SPECULATIONS ON TRAJECTORY OF PARTICLES OF MASS "m" (tangible or not) NEARBY THE SURFACE OF MASSIVE AND DENSE STARS (including the ones believed to be "black holes").

 

TOPICS TO BE DISCUSSED (“speculated”)

 

1 – SUMMARY

2 - SOME MATHMATICAL SPECULATIONS ON PARTICLES OF "mass m"

3 – MEASURING ANGULAR DEFLECTIONS DUE TO MASSIVE DENSE STARS

4 – CONSIDERATION FOR TANGIBLE MASS PATHWAY NEAR MASSIVE DENSE STARS

5 – LIGHT ENERGY PARTICLES PATHWAY NEAR MASSIVE DENSE STARS.

6 – 2nd UNIVERSAL LAW OF GRAVITATION x PATHWAY of high velocity PARTICLES NEAR MASSIVE DENSE STARS

7 – WHAT FORCES/ENERGY MAKE LIGHT ENERGY PARTICLES accelerate (even trans-light) and/or bend? As particles (tangible or “worth equivalent”) reaching velocities greater than the speed of light? What mathematical formulation is required for trans-light condition? It is like a glass separating the sub-light (our environment) to the trans-light (as if the water in an aquarium…). Relativity like phenomena stops being continuous, but only taking place when fulfill “discrete like quantum” (when conditions are fulfilled by the 2^nd type of Gravitational Inertial Energy and such energy providing explanation for light not bending. Or what energy is required for bending light or particles at very huge velocity?). Thus it provides the reason for validating Newton’s Law related to not changing rest condition or the quantity of movement of a particle in movement.

 

NOTICE: This entire message is of very speculative nature, as it will not follow what is believed (as TRUE FAITH, DOGMA) as correct in the Theory of Relativity. Thus after 1 century of viewing such Physic Events in just the same way, after 100 years it is proposed a new way of viewing such same events with other eyes and mathematical approach. Maybe it is totally wrong, or quite wrong as Caloric Theory. I hopped this way will open a new way for reasoning on things that people believe as if DEDUCTED with precision, being PERFECT in its essence: from direct revelation. When in fact it was just a FIRST STEP toward a broader understand of Physics.

 

http://www.geocities.com/celsosavelligomes/PARTICLES_BENDINGatTRANS-LIGHT_VELOCITY.htm

Besides posted material, in forum/group, the information is available at above site, with all features.

 

 

1 – SUMMARY celso-savelli

 

See the FIGURE 1, as it makes things easier. It will be available in this following site:

 

http://www.geocities.com/celsosavelligomes/DEFLECTION_NEAR-SUN.xls

In such file, at bottom, select "Chart1" to see the deflection near the Sun.

 

http://www.geocities.com/celsosavelligomes/DEFLECTION_NEAR-SUN.JPG

It is the drawing version, yet to be scanned and loaded in the NET.

 

 

I am 1,000 km far from home, visiting a farm where there is no cellular phone or NET. I have the above figure, in a more prefect way, but it requires scanning. It is easy to understand such .JPG drawing, as it is similar to the drawing "Chart1" in .xls file.

 

Consider a "hyperbole like" figure starting in the upper left side, as tangent to a horizontal line in point A (at – infinite past). Such horizontal straight line, tangent in point A, is shown going right to the point F, the interception with the other straight line, tangent in point E at + infinite future, of hyperbole after departing from A (star) which is the source of particles. The angle between the straight lines A-F and F-E, in the top right corner, is "A.D. =Angular Deflection": the deflection of trajectory (of tangible particles or light), as measured on Earth 100 years ago due pressure from Relativists (or at point E far from any nearby Massive Dense Star). In the drawing …Chart1.xls such angle of deflection at point F is almost 90 degrees=just for illustration.

 

The point F is linked by a straight line to the center "O" of such nearby Massive Dense Star, having a radius of "r" (from center to its surface) and over it there is a variable height of orbit, "h", which is "h_c" for orbit through the point C, the point of lowest height over the Massive Dense Star Surface: R=r+h. Thus, at C, particle is at greatest velocity (and kinetics energy: this is only for tangible matter "m", as electrons, neutrons…, etc.). 

 

In case of light energy (ruled by "packages" of FOTONS, each E_foton = H_Planck . f f=frequency), light velocity can’t increase (Einstein’s model they made dogma)… Thus kinetics energy of light particles remain the same, from point A to point B (generic one, between points A and C, in drawing is at half of angle A-O-C) to point C (the lowest point of orbit) to point D (generic one, between points C and E: in drawing it is at half the angle C-O-E) to point E (to be reached in infinite future time): always light particles will have the same and top velocity "C", in all such intermediate points (A to E), in hyperbole like pathway orbit around the massive dense star: velocity is constant.

 

We are only to rethink such Einstein’s model, because we are assuming Theory of Relativity as being a FIRST "GOOD GUESS" MODEL. Also because such model is so popular even among common people and in movies. Thus "relativity ideas became as true": as some cultures believes converted into unchangeable Dogmas for some faith/church of some civilizations: as 3 being 1 and vice-versa. Let us respect such civilizations dogmas and obtain what is good from them. What about keeping light speed, as first guess, as being top and constant value to obtain what is good from model?

 

Thus we are accepting, as first good guess, the centenary old model… Thus we must keep top velocity as constant for any light energy (as particles of energy which have inertia "worth" that of usual tangible mass "m", but true tangible mass can’t  reach light velocity because its "true inertia mass").

 

"BUT” for imposing light speed being constant and the maximum velocity, we have to change the way we measure distances and time intervals.  What about if there are Outer "Civilizations" measuring "Their" time in not Our linear standard time (as in Lorenz΄ theory) but based on Their TIME intervals changing in exponential power relationship in relation to Our time intervals. Should "They" change their TIME referential to our referential for measurements of our "time" for theory of relativity become universal?

