, I thought that this year I would also post on this forum what I taught, thereby allowing a more diverse critique of the model. If I was teaching something wrong, someone within this forum could show the error. (Someday, someone with authority, and more importantly, someone with courage, will acknowledge that what I am teaching is right, and it is the presently taught model that is wrong, but at this site I know I can depend upon critiques).
You can depend on the critiques (and you will get them), but are you capable of learning from them? Have you finally learned the difference between two independent dimensions and two parametrizations of one dimension? Your ideas will make no progress as long as you persist in this error. Graduate students and professors will notice this first thing. (As I have done.)
Quote:
Originally Posted by snowflakeuniverse
[Snip!]The presentation will be on Tuesday June 6.
I'm looking forward to it.
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Old 02-June-2006, 11:34 AM
Nereid Nereid is offline
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Quote:
Originally Posted by snowflakeuniverse
Critiques of Presentation of Uniform Expansion Theory

[snip]

(Specifically, the paper I wish to present will show that based on the Uniform Expansion Model, the correlation of the brightness of type 1a supernovas verses the cosmological red shift corresponds to a “flat” universe. There is no dark energy required for the model, nor is there any need for dark matter.
That is quite an achievement, if that is indeed what you have done.

However, it seems that it would create a whole host of other inconsistencies, not least due to the wide range of independent, mutually consistent sets of observations showing the existence of DM, on a range of distance scales, in a range of environments, obtained through use of a range of different kinds of processes and (ultimately) physics.
Quote:
[snip]

The presentation will be on Tuesday June 6.
Quote:
Originally Posted by Celestial Mechanic
I'm looking forward to it.
Me too!
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Old 02-June-2006, 11:58 AM
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Originally Posted by snowflakeuniverse
The presentation will be on Tuesday June 6.

Hmmmmmmm, a D-Day, of sorts. We'll be waiting snowflake.
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Old 02-June-2006, 10:23 PM
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Quote:
Originally Posted by Nereid
However, it seems that it would create a whole host of other inconsistencies, not least due to the wide range of independent, mutually consistent sets of observations showing the existence of DM, on a range of distance scales, in a range of environments, obtained through use of a range of different kinds of processes and (ultimately) physics.
Umm, I don't think anyone has shown the existence of DM, merely inferred it from the difference between calculations and observations. If anyone did, please give references, I'm very curious what DM actually is.

Cheers.
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Old 02-June-2006, 10:57 PM
Nereid Nereid is offline
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Quote:
Originally Posted by VanderL
Umm, I don't think anyone has shown the existence of DM, merely inferred it from the difference between calculations and observations. If anyone did, please give references, I'm very curious what DM actually is.

Cheers.
Not sure I follow you (nor does it seem relevant), but "merely inferred {X} from the difference between calculations and observations" pretty much describes most of astronomy, doesn't it? Think of exo-solar planets (any method of detection), star-spots, spectroscopic binaries, the SZE, even all (radial) Doppler motions, magnetic fields, ...

[Edit: as the observational basis of DM is a popular topic, I have started a thread in the Q&A section - What is the observational basis for (cold, non-baryonic) dark matter?]
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Old 03-June-2006, 03:55 AM
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Quote:
Originally Posted by snowflakeuniverse
Critiques of Presentation of Uniform Expansion Theory

Every couple of years I have the opportunity to present my Uniform Expansion Theory to a group of Advance Placement High school physics students, many of who will receive college credit for the course. These are smart kids.

Historically, I have been able to convince the students that the model makes sense and they have always signed a statement that others with more expertise in the field should review the model. This year I will be forwarding their request to the American Astronomical Society in an effort to convince the organization to allow me to present an oral paper for the January Meeting.[Snip!]
Here's another analogy: what you're trying to do is present a musical by touring dinner theaters in the Midwest, and hoping that positive reviews from the audience will land your show a run at a Broadway theater. That isn't how it is done. The standard procedure here is for the show to be given a dry run in New Haven or Philadelphia, and then after some numbers dropped and new numbers added and all the kinks worked out, then and only then does the show open on Broadway. Broadway first, then the touring companies and dinner theater productions.

