Vector field, and Lorentz Symmetry

[Mk]

What are they?

"A fundamental property of the natural world that is of supreme importance for physics. It has two components: rotational symmetry, and boost symmetry."

 

[pervect]

Do a physics experiment in an inertial frame. (Note: this disqualifies the surface of the Earth for some very sensitive experiments). Do it again, this time with your apparatus rotated by some angle theta, or phi. The fact that your results do not change with rotation is due to rotational symmetry of the laws of physics.

Now do the experiment again, this time in a second inertial frame, that's moving at a constant velocity relative to the first. The results of the experiment still do not change. This is because of the "boost" symmetry of physics.

Together, these symmetries are known as the Lorentz group.

If you add in the fact that you can move your apparatus N feet in any direction, or perform experiments at different times, and get the same results, you have a larger group of symmetries, known as the Poincare group.

 

[Mk]

Do a physics experiment in an inertial frame. (Note: this disqualifies the surface of the Earth for some very sensitive experiments). Do it again, this time with your apparatus rotated by some angle theta, or phi. The fact that your results do not change with rotation is due to rotational symmetry of the laws of physics.

Now do the experiment again, this time in a second inertial frame, that's moving at a constant velocity relative to the first. The results of the experiment still do not change. This is because of the "boost" symmetry of physics.

Together, these symmetries are known as the Lorentz group.

If you add in the fact that you can move your apparatus N feet in any direction, or perform experiments at different times, and get the same results, you have a larger group of symmetries, known as the Poincare group.

Ahh! ok, thanks a lot. But what are vector fields, and vector field lines? Do they correspond to the angle rotated for rotational symmetry, and the way it object is moving in boost symmetry? If so, do the lines curve when on a plane of positive curvature?