 

Or should They keep Their peculiar TIME referential in which velocity of light changes with "TIME", as measured in Their DAYS? With Their DAYS linked to our years as 1 Their DAY = ours 1,000 of our years? (And Their NIGHT=DAY/2 being huge amount of moon months greater than 1,000., in Kadr night as TIME interval for one event?). "Our time in Our Years referential" = 10^{Theirs TIME in Their DAYS+3} and at Their TIME=0 it started our mortality. At Their TIME=7 DAYS started Creation. Such Their TIME is "just worth", "in our mortality time referential,  = 10⁷⁺³ = 10,000,000,000 = 10 billions ours mortality years ago"! Quite strange as originated from data of some main Earth cultures + speculations (as strange as if "n" are 1 and vice-versa (a cultural fruit).

 

Such OTHER TIME referential for measuring TIME is very strange! As strange as the way we measure time in Einstein’s referential: it became like Dogma for those having faith on theory of relativity as if being something perfect inspiration an deduction. But ALL our "truth" IS only RELATIVE, generally good and useful only for a limited time and culture and civilization... Worst is that such "DAYS TIME measurement" are at the foundations of 3 main Earth civilizations: all are the same essence but with some "minor?" cultural heritage divergences. Their equal small intervals of THEIR TIME are related to growing  worth of our time, expressed into very huge number of years according our usual time. They remain true Physical things, similar to ours, but expressed in very distinct way, as TIME x time measurements. See above! Thus our light speed is decreasing if measured with Their general TIME referential used since Creation. Thus our "speculations" about our "time referential and speed of light being our limit" are nothing so important if we don’t understand about what is "time" x "TIME"…

 

Thus we can change "real trajectory" of the orbit, quite like a hyperbole from A to C and to E, without changing the trajectory itself, but changing the way we measure time and distance intervals, for them provide light velocity remaining a constant. That way our civilization "imposed" that orbit velocity is constant (something "arbitrary", as first good guesses…). Thus we must distort measurements of time and space, imposing conversion rules on how to convert measurements "to fit into model".  

 

We impose such type of distortions, even in usual real world, as when we try to provide some "worth values" that are not based on standard physics principles, rather are very "intellectually arbitrary" ones. It is like energy light being similar to SOME aspects of usual matter: as having gravitational attraction… Thus light energy is handled like we do with "present worth" of billed water becoming "worth", in present, into much smaller value than adding up historic volumes, because they are not added as the original tangible billed volumes. It is not used the plain addition of volumes: correct for the physics scientists… Thus present volume is "worth" to such series of old billed volumes, computed in "other way and purposes": distorted as Theory of Relativity… We can do the same, using not REAL time and distances in orbit going from A to B and to C… and to E, BUT using WORTH like values we impose to fulfill some our desire!

 

WELCOME TO the THEORY OF RELATIVITY, for our referential = "usual time"!!!

 

 

 

2 - SOME MATHMATICAL SPECULATIONS ON PARTICLES OF "mass m"

 

 

 

It is "believed" (as if supported by FAITH and DOGMA) that a particle of "mass m" is coming from a far away distant (infinitely) star, and is traveling in a straight line "A to F", with a velocity "v" of "v/C" <1 if tangible matter and =1 if light energy particles (FOTONS). In fact particle at initial position A, has some start velocity, usually omitted. 

 

In both case (light and tangible matter) such particles have ENERGY, as KINETICS ENERGY, as they are traveling as particles and behaving as such. It is part of our cultural "faith" that usual tangible matter "m" has an internal energy contents of E_light = m . C² being the so top greatly famous Einstein’s equation relating usual tangible matter "m" and energy "E". Such equation was greatest supporter for nuclear program (for nuclear bombs and fission reactors as source of useful energy).

 

Einstein’s famous equation is quite FALSE or TRUE, depending the way we use or understand it. It is like the equivalence of heat energy (thermal) to work energy, similar to relationship "1 calorie = 4.185 Joules", or something like that. E_light = m . C² tells us a similar relationship. But in fact it does not include the notion of "nobleness of energy" being changed from less noble energy stage requires a great amount of residual less noble energy (as heat). We have such law making E_light = m . C² being of limited value, because usually only less than 1% (up to 2%, in theory) of usual matter "m" can be converted into light energy, even in the best theoretical reactors yet devised. It is like trying to convert quite cold steam (thermal energy) into 100% work energy. Impossible!

 

E_light = "EFFICIENCY OF CONVERSION (is missing)”. "m" . C²

 

Using such Einstein’s (incomplete) equation in the opposite way, as m_worth = E_light/C²: such m_worth provides "some aspects" of light behaving as usual tangible matter "m".

 

If particles of usual tangible matter "m" are being accelerated at a  velocity "v" smaller than to "C = light speed", they increase their ENERGY CONTENTS, because it is as if MATTER (INERTIA) is increasing, according this relativistic model and believes:

 

E_total = M_relativistic .  C² = m_tangible . C² / [ 1 - (v/C)² ]^(1/2)    Eq. 1

 

Thus    M_relativistic = m_tangible . 1/ [ 1 - (v/C)² ]^{(1/2)       Eq.2}

 

As result, as v/C increases, approaching 1, M_relativistic becomes very huge, approaching infinite. Almost infinite Energy is required to create additional mass into M_relativistic

 

We can develop in Taylor’s series the above expression E_Taylor=1 / [ 1 - (v/C)² ]^(1/2)

 

 E_Taylor = 1 +1/2 . (v/C)² + 3/8 . (v/C)⁴ + 5/16 . (v/C)⁶ + 35/128 . (v/C)⁸ +  63/256 . (v/C)¹⁰ +  231/1024 . (v/C)¹² +  3003/14336 . (v/C)¹⁴ + 45045/229376 . (v/C)¹⁶ + … Eq. 3

 

Replacing Eq.3 into Eq.2, we multiply E_Taylor by m_tangible and we obtain:

 

M_relativistic = m_tangible   + ½ . [1 +  3/4 . (v/C)² + 5/8 . (v/C)⁴ + 35/64 . (v/C)⁶ +  63/128 . (v/C)⁸ +  231/512 . (v/C)¹⁰ +  3003/7163 . (v/C)¹² + 45045/114688 . (v/C)¹⁶ +…] . m_{tangible .} (v/C)² .   Eq.4

 

M_relativistic = m_tangible   + FUNCTION of (v/C)²  and of m_tangible   Eq.5

 

We can reason (SPECULATE) that it is not the usual m_tangible   which is increasing. But we can see that the original m_tangible   remained the same: it is not depending on velocity "v" or "C" or ratio "v/C". In fact the SECOND TERM in Equation 5 is telling that a SECOND TYPE OF FIELD OF ENERGY, quite like GRAVITATIONAL (E_gravity = m . g. h), is acting ((v/C)²  as some type of g),  on m_tangible, generating the storage of a 2^nd type of gravitational potential energy. But such 2^nd gravitational (or alike in electricity or magnetism fields) field is not our usual gravitational field, which doesn’t have such properties. In fact, it is a second type of gravitational energy which opposes to all change of velocity and/or direction, for all type of particles, including of light.

