Yes, both the cosmological redshift and time dilation are consistent with the principles of F=ma (Newton's second law of motion) and E=mc² (the mass-energy equivalence principle of special relativity).
The cosmological redshift is a phenomenon observed in the light from distant galaxies and other celestial objects. It is caused by the expansion of the universe, which stretches the wavelengths of light as it travels through space. This redshift is consistent with F=ma because it is a consequence of the motion of galaxies away from each other due to the expansion. Newton's second law, F=ma, describes how an object's motion changes in response to a force, and in the case of the expanding universe, the force is the result of the overall gravitational interactions between galaxies and the cosmological expansion itself.
Time dilation, on the other hand, is a consequence of Einstein's theory of relativity, particularly the theory of special relativity. According to this theory, the passage of time is not absolute but is affected by an object's motion or the strength of the gravitational field it experiences. Time dilation has been confirmed through various experiments and observations, such as the behavior of atomic clocks on fast-moving objects or in strong gravitational fields. While time dilation is not directly related to F=ma, it is consistent with the broader framework of E=mc². This equation describes the equivalence between energy (E) and mass (m) and shows that mass and energy are interchangeable. Time dilation is a consequence of how the fabric of spacetime is affected by mass and energy, as described by Einstein's equations.
In summary, both the cosmological redshift and time dilation are consistent with the principles of F=ma and E=mc², albeit in different ways. F=ma explains the expansion of the universe and the redshift of light, while E=mc² is fundamental to the understanding of time dilation and the relationship between mass and energy.