You need to take your "show" before graduate students and professors, not high-school students however gifted.
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Old 03-June-2006, 04:13 AM
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Default Re: Critiques of Presentation of Uniform Expansion Theory

There's another problem here. Since it's a course for college credit, I would imagine it's graded. And that you (SFU) would be doing the grading. That fact alone disqualifies the class members as objective reviewers. Whether unconsciously or not, the class members will consider the instructor to be the gateway to a passing grade high enough to get the college credit, and thus do what they think the instructor wants them to. For high school students in a college environment this tendency would be even more pronounced.

This isn't idle speculation. While in high school I took a number of college credit courses in such things as molecular biology, physics, astronomy, etc. We essentially took as fact whatever the instructors told us. After all, we were just high school students.
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Old 04-June-2006, 04:29 AM
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Quote:
Originally Posted by Maksutov
There's another problem here. Since it's a course for college credit, I would imagine it's graded. And that you (SFU) would be doing the grading.
I'm not sure that snowflakeuniverse is actually teaching the course. In the OP he wrote:
Quote:
Originally Posted by snowflakeuniverse
Every couple of years I have the opportunity to present my Uniform Expansion Theory to a group of Advance Placement High school physics students, many of who will receive college credit for the course.
It's probably a case of the teacher saying "And now for something completely different" and turning the floor over to Mr. Kulick for one session.
Quote:
Originally Posted by Maksutov
This isn't idle speculation. While in high school I took a number of college credit courses in such things as molecular biology, physics, astronomy, etc. We essentially took as fact whatever the instructors told us. After all, we were just high school students.
Very true, and the reason why snowflakeuniverse needs to present his ideas somewhat higher up the academic food-chain.
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Old 04-June-2006, 04:57 AM
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Default Re: Critiques of Presentation of Uniform Expansion Theory

Re:
Quote:
Originally Posted by Celestial Mechanic
Quote:
Originally Posted by Maksutov
There's another problem here. Since it's a course for college credit, I would imagine it's graded. And that you (SFU) would be doing the grading.
I'm not sure that snowflakeuniverse is actually teaching the course. In the OP he wrote:
Quote:
Originally Posted by snowflakeuniverse
Every couple of years I have the opportunity to present my Uniform Expansion Theory to a group of Advance Placement High school physics students, many of who will receive college credit for the course.
It's probably a case of the teacher saying "And now for something completely different" and turning the floor over to Mr. Kulick for one session.
However he later writes

Quote:
Originally Posted by snowflakeuniverse
In the interest of truth, I thought that this year I would also post on this forum what I taught, thereby allowing a more diverse critique of the model. If I was teaching something wrong, someone within this forum could show the error. (Someday, someone with authority, and more importantly, someone with courage, will acknowledge that what I am teaching is right, and it is the presently taught model that is wrong, but at this site I know I can depend upon critiques).
in which he uses "taught" and "teaching" twice. Then again perhaps he considers a one-session presentation to be teaching.

Quote:
Originally Posted by Celestial Mechanic
Quote:
Originally Posted by Maksutov
This isn't idle speculation. While in high school I took a number of college credit courses in such things as molecular biology, physics, astronomy, etc. We essentially took as fact whatever the instructors told us. After all, we were just high school students.
Very true, and the reason why snowflakeuniverse needs to present his ideas somewhat higher up the academic food-chain.
Agreed.
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Old 07-June-2006, 04:00 AM
snowflakeuniverse snowflakeuniverse is offline
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The students will be given this note June 6, 2006

It is my belief that I have discovered the long sought for Unified Field Theory. If I am right, then this represents a major advancement in theoretical physics. What is called modern physics will become 19th-century physics and a whole new era of physics will begin.

Such a claim deserves skepticism.

Be skeptical, if what is presented does not make sense, question it.

You will be asked to decide if the model presented seems valid to you. If you do, I will be asking you to help me have others with a more extensive knowledge and experience in physics to seriously review the work.

I want to present a paper for the members of the American Astronomical Society this coming January. The paper will take about 45 minutes explain. I will show that there is no need for Dark Energy to describe the relationship between the observed brightness of Type 1a supernovas and their corresponding cosmological red shift.

I will also show that the model can eliminate the necessity for Dark Matter.

I will also show how this theoretical model establishes the foundation for a Unified Field theory.

