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A

The following paper was taken from [http://msu.edu/~micheals/roadmap.xml Gravitation and Elementary Particles], a publication of the [http://msu.edu/~micheals Faraday Group]. The article is posted on by the author - for Gravity, Recent alternative theories.

3. Temporal Curvature

A New View of Gravity – A Distributed Compression of Time
Salvatore G. Micheal, Faraday Group, micheals@msu.edu, 11/17/2007

Y0, the elasticity of space, is defined and calculated. Linear strain is calculated for electrons and protons. In the process, after a few assumptions, a new relation between temporal curvature and spatial curvature is established. Needed work is reviewed.

From the previous paper on frame-dragging, we invented a new relation between mass and the linear strain of space:
λ0 = Y0μ0ε0(Δl/l) (1)
mass per unit length (implicit) is linearly related to extension through the three parameters of space: elasticity, permeability, and permittivity

We had some trouble defining an appropriate Y0, the elasticity of space. Recall that the basic constraint on Y0 is that it must be consistent between elementary particles (and of course its units must agree with the equation above). Let's make a few standard assumptions which should not cause too much of a ruckus. Of course, those must be verified (or at least – not disproved) – as the consequences of those assumptions must also be verified. Until now, we have not made the 'per unit length' explicit. Let's do that and assign the Planck-length:
λ0/lP = Y0μ0ε0(Δl/l) (2)
This is a place to start and we'll follow a similar convention when the need arises. Let's replace lambda with the standard notation and move lP to the other side:
m0 = (Y0lP)μ0ε0(Δl/l) (3)
Multiply by unity (where tP is the Planck-time):
m0 = (Y0lPtP)μ0ε0(Δl/ltP) (4)
Now, the first factor on the RHS is 'where we want it' (units are in joule-seconds). And, the fact we had to 'contort' the extension by dividing it by the Planck-time should not prove insurmountable to deal with later. Finally, let's assume the first factor is equal to the magnitude of spin of electrons and protons, ħ/2:
m0 = (ħ/2)μ0ε0(Δl/ltP) (5)
By our last assumption, Y0 = ħ/2lPtP ≈ 6.0526*1043 N. To simplify and isolate the extension:
m0 = (ħ/2c2)(Δl/l)(1/tP) (6)
> (Δl/l) (2c2tP/ħ)m0 = 2(tP/ħ)E0 (7)
So, the linear strain of space due to internal stress is directly related to rest-energy through a Planck-measure. Later, if space allows (pun intended), we will show that (7) reduces to an even simpler form involving only two factors. If our assumptions hold, the numerical values for (7), for electrons and protons respectively, are approximately:
8.3700*10-23 and 1.5368*10-19.
The values are dimensionless – per the definition of linear strain. The meaning is: 'locally', space is expanded (linearly) by the fractions above (assumed in each dimension). What exactly locally means – will have to be addressed later. The numerical value of Y0 is extremely high as expected. All this says is: space is extremely inelastic. The numerical values for ∆l/l will have to be investigated – perhaps as suggested in the previous paper.

Let's deal with our assumptions first. The notions of Planck-time and Planck-length are associated with 'minimum measures' conventionally. Anything less is considered physically meaningless. If there is a fundamental limit on our precision in measuring things, we consider those to be lower bounds. If we could make a 'meter stick' with a length of the Planck-length or a clock that 'ticked' per Planck-time, that would be the limit of our technology – physically imposed by the nature of our Universe. So, to use them above is not a huge stretch of our 'belief system'. Our first assumption, to employ 'mass per Planck-length', is not implying we assume electron masses are actually divided into small parts of m0/lP. It simply means that's the limit of our measuring ability – and that we associate a linear change in space (for now) with that minimum measure.

Conventionally, we think of m0, E0, ħ, c, and tP as fixed. If any of them varied, that would throw physics into chaos, right? But that is exactly what quantum mechanics has tried to cope with since inception: the seemingly statistical variation of m0/E0 about some modal value. Fortunately for science, ħ and c do not seem to vary statistically.