 

This is just one speculation originated from Einstein’s equations reasoned in other way, thus stretching the limits of the theory of relativity. Without increasing of RELATIVISTIC MASS, but with increase of a 2^nd type of Universal Gravitational Field in which energy is stored (when opposing to increase of velocity, as to approach to "C", to velocity of light) or restored (when the light particles would tend to slow down their light velocity, as trying to leave a black hole star; also it acts when tangible particles are decreasing their velocity, as when "fired out" from the surface of a massive dense star, to move outward (vertically or in ballistic trajectory). It is as if such particles have available energy greater than only their visible kinetics energy… Not all energy added for acceleration becomes kinetics energy in accelerated particle and at greater and greater speed, less efficient are the accelerators, as most of the energy is stored in the field of 2^nd type of Universal Gravitation and such conversion (or leakage of energy into such hidden field) is reasoned as being the increase of INERTIA, of RELATIVISTIC MASS of particle being accelerated…

 

The traditional Gravitational Field is based on mass (INERTIA) of particles interacting and on their distances: only. The 2^nd law of gravitation is based only on the mass of the particle that will change or start movement and/or change direction of velocity: it is for storing such inertial energy or for providing it for event being feasible. What reacts against such change of situation or start of movement or change of direction of velocity? THE WHOLE UNIVERSE through 2^nd type gravitational field.  Thus it is something beyond Newton’s law on usual gravitation.

 

According Equation 1, the m_worth of light particles energy worth to tangible mass ""m", such light energy would have infinite energy, as such mass "m" would be increasing to M_relativistic = infinite with infinite energy at v = C. But this is not true, as particles of light energy travel always at v = C and don’t have infinite energy, but usually having only modest quantum of energy, in packages having energy amount provided by the Planck’s equation, as E_light = h_Planck . f, with "f " being frequency of light.In fact the full formula for the energy E, in a single mode of radiation at frequency f, and temperature T (it measures the "nobleness of light energy, linked to its frequency"), can be written is:

Here "h" is the new Planck's constant, and "k" is Boltzmann's constant. Thus E (radiation energy) is related to the nobleness (HOTness") level of light energy required to generate it (as from heat thermal energy and temperature of it). As if "hotter light = more noble energy at greater light frequency". The nobleness of energy increases when v/C increases. When approaching 1, M_relativistic becomes huge, approaching infinite. Thus infinite Energy is required to create additional mass to keep increasing M_relativistic and increasing the nobleness of energy in particle, as is typical in accelerator of particles: very noble energy in them.

 

 

3 – MEASURING ANGULAR DEFLECTIONS DUE TO MASSIVE DENSE STARS

 

Let us return to the FIGURE 1, which is originated from Physical phenomena (well known) that was foreseen based on theoretical modeling. It was almost confirmed in field measurements, during eclipse phenomena, some 100 years ago by measuring the angular deflection, between lines A-F and F-E. We should have in mind that not all the measurements were in agreement with the theoretical value. But it was adopted some type of average, quite like adopting and justifying the best approaching values. In any way it was a good start, considering it was just the FIRST GUESS for a new model. But such values, not in perfect accordance, became the support and foundation of the theory of Relativity, since its first days, some one century ago. What was to become a new pathway, very soon was turned into dogma, closing the road to further advancements. 

 

 

4 – CONSIDERATION FOR TANGIBLE MASS PATHWAY NEAR MASSIVE DENSE STARS

 

 

The model shown in FIGURE 1 is only reasonable for tangible particles, of mass m, like electrons, neutrons, etc. coming from very far away stars. Their open orbit will be HYPERBOLIC, following the pathway A to B to C to D to E, and having the Angular Deflection, measured at point F, between the tangent lines A-F and E-F, with A and F being sited at infinite distance.

 

This orbit is SIMILAR to the parabolic (closed) orbit followed by the most far away comets orbits of our Sun solar system. They orbit with HUGEST VELOCITY at the point C, the most nearby position of Sun crust surface (the least distance "h_C"). What happens is that the hugest potential gravitational energy in the comet, that one stored between point A (at greatest distance from Sun) and C (at shortest distance "h_c" from surface of Sun), is converted into huge free additional kinetics energy at point C. Such total kinetics energy at point C generates a huge centrifugal force (outward) which counter-balances the most intense gravitational field and attraction force at point C. Thus the minimum radius "R_c” is determined by the equilibrium of such forces. Greater the kinetics energy of the particle at point A (as at infinite distance, like originated from a far away star…), greater is the total kinetics energy at point C": thus greater is the radius "R_c" and "h_c^" over star surface.

 

 F_atraction = F_centrifugal = K_{univ. gravity} . m_part . M_star / R² = m_part . v_c² / R        Eq. 6  

v_c     = ( K_{univ. gravity} . M_star / R)^(1/2)    or    R  = K_{univ. gravity} . M_star / v_c²  Eq, 7

Kinetics energy at "C" = kinetics energy already at "A" (m_particle . v_A² /2) + stored potential gravitational energy released as work between "A and C" = m_particle . v_c² /2     Eq. 8

 

It is not possible to reach V = light speed because the stored potential gravitational energy released as work between "A and C" is CONVERTED INTO ADDITIONAL MASS, which is added to the conventional mass "m" of tangible matter. Thus the gravitational potential energy, released as work, is converted into matter, making M_relativistic = m_{in usual particles} + converted gravitational energy into work and then converted such energy into "additional mass" and this becomes into INFITINITE MASS when V is just becoming equal to "C" = light speed. Thus all converted gravitational energy is being converted into additional mass Δm=ΔE/C². Such energy becomes slaved into mass (pitfall) and is not usable for kinetics energy. It is not possible to eat (or make use) twice of the same meal (or energy). Such energy ΔE used to increase RELATIVISTIC INERTIA (MASS) is not more available to increase velocity of such new additional relativistic mass Δm. Thus is not providing required kinetics energy to make additional mass Δm keep original orbiting trajectory. Thus for the whole relativistic mass (tangible matter) the global kinetics energy increases at much slower speed than the increase of additional mass, as we approach velocity in relation to "C"= light speed. Thus less centrifugal force is generated:  with smaller "v_c" the result is greater "R_c" orbit.

