Tuesday, April 27, 2010

The Beginning of Times

From time immemorial we have been asking Why?

Why might be a tall order to explain.  I might be able to tell you how?...:)

The main characteristic of our lives is causality.  You write a blog in the morning, and you might be late to work..:) (so I will be fast..)

Causality means that current events are connected to past events through some action. In physics, that action is actual action-at-distance....Gravitation, Electromagnetism are forces which act at distance. Notice that I didn't mention the others (Electro-weak or Strong).  They play no role in my theory. Anything that acts at distance implies that you are interacting with the past.  It takes time for the field (dilaton field) to reach you.

There is an Anthropic Principle (which vaguely states as an answer for the why the Universe is like this - It is like this otherwise we couldn't ask this question right now and here..:) - a circular reasoning not unlike my hypergeometrical universe cross-sections...:)

The question I will answer is if there is a deeper understanding we can derive from the Hypergeometrical Universe theory that would provide an answer to that question with a little more details.

This picture has been used to explain how we peer into the past with our telescopes.  It also can be used to explain the Universe is causal and why we are the way we are...:) 

 Ooops, I guess I will explain the WHY after all..:)

Consider a point in a four dimensional spatial manifold.  Locally deform the metric such that the total 4D volume surrounding the deformation is preserved. The initial deformational mode is debatable (Y00, Y01, TEM00..::)  Now, allow for that deformation to decay into a gazillion spinning smaller deformations.

 I used spinning instead of rotating to emphasize the fact that the smaller metric deformation (spinning deformation coherences) are rotating within a 4D spatial manifold as opposed to our 3D rotating objects.

Some of them will annihilate each other resulting in a locally flat metric. The annihilation  (not unlike a eletron-positron annihilation) will generate dilatons (Gamma Radiation) which carry momentum.

Now let's consider that the dilaton-dilator interaction depends upon cross-sections, that is, how are the dilators aligned at time zero.  Only the dilators which are perfectly aligned with their largest cross-sections perpendicular to R (the 4D radial direction) will be pushed away by the extremely intense dilaton field. This is the synchronization or selection event.  Further interactions might contain a mechanism to resynchronize  (select) dilators as the Universe travels.

I mentioned R, but at time zero, R,Z,Y,Z are indistinguishable, thus one would expect that dilators would be flying at all directions with identical speed( the maximum possible while driven by an extremely intense dilaton field).  I will postulate that the whole Universe contained in a lightspeed expanding hyperspherical shockwave shell reached the speed of light.  This postulate will be immediately tested later in this blog when we consider the nonexistence of interaction or visibility cut-offs in this Universe.

Add to that picture the Quantum Lagrangian Principle and you will have an event that accelerated equally (to our observed c) all dilators in all directions (XYZR).

That scenario would correspond to all matter in the Universe being spin synchronized and accelerated to c at time zero.

Notice that at time zero, the very small hypersphere has interaction with a very close past and the dilaton field is hyper intense.  At that level, dilators are capable of reaching the speed of light in a single or couple of de Broglie steps.

The interaction with the past should deliver the maximum kinetic energy while allowing for the dilators to surf the dilaton field.  The condition where this happens is when the average dilator interaction happens at 45 degrees, that is the shockwave hypersphere has been accelerated to the observed speed of light, which is the same as saying that the tangential speed (along X or Y or Z) is equal to the speed of light. Both are true since there isn't a difference between tangential speed and radial speed for a point.

Being spin synchronized means that we are all here interacting intermittently (as the dilators spin), living in a thin hypersphere, always interacting with our past at 45 degrees (thus preserving the constancy of the speed of light.  This angle corresponds to the maximum interaction and the equipartition of energy along all four degrees of freedom (spatial coordinates) at time zero..

Imagine otherwise that we were accelerated radially at higher speed that laterally.  This would mean that all forces would not vanish with the inverse of the square distance but just have a cut-off...  Causality would be space dependent.  We would be blind to anything further than that cut-off distance.

Thus the WHY is explained with simple geometrical reasoning based on cross-sections of dilators to dilaton interaction at the Beginning of Times. That yielded the dilator spin synchronization and the intermittently interacting Universe (Quantum Mechanics).  Of course, QM also depends upon the QLP (Quantum Lagrangian Principle) and the inherent delocalization of dilators traveling in an out of a 3D hypersurface guided by dilaton interference patterns (three dimensional Lissajous pattern).

