- Edited
Steve Dufourny I try to find the good road and several possibilities are on the road, we can write it like this in considering the cosmological constant being this fifth force also Gμν = (8πG/c4)Tμν + Λgμν + Φμν + Aμ;ν + Aν;μ
where Gμν is the Einstein tensor, Tμν is the stress-energy tensor for matter and radiation in the universe, Φμν is the tensor field that represents dark matter, and Aμ is the vector field that represents the interactions of dark energy.
In this equation, we have replaced the Ψμν term with the cosmological constant Λ. This assumption is consistent with some theories that propose a modified gravity framework, such as the f(R) gravity models, where the cosmological constant is regarded as a scalar field that can act as a fifth force. Now if we try to consider this reasoning for the standard model, The idea of an antigravity or repulsive force orthogonal to all the other forces is an interesting one, , we can explore some of the implications of this idea and how it might relate to the standard model of particle physics.
In the standard model, the electromagnetic, weak, and strong forces are all described by gauge theories, which are based on the exchange of force-carrying particles called gauge bosons. The electromagnetic force is mediated by the photon, the weak force is mediated by the W and Z bosons, and the strong force is mediated by the gluon. Each of these forces is associated with a corresponding quantum field: the electromagnetic field, the weak field, and the strong field.
If we assume that there is a fifth force orthogonal to these three forces, we might expect it to be mediated by a different kind of gauge boson, perhaps one that is yet to be discovered. This force would also be associated with its own quantum field, which we might call the fifth force field.
One possibility for the nature of the fifth force is that it could be associated with a scalar field, which is a type of quantum field that has a single value at each point in spacetime. Scalar fields are commonly used in theories of modified gravity, such as scalar-tensor theories, which propose that gravity is mediated by both a tensor field (which describes the curvature of spacetime) and a scalar field (which describes the strength of gravity).
In this scenario, the fifth force could be associated with the scalar field, and it could have an antigravitational effect that balances out the gravitational attraction of matter and dark matter. This would be similar to the way that the cosmological constant (which can be thought of as a scalar field) is thought to provide a repulsive force that counteracts the gravitational attraction of matter and dark matter on cosmic scales. if the existence of a fifth force orthogonal to the other forces were to be confirmed, it would be a major breakthrough in physics and could revolutionize our understanding of the universe. It would require a significant revision of the standard model of particle physics and could potentially lead to the discovery of new particles, fields, and phenomena that are currently unknown.
One potential implication of a fifth force is that it could provide a solution to some of the outstanding problems in physics, such as the nature of dark matter and dark energy. If the fifth force is associated with a scalar field that has an antigravitational effect, it could potentially provide a unified explanation for the observed acceleration of the expansion of the universe and the gravitational behavior of dark matter.
It is possible that the existence of a fifth force could have implications for the EPR paradox, which refers to a thought experiment in quantum mechanics that explores the concept of entanglement between particles.
The EPR paradox suggests that two particles can become entangled in such a way that the state of one particle is instantly correlated with the state of the other particle, even if they are separated by a large distance. This violates the principle of locality, which states that information cannot be transmitted faster than the speed of light.
If a fifth force exists that is orthogonal to the other fundamental forces, it could potentially provide a mechanism for entanglement that is not dependent on the transmission of information through space-time. This could potentially resolve the EPR paradox and provide a deeper understanding of the nature of entanglement and non-locality in quantum mechanics.
If a hypothetical fifth force were orthogonal to the other fundamental forces and had an antigravitational effect, it could potentially have far-reaching implications in physics. It could provide a mechanism for entanglement and non-locality in quantum mechanics that is not dependent on the transmission of information through space-time. This could potentially resolve the EPR paradox and other related issues in quantum mechanics.
Moreover, the antigravitational effect of the fifth force could also provide a unified explanation for the observed acceleration of the expansion of the universe and the gravitational behavior of dark matter. This could potentially resolve the long-standing problems of dark energy and dark matter in cosmology.
Just a thought,, An other different road with a friend Ph is this one where we must change on the left side of the equation I have used
$G_{\mu\nu}$
, which is Einstein-tensor, and it is transformed as two rank tensors but on most terms on the left-hand side of the equations look like they are also transforming as a tensor of two ranks but one of the terms, which is the second term of the left-hand side of the equation, i.e.,
$\Lambda g_{\alpha\beta}$
is multiple of $\Lambda$ which is cosmological constant, while $ g{\alpha\beta}$ is also invariant under transformation and used only for transformation of co-variant to contra-variant. , I think this equation is not possible. , I think, firstly I have to calculate the simple transformation of field, then generators, and then using gauge transformation, must calculate the gauge terms then after finding the transformation and combination of the scalar field, find the using action principle you may find the modified einstein field equation more accurately.For the lagrangian
You may calculate that every term in above equation is lorentz-invariant, this is lagrangian density and $R$ is is the Ricci scalar, which is a curvature. $F_{\alpha\beta}$ is the electromagnetic field strength tensor, which describes the electric and magnetic fields in terms of the electromagnetic potentials. $\theta$ is a coupling constant that determines the strength of
$\Psi{l}$ is a spinor field that describes a fermionic particle. $\bar{\Psi{l}}$ is its conjugate.$Y{ab}$ is a coupling constant that describes the interaction between two fermionic particles, labeled a and b, and a scalar field $H$ is higgs field. $H$ is a complex scalar field representing complex
h.c stand for the Hermitian conjugate of the preceding term.
$|D\alpha H|2$ is the kinetic term for the scalar field $H$, which describes its dynamics in terms of its derivative.
$V(H)$ is the potential energy of the scalar field H, which determines its equilibrium configuration.