If you think the theory deserves a serious review, then please contact Kelli Gilmore at the American Astronomical Socity. Email address is . gilmore@aas.org

Kelli Gilmore is a part of the Committee that decides what topics and speakers will be invited at the next meeting. Technically, we are a few days past the date for application but the members of the committee are still being assembled.

Please, if you honestly think others more experienced in the field should review the theory, make the request.

If want to review and evaluate the reactions others may have to this presentation, I have tried to include most, if not all that will be presented to you today at a web site called Bad Astronomy and Universe Today.

The direct link is
Critiques of Presentation of Uniform Expansion Theory

It might be easier use a search engine
Search for “BAUT”
Click on “Against the Mainstream”
Click on “Critiques of Presentation of Uniform Expansion Theory”

Thank you for your time and interest.

John M. Kulick



The following is roughly what I will be presenting to the Students.

The Uniform Expansion theory

The Limited Expansion Model – The mainstream model
The current expansion model is a limited expansion model in that the expansion is assumed to stop at the boundary of galaxies. The common example used in most astronomy texts is that of pennies representing galaxies, which are glued on to an expanding balloon. Another common example is that of raisins in expanding dough. Neither the pennies nor raisins expand with the expansion of the medium they are in.

The following links substantiates the assertion that the mainstream model stops the expansion at the boundary of galaxies. In the classroom presentation I will read a quote from John Wheeler, one of the authors of “Gravitation”.
http://www.madsci.org/posts/archives...1542.As.r.html
http://www.universeadventure.org/universe_15.html
http://www.astronomycafe.net/qadir/q2405.html
http://www.astronomycafe.net/qadir/q1950.html
http://www.astronomycafe.net/qadir/q1384.html
http://www.ktca.org/newtons/10/galaxy.html
http://www.as.utexas.edu/~sheila/exp...se_updated.pdf
http://msowww.anu.edu.au/cas/present...y%20Mould.html

There are several reasons or arguments for stopping the expansion at the boundary of galaxies.
1. Galaxies are gravitationally bound. A clump of distributed mass has a tendency to pull together due to gravitational interaction between the masses. Stars in a galaxy are no different and would “fall” to the center, thereby resisting the expansion of spacetime.
2. If one extended the expansion to include galaxies, where does the expansion stop?
3. If Solar systems expanded, the planetary systems would fly apart since the gravitational force would diminish faster than the centrifugal. (Fg ==1/R^2, Fc == 1/R).
4. If Atoms were expanded, electrons would no longer be bound to the nucleus for the same reason that solar systems fly apart.
5. If atoms expanded, than all rulers used to measure the expansion would be expanded. If everything expands the same amount, and all the rulers used to measure the expansion expands the same amount, then everything remains the same and there is no expansion.

No Problem
The above issues are not a problem, as will be shown in the development of the theory, but before delving into the details, there are a few statements about the proposed Uniform Expansion theory that should be made.

The effect of gravity diminishes with the passage of time
It is invalid to say that a true uniform expansion that expands matter results in no change. If objects are uniformly expanding, then the centroidal distances between the objects is increasing. This means that the effect of gravity will diminish with the passage of time. For example, if the Earth were to be expanded to twice its present size, the effect of gravity on the surface would diminish by 1/4. (1/R^2) A prediction of this model is that the effect of gravity diminishes with the passage of time. Two Nobel Prize winners in physics, Paul Dirac and George Gamow, believed the effect of gravity diminishes with the passage of time. Dirac tried to establish a model but was never successful. I have done what he tried to do. (Unless someone proves me wrong).

Stronger Gravity negates Dark matter and Dark Energy
If gravity were stronger in the past and the gravitational relationship between objects is described by when the relationships are formed, then there should be observational evidence of this effect. Orbiting objects should appear to be in a stable orbit even though it presently looks like there is not enough mass to preserve the orbit. The larger the separation in time between objects, the greater the gravitational attraction should be and if one did not know this, the amount of extra unseen or “dark” matter needed to preserve orbiting clusters of galaxies would seem to increase with scale.