The fact we had to introduce tP above in order to simplify the expression for extension, is only the completion of another expression of uncertainty. That's the conventional view. Another perspective is to view that change in space per unit time. There are two further ways to view that: as the propagation of the gravity wave of a newly minted particle – or – as the locally changing extension over time. If we tentatively adopt the latter view, this provides a natural/integrated explanation of uncertainty. The only 'problem' is that the linear increase in extension cannot go on forever. It must necessarily oscillate. The simplest form of modeling that is with a saw-tooth wave (and slope ±âˆ†l/l). We could get a little 'fancier' and model with a sinusoid. The critical factors are: amplitude and wavelength. Amplitude is associated with the variation in rest-mass/energy. Wavelength is associated with the choice of period: Planck-time, de Broglie 'period', Compton-period, or relativistic-period? The first appears too small (and arbitrary), the second is not properly defined for particles at rest, the third does not account for relativistic effects, so we are left with the fourth. The fourth is based on the third but takes into account time-dilation.

For consistency with relativistic-mass, relativistic-energy is defined as:
E ħω E0/γ (8)
where omega is the relativistic-angular-frequency and gamma = sqrt(1-(v/c)2). For consistency with time-dilation, relativistic-period must be lengthened:
T = T0/γ (9)
where T0 is the Compton-period of a particle at rest. Let's repeat equation seven here for convenience:
(Δl/l) (2c2tP/ħ)m0 2(tP/ħ)E0 (7)
If we notice that heavier particles have larger extensions (comparing protons and electrons), we can replace every variable above with its relativistic counterpart (let's also give the extension a new name, X):
X (2c2tP/ħ)m 2(tP/ħ)E (10)
But because of (8), (10) can be rewritten:
X 2tPω 4πtP/Tγ2 (11)
relativistic-extension is two times the Planck-time times relativistic-angular-frequency which is also equal to the ratio of Planck-time to relativistic-period through a solid angle! (gamma-squared is a scaling factor from the relation ν≡1/Tγ2.)
For particles at rest, (11) reduces to:
X0 = 4πtP/T0 (12)
extension is the ratio of Planck-time to period through a solid angle
You can't get much more intuitive and simpler than that!

One way to think of gravity is as curved space. Another way to think of gravity is as curved time (only). An object in a circular orbit (around Earth) is following a 'straight line' path (of least action) through curved space – or – is following a path of same temporal curvature. An object in free-fall is following a straight-line path to the maximum of spatial curvature – or – is following a path to the maximum of temporal curvature. Gravity can be analyzed exclusively as a distributed compression of time. (All trajectories can be treated as a linear combination of those two orthogonal trajectories. They are fundamentally different in terms of temporal curvature. All extended objects experience a gradient on different parts of their extension – it’s not just the ‘steepness of the hill’ which pulls them down. In the same way, time is infinitesimally slower on the ‘low side’ of an object in orbit. Objects move to maximize time-dilation.)

The analysis above has shown that, with a few assumptions, there’s an equivalence between spatial and temporal curvatures. So, another way of looking at particles is as:
charged twists of space
and localized compressions of time.
What 'local' means still needs to be defined (not in a tautological way) precisely. A preference needs to be established – in viewing curvature – such that characteristics of space-time (such as Maxwell's relations) are more easily exhibited. Those characteristics need to be derived from (1). The other theoretical tasks need to be performed (set in the previous paper). The two experiments from the previous paper need to be performed. If there is indeed a deterministic oscillation in mass/energy/extension, that needs to be experimentally verified. A small joke was forgotten to be placed in the previous paper: “Don't cross the beams .. Never cross the beams!” ;)

The following article is a list of fictional minor characters from the Japanese manga and anime series Marmalade Boy, many of whom are exclusive to the anime. For a list of other characters, see List of Marmalade Boy characters.

