A new theory of gravity
We proceed from the fact that at the quantum level Einsteinian equivalence principle is invalid (it was demonstrated in our previous contribution). In connection with this we have to look for another physical principle for description of gravity at elementary particle level. The principle we conside...
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| Date: | 2001 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2001
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| Cite this: | A new theory of gravity / S.S. Sannikov-Proskurjakov // Вопросы атомной науки и техники. — 2001. — № 6. — С. 95-97. — Бібліогр.: 7 назв. — англ. |
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| author | Sannikov-Proskurjakov, S.S. |
| author_facet | Sannikov-Proskurjakov, S.S. |
| citation_txt | A new theory of gravity / S.S. Sannikov-Proskurjakov // Вопросы атомной науки и техники. — 2001. — № 6. — С. 95-97. — Бібліогр.: 7 назв. — англ. |
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| container_title | Вопросы атомной науки и техники |
| description | We proceed from the fact that at the quantum level Einsteinian equivalence principle is invalid (it was demonstrated in our previous contribution). In connection with this we have to look for another physical principle for description of gravity at elementary particle level. The principle we consider is already found. It is ether.
|
| first_indexed | 2025-12-07T17:27:18Z |
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A NEW THEORY OF GRAVITY
S.S. Sannikov-Proskurjakov
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
We proceed from the fact that at the quantum level Einsteinian equivalence principle is invalid (it was
demonstrated in our previous contribution). In connection with this we have to look for another physical principle for
description of gravity at elementary particle level. The principle we consider is already found. It is ether.
PACS: 13.75Gx
The situation about ether is very complicated. First
of all, we would like to recall that Einstein in the
beginning of 20 century rejected the ether from physics.
But Newton, Maxwell, Lorentz considered that ether is
very useful and necessary physical substance which
causes all properties of observed world. Soon after this
Einstein understood that our physical space-time may
not exist without ether and he introduced it again.
Hereby he identified ether with metric µ νg of space-
time continuum. So according to Einstein we have
ether = metric = gravity.
We have to pay attention that in Einsteinian theory
metric is created by observed matter. Hence, the ether is
created by observed matter, too. It is typical confusion
of ideas, not admitted indeed.
Meantime, there is already present mathematical
theory in which the ether is a special entity, underlain
the elementary particle level and observed world. In the
theory the ether is the bi-Hamiltonian dynamical system
hidden in the isolated point of space-time discontinuum
and described by non-Lagrangian field f(x) grown from
the point [1]. This dynamical system is the base of
elementary particle existence and arising of all their
interactions [1].
1. In new theory gravity is originated from
flexibility (elasticity or degeneration [1]) of field )(xf ,
which described by deformation of its coordinates µx
written in the form [2,3]:
)(xaxxx µµµµ +=′→ . (1)
Non-deformed ether field )(xf obeys the equation [1]
0),( =
∂
∂ ϕ
µ
µ xf
x
p . (2)
It is the master equation of the ether, solution of which
is written in the form of [1]
)(),( 0 ϕϕ fexf ipx= . (3)
Here 0,0( 0
2 >=== ϕϕϕσϕ µµ ppp , the latter is
very important property of ether) is 4-momentum of
ether quantum f ( µµ px , are variables inside the point,
ϕ are own variables of ether).
Obviously, at deformation (1) ether field becomes
),(),( )( ϕϕ xfexf xipa=′ (3′)
and obeys the equation [2]
)()(),( )()0( xTxihxf
x
p f
µ νµ ν
µ
µ ϕ =′
∂
∂
, (2′)
where
),()()( ϕνµµ ν xfppxT f ′= (4)
is symmetric energy-momentum tensor of ether quantum
f and
)(
2
1)0(
µ
ν
ν
µ
µ ν x
a
x
a
h
∂
∂+
∂
∂
= (5)
is a symmetric tensor field playing the role of gravity.
As ether deformations take place in the point (in the
fiber, where there exists only «vertical» motion), only
«transversal» deformations )(xaµ are considered. They
obey the «Lorentzian» gauge 0=
∂
∂
µ
µ
x
a
and, hence, the
spur of tensor )0(
µ νh is equal zero
0)0( =µ µh . (6)
As these deformations are spontaneous, they have no
sources. Therefore D’Alambertian is zero: 0)( =xaµ
and conditions
0)0( =
∂
∂
µ ν
ν
h
x (7)
are fulfilled. Conditions (6)−(7) play very important role
in the theory (see further).