 

Thus, the most energetic are the particles, with high kinetics energy (as electrons, neutrons, etc.) at A, as coming from far away distant and energetic stars, and passing nearby the edge (surface) of dense and massive stars, the SMALLER is the ANGULAR DEFLECTION measured at point F.  We could guess this is the effect of tangible mass "m" increasing its INERTIA, as if gaining additional mass Δm=ΔE/C², which is added to usual mass reaching  greater and greater RELATIVISTIC MASS. The extrapolation, based on tangible particles with velocity very near light speed since point A, orbiting since point A, is that their angular deflection will be very small value at point F. Thus the same should take place with particles of light energy, orbiting since point A: no angular deflection at point F. This is something not in agreement with theory of relativity. 

 

 

5 – LIGHT ENERGY PARTICLES PATHWAY NEAR MASSIVE DENSE STARS

 

In case of light energy particles we should apply the above reasoning for tangible particles. BUT THERE IS A HUGE PROBLEM. It is not possible to increase the velocity of particles of light, as that is a physical limit (the arbitrary dogma of nowadays civilization. We should accept that as a first good guess). We could imagine v_particle as being just an infinitesimal value smaller than light velocity v = C. Thus falling into an intense gravitational field we would increase the worth mass of light particles to infinite mass, consuming all gravitational energy converted into work energy and mass, making light velocity remains nearly the same. But light energy particles would have so great mass INERTIA that it would be infinite, meaning the light would continue in its original light pathway, from point A to point F. We would have none Angular Deflection. We could guess that light particles would follow also such same straight line pathway A-F. 

 

 

For sure we can INVENT that it is possible to create MASS (inertia) from "the nothing", as some civilizations speculate about some Great Creation… Thus gravitational released energy, near v=C, could not be converted into kinetics energy particles of total M_{relativistic mass} and very near light trajectory should be a straight line. Light energy is just one type of condensed (trapped) energy, as originated from other noble energies, as energetic light noble energy (m_worth = E_light/C²). It is absurd the idea of one electron starting to breed additional .35 electrons with 0.35 of negative electrical charges at some velocities of acceleration. According Planck's reasoning, things take place like walking in full steps on stairway, not as in a continuous way of increasing, as suggested by the Relativity equations. Because the 2nd type of gravitational energy, to come from tangible matter (removed for storage, to oppose to increase of velocity) and vice-versa (as to make a particle move out of a black star like), it is required to envolve the radiation energy and thus all relationship from E2nd type to Tangigle matter energy is made through LIGHT (RADIATION is better) energy. Thus such transformation toward E2nd (and thus to THEORY OF RELATIVITY) is linked to QUANTUM of energy filling package of energy from E2nd to Tangigle matter and vice-versa, thus relativity is linked to PLANCK's formula.

 

If we reason the "worth mass m_light" is not increasing while light particles energy are moving closer and closer to a massive dense star, and also that the kinetics energy of light particles remains the same (because light particle velocity "v = C" can’t be increased, as it is at the limit), the gravitational force making the light particles moving down (toward the center of the Star), should release gravitational energy, from A to C, that should be converted into "something".  One guess is that frequency of light energy is increasing in the trajectory pathway from A to C (deviation to blue) and is decreasing in the trajectory pathway from C to E (deviation to red), according (speculativelly) Planck’s equation, as E_light = h_Planck . f, with "f " being frequency of light. But what would make light energy particles change their inertial original pathway, of trajectory A-F, into the hyperbolic like pathway A-B-C-D-E? Remember light particle energy remained always the same, as we had NONE INCREASE of KINETICS ENERGY (none conversion of gravitational energy into kinetics energy and into centrifugal inertial force for orbiting).

 

Should the orbit trajectory (pathway) A-B-C-D-E be very almost the same (with only very minor differences, as on value of height of orbit "h_c" over star surface at the lowest point C of orbit) for a light energy particle and for an electron traveling at (v_{at A})/ (light velocity) = 99.99999%  and for 99.999999999999999999999%? What makes light energy particles behave like having tangible worth mass "m" as m_worth = E_light/C²?

 

 

6 – 2nd UNIVERSAL LAW OF GRAVITATION x PATHWAY of high velocity PARTICLES NEAR MASSIVE DENSE STARS

 

 

There is other reasoning, originated from equations 1 to 4, already reasoned as being something awkward, very un-usual in modern physicists’ minds.

 

M_relativistic = m_tangible   + ½ . [1 +  3/4 . (v/C)² + 5/8 . (v/C)⁴ + 35/64 . (v/C)⁶ +  63/128 . (v/C)⁸ +  231/512 . (v/C)¹⁰ +  3003/7163 . (v/C)¹² + 45045/114688 . (v/C)¹⁶ +…] . m_{tangible .} (v/C)² .   Eq.4

 

M_relativistic = m_tangible   + [FUNCTION of m_tangible   and of  of (v/C)²         Eq.5

 

We can reason (SPECULATE) that it is not the usual m_tangible   which is increasing (breeding reproducing, as if a living organism…), but we can see that the original m_tangible   remained the same: because it is not linked or depending on changes of velocity "v" or "C" or ratio "v/C".

 

In fact the SECOND TERM in Equation 5 is telling that a SECOND TYPE OF FIELD OF ENERGY, quite like GRAVITATIONAL (E_gravity = m . g. h), is acting ((v/C)²  as some type of g),  on m_tangible, generating the storage of a 2^nd type of gravitational potential energy. But such 2^nd gravitational (or alike electricity and/or magnetism fields) field is not our usual Newton’s gravitational field, which doesn’t have such properties. In fact, we are proposing the second type of gravitational energy which acts opposing to all change of velocity and/or direction (as if INCREASING some type of INERTIA, gravitational inertia), for all type of particles, including of light. Thus its line of action has nothing to do with the straight line linking the center of the star with the center of the particle while it is orbiting nearby the star, from point A to C to E, as it is not always attraction force and it is not based on 1^st law of gravitation which is for force being in the same straight line linking the center of mass of attracting objects. 

