Galilean experiment at the elementary particle level
As is well known Einsteinian theory of gravity is based on he so called equivalence principle according of which gravity is identified with accelerated frame and therefore both - acceleration and gravity - are described by means of metric given on the space-time continuum. 
 Here we demonstr...
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| Опубліковано в: : | Вопросы атомной науки и техники |
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| Дата: | 2001 |
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| Формат: | Стаття |
| Мова: | Англійська |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2001
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| Цитувати: | Galilean experiment at the elementary particle level / M.J.T.F. Cabbolet, S.S. Sannikov-Proskurjakov // Вопросы атомной науки и техники. — 2001. — № 6. — С. 88-90. — Бібліогр.: 5 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860021994727145472 |
|---|---|
| author | Cabbolet, M.J.T.F. Sannikov-Proskurjakov, S.S. |
| author_facet | Cabbolet, M.J.T.F. Sannikov-Proskurjakov, S.S. |
| citation_txt | Galilean experiment at the elementary particle level / M.J.T.F. Cabbolet, S.S. Sannikov-Proskurjakov // Вопросы атомной науки и техники. — 2001. — № 6. — С. 88-90. — Бібліогр.: 5 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | As is well known Einsteinian theory of gravity is based on he so called equivalence principle according of which gravity is identified with accelerated frame and therefore both - acceleration and gravity - are described by means of metric given on the space-time continuum. 
Here we demonstrate that at the elementary particle level (in the framework of the quantized field theory) there is no equivalence between gravity and acceleration. As a result we may formulate the following statement: two particles with different masses (for example electron and proton) move in one and the same given external gravitational field not identical, they move with different accelerations.
|
| first_indexed | 2025-12-07T16:48:14Z |
| format | Article |
| fulltext |
GALILEAN EXPERIMENT AT THE ELEMENTARY PARTICLE LEVEL
M.J.T.F. Cabbolet, S.S. Sannikov-Proskurjakov
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
As is well known Einsteinian theory of gravity is based on he so called equivalence principle according of which
gravity is identified with accelerated frame and therefore both - acceleration and gravity - are described by means of
metric given on the space-time continuum.
Here we demonstrate that at the elementary particle level (in the framework of the quantized field theory) there
is no equivalence between gravity and acceleration. As a result we may formulate the following statement: two
particles with different masses (for example electron and proton) move in one and the same given external
gravitational field not identical, they move with different accelerations.
PACS: 13.75Gx
INTRODUCTION
In articles about GR [1] Einstein had very often
referred .on the two following circumstances: i) For any
body its inertial mass im is equal to its gravitational one
gm , ii) In given gravitational field all bodies move
identical. So that in particular at the motion in a
homogeneous gravitational field all they will have one
and the same acceleration (Galilean gedanken
experiment). It permits (in Einstein opinion) to identify
such a field with accelerated frame.
In connection with i) we have to indicate on the
other obvious circumstance: mass of any body is made
up from masses of elementary particles (nucleons and
electrons) consisting it and their interactions. Hereby an
elementary particle is characterized by only one mass m
, which is calculated in the theory, see [2]. There is no
another mass of particle (called gm ) and hence of body.
Therefore in our opinion there is no indeed problem of
identity gi mm = , lying in the ground of so-called
equivalence principle. Moreover, in [3] it is shown by
means of the simple calculations in the framework of
quantized field theory 1 that at the elementary particle
level there is a renormalization of gravitational vertex
that means the renormalization of the Newtonian
constant of gravitational interaction γ . As a result the
latter begins to depend on mass of particle which moves
1 Hereby it is very important to know at what level (classical or
quantum) gravitational interaction is switching on. Physical meaning
and mathematical tool of the theory depend on this.
As is well known first pure phenomenological theory of gravity was
given by Newton without explanation of the physical reason of
gravitational force. Einstein considered that the reason is in the metric
of space-time. In connection with this we would like to recall that the
idea about applying of Riemannian geometry for gravity description
was prompted to Einstein by Grossmann. Soon after this Einstein
deflected such an approach, but then returned to it again.
We consider nevertheless that the metric and gravity are quite
different things: the first is connected with co-tangent fibration of
space while the second is connected with so called material one.
More over to apply a quantization procedure to the metric (and to
identify this with space quantization) makes no sense: metric is not
characterized by energy-momentum tensor [1] therefore from physical
point of view quantum of metric is a bad defined notion.
in the field. Therefore for example electron and proton
(or neutron) will move in one and the same external
gravitational field by different way. Universality of
motion mentioned by Einstein (universality of space and
geometry) is not indeed. This means that it is impossible
to reduce the gravity to the metric and curvature of
space-time: at elementary particle level there is no
equivalence principle. Therefore we consider that the
metric approach to gravity is not adequate.