Obviously, symmetric tensor )()( xT f
µ ν (4) satisfies
all these conditions too:
0,0
)(
)( =
∂
∂
=
ν
µ ν
ν µ x
T
T
f
f . (8)
Further we may go over from special )0(
µ νh to the more
general functions µ νh conserving all these conditions
and having sources. Hereby the integral ∫
Γ
=
x
dxha νµ νµ
~
will depend on final point x and else on contour Γ
coming in x. (It is interesting to notice that since the
space of coordinates x is a vector space so the exact
forms exhaust all closed differential forms on it: it is the
well known Poincare lemma, see for example [4]). Due
to the Stocks theorem we may write
ν ρν ρµνµ ν dShdxh
S
∫∫ =
Γ
][ (9)
where S is a surface limited by the closed contour Γ
and ρνν ρ dxdxdS ∧= ( ∧ is external multiplication). So
we come to the tensor
ν
µ ρ
ρ
µ ν
ν ρµ x
h
x
h
h
∂
∂
−
∂
∂
=][ (hereat
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2001, № 6, p. 95-97. 95
)()0(
][
ν
ρ
ρ
ν
µ
ν ρµ x
a
x
a
x
h
∂
∂
−
∂
∂
∂
∂= ). Functions µ νh and ][ν ρµh
are called to be potentials and strengths of gravity
correspondingly
2. As usually equation (2′) describes only
perception process of gravity (term )()( )()0( xTxh f
µ νµ ν ).
There is no equation of the type )0(
µ νh )( fTµ νγ= yet,
which describes the creation process of gravity, because
for fields f(x) there is no Lagrangian [1].
However if to build coherent states [1]
)()()( ϕµϕ ∫= fdxfx
from ether fields )(xf , integrating over own variables
ϕ with measure )(ϕµ fd (details see in [1]), we get the
fields with zero mass and positive energies (see above;
such fields may not be quantized [1]), for which there is
already Lagrangian in the form
))((
2
ϕσϕϕσϕ µ
µµ
µϕ
++
∂
∂−
∂
∂=
xx
iL (10)
(in the case of spin 1/2) or in the form
µµ
ϕ
ϕϕ
xx
L
∂
∂
∂
∂=
(in the case of zero spin).
From point of view of coherent states ether is two
component gas: spinor and scalar. This gas is a pre-
matter from which our Universe consists of before the
first Big Bang.
Equation for spinor states ϕ is
0=∂
+
ϕσ µµ (11)
(here µµ x∂∂=∂ / ). It looks like the well-known Weyl
equation, although here ϕ is not neutrino field but it is
coherent state of ether. At ether deformation (1) this
equation transits into the equation with interaction
ϕσϕσ νµµ νµµ )(
)0( ∂=∂
++
h (12)
here )(
2
1
)(
µ
ν
ν
µνµ σσσ
xx ∂
∂+
∂
∂=∂
+++
is a symmetric
tensor (compare with (2’), (skew symmetric part, due to
the condition
0)()( =−≈
∂
∂−
∂
∂ ++
ϕϕσσ µννµ
µ
ν
ν
µ pppp
xx ,
see [5], does not work).). Hereby, the interaction term
)()0( ϕ
µ νµ ν ThLi = arises in Lagrangian in which energy-
momentum tensor is (in the case of spin 1/2)
)(
2
)()(
)( ϕσϕϕσϕ µννµ
ϕ
µ ν
++
∂−∂= iT . (13)
So, the field system },{ hϕ is quasi-Lagrangian one
(canonical momentum of this system is obviously
)}(
4
1,{ 0
ν
µµ ν
π γ
ϕ
x
h
t
h
∂
∂
−
∂
∂
; before the first Big Bang it is
the only field system in Universe) and we may close it
adding to the Lagrangian iLL +ϕ the Lagrangian hL of
gravitational field µ νh . Hence total Lagrangian is L=
iLL +ϕ + hL . In the case of small and slowly changed
functions µ νh we can write Lagrangian hL in the form
of gauge invariant quadratic form 2
][
3
8 ν ρµπ γ
hcLh = and
action as an integral ∫= xdLA 4 . Here
2
3
2
hk
cνγ = (14)
is the Newtonian constant of gravitational interaction [2,3].