Also, if the effect of gravity were stronger in the past, it would take less mass for a Type 1a supernova to reach the Chandrasekhar limiting pressure. Less mass would mean a smaller supernova that would be dimmer. If one did not know this one would assume that the supernova was further away, requiring the existence of some kind of dark energy moving these galaxies further away. (The paper I wish to present to the AAS is the application of the relationships predicted by the Uniform Expansion theory to 1asn’s. It turns out that the expansion rate conforms to a flat and not an accelerating universe).

Uniting Gravity with Electromagnet relationships
One advantage of a uniform expansion theory is that it is a process that can be geometrically applied to all physical properties. It will be shown that with the proper rate of geometric expansion, the inverse square laws are derived as a characteristic of spacetime, thereby uniting the force of gravity with electromagnetic forces under the same causative structure. The principles of conservation of momentum and energy, which are observationally assumed, become geometrically established by a uniform expansion.

Quantum Physics
A uniform expansion theory also creates a physical explanation for Quantum physics. If the expansion of spacetime occurs a small “piece” at a time, then as each infinitesimal piece of spacetime integrates itself upon the existing structure of reality, there will be a probabilistically determined variance or disturbance.

A True Unified Field Theory
Since the relationships of Quantum Physics and the inverse square laws can all be predicted as a result of the same physical process, the uniform expansion theory represents a major step in establishing a Unified Field Theory. A fundamental property of this theory is that all physical relationships are the result of a geometric expansion of spacetime. It is all geometry.

Continued with next post.
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Old 07-June-2006, 04:05 AM
snowflakeuniverse snowflakeuniverse is offline
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A True Uniform Expansion Model

Absolute Measures

Absolute and Relative measures of Distance (Expansion and the “Eye of God”)
We can use a ruler to measure the size of a pizza. If the pizza and the ruler proportionally expand the same proportional amount, it is impossible to describe the change using our relative rulers. However, if we look at the expanding ruler and pizza from an “Eye of God” perspective we can see how much bigger the ruler and the pizza have gotten compared to their initial observed size. A uniform expansion introduces two measures of length, relative and absolute. Humans measure the Universe in relative terms and God measures it in Absolute terms. As humans we would have no direct local measure of a uniform expansion and it takes an “Eye of God” like perspective to describe the expansion.

Absolute and Relative Time
Relative time is defined as the time interval between points, with the speed of light defining the interval of time. Relative time is also the measure of time we use locally. The cumulative measure of relative intervals of time is experiential time.

Absolute time demarcates a point’s location historically, relative to the moment of creation, the beginning of time, or the “Big Bang” if you prefer. We each have a unique moment in history. Absolute time is unique.

An Absolute measure of time is needed in this model for the same reason an absolute and relative measure of length is necessary to describe a uniform expansion. All clocks and physical process slow down at a geometrically defined proportional amount with the expansion of spacetime. In order to describe how our relative measures of time are all slowing down, an absolute or fixed reference to measure time is necessary, it is necessary to use an “Absolute Clock”.

All Clocks slow with the expansion of spacetime
A brief explanation as to why clocks must slow with the expansion of spacetime is realized by considering a Pendulum. If the length of a pendulum increases, the period increases. It was also stated that in this model the effect of gravity diminishes with the expansion of spacetime, since the centroidal distance between the center of mass of the pendulum and the Earth increases. This diminished effect of gravity would also increase the period of a clock. What is especially surprising is that all clocks and physical process slow down the same proportional amount, preserving the relative measure of time. The only way to describe how our relative measures of time are slowing down is to establish a “fixed” or absolute measure of intervals of time.

Why use “absolute” measures?
The advantage of using absolute measures is that they reveal a hidden geometry of nature. The inverse square laws become based upon a specific geometric expansion described by absolute measures of spacetime. Principles of conservation of Energy and momentum become geometrically defined by absolute measures. It is all geometry.