It is very important to understand that the reducing
of gravity to the space geometry does not permit us to
discover true nature of this kind of interaction. In our
opinion it hides in properties of physical substance
which causes the existence of space-time as well as
fundamental particles with all their inner properties and
interactions. For a long time it is called as ether however
in the beginning of the 20-th century it was (by mistake
of course) rejected from physics.
Here we first of all try to answer the question lying in
the ground of equivalence principle: whether indeed
different particles move in given gravitational field by
identical way or not? As the answer turns out negative we
will further formulate a new approach to the gravity based
on the notion of deformation of ether field lying in the
ground of elementary particle theory suggested in [2].
CALCULATIONS
In quantum theory gravitational interaction is
described by the Lagrangian )()( XTXh νµνµ
where
)(Xh νµ is an external gravitational field and νµT is the
energy-momentum tensor built from particle field
operator ψ . This process is shown in the Feynman
diagram a (see Fig. 1).
Further we are interested in the case of zero
transferred momentum k=0 of external gravitational
field only (i.e. hµν(k=0)).
If a particle is charged (like electron or proton) it is
necessary of course to take into account electromagnetic
radiative corrections [3] described by Feynman
diagrams b, c, d, where wavy lines represent virtual
photon from own electromagnetic field of particle.
88 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2001, № 6, p. 88-90.
(Graphs b, c look like the Schwinger’s effect containing
the anomalous magnetic moment and renormalization of
electric charge, graph d is described the interaction of
photon with gravitation field). In our case all these
effects lied to the renormalization of gravitational vertex
or to the renormalization of the Newtonian constant γ .
Fig. 1. Feynman’s graphs of the process.
Continuous, broken, and wavy lines are the charged
fermion, external gravitational field, and virtual
photon, respectively; dark spot is the form-factor
Proceeding from general reasoning we may write for
renormalized Newtonian constant γ ′ the following
expression
))(1( 2mf
π
αγγ −=′ ,
where γ is the «bare» constant and
π
α
4
2e=
is the Sommerfeld fine structure constant. Function f
depends on mass of particle and its spin only. Namely
γ ′ is experimentally observed quantity.
In the framework of the local interaction theory to
calculate f is impossible because ultraviolet divergences
are present in the theory [4]. But we use a new (if it may
be said) improved quantized field theory of interaction,
see [2], in which particle is non-point, smearing object
describing by the bilocal field ),( YXψ (here µX are
usual space-time coordinates and µY are inner
coordinates describing the spatial structure of particle).
Interaction of such a particle is described by usual
Feynman diagrams in which at vertex there is a form-
factor ),( kpρ shown in Fig. 1 by a dark spot. In the
case of massive particle (for example, electron)
interacting with zero mass particle (photon) ),( kpρ has
the form
I
IIkp sin)(),( θρ = ,
where
222)( kppkI −=
and θ is the Heaviside function. As a result all
Feynman’s diagrams become convergent.
Contribution from diagrams b, c into function f is
found in [3] and equal
,)]()1(
3
2)()1(2[ 2
1
22
1
0
2
0 zmKzzmzmKzzdz ++−∫
where nK are the Macdonald functions. Contribution
from diagram d is
)].(
3
1)()[1( 2
1
2
1
0
2
0 zmKzmzmKzdz∫ −−
In the sum we have for )( 2mf :
)].()132(
3
1
)()21)(1[()(
2
1
22
1
0
2
0
2
zmKzzzm
zmKzzdzmf
−++
++−= ∫
In the case of small masses 1< <m (here khmc / is
a dimensionless mass; in the theory there are three
fundamental constants c, h, k, [2]) we have
22 ln
6
510C)-10ln2(17
12
1 )( mmf −+=
( C is the Euler constant). For example for electron its
dimensionless mass is
310.5,0 −=
kh
cme
( GeVkhc 1= ), for proton we have
938,0=
kh
cmp .
In another limit ∞→m we have
,
3
)( 2
2
m
mf π=
and we may consider the correction to be zero.
So we see that particles with different masses are
characterized by different Newtonian constants γ ′
depending on mass of particle. Namely renormalized
constant goes into all experimentally observed effects.
Dependence of γ ′ on particle mass is shown in Fig. 2.
Obviously we have the following expression for
difference ep γγγ ′−′=∆ between γ ’s for proton and
electron
,),(ln
3
5 γε
π
αγγ ep
m
m
e
p ==∆
where
),( epε =
e
p
m
m
ln
3
5
π
α
= 210.3 − .
It follows from here: electron interacts with gravitational
field weaker than proton (we did not take into account
89
strong interaction of proton yet!). This circumstance is
expressed in the character of electron motion in
comparison with proton, namely, in time delay.