 

When a PHOTON is orbiting the quite Hyperbolic pathway, since point A to B to C to D to E, "because it has worth mass m", it is subject to the 1^st type of universal gravitational attraction, according Newton’s law, and thus such attraction FORCE (due gravitational field) makes the particle of light energy of worth mass "m" move down along the vertical straight line linking the center of star to the center of the particle, in all points along its trajectory from A to E. This force makes particle of light energy of worth mass "m" moves vertically down releasing gravitational energy into work energy (kinetics energy) and the particle would accelerate toward star center, reaching greater and greater vertical velocities. This is NOT TRUE, and velocity (and kinetics energy) grows slower and slower, in relation to Newton’s formula, as (v/C) is increasing more and more. The gravitational energy not converted into kinetics energy is converted into the 2^nd type of gravitational energy, and stored as some type of GRAVITATIONAL INERTIA. 

 

See the end of this text… But the composition of such falling (vertical) velocity (having kinetics energy) with the tangential velocity along the orbit A to B to C to D to E (LIGHT VELOCITY, having other kinetics energy, in near horizontal direction, it is at point C), generates a TRIANGLE, with vertical velocity being computed in the above mentioned way (some of acceleration energy, Star gravitational field, is stored as 2^nd type of gravitational energy). Thus the composition of a triangle of velocities, with one side being "C=speed of light" (almost at horizontal inclination, it is horizontal at lowest orbital point "C") with other being the velocity of fall (or upward) into Star would result a hypotenuse with VELOCITY GREATER THAN VELOCITY OF LIGHT. Thus the resulting velocity is the NEW DIRECTION of LIGHT (thus vertical velocity and gravitational field makes light deviates its trajectory to A-B-C-D-E) and the 2^nd gravitational field  opposes to increase of velocity, thus resulting velocity (at orbit) is reduced to the velocity of the light, but a force that opposes to such change. In case of orbit C-D-E the gravitational velocity will decrease the resulting velocity (in the triangle), thus 2^nd type of gravitational inertial energy will provide energy for velocity of travel, along orbit pathway, from C to D to E, remains velocity of light.

 

Let us reason in the orbit pathway from point A to point B to point C. In this case the velocity of attraction is vertical, attracting from center of sun to the center of each particle. As result of gravitational field, falling from the distance R_A = infinite at point A to the radius distance R_B (the distance from the point "B" to the center "O" of the Star) will release a gravitational energy, that is converted into kinetics energy. Thus in lower orbit position (minimum "h_c" height at point C) we will have the greatest kinetics energy and the greatest vertical velocity of fall (v=v_C) and eq.4:

 

F_attraction = K_univ.const. . M_{particle at great velocity} . M_star / R² = K_univ.const. . M_star / R² . M_{particle at great velocity} =

 

= K_univ.const. . M_star / R² . m_tangible   +  K_univ.const. . M_star / R² . ½ . [1 +  3/4 . (v/C)² + 5/8 . (v/C)⁴ + 35/64 . (v/C)⁶ +  63/128 . (v/C)⁸ +  231/512 . (v/C)¹⁰ +  3003/7163 . (v/C)¹² + 45045/114688 . (v/C)¹⁶ +…] . m_{tangible .} (v/C)²  =  

₌ K_univ.const. . M_star / R² . m_tangible   +  K_univ.const. . M_star / R² . m_{tangible . .} ½ . [1 +  3/4 . (v/C)² + 5/8 . (v/C)⁴ + 35/64 . (v/C)⁶ +  63/128 . (v/C)⁸ +  231/512 . (v/C)¹⁰ +  3003/7163 . (v/C)¹² + 45045/114688 . (v/C)¹⁶ +…] .  (v/C)²     =

=  ₌ K_univ.const. . M_star / R² . m_tangible   +  K_univ.const. . M_star / R² . m_tangible . FUNCTION (v/C)²   Eq. 9

 

FUNCTION (v/C)²  = ½ . .  (v/C)²  .  [1 +  3/4 . (v/C)² + 5/8 . (v/C)⁴ + 35/64 . (v/C)⁶ +  63/128 . (v/C)⁸ +  231/512 . (v/C)¹⁰ +  3003/7163 . (v/C)¹² + 45045/114688 . (v/C)¹⁶ +…]     Eq.10  (depends only of relative velocity   (v/C)²  affecting m_tangible).

 

We can see that the conventional gravitational force (the first term of equation) is being increased only by the 2^nd type of force, which is linked to opposing the increase of velocity to reach the velocity of light. According the second term of equation 9, we can expect such "strange conservative force" becomes INFINITE, because function (v/C) becomes infinite when "v" is an infinitesimal value smaller than light speed. Into practice it becomes, even for moderate values v/C, is almost impossible to increase further V as we are facing huge growing gravitational INERTIA. Should it be MASS INERTIA, increase of MASS?  No… it can be something similar to Electrical and Magnetism field for storing energy or providing it, as required, as in gravitation… 

 

A direct impact of one particle (even of light energy particles), on Sun surface, according the pathway of a straight line A–O, would release, at the impact, all such energy added to the particle (and also that present at A…), as potential gravitational energy converted into kinetic energy, available as particle velocity… the energy converted into additional mass (relativistic one) is to "burst" and release noble light energy and originate particles with high speed (energy) as in accelerators...

 

But there is another type of GRAVITATIONAL FIELD, implicit in equation 10

 

In the part of orbit A-B-C we have (according Galileo’s principle of independence of movements) the falling of particle in vertical movement, releasing gravitational energy which is converted into kinetics energy, which generates the centrifugal energy which causes the trajectory of the particle be curved, around the Star, in one open orbit, according an open trajectory which counterbalance centrifugal forces and gravitational forces, with  creation of mass (inertia) as approaching the velocity (v/C) = 1.

