Abstract (MT)
The Lorentz transformations have a solution different from that of the Special theory.
On this basis, without prerequisites, follows the conclusion: L'=L/b ; t'=t/b ; m'=mс/b – moving viewpoint K';
L=L'.b ; t=t'.b ; m=mс'.b –
stationary viewpoint
K; (b=(1-v2/c2)1/2
and mс=m'с). These dependences suggest that between the systems K and K' is in force similarity – Principle of similarity (Principle of
difference in proportion).
In summary,
(parameters K')=κ(parameters K), where κ is a coefficient of similarity. It follows from here that the Principle of
relativity will be in force only to isolated laboratory, because solely then in no way can be established
whether κ is b or 1/b. According to viewpoint K, with
increasing the velocity v, kilogram K' decreases, from where are decreasing meter K' and second K' in the same degre. I.e, the scale of system K' alter simultaneously, in
one direction and to the equal degree (in the Theory the changes are in different directions: meter
K' is shortened, second K' is extended, kilogram K' increases). Here it is obligatory to test above dependencies for compatibility with "condition
for preservation the form of laws". The result of the check is positive. To the same test,
conclusions of the Theory fail, which is expected. Suffice it to mention only
its monstrously outrage over reason with "the infinitely big mass in zero
length" and the misapprehension:
in dx'/dt'
– dx'
(meter K') tends to zero, dt'
(second K') tends to infinity.
The
Planck's law E=hf also fails. His coordination with
the prescribed "condition
for preservation the form of laws" leads to the
conclusion that the Planck's
constant h should represent a border discrete portion of energy
Е0 , i.e. h=Е0 .
On the portion of energy h must correspond a portion of mass
m0 , according to the requirement E/m
– const.,
respectively, h=m0c2.
The quantity m0 should represent a border discrete portion of mass – the indivisible atom of Democritus. The constants
m0, h
and c will be the mainly definitions of substance and
matter field - the so-called "ether" (which is absolutely motionless
according the experiments
of: Bradley-1725, Michelson-Morley-1881,
Fizeau-1851, Sagnac-1913 etc.). The
ether forms the space and gives the relationshipe "relativism-quantum mechanics". Here I will mention only that the Gravitational constant is a
combination of them and reports the linear density of matter (the linear
density of ether,
respectively, of space, respectively,
of masses m0).
Keywords: Lorentz transformations, Principle of similarity,
Planck's
constant, atom
of Democritus
INTRODUCTION
It is by all means proven
fact that the World is organized
on the Principle of opposites. But the latter goes into a frank conflict with today's
philosophical and physical conception
"the movement is
an only reality", without
the presence of peace as its antipode (unlike classical views). I.e., the physics
assumed a priori (and the philosophy trustfully follows it)
that the inertial systems are absolutely identical, making an exception to the principle in
question. This incompatibility requires
a redefining the conclusions of relativism.
Because the World is
arranged on the principle of opposites, in this way was formed
and the condition of the Special Theory: "Inertial system K'(x', t') moves towards a stationary system K(x,
t) with velocity v along the axes X'=X ". Be assumed a priori that this
opposition is simulated,
as it does,
there is not a
scientific approach. Because
only thanks to him is reaches to the Lorentz transformations.
Because without this polarity (with
text "systems K and K' are moving relative to each other
...") cannot be compiled equations, the mathematics does not work. But with the normal opposition to systems K and K', the
Lorentz transformations have a solution different from that of the Theory. For clarity of the upcoming analysis
should specify: 1) the dialectics of the cognitive
process, 2) the meaning of the basic physical
quantities, 3) the solution of the relative mass and 4) the solution of the
relative time.
EXPOSITION
1. Dialectics of the cognitive process
From a philosophical point
of view, the principle of opposites raises the almighty dialectic. Namely, it dictates the course of the cognitive process. According to it, the motion
to truth is realized in three phases of cognition in which the ideas of Special
theory are appeared as the second intermediate, antithesis element – "opposite point of view ". This actually
is the transitional form –
"negation for creating a contradiction". Nothing more.
The contradiction is solved in the next third phase of the scheme "negation of negation" – by closing the cognitive outline through
a synthesis returning to the pre-relative positions. So the final resolution of the
problem is obtained as an alloy between the truth of the classical thesis and the relative antithesis, and the
incorrect fragments become irrelevant.
Precisely the described third stage of synthesis is a purpose of this article.
