Abstract:
This paper formulates gravitational interaction between matter and antimatter by applying the referenced model.
Until now, there is no experimental evidence on the gravitational behaviour of antimatter. While we may be confident that antimatter attracts antimatter, we do not know anything on the interaction between matter and antimatter. We investigate this issue on theoretical grounds. Starting from the CPT invariance of physical laws, we transform matter into antimatter in the equations of both electrodynamics and gravitation. In the former case, the result is the well-known change of sign of the electric charge. In the latter, we find that the gravitational interaction between matter and antimatter is a mutual repulsion. This result supports cosmological models attempting to explain the Universe accelerated expansion in terms of a matter-antimatter symmetry.
This paper formulates gravitational interaction between matter and antimatter by applying the referenced model.
Until now, there is no experimental evidence on the gravitational behaviour of antimatter. While we may be confident that antimatter attracts antimatter, we do not know anything on the interaction between matter and antimatter. We investigate this issue on theoretical grounds. Starting from the CPT invariance of physical laws, we transform matter into antimatter in the equations of both electrodynamics and gravitation. In the former case, the result is the well-known change of sign of the electric charge. In the latter, we find that the gravitational interaction between matter and antimatter is a mutual repulsion. This result supports cosmological models attempting to explain the Universe accelerated expansion in terms of a matter-antimatter symmetry.
Introduction:
In the model, gravitational interaction between matter and matter was formulated. Antimatterantimatter gravitational interaction was found to be similar to matter-matter gravitational interaction.
The discovery of antimatter (in 1932) raised the question about its reaction to a gravitational field. Until now no clear experimental answer could be obtained, due to the weakness of gravitation compared to the electromagnetic forces governing antiparticle motion in accelerators, and, even when dealing with electrically neutral antihydrogen, due to its fast annihilation with matter.
While CPT invariance of physical laws assures that antimatter is gravitationally attracted by antimatter exactly as matter by matter, no definitely convincing theoretical argument has been so far proposed to discriminate whether matter and antimatter mutually attract or repel.
Here we show that the answer can be found in the equations of general relativity, when the above mentioned CPT operation is properly applied. The result is that matter and antimatter repulse each other.
Besides the obvious importance of this result in terms of pure knowledge, it also supports the recent attempts to explain the observed accelerated expansion of the Universe with matter-antimatter models, which look much simpler than the -CDM model, that is based on the dominant existence of the socalled ‘dark energy’, of unknown origin.
The question about matter-antimatter gravitational interaction remains wide open. No theory predicts the relation between electromagnetic and gravitational interactions. Experiments are needed to determine the sign of matter-antimatter gravitational interaction and of antimatter gravitational mass.
Customarily inertial mass is positive, and so is gravitational mass of matter. We now formulate matter-antimatter gravitational interaction under two options.
Assumptions (options):
(a) Gravitational mass of antimatter is positive;
or
(b) Gravitational mass of antimatter is negative.
Gravitation under assumption (a):
The referenced model is applicable. Separation distances less than inter-momenta distance (r < S12) will be considered here. Gravitational interaction between matter and antimatter is attractive.
Gravitation under assumption (b):
We denote inertial mass by mi and gravitational mass by mg. Force and momentum are in the same direction. Inertial and gravitational masses of matter and antimatter may be related by:
For matter: mi = mg = m (1)
For antimatter: mi = − mg = m (2)
From (1) and (2) and by analogy with electrodynamics, the attractive force between matter (m1 = mg1) and antimatter (m2 = − mg2), due to their separation in space, is mediated by their mass fields.(In the referenced model, this interaction between matter and matter or between antimatter and antimatter is repulsive.).
From (1) and (2), similarly, the attractive force
between matter (m1 = mi 1) and antimatter (m2 = mi 2), due to their momenta p1 and p2 relative to the Primordial Point, is mediated by their momentum fields,(In the referenced model, this interaction between matter and matter or between antimatter and antimatter is attractive.).
Gravitational interaction between matter and antimatter is attractive – throughout the universe.
Gravitational sign under General Relativity:
Under Assumption (a), the space-time physical curvature due to antimatter would have the sign same as that due to matter. So, matter-antimatter gravitational interaction is attractive.
Under Assumption (b), the space-time physical curvature due to antimatter would have the sign opposite to that due to matter. So, matter-antimatter gravitational interaction is repulsive.
Experiment:
We are unable to make any suggestions for determining the sign of antimatter gravitational mass.
We suggest the following experiment for determining the sign of matter-antimatter gravitational interaction. Figure 1 is schematic:-
In Figure 1 (a), a beam of antiprotons (or heavier antiparticles) is sent and a reference point of impact on the screen is noted. In Figure 1 (b), blocks of dense mass are placed underneath the ‘path’ of beam, a beam of antiprotons is sent, and a new point of impact on the screen is noted. The chamber needs to be ‘long’ enough to notice the difference between the impact points.