 

Because there is a NET RESULTING VERTICAL FORCE, toward the center of the Sun, in all points of trajectory from A to B and to C and to D and to E, and some velocity is available at point A (or particles would have a free fall up to collide toward the center of the Star), it is evident that the LIGHT PARTICLES (and even USUAL MASS m) have to FALL toward the surface of the STAR, following a HYPERBOLE LIKE trajectory, as in FIGURE 1. Because some of the conventional gravitational energy is not converted into kinetics energy, but rather into the 2^nd type of gravitational energy (conservative one), conventional tangible particles (as electrons) "m" will travel slower at their lowest point C and thus they will follow more distant orbits (requires less kinetics energy) and will provide smaller ANGULAR DEFLECTIONS from point A to E (all the orbit). 

 

In the case of net VERTICAL FALL VELOCITY (when downward and then upward), it is usually so small relative to velocity of light, that its main effect is to cause the small CHANGE OF DIRECTION of a greater velocity, which is of LIGHT SPEED and it is kept tangent to each point of ORBIT, from A to B to C to D to E, thus from – infinite (coming from a distant star, having some self velocity…) to + infinite (to physicians at future infinite distance: yet making measurements to be sure about relativity model!).

 

7 – WHAT FORCES/ENERGY MAKE LIGHT ENERGY PARTICLES accelerate (even trans-light) and/or bend? And particles (tangible or “worth equivalent”) reaching velocities greater than the speed of light? What mathematical formulation is required for trans-light condition? It is like a glass separating the sub-light (our environment) to the trans-light (as if the water in an aquarium… ). Relativity like phenomena stops being continuous, but only taking place when fulfill “discrete like quantum” (when conditions are fulfilled by the 2^nd type of Gravitational Inertial Energy and such energy providing explanation for light not bending. Or what energy is required for bending light or particles at very huge velocity?). Thus it provides the reason for validating Newton’s Law related to not changing rest condition or the quantity of movement of a particle in movement.

 

Let us see, again, the file

 

http://www.geocities.com/celsosavelligomes/DEFLECTION_NEAR-SUN.xls

In such file, at bottom, select "Chart2" to see what causes and how to evaluate the angular deflection of the velocity of light (and of other particles) near the sun.

 

Let us reason, first on VERTICAL FORCES and on VERTICAL VELOCITIES. It the particle had none velocity when departed from point A (like from a distant Star), it would be difficult for it reach a massive and dense star (quite like a black hole), or even our Sun (assumed as being almost massive and dense, but not so much…) . In fact instead of ORBITING around such dense and massive star (as shown in Chart2) it would fall as a stone according to the vertical line from it (point A) to the center of the star, with collision taking place at the surface of star (in worst situation, as some collisions could take place in the pathway through sun atmospheres…). In such situation, all the energy the particle had in position A (entering the solar system, is more correct) and that it gained (as gravitational potential energy converted into kinetic energy) it would be released, as a "burst (sudden explosion)" when collision is against planets without atmosphere (as our Sun…). For sure gravitational energy that was converted into relativistic mass (making mass "m" increase, something ABSURD!…) and even conventional tangible mass "m" (having internal energy E_light = "m" . C²) also can release their stored energy, generating huge emission of light and of high speed particles… This is what takes place in our accelerators, when particles collide against a target, releasing the huge useful energy that was added to particles. "Thus" what about the HUGE added energy (for acceleration) that was not used to increase RELATIVISTIC MASS? And in fact is a NOBLE ENERGY stored as 2^nd type of GRAVITATIONAL INERTIA energy.

 

Thus a free fall of particles directly toward the center of the star, requires no another inclined velocity, as they could cause particles to ORBIT (in open orbit) around the star, or even collide with surface of star, in other points, like the result of ballistic trajectory, if such inclined velocity is too small. Human accelerators of particles are like making the perfect accelerators of particles, in perfect vertical pathway all the way down, using gravitational energy field, which is being converted into kinetics energy and also into 2^nd type of gravitational energy (as if some type of inertia, going against increase or decrease of velocities or change of direction) which becomes infinite at speed of light. None tangible mass "m" increase. Because humans yet don’t understand how to handle gravitational field, they use electrical and/or magnetic fields, heat and radiation pressure. All such means are very less efficient. Otherwise nuclear fusion would be at hand/easy. 

 

CHART 2 is an attempt to evaluate the problem of ORBITING not only in one straight line, but along a pathway which is alike a HYPERBOLE, as shown from points A, to B, to C, to D and to E (as shown in CHART1). This is the composition of ORBITING only in vertical line A-O and if an endless hole crosses the star (as if the deep well in which fell Alice in Wonderlands) the particle will continue traveling to point E, now symmetrical to point A, in relation to "O", the center of star. What makes the difference is that vertical velocity, along A-O-E, is turned into centrifugal force (related to inertia of mass "m") which allows the particle to orbit around the star and it defines the minimum height "h_c" particles will reach traveling over the star surface (see Chart1).

 

Thus what is more important is the VERTICAL FORCE making the FALL DOWN, toward star center, and the WORK generated by such attraction force, which is the gravitational field energy converted into it and into fall vertical force (at very high velocities, near the speed of light, greater and greater of such usual gravitational energy of attraction is stored not as WORK but as 2^nd type of gravitational inertia energy, which increases more and more intensely as the particle velocity is reaching the velocity of light, making acceleration less and less effective… it is like stealing most of useful required energy with electricity leaks as a motor is approaching some top velocity…).

 

In CHART2 we have a figure showing in "O" the center of a dense massive star, and C being the lowest height position "h_c" of the particle orbiting from A to B to C to D to E. Guess G – C as representing the total force of gravitational attraction, according to Newton’s theory, for our normal conventional mass "m": see equation 6

 

F_attraction = F_centrifugal = K_{univ. gravity} . m_part . M_star / R² = m_part . v_c² / R        Eq. 6  

 

K_{univ. Gravity is known.} m_{part is known.} M_{star is known. With the maximum force of attraction, and minimum R and with the height of orbit above the star surface at position "C" (with height} "h_c") we can compute the whole orbit trajectory pathway, from C toward A and toward E: as with comets. Better: we can compute directly from A to B and to C, and (by symmetry) to D and to E.