Fig. 2. The γ constant vs the charged particle mass
NUMERICAL RESULTS
With this aim we consider the simplest case of free
falling of charged particle in homogeneous gravitational
field of Earth. To estimate macroscopic time delay we
can use the classical non-relativistic formulas in
particular the formula for passed path
2
2tgl
′
= ,
where
2/ EE RMg γ ′=′
( EE RM , are mass and radius of Earth) 2. For passing
one and the same path l electron and proton demand
different times et and pt correspondingly. Hereby the
difference
p
p
p
p
pe g
l
ep
g
gt
ttt
2
),(
2
ε=
∆
=−=∆ .
At free falling electron will come off from proton in
the distance
p
p
ep l
gt
lll ε=
∆
=−=∆
2
2
.
These differences might be compensated by the
initial velocity of electron according to the formula
pe
pepp tv
tgtg
+
′
=
′
22
22
.
Hereat ev is equal
22
pp
e
lg
v ε= .
2 It is well known that at
3/1
2
2
> >
gm
hl (for electron the latter
magnitude is 0,1 cm ) the motion may be considered to be
quasiclassical one, see [5].
If ,/10,10 232 scmgcml pp == so
st p 44,0= .
In this case differences in time and distance are
correspondingly
st 310.6 −=∆
and
cml 3=∆ .
Hereby initial velocity of electron must be
scmve /3,3= .
CONCLUSION
So, we may conclude: at quantum (micro) level
equivalence principle is invalid. Therefore it is very
interesting to carry out the Galilean experiment at the
elementary particle level with electrons and protons.
ACKNOWLEDGMENT
We are indebted to M.I. Konchatny and
A.S. Omelaenko for some kind of assistance.
REFERENCES
1. A. Einstein. Selected Scientific Works. V. 1, M.:
«Nauka», 1965, 700 p.; v. 2, M.: «Nauka», 1966, 880 p.
2. S.S. Sannikov-Proskurjakov. A New Field
Theory of Fundamental Particles //
Ukr. J. Phys. 2001, v. 46, p. 5-13.
3. S.S. Sannikov-Proskurjakov, M.J.T.F. Cabbolet.
About Some Processes in Quantum Gravitation
(Radiative Corrections) // Russian Physical
Journal, 2001, №4, p. 81-86 (in Russian).
4. A.I. Akhiezer, V.B. Berestetskii. Quantum
Electrodynamics. New York: «Interscience
Publ.», 1965, 868 p.
5. L.D. Landau, E.M. Lifshitz. Quantum Mechanics,
M.: “Nauka”, 1963, 704 p.
90
GALILEAN EXPERIMENT AT THE ELEMENTARY PARTICLE LEVEL
M.J.T.F. Cabbolet, S.S. Sannikov-Proskurjakov
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
INTRODUCTION
CALCULATIONS
REFERENCES
|
| id | nasplib_isofts_kiev_ua-123456789-79431 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T16:48:14Z |
| publishDate | 2001 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Cabbolet, M.J.T.F. Sannikov-Proskurjakov, S.S. 2015-04-01T19:45:38Z 2015-04-01T19:45:38Z 2001 Galilean experiment at the elementary particle level / M.J.T.F. Cabbolet, S.S. Sannikov-Proskurjakov // Вопросы атомной науки и техники. — 2001. — № 6. — С. 88-90. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS: 13.75Gx https://nasplib.isofts.kiev.ua/handle/123456789/79431 As is well known Einsteinian theory of gravity is based on he so called equivalence principle according of which gravity is identified with accelerated frame and therefore both - acceleration and gravity - are described by means of metric given on the space-time continuum. 
 Here we demonstrate that at the elementary particle level (in the framework of the quantized field theory) there is no equivalence between gravity and acceleration. As a result we may formulate the following statement: two particles with different masses (for example electron and proton) move in one and the same given external gravitational field not identical, they move with different accelerations. We are indebted to M.I. Konchatny and A.S. Omelaenko for some kind of assistance. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Quantum field theory Galilean experiment at the elementary particle level Галилеев эксперимент с элементарными частицами Article published earlier |
| spellingShingle | Galilean experiment at the elementary particle level Cabbolet, M.J.T.F. Sannikov-Proskurjakov, S.S. Quantum field theory |
| title | Galilean experiment at the elementary particle level |
| title_alt | Галилеев эксперимент с элементарными частицами |
| title_full | Galilean experiment at the elementary particle level |
| title_fullStr | Galilean experiment at the elementary particle level |
| title_full_unstemmed | Galilean experiment at the elementary particle level |
| title_short | Galilean experiment at the elementary particle level |
| title_sort | galilean experiment at the elementary particle level |
| topic | Quantum field theory |
| topic_facet | Quantum field theory |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/79431 |
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