Here's my ELI5 attempt of the time/energy relation:
imagine a spring at rest (not moving)
strike the spring, it's now oscillating
the system now contains energy like a battery
what is energy? it's stored work potential
the battery is storing the energy, which can then be taken out at some future time
the spring is transporting the energy through time
in fact how do we measure time? with clocks. What's a clock? It's an oscillator. The energized spring is the clock. When system energy is zero, what is time even? There's no baseline against which to measure change when nothing is changing
There are many machine learning problems which should have symmetries: a picture of a cow rotated 135 degrees is still a picture of a cow, the meaning of spoken words shouldn't change with the audio level, etc. If they were doing machine learning on tracks from the LHC the system ought to take account of relativistic momentum and energy.
Can a model learn a symmetry? Or should a symmetry just be built into the model from the beginning?
Equivariant machine learning is a thing that people have tried... Tends to be expensive and slow, though, and imposes invariances that our model (a universal function approximator, recall) should just learn anyway: If you don't have enough pictures of upside down cows, just train a normal model with augmentations.
imagine a spring at rest (not moving)
strike the spring, it's now oscillating
the system now contains energy like a battery
what is energy? it's stored work potential
the battery is storing the energy, which can then be taken out at some future time
the spring is transporting the energy through time
in fact how do we measure time? with clocks. What's a clock? It's an oscillator. The energized spring is the clock. When system energy is zero, what is time even? There's no baseline against which to measure change when nothing is changing