In the theory there are three fundamental
dimensional constants: c (light velocity), h (Planck
constant) and k (universal wave number with dimension
1−cm ). They are proper characteristics of ether. In (14)
dimensionless normalization constant 201 9=−ν is the
number of mapping of the set from 20 elements ][ν ρµh
into the set from 9 elements µ νh [2,3]. This statement
follows from the set theoretical analog of the Stocks
formula (9), which gives the connection between µ νh
and ][ν ρµh (strictly speaking in fiber there is neither
space-time nor measure and integral on it, only the set
theory methods may be used there). As
cmlk Pl
3310/ −≈=ν is the Planck length, so we have
11410 −≈ cmk .
Further varying total Lagrangian over µ νh we get
the equations
µ νh )(4 ϕ
µ νπ γ T= (15)
describing creation process of gravity.
We think, the physical meaning of new theory is,
first of all, in possibility to determine numerical value of
the Newtonian constant γ .
Now we can construct the energy-momentum tensor
)(hTµ ν for gravitational field ][ν ρµh writing the formula
)
4
1(
8
1 2
][][][
)(
σ τρµ νσ νρσ µρµ ν δ
π γ
hhhT h −= (16)
It satisfies the condition 0)( =hTµ µ . It is not difficult to
get using the equations (12),(15) that the conservation
law is fulfilled:
0)( )()( =+
∂
∂ ϕ
µ νµ ν
ν
TT
x
h . (17)
It is very important to emphasize that as quanta f and
their coherent states ϕ are c-number fields (see [1]) so
gravitation µ νh is a c-number field, too. So at the ether
level gravity is a pure classical phenomenon.
3. After irreversible quantum transition ff → ,
taking place in the bi-Hamiltonian system,
Lagrangian fields ),( YXψ of fundamental
particles arises, see [1] (here f is the second
component of the bi-Hamiltonian system).
Of course, ether deformation (1) is transferred from
field )(xf onto transition matrix elements
96
)(),( xfxf (definition see in [1]) and particle fields
))(
2
1),(
2
1(),,( xxYxxXYX −=+=ψ . Not difficult
to obtain equations for these fields ψ
ψψ νµµ νµµ )()( ∂Γ=+∂Γ hM (18)
(here µµ X∂∂=∂ / ) following from the explicit form of
matrix elements, and to construct the energy-momentum
tensor for these fields
])([
2 )()(
)( ψψψψ µννµ
ψ
µ ν Γ∂−∂Γ= iT , (19)
which creates the gravity field µ νh by means of
equation (compare with (15))
µ νh )(4 ψ
µ νπ γ T= . (20)
As Lagrangian (elementary particle) fields ψ are q-
number quantities so µ νh in (20) must be q-number
quantity too. Hence at the elementary particle level gravity
is quantized. We see that the gravitation interaction of
observed matter is caused by gravity of ether.
It is seen also that for description of gravity at the
ether level the theory of deformation (see for example
[6]) applied to the ether medium is used. Note, that this
theory deals with linear differential forms only. Hence
our approach is principally distinguished from
Einsteinian one, using bilinear (quadratic) differential
forms and Riemannian geometry.
Now, proceeding from the equations (18) and using the
standard «averaging technique» we may obtain gravity
equations at the macro level. Important question is: what is
connection of these equations with equations of GR?
First of all, it should be emphasized that in the
suggested theory the case of strong (non-linear)
gravitational fields µ νh is connected with consideration
of arbitrary Lagrangians hL , but not Hilbert-Einstein
Lagrangian - scalar curvature R . In the given form new
theory is the linear approximation of Einsteinian one.
4. It turns out, besides the elementary particles and
their interactions ether is responsible also for creation of
space-time continuum. Individual quanta f is responsible
for particles arising. But ether in whole (as an ensemble
of quanta f) is else a source of space-time continuum.
First this continuum arose before the first Big Bang
(which is the total irreversible quantum transitions
ff → because the theory of the bi-Hamiltonian
system is non-unitary; from here time arrow originates).