As you can see, if the Big Bang wasn't really Big (accerating everything to the maximum velocity) and if the Bang wasn't really isotropic (along all four spatial dimensions) we wouldn't have Cosmological Causal Relationships today.  The night sky would be darker and we wouldn't be allowed to see beyond a point in the Cosmos - Cosmic Censorship...:) of the worse kind.

The isotropy (Michelson Morley) of the speed of light is the direct result of the initial isotropic acceleration.
The causality is because we interact perfectly at 45 degrees with the past hypersphere, thus creating a no cut-off interaction....:)

Thus permitting us to stand in a cloudless night and watch the whole Universe ...

and ask that question...:) WHY?



Friday, April 23, 2010

Darn Retarded Potentials and the Beginning of Times…:)

Darn Retarded Potentials and the Beginning of Times…:)

In the past few postings I reached a conclusion which I cannot refute within the logical framework of my theory.

The conclusion I reached is that the actual speed of light is Sqrt(2) times the measured speed of light.:)

Or that light is faster than itself (or what we perceive as being its speed..:)

Up to now my mind has been living with a conundrum… a paradox. The equations of motion, the Unification Equation is derived from a simple principle that dilators never do any work as they move. There are two kinds of motion. Radial and lateral, where lateral means within our 3D Universe (a lightspeed expanding Hypersphere).

The equations of motion for lateral movement required the mapping of inertia to the footprint (on specific phases of the spinning motion) of the dilator on our 3D Hypersurface.

There was no equivalent inertia mapping for radial motion. That never caused a problem because we never had time to fully develop the initial Cosmogenesis process.

When I worked on calculating the age of the Universe from the Pioneer Anomaly, I had to struggle with something obvious that I had overlooked for a few years. The problem is the following: If I am surfing, can I make a wave on the surface of the wave and see it propagate? The solution to the old problem of waves in a wave eluded me for many years.

For a dilator to move always without doing any work, the fastest it can ever travel is surfing the dilaton wave generated by other dilators. The larger the dilaton field the highest the acceleration but the highest speed is always c (the observed speed of light).

The paradox is that lateral motion requires inertia while the initial setting in motion of the whole Universe never seemed to require inertia…:) I considered the motion of the dilator (which is a coherence thus not unlike a wave) to be traveling at its natural speed. That was satisfactory explanation until I faced the Pioneer Anomaly problem…;)

The dependence of the observed velocity as a function of observed Epoch (beta angle) was necessary to keep the dilator frequency unchanged. The Hubble related red-shifting had to do only with the geometric projection of the waves into the lightspeed expanding Hypersphere (our Universe).

For that to happen the actual speed of light had to be higher than the observed speed of light by a factor of sqrt(2).

This means that dilators always have the same amount of Inertia for both lateral and radial motion.

Retarded Potential

I remember when I read Landau and Lifshits for the first time about Retarded Potentials. We all know that the Sun is eight light minutes from us, that is, we are always seeing what was happening to the Sun eight minutes ago. The field propagation travels at the speed of light for both Gravity and Electromagnetism. This is convenient since both are described as dilaton field modulations in my theory.

First let's consider that the 3D Universe is already in motion. Here we have the Universe already in motion and all interaction between particles in different positions (relatively close) travel at 45 degrees and thus at c.
This is consistent with my Quantum Lagrangian Principle where dilators always surf the local metric dilaton field. The fastest this dilaton field can drag a dilator with its own local velocity or the observed speed of light (consistent with observation and relativity).

Figure 1 displays the geometry for peering or interacting with the near past. From the past blog, we established that the actual speed of light is sqr(2) times the observed speed of light.

I cannot create a perfect explanation. It would take time. On the other hand, it should be self-evident that this is the only solution to the beginning of times..:) just by looking at the following figure:

Figure 2. Interacting with the past.  One always interact with the past through Retarded Potenials...:)

It turns out that the same picture that describes how do we currently look into the past can provide insight on the first moment of this Universe.

Let's consider that in the first instant of this Universe there was two layers of Universe (Biverse)…:) strongly interacting (Gravitation, radiation) etc.