It is time for the contemporary philosophy and physics to realize this dialectic of the process
and the whole absurdity of the attempts to ignore it.
2. Fixation the meaning of the output quantities and
concepts
Objective reality is a material, spatial and changeable. The physics covers this
picture by introducing the quantities: mass – for its materiality, length – for
its spatiality and time – for its mutability. But to this day is not aware
of the logics of these basic concepts (the Theory disfigures their meaning).
In this respect, our treatment is
categorical.
At the base of the World stands a
dualistic matter.
It is both a source and object of
its development, which is due to the force of attraction between the two
opposing sides.
This force provokes activity –
ability to action, to automotion. [1]
Matter, in its turn, forms a power space. Moreover, development of the space starts
the course of time.
The basic physical quantities
represent qualitative and quantitative definitions of this organization of
Nature, namely:
2.1. The term mass (m) means a quantity of
matter.
2.2. The term energy (E) means a quantity
of ability to action of the mass.
2.3. The term length (L) means a quantity
of space.
2.4. The term time
(t) means a quantity of time.
2.5. By reason of its dualism, the matter is
"charged" with energy, from
where comes its mainly connection and ratio E/m=k – const. The parameter k has the meaning of degree
of saturation the mass with energy (or energetic capacity of the
mass). Accordingly, k=c2, where the factor c
is the speed of light. From the inviolable ratio E/m – const. follows:
2.5.1. This ratio is in
force for any point in space.
2.5.2. Under no circumstances cannot have a mass without energy (only mass) and
energy without mass (energy only).
2.5.3. Under no circumstances, the
mass cannot be converted into energy and energy into mass.
2.5.4. Under no circumstances, the
energy cannot be changed without changing the mass and vice versa.
2.5.5. The energy can be
increases
/ decreases only by increasing / decreasing the mass.
2.5.6. The dualism of matter
predetermines a dualism of the mass and energy.
2.5.7. The energetically processes do not present transmission
/ acceptance of energy, but only transforming of
the
energy (and the mass) from one state to another.
3. Specifying the solution of the relative mass
In contrast to
the opinion of Theory the mass,
as a quantity of matter,
should be uncreated and indestructible.
In particular,
the mass mс of an arbitrarily body
(corpus – Lat.) should be constant, independent
of any conditions and prerequisites. [2, p. 311-334]
But as a quantity of matter dualistic, it will consist
of two opposing components dependent on the speed
– potential mass
mp (potentialis –
Lat.) and
kinetic
mass mк
(kinetikos
– Gr.).
More specifically, the mass (at rest) m'с
of moving body – system K', will be
constant. The same mс=m'с
in the stationary system K will
consist of ingredients mp (potential) with
power characteristics and mк
(kinetic) with speed characteristics:
mс=mp+mк -
const. – viewpoint
K (3.1)
With increasing the velocity v (on the
quantity of movement Q'), the
mp component decreases,
and the mк component grows and vice versa. Let us specify that
what the Theory (Physics) called a changing mass of the body is actually the
component mp (the length L and the time t are its attributes), because
the other
(mк) is not susceptible of measurement with power methods
- through the gravity or acceleration(as weightless and
no inert, it remains hidden).
Follows the relationship between mp mass, gravitation and time: With increasing the
velocity v (on the quantity of movement Q'), the mp
mass decreases
(the kilogram
decreases, becomes a lighter), the gravitation decreases (as
an example: low gravitation - an emergence of dinosaurs), the second decreases (becomes a shorter) – the time
speeds up his move.
And vice versa: With decreasing the
velocity v (on the quantity of movement Q'), the mp mass increases (the kilogram increases), the gravitation increases (dinosaurs disappear), the
second increases (becomes a longer) – the time slows down his move.
We derive the
mp mass from the energetic equation:
mр.c2=m'с.c2-1/2m'с.v2 or
mр=m'с.b (i.e. m=m'.b)
wherever b=(1-v2/c2)1/2
(3.2)
The opposite viewpoint m'= m/b is obtained in the same way (either directly from 3.2). But because it is a mirror, here the coefficient is
1/b. This, in short, as a principle, is the philosophy and
physics on the masse. Dualism is everywhere. Where "is missing" (in the inertial systems) the things
are not in order.