It is remarkable, that ensemble of quanta f is
characterized by the macroscopic energy-momentum
tensor )()( XT f
µ ν (definition see in [2]; it is hydro-
dynamical tensor), principally distinguished from
microscopic one )()( xT f
µ ν (4) or )(ϕ
µ νT (13). This tensor
generates absolute Newtonian space-time continuum
(space-time filling by ether; µX are measurable
coordinates of this space [2]). Remarkable, that its
metric )( Xg µ ν and curvature )(XRµ ν ρ σ are
determined exactly by the Hilbert-Einstein equations. In
the theory space-time continuum is appeared in the form
of compact closed Friedmann manifold 1
3 RS ⊗ (or 4S
). It is atlas of our Universe which is originated in the
process of sticking together of local maps (see [2])
which are Poincare-Minkovski space-time 1,3A with
coordinates µx (the set of non-measurable maps is a
differential system in the sense of [7], the infinite small
(indivisible) part of which is a speceuscula- carrier
space of the field )(xf ). Spaceuscula is identified with
the mini-map 1,3A (maximal size of which is cm810−≈ ,
[2]).
In the framework of new theory the question about
unification of gravitational field )(xhµ ν with metric
field )( Xg µ ν raised by Einstein will probably have
negative answer because it is obviously that ≠)(xhµ ν
)(Xg µ ν and ether ≠ space-time.
In spite of this in the suggested theory all three
famous phenomena (they are: motion of the Mercury
perigee and deviation of light rays - they are gravity
effects, and also red shift - it is metric effect)) are of
course the same.
So, at the ether level two problems of fundamental
importance are solved: switching on gravitational
interaction (and also other kinds of interactions) at
micro level and creation of the space-time continuum at
macro level. They are quite different things although
gravity plays an important role in the forming of space-
time continuum: it pastes together various maps A3,1.
In connection with this we can say that the
Einsteinian GR is the theory of physical space-time
originating (but not gravity). Hereby the GR is the main
part of cosmological theory of our Universe.
REFERENCES
1. S.S. Sannikov-Proskurjakov. Fundamental particles
in a new quantum scheme // Ukr. Journ. Phys. 2001,
v. 46, p. 5-13, p. 775-783, p. 1019-1027; v. 45, p. 778.
2. S.S. Sannikov. Cosmological aspects of the bi-
Hamiltonian dynamical systems // Russian Physical
Journal. 1996, №2, p. 106-115; №8, p. 106-115.
3. S.S. Sannikov-Proskurjakov, M.J.T. Cabbolet.
Interaction problem: gravitational interaction
(submitted to Russian Physica Journal).
4. V.I. Arnold. Mathematical methods in classical
mechanics. M., 1979, p. 431 (in Russian).
5. L.H. Ryder. Quantum field theory. London, 1985, p. 512.
6. V.A. Dubrovin, S.P. Novikov, A.T. Fomenko. Modern
geometry. M.: “Nauka”, 1986 p. 760 (in Russian).
7. S. Sternberg. Lectures on differential geometry. Inc.-
1964, p. 410.
97
A NEW THEORY OF GRAVITY
S.S. Sannikov-Proskurjakov
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
REFERENCES
|
| id | nasplib_isofts_kiev_ua-123456789-79433 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T17:27:18Z |
| publishDate | 2001 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Sannikov-Proskurjakov, S.S. 2015-04-01T19:47:39Z 2015-04-01T19:47:39Z 2001 A new theory of gravity / S.S. Sannikov-Proskurjakov // Вопросы атомной науки и техники. — 2001. — № 6. — С. 95-97. — Бібліогр.: 7 назв. — англ. 1562-6016 PACS: 13.75Gx https://nasplib.isofts.kiev.ua/handle/123456789/79433 We proceed from the fact that at the quantum level Einsteinian equivalence principle is invalid (it was demonstrated in our previous contribution). In connection with this we have to look for another physical principle for description of gravity at elementary particle level. The principle we consider is already found. It is ether. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Quantum field theory A new theory of gravity Новая теория гравитации Article published earlier |
| spellingShingle | A new theory of gravity Sannikov-Proskurjakov, S.S. Quantum field theory |
| title | A new theory of gravity |
| title_alt | Новая теория гравитации |
| title_full | A new theory of gravity |
| title_fullStr | A new theory of gravity |
| title_full_unstemmed | A new theory of gravity |
| title_short | A new theory of gravity |
| title_sort | new theory of gravity |
| topic | Quantum field theory |
| topic_facet | Quantum field theory |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/79433 |
| work_keys_str_mv | AT sannikovproskurjakovss anewtheoryofgravity AT sannikovproskurjakovss novaâteoriâgravitacii AT sannikovproskurjakovss newtheoryofgravity |