VERY SUMMARIZED KEY INFORMATIONS ABOUT
PARTICLES TRAVELLING TRANS-LIGHT VELOCITIES
This information came from http://www.geocities.com/celsosavelligomes/DEFLECTION_NEAR-SUN.xls
Answering questions from ZEPHIR to present a very concise summary of my postings on
http://www.geocities.com/celsosavelligomes/PARTICLES_BENDINGatTRANS-LIGHT_VELOCITY.htm
Newton’s Law for REST CONDITION (v = velocity
equal ZERO ("WHERE/WHEN v=0 in UNIVERSE? In/for what referential?): it results also v/C=0)
F = m .
a (m is
related to INERTIA at REST; F is force opposing movement of “m”).
If an external true force is applied to the tangible matter, the usual "m, as INERTIA”, then its "rest mass" would increase (procriating 33% of an electron? Breeding additional mass?)
and becoming “Mrelativistic” according Einstein’s equation:
Mrelativistic = m
/ [1
- (v/C)^2]^(1/2)
(Mrelativistic
would increase to infinite for v/C approaching 1 in accelerator)
How does it increase the opposing Force F due
increasing INERTIA, in accelerators? (including particles falling over crust of dense massive stars and pseudo "black holes" and their intense gravitational forces provided by Newton´s Law of attraction).
Faccelerator = M . a = m / [1 - (v/C)^2]^(1/2) . a =
Faccelerator = m . a . [1 - (v/C)^2]^(-1/2) = m . a . Taylor’s series
(Notice: in some
articles m and M notation is shown in the opposite).
Faccelerator would become infinite for v/C approaching 1 in accelerators, thus preventing efficient further acceleration (nearly zero further increase of v/C) at already very great values of v/C, as if the Relativistic Mass of particles being accelerated becoming infinite.
a=1
b=-(v/C)^2
n
= -1/2
SOLUTION through Taylor’s series:
(a+b)^n = ( 1 +b)^n = [1 -
(v/C)^2]^(-1/2) = 1 + n/(1!).(b)^1 + n.(n-1)/1.2.(b)^2
+ n.(n-1).(n-2)/1.2.3.(b)^3 + n.(n-1).(n-2).(n-3)/1.2.3.4.b^4 +
n.(n-1).(n-2).(n-3).(n-4)/1.2.3.4.5.b^5 + etc.
[1 - (v/C)^2]^(-1/2) = 1 +
(-1/2)/1!.[-(v/C)^2]^1 + (-1/2).(-3/2)/1.2[-(v/C)^2]^2 +
(-1/2).(-3/2).(-5/2)/1.2.3.[-(v/C)^2]^3 +
(-1/2).(-3/2).(-5/2).(-7/2)/1.2.3.4.[-(v/C)^2]^4 + etc. =
= 1 + ˝ . (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 + etc. (TAYLOR’s
series) =
= 1 + (v/C)^2 . [ ˝ + 3/8 .
(v/C)^2 + 5/16 . (v/C)^4 + 35/128 . (v/C)^6 + 63/256 . (v/C)^8 + 231/1024 .
(v/C)^10 + 3003/14336 . (v/C)^12 + 45045/229376 . (v/C)^14 + etc.) =
= 1 + FUNCTION of (v/C) = 1 +
f(v/C) = [1 - (v/C)^2]^(-1/2)
FUNCTION of (v/C) = f(v/C) = (v/C)^2 .
[ ˝ + 3/8 . (v/C)^2 + 5/16 . (v/C)^4 + 35/128 . (v/C)^6 + 63/256 . (v/C)^8 +
231/1024 . (v/C)^10 + 3003/14336 . (v/C)^12 + 45045/229376 . (v/C)^14 + etc.)
THUS:
Faccelerator =
m . a
. [1
- (v/C)^2]^(-1/2) = m . a . Taylor’s series = m .
a. [1+f(v/C)]
Faccelerator =
m . a + m . f(v/C) . a = acceleration of (USUAL
INERTIA + 2nd type
gravitational INERTIA).
.This is the MAIN SUMMARY of these messages, to be posted + COMMENTED up to item 7, thus introducing big SPECULATIONS, as COLEBROOK did with the data provided by HUNTER ROUSE who was not able to provide a compact solution, make it practical, simple and useful.
By CELSO SAVELLI GOMES
(M.Sc. Univ. California, Berkeley).