If you consider that the Hypersphere to be a point, tangential motion is the same as radial motion. The only angle which allows dilators to travel at the same tangential speed as the radial speed is 45 degrees interaction.

The symmetry of the problem forces that the radial acceleration to be equal to the tangential acceleration (think about this as basically a point in the 4D spatial manifold).

This means that if one consider that radial and tangential accelerations or speed should yield the same hyperspherical topology at the end if one starts from a point, them the interaction has to take place at 45 degrees and the equilibrium condition is all dilators traveling at the observed speed of light tangentially and radially at the beginning of times.

That acceleration took no time as motion is just the surfing upon the dilaton field. Given a strong enough dilaton field and everything will travel at the speed of light…:)

Is there a need for an initial Biverse? No it was just drawn to show the interaction symmetry. When one interacts with another the other is always in the past.  If this interaction is repulsive (as being blown away by gamma radiation, neutrino flows) the originator of the neutrino and the receiver of the momentum are always in different epochs (different radius) of the Universe.

When the Universe is a point, interaction that produces tangential motion also produces radial motion. From a point tangential motion is the same as radial motion.

If you consider that the Four Dimensional Big Bang (created by the dilaton field) creates equally distributed radial and tangential motions, then the speed of the shock wave Hypersphere has to be equal to the dilaton field speed divided by sqrt(2).

From that point on, all potentials were called Retarded Potentials…:)

One more point, in the past I proposed a bipolar (TEM01) initial metric deformation as the format of the initial metric deformation:

 This would lead to a bipolar hyperspherical Universe, that is, matter and antimatter would exist in different halves of the Universe with an empty boundary due to mutual assured annihilation of matter and antimatter...:)

It just happens that it is impossible to see anything farther than 45 degrees away from you, let alone 180 degrees from you.  By this reasoning we could never see any sign of the original annihilation unless we lived in that neighborhood.

Since then, I started thinking about TEM00. Well, that is also a possibility, in this case the Universe would be perfectly symmetric (not perfectly homogeneous).
In my Cosmogenesis reasoning, I considered that the creation of the Universe occurred together with a dimensional unfolding, that is, metric fluctuations not only changed the local spatial density but also the dimensionality of the space.  This reasoning was based on entropy considerations, after all the Universe where we live is a long lived fluctuation, certainly reversible but long lived due to entropy.

Not unlike finding your other half... It is possible but might take the age of the Universe..:)



PS- I found a more succinct argument.  Consider my Quantum Lagrangian Principle which I used to unify all forces and  to calculate form first principles Cosmological Constants (G, epsilon0, mu0 etc).  I explained that the dilators should always surf (dilate in phase with the surrounding dilaton field).  To dilate in phase, each dilator has to move at each de Broglie step of the hyperspherical Universe expansion.
This surfing takes place on both 3D and 4D, that is the dilator is always in phase with the dilaton field which is a metric deformation in a 4D spatial manifold. The only way that the dilator will be in phase with both the 3D projection of the dilaton field  and with the 4D dilaton field itself is if initially accelerated to the speed of light both tangentially and radially.  Starting from a point, the Universe was formed as a flash of lighspeed traveling dilators traveling within a lightspeed expanding hyperspherical shockwave. 

This is kind of succinct.  Please let me know if you can articulate it better.  I will be happy to post it and acknowledge your contribution to the discussion..:) Cheers

Sunday, April 04, 2010

Hubble Expansion and the Hypergeometrical Universe

Hubble Expansion and the Hypergeometrical Universe

Given that the Hypergeometrical Universe proposes a dynamic (lightspeed expanding hyperspherical Universe) topology for our Universe, it shouldn't be surprising that we have to revisit the interpretation of the Hubble constant and how one measures distance across the vast expanses.

Figure 1 displays the geometry for peering into the past. From the past blog, we established that the actual speed of light is sqr(2) times the observed speed of light.

I struggled a lot with this problem because it requires a Gedanken Experiment which I wasn't 100% sure about the outcome. The question is:
  1. Can one make waves on a wave and see them propagating along the wave?
  2. Can two pilots traveling in an open cockpit at the speed of sound hear each other speaking?
These seemingly simple questions (for a fluid dynamicist) bothered me a lot. If the two pilots could not hear each other that would imply that the speed of light is actually faster (sqr(2)* c) than the observed speed of light.