4. Specifying the solution of the relative time
Now we will show exactly where and how
the Special Theory makes a mistake as regards the time. For this purpose, first we have to pay
attention to the complete formulation that the Lorentz transformations are derived from, namely:
Inertial system
K'(x', t') is moving to the right towards a stationary
system K(x, t) with velocity v along the axes X'ºX. At the time of concurrence of
the origins O'ºO, from this common center a light
signal is radiated to the right
along X'ºX.
After a time t in K, respectively t' in K', the front of
the signal will have a coordinate х, respectively x' in K'. The ratios x'/x и t'/t are wanted (we replace b=(1-v2/c2)1/2).
We emphasize
heavily that this is the only condition that leads to the dependencies:
x'=1/b(x-vt) ; t'=1/b(t-v.x/c2) –
viewpoint К' (4.1)
Let us explain: As seen from the scheme, for the
juxtaposition (4.1) are needed two clocks, in K and
К', and the "light signal" event whose parameters x, x' and t,
t' are registered (the other possibility is with three clocks
– results from the
first one, the signal is in implicit form).
As a second responsible moment, in order to
no room for speculations, verbatim
we will quote the text about the
time from the original article (A. Einstein – On the Electrodynamics of Moving Bodies, 1905, part
I, §4, http://www.fourmilab.ch/etexts/einstein/specrel/www/), where for convenience we will use the above
designation of the systems only and we will also add some notes
in italic. And here are the author’s reasonings:
"Further, we imagine one of the clocks which are
qualified to mark the time t when at rest relatively to the
stationary system K, and the time t' when
at rest relatively to the moving system, to be located at the origin of the co-ordinates of K', and so adjusted that it marks the time t' (this design eliminates the light
signal). What is the
rate of this clock, when viewed from the stationary system (no way to establish with two clocks only)?
Between the quantities x, t, t', which refer to the position of the clock, we have, evidently,
t'=1/b(t-v.x/c2) (the formula is 4.1 – here x is the abscissa in K
of the light signal)
and x=vt
(here
x is the abscissa in K of the origin O')
Therefore, t'=t.b whence it follows that the time marked by the clock
(viewed in the stationary system) is slow…"
In a word, Einstein arrives at the conclusion t'=t.b, putting x=vt at the place of x in
relation (4.1). However, it is obvious that the two
abscissas are not equivalent. Before us is a wrongful manipulation
of formula (4.1). According to the initial treatment it compares the light signal’s
parameters x, t, t'.
While in the scenario of the quoted text this event is discarded.
But with his falling
off, drop out and the top speed с, coordinate x' and time t'. Then,
the times t' and t of which event does the author
compare...and
how does he compare them once formulas (4.1) do not make sense anymore?
In order to show even more clearly the whole untenability of his reasonings at this point we will adapt the problematic treatment to the initial one by replacing the light signal with
a conditional one* whose velocity is v.
I.e., in system K'
the front of the signal does not leave the origin O' and therefore
it has a coordinate x'=0 and time t'=0.
And in system K,
after the time t,
it will have a coordinate x. So the situation is adjusted to
transformations (4.1),
with a result:
0=x-vt
, respectively x=vt
; 0=t-x/v
, respectively t=x/v (4.1*)
Therefore, the
author’s idea of x=vt will be in force only when x'=0, t'=0,
which makes the conception a classical one – the ongoing event in K is the movement of K', ergo, the conditional signal with its
front in O'. Nothing more! In this case, one cannot draw a
conclusion about the relation t'/t…besides in the way of incorrect
physical and mathematical operations (the light signal is
the heart of the Theory).
While here, we are going to present a scientifically consistent approach
to finding the required relations, based on strict adherence to the initial
formulation, with solution to the end of the transformations derived from it.
[3]
In short, because of displacement of the
systems К and К',
reports x', t' in K' are mono-dimensional (x'=x'mon, t'=t'mon), while reports x, t in K are formed as summary (x=xsum, t=tsum).
I.e., the exact description of
transformations (3.1) is:
x'mon=1/b(xsum-vtsum)
; t'mon=1/b(tsum-v.xsum/c2)
– viewpoint К' (4.1)
Now we must to
solve the expressions in brackets. The coordinate xsum consists of
mono-dimensional coordinate xmon (corresponding to x'mon) and the additional distance v.tsum=OO', i.e. xsum=xmon+v.tsum.
The time tsum consists of mono-dimensional time tmon
(corresponding to t'mon)
and a time supplement
v.xsum/c2
for
distance OO', i.e. tsum=tmon+v.xsum/c2.