 

In case of very intense gravitational field nearby a massive dense star, it is replaced m_part by m_relativistic for computing the trajectory of particle orbiting around the star. This is one approach. The other is to use equation 9:

 

F_attraction = K_univ.const. . M_star / R² . m_tangible   +  K_univ.const. . M_star / R² . m_tangible . FUNCTION (v/C)²   Eq. 9

 

FUNCTION (v/C)²  = ½ . .  (v/C)²  .  [1 +  3/4 . (v/C)² + 5/8 . (v/C)⁴ + 35/64 . (v/C)⁶ +  63/128 . (v/C)⁸ +  231/512 . (v/C)¹⁰ +  3003/7163 . (v/C)¹² + 45045/114688 . (v/C)¹⁶ +…]     Eq.10  (depends only of relative velocity   (v/C)²  affecting m_tangible).

 

In this way the problem is the composition of two problems, one (first part) based on classic Newton’s model for attraction according universal gravitation and the other (second part) based on 2^nd law of universal gravitation, which is ruled by the values (v/C). The reasoning is the OPPOSITE people make use.

 

F_attraction   - K_univ.const. . M_star / R² . m_tangible . FUNCTION (v/C)²  = NET 2^nd GRAVITY FORCE = K_univ.const. . M_star / R² . m_tangible traditional Newton’s gravitational attraction force.   Eq. 11

 

This means that ALLWAYS the "tangible conventional mass m" remained the same (no mass increase with velocity v approaching light speed (v/C almost 1), as when without velocity (v=0 / C=light speed) and that it remains like the fall of a particle "m" (tangible, or "m" as worth light particle energy) over a planet without atmosphere: that is shown in the right side (end) of equation 11.

 

The first part of equation 11, F_attraction, shows that the usual gravitational field energy converted into work is mostly released to become stored as 2^nd type of gravitational inertial energy: such amount of stored inertial energy grows very fast and strongly. Thus only a small amount (and decreasing very fast…) of total released gravitational energy will be left (available) to accelerate the particle "m" (which remains the same conventional tangible matter "m", without breeding new particles and new electrical charges…), now storing in it the inertial energy.

 

Thus let return to CHART2. G-C is the total gravitational energy released since infinite distance to the point C, here replaced with F_attraction. (Or make the integration, considering Newton’s law). Also in scale, G-H is the inertial energy stored based on the 2^nd type of gravitational energy (stored into the particle, quite like light) and thus it is not something tangible (as conventional matter) and it is the 2^nd term of first side of equation 11.

 

Thus H-C is the classic Newton’s force, from conventional gravitational energy field, used to accelerate a particle, with (tangible or WORTH) mass m, but as if acts only the LEFT (NET) AVAILABLE GRAVITATIONAL FORCE, which  is becoming weaker and weaker, as particle velocity approaches of light speed.

 

Lets return to CHART2. Particle was ORBITING around the STAR according the pathway trajectory C-I (traveling at the SPEED OF THE LIGHT, or other value: you may decide, as to "accommodate measurements results") and now, WHAT IS LEFT FROM GRAVITY RELEASED ENERGY, was able to become accelerated to the velocity "v" (at ratio v/C) plain particle of mass "m" (tangible or "worth value m"). Because of Galileo’s principle, of independence of movements, we compose such vertical velocity (H-C = I-J) with the orbit velocity at C (C-I = velocity of light) and we obtain the composed velocity, C-J, and it will be greater than the velocity of light. Thus such excess of kinetics energy, in the combination of movements, is converted in a FORCE that OPPOSES to the excess of movement, and thus excess energy is stored as 2^nd type of gravitational inertial energy. Energy to break the excessive velocity is not originated from the NOTHING….

It is interesting to compare the transition of our sub-light velocity condition as being our atmosphere environment(and with peculiar low index of refraction value) separated by a thick transparent glass of an aquarium filled with other liquid environment, water, with its other peculiar higher index of refraction. Thus velocity of light is distinct in the two environments. In our case we could just adjust the FUNCTION (v/C) series" (changing functions and fractions) in such a way to impose the desired limit for the other environment (as trans light) to adjust the proper and limited velocity of displacement for ligh energy, as fulfilling the equation 11, with just a small part (eventually) of the energy stored in the particle (as 2nd type of inertial gravity and kinetics and others) remained available as kinetic energy, quite like the visible "tip" of a huge iceberg.

SIMILAR FUNCTION, for TRANS-LIGHT, similar to: (v/C)² = ½ . . (v/C)² . [1 + 3/4 . (v/C)² + 5/8 . (v/C)⁴ + 35/64 . (v/C)⁶ + 63/128 . (v/C)⁸ + 231/512 . (v/C)¹⁰ + 3003/7163 . (v/C)¹² + 45045/114688 . (v/C)¹⁶ +…] Eq.10 (depends only of relative velocity (v/C)² affecting m_tangible).

 

The excess of velocity is NOT KEPT remaining only BECAUSE OF OURARBITRARY MODEL (as it was "imposed" to fulfill a model one century old, departing from its equations). Thus we IMPOSED the RULE that the MAXIMUM SPEED is the SPEED OF LIGHT (valid for light energy particles and for tangible mater, any as "m" or "m_worth"). THUS we "deform" the space and time when we make measurements in our environment, in such a way we measure velocities in it according "our desires" and the model we imposed: thus the new vector of velocity will be C-J.

We must have in mind that the VELOCITY OF THE LIGHT allways must follow a trajectory (pathway) of a STRAIGHT LINE, if none force or energy is causing its deflection. In case there is any tendency of changing the value and/or the deflection of light trajectory, as due a strong gravitational field, it is the Force/ENERGY originated from the 2nd GRAVITATIONAL INERTIAL FIELD that "resist to such change of velocity or direction".

Thus, it is because of the existence of 2nd GRAVITATIONAL INERTIAL ENERGY, latent or when acting in a particle ( tangigle or light energy particle) is that any particle remains travelling into a straight line (which may means stay at rest condition for other observers in other proper referentials).

Thus the WHOLE and SUPREMME UNIVERSE reacts, through the 2nd type of gravitational fiel energy (/FORCE), opposing such changes of velocity and/or of deflection, and imposing limits (as C"máximum" = velocity of light).

