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Faces of Physics:

FAKE or FACT?

Diederik Roest

Feb 13, 2020

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Can we understand the hydrogen atom?

Quantum Mechanics

Wave function

Wave function

Linear superposition of simple states

Three quantum numbers:

n - excited state

l, m - magnitude and orientation

of angular momentum

Energy spectrum

Energy spectrum

Time-independent systems: energy conserved

Spectrum of states in general very complicated

Rotational symmetry: independent of orientation

Energy depends on n and l

Special case: hydrogen atom with Coulomb potential

Energy depends only on n... why?

Claim: due to additional symmetry!

Can we include gravity?

Special Relativity

Newton

Newton vs Einstein

Problems with Newton's gravity:

- instantaneous (what about c?)

- distance (according to whom?)

- why are inertial and gravitational mass identical ?!?

Einstein

From special to general relativity?

Einstein: the solution is General Relativity, with a spin-2 field (curved space-time).

Propagation through field addresses problems, and includes equivalence principle

Claim: alternative with spin-0 field, also compatible with equivalence principle

Answers

Symmetry

Hidden symmetry

Any non-relativistic system with a 1/r potential has additional symmetry

Hydrogen atom

Kepler problem

Relativity

Including relativity

Most relativistic systems break this symmetry:

spin-0 field

spin-2 field

goes in the wrong direction...

explains anomalous orbit of Mercury

Modern physics

Quantum gravity?

Hidden symmetry important for quantum gravity:

Can be preserved by including both spin-0 and spin-2 fields. Toy model?

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