Hans Albert Einstein:
Innovation and Compromise in Formulating ... I - SAVELLI - provided a fast and practical solution
for using bedload equation (in 1970), in explicit direct solution, that
could be solved in fraction of second, in computer, instead in tedious manual
labor computations and use of charts and diagrams. Just because I got
“revolted” with such tedious computations, caused by mathematics like Einstein (son)... As Einstein
saw things, accurate estimation of bed-sediment load, ...
rates of bed-sediment transport through the
river was the bedload equation proposed by ... link.aip.org/link/?JHEND8/130/477/1
http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JHEND8000130000006000477000001&idtype=cvips&gifs=yes
FOR A FISH, living into WATER (as if with great INDEX OF REFRACTION) and
separated by a thin wall of transparent glass (a BARRIER THAT CAN’T BE CROSSED,
as if LIGHT can’t create such type of barrier, WE IMPOSED THAT BY OUR CULTURAL
VALUES AND REASONING…) we are like IMAGINARY BEINGS living in an IMAGINARY
ENVIRONMENT (atmosphere, index of refraction near 1), quite like SUB-LIGHT
environment if the fish is living at TRANS-LIGHT environment. What changes of
velocity takes place when CROSSING THE BOUNDARIES? Two reflex of light at glass
boundaries? Refraction of light through glass? Should be glass be made like
mirror or half-mirrored? What about jumping over the very thin wall of aquarium (made in glass) and diving directly into the swimpool? Breaking a "barrier", very stiff to break...
(****) = 1 + ˝ .
(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 + etc. (TAYLOR’s series)
|
v/C values |
(*****) Taylor´s 8 terms |
Value original
equation 1/[1-(v/C)^2)^(-1/2) |
|
0 |
1 |
1 |
|
0,1 |
1,005037815 |
1,005037815 |
|
0,2 |
1,020620726 |
1,020620726 |
|
0,3 |
1,048284837 |
1,048284837 |
|
0,4 |
1,091089436 |
1,091089451 |
|
0,5 |
1,15469961 |
1,154700538 |
|
0,6 |
1,249971339 |
1,25 |
|
0,7 |
1,399713202 |
1,400280084 |
|
0,8 |
1,658061791 |
1,666666667 |
|
0,9 |
2,168648756 |
2,294157339 |
|
0,95 |
2,625640059 |
3,202563076 |
|
0,99 |
3,168506085 |
7,08881205 |
|
0,999 |
3,32074868 |
22,36627204 |
|
0,9999 |
3,336690778 |
70,71244595 |
|
1,0001 |
3,340251814 |
No original
mathematical numerical solution, but we could
have other meaning through Physics |
|
1,001 |
3,356359608 |
The same |
|
1.01 |
3,525186796 |
The same |
|
1,1 |
6,337912679 |
The same |
|
1,2 |
14,46177228 |
The same |
|
1,3 |
36,61847991 |
The same |
|
1,5 |
248,1928718 |
The same |
|
2 |
17577 |
The same |
|
3 |
9591917,692 |
The same |
|
5 |
31301413362 |
The same |
|
10 |
1,98498E+15 |
The same |
Warning: Coma and points are INVERTED (Excel in Portuguese!)
NOTICE that the
FUNCTION (v/C) continues to provide a numerical answer (not an IMAGINARY number), even if (v/C) is equal or
greater than 1.0. In fact such number is infinite (your guess is correct... you have only additions between the terms and (v/C) are all in the square power (v/C)^2...). And for v/C f(v/C) will provide infinite for v/C = 1 or greater than 1: the same result. But we need to use very HUGE number of terms from Taylor’s series. In any way series continues
to exist and can provide an ANSWER (not imaginary) when computed beyond, for (v/C) = 1.0 or greater.
It is not known exactly what could be the FUNCTION
(v/C) for v/C greater than 1: we are here to make such SPECULATIONS, from the
ACADEMIC COMMUNITY in general, thus including you. In chapter 7 of the article
being posted here, http://www.geocities.com/celsosavelligomes/PARTICLES_BENDINGatTRANS-LIGHT_VELOCITY.htm,
.It was suggested how such FUNCTION (v/C) could be made (constructed) for v/C greater than 1. One use would be the composition of sub-LIGHT velocities generating TRANS-LIGHT velocity (v/C greater than 1), and how strong should be the opposition to such (as if f(v/C)) to turn it from TRANS-LIGHT into LIGHT boundary. It would be like computing some fish (density nearly 1) jumping into air (density nearly 0) for some time, and facing a huge opposition (“gravity”) for making dive again. Even huge “fishes” and whales do that…
It is absurd
to believe that because one physical law is limited or ends abruptly at one boundary,
it is not possible to cross it. One very classic example is the transition of
sub-sonic to ultra-sonic flow regime, as they change drastically, suddenly. One
thing that heroic pilots had to learn even with their lives. It was not because
of resulting sonic shock wave that airplanes and rockets do not cross such barrier…
even if in quite recent past it was “believed” that none airplane could travel at
supersonic regime, as Concord airplanes did so well.
Best personal regards, to our readers, sincerely yours,
CELSO SAVELLI GOMES (“SAVELLI, celosavelli, all ijah”) Aug. 9th, 2006