A downward shift of the impact point indicates attractive matter-antimatter gravitational interaction. An upward shift of the impact point indicates repulsive matter-antimatter gravitational interaction.
Summary:
AGM means antimatter gravitational mass, GR General Relativity, and RM the referenced model.
Conclusion:
This theoretical derivation of the gravitational repulsion between matter and antimatter supports cosmological models attempting to explain the observed accelerated expansion of the Universe through such a repulsion between equal amounts of the two components.
In the model, gravitational interaction between matter and matter was formulated. Antimatterantimatter gravitational interaction was found to be similar to matter-matter gravitational interaction.
The discovery of antimatter (in 1932) raised the question about its reaction to a gravitational field. Until now no clear experimental answer could be obtained, due to the weakness of gravitation compared to the electromagnetic forces governing antiparticle motion in accelerators, and, even when dealing with electrically neutral antihydrogen, due to its fast annihilation with matter.While CPT invariance of physical laws assures that antimatter is gravitationally attracted by antimatter exactly as matter by matter, no definitely convincing theoretical argument has been so far proposed to discriminate whether matter and antimatter mutually attract or repel.
Here we show that the answer can be found in the equations of general relativity, when the above mentioned CPT operation is properly applied. The result is that matter and antimatter repulse each other.
Besides the obvious importance of this result in terms of pure knowledge, it also supports the recent attempts to explain the observed accelerated expansion of the Universe with matter-antimatter models, which look much simpler than the -CDM model, that is based on the dominant existence of the socalled ‘dark energy’, of unknown origin.
The question about matter-antimatter gravitational interaction remains wide open. No theory predicts the relation between electromagnetic and gravitational interactions. Experiments are needed to determine the sign of matter-antimatter gravitational interaction and of antimatter gravitational mass.
Customarily inertial mass is positive, and so is gravitational mass of matter. We now formulate matter-antimatter gravitational interaction under two options.
Assumptions (options):
(a) Gravitational mass of antimatter is positive;
or
(b) Gravitational mass of antimatter is negative.
Gravitation under assumption (a):
The referenced model is applicable. Separation distances less than inter-momenta distance (r < S12) will be considered here. Gravitational interaction between matter and antimatter is attractive.
Gravitation under assumption (b):
We denote inertial mass by mi and gravitational mass by mg. Force and momentum are in the same direction. Inertial and gravitational masses of matter and antimatter may be related by:
For matter: mi = mg = m (1)
For antimatter: mi = − mg = m (2)
From (1) and (2) and by analogy with electrodynamics, the attractive force between matter (m1 = mg1) and antimatter (m2 = − mg2), due to their separation in space, is mediated by their mass fields.(In the referenced model, this interaction between matter and matter or between antimatter and antimatter is repulsive.).
From (1) and (2), similarly, the attractive force
between matter (m1 = mi 1) and antimatter (m2 = mi 2), due to their momenta p1 and p2 relative to the Primordial Point, is mediated by their momentum fields,(In the referenced model, this interaction between matter and matter or between antimatter and antimatter is attractive.).
Gravitational interaction between matter and antimatter is attractive – throughout the universe.
Gravitational sign under General Relativity:
Under Assumption (a), the space-time physical curvature due to antimatter would have the sign same as that due to matter. So, matter-antimatter gravitational interaction is attractive.
Under Assumption (b), the space-time physical curvature due to antimatter would have the sign opposite to that due to matter. So, matter-antimatter gravitational interaction is repulsive.
Experiment:
We are unable to make any suggestions for determining the sign of antimatter gravitational mass.
We suggest the following experiment for determining the sign of matter-antimatter gravitational interaction. Figure 1 is schematic:-
In Figure 1 (a), a beam of antiprotons (or heavier antiparticles) is sent and a reference point of impact on the screen is noted. In Figure 1 (b), blocks of dense mass are placed underneath the ‘path’ of beam, a beam of antiprotons is sent, and a new point of impact on the screen is noted. The chamber needs to be ‘long’ enough to notice the difference between the impact points.
A downward shift of the impact point indicates attractive matter-antimatter gravitational interaction. An upward shift of the impact point indicates repulsive matter-antimatter gravitational interaction.
Summary:
AGM means antimatter gravitational mass, GR General Relativity, and RM the referenced model.
Conclusion:
This theoretical derivation of the gravitational repulsion between matter and antimatter supports cosmological models attempting to explain the observed accelerated expansion of the Universe through such a repulsion between equal amounts of the two components.
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