When I first derived the "solution" to this problem I simplified the problem just by considering a static hyperspherical reference frame. That introduced another constant into the problem (pi/3). The reason was the at any given Cosmological Angle, light travels in straight lines through the 4D spatial manifold, while we traveled along an arc. By the time light traveled all the distance to the 4D Center of the Universe, we would have traveled around the arc on an equilateral triangle inscribed inside a circle. I have to confess that this seems to be an artifact of how I tried to solve that problem. It gives a slightly older Universe than what we obtain when using the proper geometry:

The full treatment of the Pioneer Anomaly problem doesn't seem to require that constant.

Figure 1. Looking deep into the past.

This picture is quite telling. It shows the L0 radius of curvature of the time when the first stars lightened. At that time and at that radius of curvature, There was light… It is important to notice that light always travels at 45 degrees with the Fabric of Space – 45 degree with the tangential line at point A.

Under those conditions one can write the following equations for the relating L0, R0, Beta, LambdaObseved, CObserved – yes even the speed of light depends upon what are you looking at…

Let's start with the speed of light. Normally we are observing things close, in our neighborhood… solar system, galaxy… Under those conditions, beta is 45 degrees and point A is almost right radially aligned with B. The two hyperspheres look like two hyperplanes and can be represented by the figure below:

Figure 2. Pioneer Radar Gun Experiment. Looking into a few minutes in the past.

This picture shows the Pioneer experiment. Light, microwaves leave Earth on point A and bounce back from the Pioneer spacecraft on point B. This all happens as the Hyperspherical Ligthspeed Expanding Universe expands at velocity Cobserved. The observed value for the speed of light is c, what we are used to think at the velocity of light. It just happens that the observed velocity depends upon the angle of observation. If you are observing the beginning of times, them the angle Beta will be very small, otherwise it will be around 45 degrees.

where beta ranges from 45 degrees to zero degrees

is the actual speed of light which is faster than the speed of light we are used to… by a sqrt(2) factor.

Similarly, the wavelength of light depends upon what is the angle beta of observation.

This is expected, since the actual frequency of light shouldn't change. This also means that Hubble constant should depend upon how you calibrate it. Calibration is done using parallax and red shift or stellar candles and red shifts. These two calibrations are inconsistent since they look at different angles. One should use the near field calibration and then extrapolate it using the hypergeometrical argument.

Hubble equation relates distance with the receding velocity:

The Shifted Frequency is related to Hubble constant by the following equation:

Doppler effect equation.

The value of H is obtained when L is Ro. Under those considerations v becomes Cactual:

In summary, here we presented a geometric model for the Doppler Shift, that is, the change in wavelength has only to do with the 4D angle of observation. This angle cannot be drawn within the 3D Hypersphere since when looking into the past, one is looking outside the hyperspherical hypersurface.

Numerically, the modeled Hubble coefficient is a match to the experimental Hubble coefficient.

H=2.0637E-18 s^-1



PS - The most recent observational determination of the proportionality constant obtained in 2009 by using the Hubble Space Telescope (HST) yielded a value of H0 = 74.2 ± 3.6 (km/s)/Mpc.[4] The results agree closely with an earlier measurement of H0 = 72 ± 8 km/s/Mpc obtained in 2001 also by the HST.[5] In August 2006, a less-precise figure was obtained independently using data from NASA's Chandra X-ray Observatory: H0 = 77 (km/s)/Mpc or about 2.5×10−18 s−1 with an uncertainty of ± 15%.[6] NASA summarizes existing data to indicate a constant of 70.8 ± 1.6 (km/s)/Mpc if space is assumed to be flat, or 70.8 ± 4.0 (km/s)/Mpc otherwise.[7]

1 megaParsec = 3.08568025 × 1022 meters

1megaparsec/Km=3.08568025 × 1019


H=2.0637E-18 s^-1=2.0637E-18 s^-1* 3.08568025 E19 km/s/mpc=63.63 km/s/mpc

Where discrepancies are likely due to NASA averaging values from different epochs (beta angles).