The substitution of the summary
quantities leads to the correct direct comparison:
x'mon=xmon/b ;
t'mon=tmon/b
(as a generalization x'=x/b ; t'=t/b ) –
viewpoint К' (4.1)
xmon=x'mon.b
; tmon=t'mon.b
(as a generalization x=x'.b ; t=t'.b ) –
viewpoint К (4.2)
(the effect of the movement is reported without displacement
of the systems (O'=O))
And let us repeat the conclusion: With the increasing
velocity, second К' is shortened and
time К' accelerates. With top speed с, mathematical properly dt'
(second К') tends
to zero (as well as dx' - meter К'). [4]
5. Principle of
similarity
On the basis of specifications made, without prerequisites, follows the
conclusion:
L'=L/b ; t'=t/b ;
m'=mт/b
– viewpoint
K' (5.1)
L=L'.b ; t=t'.b ;
m=mт'.b
– viewpoint
K (5.2)
The combination equations (5.1)-(5.2) suggest that between the systems K and K' is in force similarity – Principle of similarity (principle of
difference in proportion, dependent on the velocity v). This, in summary form, is given by the ratio:
(parameters K')=κ(parameters K), where κ is a coefficient of similarity (5.3)
According to (5.2), with increasing the
velocity v, kilogram K' decreases, from where are decreasing meter K'
and second K' in the same degre.
I.e, the scale of system K' alter simultaneously, in one direction and to the same degree (in the Theory the changes are in different
directions: meter K' is shortened, second K' is extended, kilogram K' increases).
The scale of system K do not
change – there is missing a reason
for it. But they seem growing, according to (5.1), as a mirror effect from decreasing of the scale K'. Dependences (5.1)-(5.2) are confirmed by experiments on Michelson-Morley, Tolman-Lewis and
others. [5]
6. Preservation the form of laws
Here again we will quote the article "On the Electrodynamics of Moving Bodies", 1905,
part I, §2 – A.
Einstein (http://www.fourmilab.ch/etexts/einstein/specrel/www/):
The
laws by which the states of physical systems undergo change are not affected,
whether these changes of state be referred to the one or the other of two
systems of co-ordinates in uniform translatory motion.
In the veracity of this situation, there can be no
doubt. It understands itself. Otherwise, what reality would have been one in which
each system has its own laws?! Only, as it is known, the author moistures in the quoted text meaning of the valid Principle
of absolute relativity (identity) in systems and
assigns
on the last the role of Postulate
(first), which an outside
experimentally enterprise is
questionable.
It is clear that dependences (5.1)-(5.2) must meet unconditionally of
the cited requirement. That is, it is obligatory to test them for compatibility with
"condition for preservation the form of laws". The check will do with the law of the gravitational pull.
For this purpose, we build the following treatment: Inertial
platform (system K') moves on rails with velocity v towards the
stationary Earth (system K). The rails are the axes X'=X. There is an appliance with
masses m1 and m2 on the platform
whose distance
R between the centers is parallel to the axes X'=X, ergo, to the
direction of movement. Let the force of attraction between the masses gives an indication
unit on the screen of the appliance.
Check
the conclusions of Similarity of experience, positioned in K' (on the platform).
Observation in K':
F'=G(m'1.m'2)/R'2=1
Observation
from K, according to (5.2): F=G(m'1.b).(m'2.b)/(R'2.b2)=G(m'1.m'2)/R'2=F'=1
Results:
In both systems the law is the same (keeps its shape).
Now we transfer the appliance
onto the stationary Earth under the same conditions.
Check
the conclusions of Similarity of experience, positioned in K (on the Earth).
Observation in K:
F=G(m1.m2)/R2=1
Observation
from K', according to
(5.1): F'=G(m1/b).(m2/b)/(R2/b2)=G(m1.m2)/R2=F=1
Result:
Again, in both systems the law is the same (keeps its shape).
To the same
test conclusions of the Theory fail, which is expected. Suffice it to mention
only its monstrously outrage over reason with "the infinitely big mass in
zero length" and the misapprehension:
in dx'/dt' – dx' (meter
K') tends
to zero, dt' (second K') tends to infinity.
