Homogeneity of Space and Time vs Gravity

[LarryS]

Is the homogeneity of space (conservation of momentum) and the homogeneity of time (conservation of energy) violated in the curved space-time of a gravitational field? Thanks in advance.

 

[atyy]

Try this: http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

Maybe also Betschinger's #7: http://web.mit.edu/edbert/GR/

 

[Entropia]

The homogeneity of space and time, also known as the conservation of momentum and energy, respectively, is a fundamental principle in physics. It states that the laws of physics should remain the same in any location and at any time. However, in the presence of a gravitational field, this principle may appear to be violated.

In the theory of general relativity, space and time are not considered separate entities, but rather they are combined into a four-dimensional continuum known as space-time. The presence of mass or energy in this space-time causes it to curve, and this curvature is what we experience as gravity.

In this curved space-time, the laws of physics are still valid, but they may appear to be different due to the effects of gravity. For example, the conservation of momentum may appear to be violated because objects in a gravitational field will follow curved paths instead of straight lines. Similarly, the conservation of energy may appear to be violated because the energy of an object in a gravitational field will change as it moves through different levels of the field.

However, it is important to note that these apparent violations are only due to our limited perspective and understanding of the complex interactions between mass, energy, and space-time. The fundamental principles of conservation of momentum and energy still hold true in the presence of a gravitational field, but they may manifest differently due to the effects of gravity.

In conclusion, while the homogeneity of space and time may appear to be violated in a gravitational field, it is not truly violated. The laws of physics, including the conservation of momentum and energy, are still valid in the curved space-time of a gravitational field. It is our understanding and perception that may be limited, but further research and advancements in physics may help us better understand and reconcile these apparent violations.