Also the transference of light energy into 2nd type of gravitational inertial energy and vice-versa, is direct one. Not the case of tangigle matter, in which matter receive "packages" of energy (including of opposition to increase or decrease the velocity, at very high v/C ratio), from 2nd type of gravitational inertial energy into light energy. It is speculated that the work (kinetics) energy to accelerate (or de-accelerate particles), in a not a continuous variable, but rather quite like provided in Planck's packages of energy, now of 2nd type. The process of conversion of energy is less efficient from tangigle matter energies into nobler energies (as light and 2nd type of gravitational inertial energy), as if from less noble energy into more noble energy type. INERTIA is quite like similar to the WHOLE UNIVERSE presenting its opposition (through force and energy) against any change of velocity or direction of particles. Such second type of gravitational energy is not more linked to two particles being attracted (Newton's law), but rather to an Universal Field, which is the same anywhere and toward any direction.

Whe should make an obvious comment in relation to the orbit trajectory of particles of light energy (or tangible particles) of value "m". Orbit do not depends on the value for whole "m" but is the same for each of what composes the value "m" or for values greater than "m". Thus a neutron and an electron travelling with same velocity and direction at position "A", infinitelly distant from the center "O" of a massive and dense star, will have the same trajectory. We can see that with Newton's formula for gravitational attraction between two particles and counterbalancing such Attraction Force with centrifugal force for bending orbit trajectory. But the relative position of A and O will determine the pathway.

If velocity of particle at A is pointing directly to the point "O", the center of massive dense star, and both A and O are travelling in the same general velocity (as of around a Galaxy), then the particle coming from "A" will remain travelling in the straight line and it will strike directly the surface of the star and would hit the central point "O" if a very deep well exist from star surface to its center.

If this ray is of light energy particles and/or also of tangible particles, quite like in a laser beam, there will be none velocity in particles at point "A", spreading perpendicular to the pathway A-F. Thus there will be none gravitational lense effect, and what reported in literature would be false and generally is false, because there is not such "beam of particles travelling in parallel" and only through a limited cross-section. Emissions of particles are usually made to all directions and they reach us all over our solar system, as equal and same beam of light, because they come from so far away that their particle pathway is usually very parallel (unless some high intense gravitational field, along/nearby such pathway of particles make them bend...). But most of the particles will fall directly on the massive dense star,or will travel so far away its surface that the effect of such massive dense star will be negible on the trajectory of such beam of particles and/or or light energy particles. Otherwise we could not examine the universe and see what light would be coming from what source... What is presented below is impossible: to see the light of particles travelling (as if in laser beam) in the other side of the massive dense star (a beam with the diameter of such star): all light would had fallen, because there would be no transversal velocity (to the pathway to the massive star) and none movement can be generated without a source of energy (even the 2nd type of gravitation).

See GRAVITATIONAL LENSES: If the source, massive object, and the observer lie on a straight line ("A-O-E" points of the same straight line), the source will appear as a ring behind the massive object. This phenomenon was first mentioned by Chwolson in 1925, and quantified by Einstein in 1936. It is usually referred to in the literature as an Einstein ring, since Chwolson did not concern himself with the flux or radius of the ring image. Consider such direct line A -O remains bound to the center "O" of the star, and that the position A is moved up, in a distance "d", perpendicularly from previous position A, and particle is released from point A at the same previous velocity and direction. We will see that for very large values of distance "b", the trajectory of particle will remain nearly the same original straight line (paralel to old "A-O" straight line), with minimum angular displacement. But as distance "d" is decreased, the angular displacement will increase more and more (measured at point "F"), as the lowest point ("C") of the orbit around the massive star (at height "h") is approaching star surface. Eventually such minimum distance of orbit comes to zero and the particle is captured by the star, like what happens with our satellite when their orbit becomes too close to Earth or other planet or satellite, etc. It is evident if we increase or decrease the velocity of the particle in the infinitelly distant position A, we change the trajectory of the particles around/nerby a massive and dense star. It is because of GRAVITY, and the falling down velocity (approaching the speed of light) of orbiting particles, that the light trajectory is "curved, bended" around a massive and dense surface, with greatest "angular deviation" taking place when ligh particles are almost colliding with star surface, in very low orbit (with minimum heigh "h" being really very small, as possible to block star light emission with an eclipse).

One use of strong gravitational field is to generate the "lenses effect", Gravitational lens - From Wikipedia, the free encyclopedia

quite like we have by making light particles travel along environments of distinct refraction index, as a lense of glass or plastic materials surrounded by vacuum or by our atmosphere (in one or both sides) and/or by water (for water divers): in one or both sides, etc.. In these cases for bending light trajectory (pathway) it is required to have a changing index of refraction, thus it is not possible in absolute vacuum, which is required for top (maximum) velocity of light. If it travels through any distinct material contents (as gas or ions) along the pathway (as perfect vacuum in some portions), than the light deflection is possible. We can see that in the mirage phenomena, in which it changes the index of refraction in our atmosphere, as light travels through it (as caused by distinct air temperatures). Other type of phenomena which is similar to lenses caused by intense gravity field (of massive and dense stars), is that used with electrical and/or magnetical fields replacing the gravitational field, as we have with electronic and protonic microscopes. In these cases, nothing tangible (as causing change of refraction index) is causing the change of the velocity and/or direction of particles: three very similar energetic fields (gravitational, electric and magnetic). The fourth one is the 2nd type field of gravitational inertial energy (it is not based on Newton's Law for Universal Gravitation), which acts (all time, as INERTIA LIKE EFFECT) on all particles on whole Universe, opposing to the change of INERTIA, as increase or decrease of velocity and/or change of direction of velocity (including of light).

Thus the way for making light pathway deviates, curving/bending, is through providing external energy (as from the gravitational energy of the dense and massive Star) and that is possible, but must overcome such 2nd gravitational inertial forces/energy, in opposition. Only what is left, as in Equation 11, for right side of equation, is the net resulting force or energy, which will be available for bending and/or changing velocity. Thus it is because of gravitation (and vertical huge velocity of falling down) that we can change the direction of orbit, along the trajectory pathway A-C-E, in which we used vertical velocity of fall to "bend light". Velocity of fall is kept constant, even being counterbalanced continously, as when we keep a geo-stationary satellite, at 38,000. km, orbitting according a perfect geo-stationary circle): Fa=Fc. In fact the satellite is constantly falling down while centrifugal force is pushing it upward, preventing it collide against Earth surface.

 

END