Preprint
(17.01.2003)
Date: Fri, 17 Jan 2003
21:08:18 GMT
From: redshift0@narod.ru (Alexander
Chepick)
Organization:
Newsgroups: sci.physics, sci.astro,
alt.sci.physics.new-theories
Subject: new particular relativity theory
(NePaRT)
Key words: particular relativity theory
Principles of a New Particular Relativity Theory
A.M. Chepick, Nizhni Novgorod
e-mail: redshift0@narod.ru
Abstract
In this article the
hypothesis about a possibility of distinction of the speed's supremum of speed
of substance interaction from speed of light in vacuum is offered, arguments in
favor of it are suggested, the possibility of construction of a New Particular
Relativity Theory (NePaRT) without a principle of independence of the light's
speed is demonstrated.
1. Introduction
Basis of the
Einsteins particular (special) relativity theory (PRT) are two postulates: the
Principle of independence of lights speed : " Speed of light in vacuum in
all inertial systems of reference(ISR) is constant and does not depend on speeds
of a source and a receiver of light "; and the Principle of a relativity: "
All physical phenomena at identical entry conditions are equally resulted in all ISR ". (in Einstein's
formulation [5, c.147]). With their help it is possible to deduce Lorentz's
transformations - the ratio, which tied values of all coordinates in various
inertial systems of reference. In PRT the formula of Doppler effect expressing
dependence of received frequency of light from emitted frequency of light is
well known. Check of this formula has served as confirmation of Einsteins PRT.
In "The Encyclopedia of Physics" [3, v.3, p.501] it is told, that in 1986
formula Doppler effect is checked up with accuracy 310-4. Check of
this formula has served as confirmation of the Einstein's relativity theory. But
why accuracy of performance of this formula is so insignificant? In fact values
included in it are measured with much more accuracy: frequency -
10-16, speed - 410-9, a corner -
510-10.
Whether there are
no the physical reasons, which not allow to increase accuracy of check of
performance of this formula? In fact opportunities for this purpose are
available, moreover, the formula is applied as to calculations of speeds of
streams of gases in galaxies, so and other appendices where required accuracy of
calculations should be not less than 10-5. There are also other
reasons for doubt in accuracy of this formula, for example, non symmetric
distance and redshift from jets, removing from us, for some quasars in
comparison with redshifts of these quasars and their jets approaching to us.
As the inference of
formula Doppler effect is based on PRT, maybe, the point is in this
theory?
Logunov [2] has
shown, that for an inference of Lorentzs transformations
in the flat Euclidian static universe the Principle of an independence of
lights speed is not required, enough one Principle of relativity. Moreover,
from the Principle of a relativity
an existence some constant (we shall designate it cL
a Logunovs-Lorentz's constant) follows in all ISR. It
has dimension of a speed, and on sense of these transformations it is the
maximal allowable speed. But as this value at measurements appeared with the big
accuracy is equal to speed of light Einstein has made the decision to postulate
the Principle of an independence of lights speed. As to the theoretical proof
of that the constant "" in the equations of
transformation of time and metric coordinates from one system of reference in
another also is speed of light, so without the Principle of a constancy of
lights speed such proof simply is not exist!
Therefore we
offered a hypothesis:
Logunov - Lorentz's
constant cL differs from speed of
light.
It is natural that
this difference if it exists should be close to a modern accuracy of measurement
of lights speed.
Concerning the term
"speed of light" in the formulation of this hypothesis is necessary to note,
that here it is speed of photons in a system of reference of the motionless
source. Photons of a given frequency radiated by a source, have some speed
c, identical in all directions, by virtue of an isotropy of a conditions
of their spreading.
Landau and Lifshitz
in [1] have shown independence from ISR of the supremum of speed of substance
interaction (that gives equivalence
of this value and the Logunovs-Lorentz's constant, because in one space
two different constants can not be maxima). And for speed of light they esteemed
only two hypotheses: the Einsteins principle of independence and "ballistic"
hypothesis ", which states: c'=c+V, where c' is speed of photons
in the reference system moving by speed V relatively the reference
system, in which one the speed of photons equals "c". Having produced
arguments against the second hypothesis, they have considered, that have
demonstrated necessity first one, though there was not demonstrated alternation
of these hypotheses. Actually in conditions of Einsteins Principle of
relativity alternative to an Einsteins Principle of independence is the
hypothesis tendered to consideration in this article, but it is not a ballistic
hypothesis.
As a consequence of
the offered hypothesis it turns out, that many conclusions PRT are carried out
with small updating, namely:
- The value of
relative speed of one body in system of reference of the second body is equal to
value of relative speed of the second body in system of reference of the first
body;
- There is a factor
of delay of rate of time ?L which looks like:
?L=[1-(V/cL)2]-1/2;
- Lorentz's
transformations are carried out connecting values of coordinates in two ISR
the;
- There are
formulas of the relativistic sum of speeds and formulas of the sum of their
projections; in particular, for the motionless receiver the speed of a photon
from a source which is strictly keeping away from the receiver with speed
V, it looks like:
c2 = (c-V) /
(1 - c V / cL2)
(1)
But now speed of
photons of a given frequency is constant only in ISR a source, in others ISR,
moving concerning a source, speed of a photon can have different value, it can
be both more c, and less c, in particular, it is equal to zero for
a photon flying in parallel. The exclusiveness is taken off from photons, they
were made even to usual particles. Only in NePaRT photons can have
mass.
