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The connection between energy (measured in joules) and the space-time continuum comes mainly from relativity, where energy and matter directly influence the geometry of spacetime.
1. Energy curves spacetime

In General Relativity, developed by Albert Einstein, the key idea is:

Energy and mass tell spacetime how to curve, and curved spacetime tells matter how to move.

Energy is measured in joules, and all forms of energy contribute to spacetime curvature:
Mass energy
Kinetic energy
Radiation energy (light)
Pressure and stress in matter

These appear in Einstein’s field equation:
Gμν=8πGc4TμνG_{\mu\nu} Gμν​=c48πG​Tμν​

The stress-energy tensor represents energy density and momentum flow — essentially how many joules per volume are present and how that energy moves.

So:
More energy (joules) → stronger curvature of spacetime.