Actually, this
outcome was clear without testing – we know that in similarity all proportions (laws)
are preserved. In this connection, pay attention to the fact that Planck's law E=hf (h – const., f –
frequency, respectively, f=n/t –
number of oscillations n per unit of
time t), does not cover the "condition for preservation the form of laws
", namely: with E'=hn/t' in K', we have E=hn/(t'.b) in K
and vice versa – with E=h.n/t
in K,
we have E'=h.n/(t/b)
in K'. I.e., the preservation does not happen. Then should suppose that the law
in question is wrong? Its precise form is achieved with correction or so E/t=hn/t, or so E=hn.
7. Planck's constant
In principle, the
energy E is a quantity that never,
nowhere does not depend on the time t . In this sense, M. Planck's formula for the energy (Е=f.h) is not
correct!
The analysis of
the periodic processes [6], such as actually are the electromagnetic waves, shows that their energy E is equal to the constant energy of one
cycle Е0 (in the case Е0=h), multiplied by the number n of cycles performed:
Е=Е0.n=h.n
wherever Е0=h –
const.
(7.1)
While the energy per unit time E/t (or the power N) of
the periodic processes, ergo, of the electromagnetic waves, is equal to the energy h
of one cycle,
multiplied by the number of cycles performed per time unit n/t
(or the
frequency f
of oscillations):
N=E/t=h.(n/t)=h.f (7.2)
Therefore, it is not the energy of electromagnetic
waves, but their power is in proportion to the frequency. The Planck's constant h
represents a border discrete portion of energy.
8. Atom
of Democritus
From the mainly connection and
ratio of the matter will be in force dependence:
E/m=Eр/mр=Eк/mк=Е0/m0=h/m0 –
const. (or Е0=h=m0c2 and h/c2=m0 – const.) (8.1)
The constant m0 represents a border discrete portion of mass,
"charged" with energy h.
The masses m0 should be the indivisible particles of the
matter field (the so-called Ether) and of the objects from substance. I.e., the particle m0 will be the indivisible
atom of Democritus, which builds the Universe. In this sense will have a mass m0 and energy h in each point of the space. Another reality (another matter) does not exist.
From the ratio h/m0 - const. comes the invariable speed of light. Precisely the particles m0
are that shine,
being
set in oscillation.
The constants
m0, h
and c will be the mainly definitions of matter. Here I will mention only that
the gravitational constant is a combination of them and reports the linear
density of matter (the linear density of ether, respectively, of space, respectively,
of masses
m0).
CONCLUSION
Based on the
extracted regularities, we can make some important conclusions. When
the system K' moves relative to a
stationary system K, both systems
already becoming different amounts of motion Q'>Q. But the parameters m',
l', t' are changing simultaneously in one direction and to the same degree. So
the identical (at standstill) systems stand in a respect of similarity. Therefore:
a) Preservation
the form of laws – this is
a natural
law.
b) By no law cannot be
found the inertial motion – this is a natural law.
c) By
no way cannot be found the inertial motion – this is an assertion which (5.1), (5.2), a) and b) disprove. It is in force only for
isolated laboratory.
Solely
then no way to ascertain whether κ
from (5.3) is b or 1/b. But systems K and K' are connected, whence we have the following
equations:
(parameters K')=1/b(parameters K) – viewpoint К' (9)
(parameters K)=b(parameters K') – viewpoint К (10)
This is the usual, ordinary,
natural mathematics. The two sides of the equations are always opposite (in accordance with
the Principle of opposites). Another mathematics we know no (because
it do not exists).
All known experiments prove
that the material environment called "ether" is absolutely motionless
(the full and partially entrainment are a naive notions). [2, p. 365-385] It consists of particles
with m0 mass and h energy. Thus, the ether gives the relationship "relativism-quantum
mechanics".
Reference
[1] Nikolov A. – For
the driving force in nature and society (in Bulgarian)
http://alniko.log.bg/article.php?article_id=80360
[2]
Nikolov A. –
To change of ideas in philosophy and physics, Sofia, 1999 (in Bulgarian)
[3] Nikolov A. – Logical and mathematical
reconsideration of the Lorentz transformations
(in English),
[4]
Nikolov A. – Removing
the make-up (17), (18), (19) of the Special theory
(in Bulgarian)
http://alniko.log.bg/
[5] Nikolov A. – Working out of the Lorentz
transformations from the
Michelson-Morley experiment (in
English)
[6] Nikolov A. – Physics of the matter field (in
Bulgarian)
http://alniko.log.bg/article.php?article_id=97416
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