Only
now it has appeared the opportunity to receive answers to many questions
connected to photons, for example: to what is equal a relative speed of two
photons? - a question which standard PRT is powerless to answer unequivocally,
namely: if speeds vectors of photons are not parallel, their relative speed is
equal c; if they are collinear - it is not determined. But why it is not
determined? Unless two in parallel flying photons should not have zero relative
speed? For real objects it is conclusive. If photons are real... That is,
formulas PRT are reflect reality inexact.
Therefore the
theory that has grown out of this hypothesis is named as the New Particular
Relativity Theory, or NePaRT (NeoPRT).
2. Restrictions of
applicability of physical theories, principles and postulates; and Supremum of
speed of substance interaction
1. Any physical theory has the limited scope.
First,
it is applied to the limited class of the phenomena.
Second,
it has the limited range of definition that is carried out with some given
accuracy for the parameters limited in the values in aggregate and-or
separately. For unlimited basically parameters such restriction always happens
both from above and from below, for limited - near to limiting
values.
2. The formula of any theory treating
the physical law corresponding to it, gives approached (and sometimes probable)
value.
First,
because of the limited accuracy of definition of parameters and constants
included in the formula.
Second,
because of the approached formula representing this law. Frequently in formulas
insignificant members because of their small value are rejected. There are
formulas for which there is no exact expression (such as not taken
integral).
Third,
because of the approached, idealized form of the description of this
law.
For
example, Coulomb formula F=KQq/r2 expressing
dependence of force of an attraction (pushing away) between electric charges.
The formula is carried out for motionless charges which sizes are considered as
dot, that is infinitesimal in comparison with distance between them. The formula
is not carried out for small distances, smaller the size of atom, but not for
the reason, that we do not know the size of a charge in the charged particles
(the size of an electron with sufficient accuracy is dot in comparison with the
size of atom) but that on such distances there is a phenomenon of shielding. The
formula cannot be checked up for very big distances and for very big charges. It
is unknown also a feasibility of the formula for charges smaller than quark
charge as we have not those.
3. As principles and the postulates
concerning to physical values, inherently are physical theories they, as well as
theories, can be applied only with the certain
restrictions.
For
example, Einstein's postulate on a constancy of lights speed in any inertial system of reference. It
concerns to real physical parameter - speeds of photons. It is possible to check
up a postulate only for a limited speed of a source. And for the speed of a
source close to limiting value, the postulate obviously cannot be applied by
virtue of the previous reasons. So it is quite natural, that in the theories
constructed on its basis the results can turn out, which are not compatible with
physical sense.
4. Supremum of
speed of substance interaction is the constant
How then to act
with the statement that supremum of speed of substance interaction in the
universe is the constant?
First,
it is not a postulate, only the theorem. Really, if to assume, that this value
depends on speed of a source or the receiver it will not be the top
side.
Second,
this value does not correspond with any physical object. It is not speed of any
object, it is the top limit of such speeds.
Therefore the
destiny of the theory or a postulate does not threaten this statement, it will
exist in a constant kind until the universe exists and there is substance in
it.
3. Calculation of
speed of photons
It is obvious that
in own system of reference of the source
(OSRS)
where the source is motionless, the photons of the given frequency radiated by
it, have some speed c, identical in all directions, valid isotropic
conditions of their distribution. In
OSRS for the photon has got in the moving receiver, direction of speed of a
photon should "outstrip" the receiver. Let the source has velocity V and
the corner ? between a direction of movement of photons from a source and
vector V. Thus this corner ? does not vary during movement.
Then in own system
of reference of receiver (OSRR) where the source
moves with speed V, the photons radiated by it, get additional speed
depending on a direction of movement of a photon, NePaRT agrees. Resulting speed
of photons 2 in OSRR
and the corner a between a direction of their movement from a
source and vector V is determined under formulas of the relativistic sum
of speeds projections on a direction of speed V:
c2,X= c
+V)/(1+ c Vcos ?
/cL2)
c2,Y=csin
? [1- (
V/cL)2 ]? / (1+ c V
cos ? d
/cL2)
c2=(c22,X
+c22,Y)1/2
cos a =
c2,X/ c2
where
c2,X and c2,Y -
accordingly x-and y-projections of speed of photons c2
.
Whence we receive
speed c2, expressed through c,
V, cL and a. We carried out
transformations in condition of the real assumption in our validity: V
<c. Condition V>=c in this article is not considered.
Let's choose that
decision of this system of the equations which at aspiration c
and cL to infinity gives a parity cos
? =cos
a.