Minor characters
Yoshimitsu Miwa
:
:

Satoshi's father and a renowned architect. Yuu suspects that Yoshimitsu may be his actual biological father based on a letter his grandmother had written to Youji Matsura when he was engaged to Chiyako while she was working for Yoshimitsu. Satoshi suspects this as well based on the mention of Chiyako in his mother's diary as the woman his father was having an affair with.

When confronted with the accusations by both Yuu and Satoshi however, Yoshimitsu denies that he is Yuu's father. He explains that he was interested in Chiyako, but she was in love with another man and continually rebuffed him. He did not attempt to dissuade his wife that he was seeing her because it served as a cover for him to see other women. His son Satoshi is exasperated by his admissions of his past misbehavior.



Takuji Kijima

:

The owner of "Junk Jungle", a clothing store where Yuu works part-time. He has known Ryoko and Namura since college and dated Ryoko during that time. However, when he realized that she was falling in love with Namura, he distanced himself. Ryoko comes to confide more in him as she attempts to reconcile her feelings about Namura.



Chigusa, Keiko & Mari
:Chigusa voiced by:Yuko Nagashima (Japanese), Wendee Lee (English)
:Keiko voiced by: Naoko Nakamura (Japanese), Cindy Robinson (English)
:Mari voiced by: Mariko Onodera (Japanese), Kate Davis (English)

The friends of Miki and Meiko in Toryo High School. Chigusa is the one with pigtails, Keiko wears glasses, while Mari has short hair. Chigusa and Mari are in the tennis club along with Miki and Ginta.

Furukawa
A reporter for Toryo High School.

Principal
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The principal of Toryo High School. He is quite kind-hearted and understanding of the teachers and students. He likes Namura and is reluctant to see him go after his relationship with Meiko is exposed, but is forced to accept his resignation.

When Miki and Yuu's family backgrounds were exposed and the two were summoned to the Principal's office, the Principal tried to calm their nervousness by telling them that the school was only trying to understand the whole situation. After Miki and Yuu's parents arrived and explained their circumstances, the Principal gave Miki and Yuu his approval, telling them that they have wonderful parents. This approval finally relieved Miki of the pressure and uneasiness she had for her new family, allowing her to see them in a new light.


Vice Principal

:

The Vice Principal of Toryo High School. Unlike the Principal, she is more cold, severe, and unsympathetic towards the teachers and students. He is surprised at the regard Namura's class holds for him, especially when Ginta firmly stands up to her for openly criticizing Namura in front of them.

When Miki and Yuu's family backgrounds were exposed and the two were summoned to the Principal's office, the Vice Principal openly criticized Miki and Yuu's parents, and was shocked when Yuu firmly talked back to her. However, she was forced to silence herself when the Principal gave his approval to Miki and Yuu.

While often referred to as "Kyoto", this is not actually a proper name; the term translates as Vice Principal. Like the Principal, the Vice Principal's name is never given throughout the course of the series.



Raihito Sakuma
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Suzu Sakuma's father and the brother of Satoshi's deceased mother. He is also a famous architect, and helps Yuu with his dreams, telling him to transfer to the USA.

Anime-only characters
Ryoko Momoi

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A teacher at Toryo and friend of Namura since they were younger, Ryoko is in love with him, but the feeling is not mutual. In fact, Namura didn't know about Ryoko's love for years, until she confessed to him during Christmas. That surprises him so much that, in the end, he actually apologizes for all the hurt he inflicted into her without knowing it. Ryoko works hard to get over Namura and succeeds, later hooking up with Akira Mizutani, a young man who is the brother-in-law of her friend Takumi Kijima.

She is also a coach in the tennis club along with Namura, later becoming the homeroom teacher of Miki, Yuu, Ginta, and Meiko's class after Namura's resignation.

Anju Kitahara
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:

Yuu's old childhood friend and first love. He calls her "Anne" because of her favorite book, "Anne of Green Gables". She suffers from a heart disease that she has had since childhood; in fact, they met in the hospital. Although she still harbors feelings for Yuu, she understands that Miki is his true love, and tries her best not to get into their relationship; in her own words, she only wants to be second in his heart.

