Questions

Kant's distinction

• Phenomenon: what we can observe and measure (interactions)
• Noumenon: the "thing-in-itself" (essence)

Kant's claim: we only ever access phenomena. The noumenon is forever hidden.

But is "essence" even coherent?

If something has no interactions whatsoever — doesn't affect anything, can't be measured, leaves no trace — in what sense does it exist?

Maybe asking "what is it really, beyond all interactions?" is like asking "what is north of the North Pole?" — grammatically valid but meaningless.

Ontic structural realism

Some physicists argue: things ARE their relationships. There's no hidden essence beneath.

The electron IS the thing that has charge -1, spin ½, mass 0.511 MeV. That's not a description of the electron — that IS the electron. Nothing is hiding.

Quantum mechanics pushes us here

A particle doesn't have definite properties until measured. Properties seem to emerge from interactions, not exist prior to them. This suggests reality might be fundamentally relational.

Physics describes behavior, not essence

Physics doesn't tell you what things ARE. It tells you what things DO.

We can't define energy, mass, time, charge, or space in terms of something more fundamental. They're the rock bottom. Instead, we define them operationally:

• Energy: the thing that's conserved when physics doesn't change over time
• Mass: the thing that resists acceleration, and curves spacetime
• Time: what clocks measure
• Charge: the thing that couples to electromagnetic fields

These aren't definitions of essence. They're definitions of behavior and relationship.

Why does this work?

Because physics is about structure, not substance. We don't know what an electron "is" — but we know exactly how it behaves in every situation. And that's enough to build semiconductors, lasers, and MRI machines.

The philosopher Russell called this "knowledge by description" vs "knowledge by acquaintance." We know energy by its relationships, not by meeting it directly.

Is this a problem?

Maybe. Two views:

1. Structural realism: Reality IS structure. It's relations all the way down, with no "stuff" underneath. Mathematics describes reality because reality is mathematical.
2. Hidden ontology: There's something beneath the math — some fundamental "substance" — but physics can't access it. We only see the shadows on the cave wall.

This connects to the question: what is quantum mechanics really telling us about reality?

The honest answer

We don't really know what energy "is." Feynman said it directly: "It is important to realize that in physics today, we have no knowledge of what energy is."

What we do know is that energy is a conserved quantity — a number we can compute that doesn't change over time in a closed system. That's its definition in practice.

Why call potential energy "energy"?

A ball held high doesn't glow or vibrate or look different. Where's the energy?

The key: potential energy is about what could happen, not what is.

• Hold a ball at height h. It just sits there.
• Release it. It accelerates, gains speed, gains kinetic energy.
• Where did that kinetic energy come from?

It came from somewhere. We call that somewhere "potential energy." It's a bookkeeping device that makes conservation work: as kinetic goes up, potential goes down, and the sum stays constant.

Is it "real"?

Two philosophical views:

1. Instrumentalist: Potential energy is just a mathematical trick to make conservation laws work. Only changes in energy are measurable — it's not "real."
2. Realist: Potential energy is stored in the field (gravitational, electric). When you lift a ball, you're doing work against gravity, and that work is stored in the configuration of the ball-Earth system.

The realist view becomes more compelling in electromagnetism, where field energy has real, measurable effects.

The deepest answer (Noether's theorem, lesson 1.3)

Energy is the conserved quantity that exists because physics doesn't change over time.

If the laws of physics are the same today as yesterday, then mathematically, there must exist a quantity that is conserved. We call that quantity energy.

Energy isn't a "thing" — it's a consequence of time-translation symmetry.