Continued next post
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Old 07-June-2006, 04:06 AM
snowflakeuniverse snowflakeuniverse is offline
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Physical description of the model
The Physical Characteristics of the Uniform Expansion Model are as follows:
1. The expansion is uniform, meaning that matter expands with the expansion of spacetime
2. The expansion is easiest to describe in absolute measures since all local or relative measures appear constant.
3. The expansion occurs at a specific geometric rate, double the age of the universe and the volume of absolute space increases 4 times. (Relative measures of spacetime remain constant)
4. The expansion includes an extra dimensional relationship. Just as we can imagine a Flatland universe moving from expansion along an unobserved dimension, so too is our universe moving and expanding along an unobserved dimension.
5. The velocity of our Universe along the unobserved dimension is conjectured to be the square root of two times the speed of light. This way the Kinetic Energy of a Mass moving along the unobserved dimension corresponds to what Einstein called the “intrinsic” energy of a rest mass. Va = sqrt 2 c. (c = speed of light) K.E = 1/2 mVa^2, = mcc.


All the fundamental laws or principles of physics are based upon a geometric expansion of Spacetime.

Continued next post
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Old 07-June-2006, 04:10 AM
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Derivation of the Ratios of Time Formulas
The derivation of the formulas describing the uniform expansion of spacetime was originally posted in this thread My (Discovered) Unified Field Theory . I have neatened a few things up for repeating them here but I do not wish the comments and analysis of others who have already reviewed the formulas to be ignored since the comments and insight they provided was good and they helped me to improve or make clearer this explanation.

The basic geometry

Nomenclature
Relative measures of time and distance are written with lower case letters. Absolute measures are capitalized. When a letter is followed by a 1 or 2, such as T1 or T2, this establishes which measure is earlier and which is later respectively.

Before delving into the details the result can be simply stated. A volume of spacetime varies to the square of the absolute time elapsed. If you double the age of the universe, the absolute volume enclosed increased 4 times. Simple but tricky. There will be no local indication of the increase in size since all local relative measures of distance have similarly expanded.

The initial idea.
One day I realized that if nothing ever changed, time would not exist. Stated in the positive I thought; “Because space changes, time exists”. This led to the following equations.

S = Volume of Spacetime
T = Absolute time

dS/dT = T, Because space changes, time exits.

Integrating this relationship yields, in its simplest form,

S == T^2

(The == notation can be considered as meaning “proportional to”, but the relationship is more analogous to the relationship described by the speed of light, a relationship between distance and time).

The volume of any object is a distance measure cubed, times some constant,

D^3 x k = S = A Volume of spacetime.

Combining the relationships results in the following

D^3 = k T^2[/b]

Note; this is the exact form of Kepler’s Third Law. This is not a coincidence; the theoretical model truly produces Kepler’s law. It will be shown that this is indeed the relationship predicting the inverse square law required for celestial stability and the principle of conservation of momentum. Kepler’s law, which was experimentally established, is now theoretically predicted from a geometric model. Epistemologically, the relationship proposed, (dS/dT = T ), is as important a relationship as E= mcc, or e = hv

Rewriting the above equation we get

D = k T^(2/3)

Taking the first derivative with respect to absolute time we get how the absolute velocity will vary for two points in spacetime

V = k (2/3) / T^1/3

Similarly for Acceleration we get

A = (-k 2/9)/T^(4/3)

We do not know the value for k but since this is a geometrically described rate of expansion, it is possible to state that at a particular time, T1, points in spacetime are a particular distance D1. Similarly at another later time, T2, the objects are at location D2. Dividing the two relationships by each other eliminates the constants resulting in

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

Similarly for Velocity and Acceleration we get

V2/V1 =(T1/T2)^(1/3)
A2/A1 = (T1/T2)^(4/3)

These formulas are actually field formulas in that they describe, in absolute measures, the properties of an object when associated with a point in free space. (Free space means that no other unaccounted force is acting.)

The Ratios of Time
(Capitol letters indicate “absolute measures”, 1 and 2 are earlier and later measures respectively)
D1/D2 == (T1/T2)^(2/3)
V2/V1 == (T1/T2)^(1/3)
A2/A1 == (T1/T2)^(4/3)
E2/E1 == (T1/T2)^(2/3)


E = energy, which for now can be considered just the square of the velocity term but this relationship is valid for all forms of energy in which spatial relationships are involved.

(Nuclear energy appears to be a partial exception to these relationships of expansion. It seems that at the nucleus, the expansion of spacetime does stop; nuclear relationships involve measures that are essentially fixed in size. This is discussed in more detail in the paper on Type 1a supernovas).