Let's
designate ?=V/cL; ?L=[ 1-
(V/cL)2 ]-? ; ?=[ 1- (V/c)2
]-1/2
?K-1=(? -2sin2a
+ ?L-2cos2
a)?
The size
?K can be named scale circular
as by the definition it changes from ?L up to ? depending on a
corner a.
Let k=1-
c/cL is a factor of
difference between speed of light and supremum of speed of substance
interaction. In article [4] this factor is approximately empirically determined,
as k = k= 2.810-11.
In these
designations it is received:
|
c2=
cL[1
|
(1-(1-k)2)
(1- ?2cos 2a)
2 |
]
1/2 |
(5) |
|
(?L-1 +?(1-k) ?K-1 cos a )
2 |
In particular, at
strict moving away of a source from receiver, that is, at cos a = -1, the
formula (1) turns out. This formula gives value of speed of a photon in
OSRR depending on a
direction and velocity of a source, therefore it is possible to use it for the
proof or refutations of NePaRT.
4. The analysis of
the formula of photons speed
In "The
Encyclopedia of Physics" [3, v.4, p. 549] speed of light is determined for the
present moment, as c =299792458,0 (+-1,2) [m/s]. Though accuracy here
makes 410-9, at the present stage accuracy of measurement of speed
of light 510-11 is achievable.
Probably, the
reason of this insufficient accuracy of definition of speed of light is made in
inconstancy of speed of photons.
For the analysis of
the formula (2) we shall consider the ratio of speeds
c2 and cL:
u(?,a)=c2/cL .
As distinction
between cL and c is outside accuracy of
definition of speed of light accessible now, it is possible to suggest, that in
formulas (1) and (2) cL coincides with the
above-stated size 299792458,000 [m/s], and speed of light c =
(1-k) cL = 299792457,992 [m/s]. Here
k=1-c/cL=2.810-11 is factor of difference between speed of light and
supremum of speed of substance interaction, approximately empirically determined
in article [4]. But it is possible to count, that speed of light c
coincides with the above-stated size 299792458,000 [m/s], and
cL=c/(1- k)= 299792458,008 [m/s], - on size u (?,
a) this choice practically will not affect. Most likely, in vacuum size of
factor of difference between speed of a photon and supremum less than one
calculated in article [4], as in real intergalactic and interstellar space
density of substance (and, hence, an optical density) not zero, and consequently
the measured effect of change of speed of photons for Supernovae accumulates
from an influence of environment (delay plus redshift) and the contribution of
formulas for a relativistic difference of speeds of Supernovaes parts and
photons radiated by it.
The analysis of the
formula (2) shows, that at anyone a for ? <0.55 it turns out
|u(?,a)-1| <10-10, and at ? <0.95 it turns out
|u(?,a)-1| <10-8, that is distinction of values of formulas
in this range of definition is within the limits of detection at the present
stage. The greatest rejection from 1 at ? <=1-10-9 is marked in
area a =p. We receive at ?
<=0.972 accuracy of concurrence with 1 u(0.972,a) = 1 -
210-9. At the greater speed it is received the big distinctions: u
(0.99999972, a) = 1 - 210-4 and it is clean at a
=p, at other corners
- distinction is less.
5. Conclusions
1. In the flat Euclidian static Universe in
condition of the relativity principle of it is possible to construct
a New
relativity
theory without the Principle of an independence
of lights speed.
2. The size
c2/cL,
differs from 1 less, than on 210-N, for relative speed of
source V<(1-2,810-11+N)cL at N = (1-10). At
V> = (1-2,8 10-10)cL difference of this
attitude from 1 can make more than 20 %.
3. Accuracy of
10-4 concurrences from 1 relation
c2/cL in the formula of speed of a photon
(2) is achieved for all corners a and almost all range of speed of a
lights source, namely at V<(1-5,6 10-7)cL
.
4. Orbital speed of
the Earth practically does not influence speed of photons from stars, only on a
corner of an aberration. Speed of stars and galaxies concerning the Earth almost
does not influence speed of photons from them.
5. The above-stated
calculations show, that all experiences spent till now by definition of speed of
light do not contradict NePaRT.
6. Formulas (1) and
(2) can be used for check of speed of photons from a moving source with the
purpose of a refutation or confirmation of an offered hypothesis.
7. There is an
interest for check of NePaRT be supervision of the secondary photons flying in
various directions from a downpour of ions, formed by a space particle with
ultrahigh energy.
8. The
exclusiveness is taken off from photons, they were made even to usual particles.
Only in NePaRT photons can have mass.
Referenses:
[1]
L.D.Landau, E.M.Lifshits. The field theory
, (., the Science, 1988.)
[2] A.A.Logunov. Bases of the relativity
theory, (., 1982.)
[3] The
Encyclopedia of Physics, (., the Soviet encyclopedia, 1988-1992.)
[4]
A.M.Chepick, Supremum speed of interaction of a matter,
Spacetime and Substance, No. 3(13)-2002, p. 122)
[5] A.Einstein, L.Infeld.
Evolution of physics, (., the Science, 1965.)