Anju decides to go to the USA to both have an operation and take violin classes after she has a heart attack during Christmas and almost dies. In America, she reestablishes contact with Yuu and befriends Bill Matheson.

Yayoi Takase

:Voiced by: Mariko Onodera and Miki Inoue (Japanese), Jennifer Sekiguchi (English)

A girl whom Tsutomu meets at the temple on New Year's Day while he is walking around cursing the bad luck fortune that he received. The two hit it off, but Tsutomu forgets to get any more information from her other than her name and that she is about the same age as him. He does not run into her again until Valentine's Day, while he is bemoaning not receiving any Valentine's chocolate while in the park. Tsutomu overhears Yayoi get turned down by a boy she is interested in, and encountering her again, cheers her up and shares her chocolate with her. Yayoi then officially became Tsutomu's girlfriend, often appearing with him later on as a couple.

Michael Grant
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:

An American exchange student from Toryo's sister school in New York City who stays with the Matsuras and Koishikawas. He is a year younger than Yuu and Miki. Michael develops a crush on Miki and tries to come between her and Yuu when Yuu is in New York, due to some information that he misinterpreted, thinking that Yuu is a two-timer and cheated on Miki with Jinny.

Brian Grant

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Michael's older brother, good-hearted yet with a horrible temper. He thinks of Jinny as his girl, but her flightiness and flirtation with Yuu frustrate him. Brian eventually challenges Yuu to a basketball game over Jinny that he ends up losing, but the two end up as best friends as a result.

William "Bill" Matheson
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Brian's friend and Yuu's roommate. His behavior leads his friends to think that he is gay, but this just an act on Will's part to get closer to Jinny. He is witty, intuitive, and supportive, and gets along well with everyone.



Doris O'Conner

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A voice of reason and counterpoint to Jinny, Doris likes Brian but has not made her feelings known to him, since she thinks men will only see her as a best friend but not date material. She finally declares her love for Brian when Jinny gets together with Bill.



Jinny Golding
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:

Highly attractive, childlike and well-intentioned yet very impulsive, Jinny develops a crush on Yuu as soon as she sees him and tries very hard to make him forget about Miki, even playing a bad prank on Miki by leading her to think that she had a one-night stand with Yuu, who in fact was not even in the dorms. Unbeknownst to her, this triggers Yuu and Miki's break up. Bill and Doris make Jinny take conscience of what she had done and sincerely repentant, she apologizes to Yuu. After Yuu finally rejects her, she starts to become anxious of the attention Bill gives to Anju. When she confronts him about this, Bill tells her he has been in love with her from the beginning.



Rei Kijima
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Takuji Kijima's wife. She helps Miki overcome her doubts over Yuu's behavior in relation to her while he is in New York, since she went through a similar experience with Takuji when they were younger.



Akira Mizutani

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:Rei Kijima's brother and Takumi's assistant. He has a crush on Ryoko, and she slowly comes to reciprocate his feelings.



Mr. Rainy
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The teacher of Yuu and the American characters in Yuu's boarding school.

Eddy and Chris
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: Eddy voiced by: Mami Matsui (Japaneses), Doug Erholtz (English)
: Chris voiced by: Naoko Watanabe (Japaneses), Jennifer Sekiguchi (English)

A pair of siblings Miki meets in New York City who help her escape from some thugs who target her, and help Miki reconcile the feelings she has for Yuu with knowledge of their possible blood ties.



The Gastman Team
:A group of five boys who are costumed and act as the super sentai team Gastman. They come across Miki when she is out one day and force her to play along with their games, but unexpectedly, Miki wholeheartedly jumps in. Unbeknown to Miki, her interaction with the boys is witnessed by Yuu, who falls in love with her before they actually meet. The Gastman Team only appears in the Marmalade Boy Movie.

Marmalade Boy minor characters