Physical Explanation
The physical relationships that the Ratios of Time formulas describe need some explanation. The basic derivation of the formulas was based on considering a small discrete volume of spacetime. Within this discrete volume of spacetime physical relationships concerning Absolute measures of Distance, Velocity, Acceleration, and Energy are described.

Consider a Balloon and its enclosed volume to represent the discrete absolute volume of spacetime. If we were to reduce the surface tension in the balloon, the balloon would expand, which is analogous to our expanding spacetime. Molecules of air hitting the retreating walls of the expanding balloon would rebound with less energy and the velocity of the rebounding air molecules would decrease. This slower velocity would eventually be shared with all the molecules in the balloon and the temperature of the air in the balloon would drop. Similarly a discrete or infinitesimal object with its own velocity within a discrete or infinitesimal volume of spacetime will also “lose” velocity as spacetime expands.
(Drawing of expanding balloon with “relaxed” walls used for class).

A mass can be considered a collection of discrete points residing in a collection of discrete absolute volumes of spacetime. Since the collection shares the same physical relationships as its parts, it is possible to generalize the relationship to the entire collection.

If an object has a given absolute velocity, then according to the derived relationships, the absolute velocity of the object should slow with the expansion of spacetime, just as the molecules within an expanding balloon all slow down in an expanded balloon.

Now comes the amazing part , Time
These changes in absolute measures of distance, velocity, acceleration and energy cannot be locally observed using relative measures. It is only from the “Eye of God” perspective that these changes can be described. If an object slows to 1/2 its original absolute velocity, all local measures of time, or all local physical process will also slow to 1/2 their original rate. Just as all relative measures of length maintain their proportional measure in a uniformly expanding spacetime field, all relative measures of time keep their proportional measure.

Continued
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Old 07-June-2006, 04:15 AM
snowflakeuniverse snowflakeuniverse is offline
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Physical relationships and Time

It has been proposed that all relative measures of time slow with the expansion of spacetime. This will be verified for the following physical processes.
1. A light Clock
2. A pendulum
3. A spinning planet or object
4. An orbiting planet or object


The Ratios of Time
(Capitol letters indicate “absolute measures”, 1 and 2 are earlier and later measures respectively)
D1/D2 == (T1/T2)^(2/3)
V2/V1 == (T1/T2)^(1/3)
A2/A1 == (T1/T2)^(4/3)
E2/E1 == (T1/T2)^(2/3) [/b]

The light clock,
Based upon absolute measures, the speed of light slows and the distance the photon must travel increases with the expansion of spacetime. This means that based upon absolute measures it is going to take a photon longer to travel back and forth between two mirrors. Locally there should be no indication of the change, which requires all physical measures of time (except nuclear decay rates) to all slow down the same proportional amount. Sounds impossible, but it is actually amazing.

First off, the change in distance is not observed since proportionally everything else proportionally expands. This leaves the challenge of checking that all measures of relative time also stay the same.

Using the Ratio of time formula describing how the distance the photon travels will vary, we have
D1/D2 == (T1/T2)^(2/3)
If the age of the universe were to double, the corresponding increase in absolute distance is
D2/D1 == (T2/T1)^(2/3) = 2^(2/3) = 1.59… The light clock is longer by this proportion.

Note that since the age of the universe is billions of years old, and the ratios of time formulas use this measure of time as a basis for describing relationships, events over a few thousand years represent a small, almost insignificant change.

Using the Ratio of time formula describing how the speed of a photon changes with the expansion of spacetime,
V2/V1 == (T1/T2)^(1/3)
If the age of the universe were to double, the corresponding decrease in the absolute velocity of the photon is
V2/V1 == (T1/T2)^(1/3) = (1/2)^ (1/3) = .79….

In the case where the age of the universe doubles, it would take the photon D/V = 1.59/.79 = 2 times longer to describe a cycle.

Generally the relationship is
D/V = interval of time = D2/D1 / V2/V1 = (T2/T1)^(2/3) / (T1/T2)^(1/3) = T2/T1. Double the age of the universe and the interval of time described by a light clock doubles.

A pendulum
The Period of a pendulum is = 2 pi x (l/g)^(1/2).

The length of the pendulum changes with the expansion of space-time. The locally experienced acceleration is also effected since the centroidal distance is increased with expansion. Rather th