Symmetry: Where the Universe and Physics (and Consciousness) Begins - The Origin of Causality (the c in e=mc^2)

Plato, "Philebus"

SOCRATES: What, then, is there in the mixture which is most precious, and which is the principal cause why such a state is universally beloved by all? When we have discovered it, we will proceed to ask whether this omnipresent nature is more akin to pleasure or to mind.

PROTARCHUS: Quite right; in that way we shall be better able to judge.

SOCRATES: And there is no difficulty in seeing the cause which renders any mixture either of the highest value or of none at all.

PROTARCHUS: What do you mean?

SOCRATES: Every man knows it.

PROTARCHUS: What?

SOCRATES: He knows that any want of measure and symmetry in any mixture whatever must always of necessity be fatal, both to the elements and to the mixture, which is then not a mixture, but only a confused medley which brings confusion on the possessor of it.

PROTARCHUS: Most true.

SOCRATES: And now the power of the good has retired into the region of the beautiful; for measure and symmetry are beauty and virtue all the world over.

PROTARCHUS: True.

SOCRATES: Also we said that truth was to form an element in the mixture.

PROTARCHUS: Certainly.

SOCRATES: Then, if we are not able to hunt the good with one idea only, with three we may catch our prey; Beauty, Symmetry, Truth are the three, and these taken together we may regard as the single cause of the mixture, and the mixture as being good by reason of the infusion of them.

PROTARCHUS: Quite right.

Then what does it mean to "break symmetry"? (from Google AI): 

Symmetry breaking in physics occurs when a symmetric system (ordered or law-based) transitions into a less symmetric, often more ordered, state, or when fundamental laws lack symmetry. Key mechanisms include spontaneous symmetry breaking (e.g., Higgs mechanism, phase transitions like freezing) and explicit symmetry breaking (e.g., gravity, magnetic fields).

Spontaneous Symmetry Breaking: The underlying physical laws are symmetric, but the actual state of the system is not. As explained in the Wikipedia entry on Symmetry Breaking, a common analogy is a ball on a symmetric hill falling to one side; the hill is symmetric, but the ball's final position is not.

• Higgs Mechanism: Gives mass to particles; the vacuum breaks electroweak symmetry.
• Phase Transitions: Water freezing into ice (loses continuous translation symmetry) or magnets forming, as discussed in this Reddit thread and this Quora answer.

Explicit Symmetry Breaking: The fundamental equations or Lagrangian of a system themselves lack symmetry, as detailed in the Stanford Encyclopedia of Philosophy entry.

Gravity: A magnetic field or gravity pointing down breaks rotational symmetry.

Commonly Broken Symmetries

• Rotational Symmetry: A system changes when rotated (e.g., a stick buckling), noted in this Youtube video.
• Gauge Symmetry: Fundamental symmetries of nature that, when broken, allow particles to acquire mass, explains the Department of Energy.
• Parity (P-Symmetry): Left/right reflection symmetry, broken in weak interactions.

Examples in Physics

• Magnetism: Atoms align in one direction below the Curie temperature, as mentioned on Quora.
• Cosmology: The inflationary field decay after the Big Bang.
• Fluid Dynamics: Water flowing from a tap forming distinct, non-circular shapes as shown by Sabine Hossenfelder.

As highlighted by the Stanford Encyclopedia of Philosophy, these concepts are foundational to understanding the diverse structures in the universe, as a perfectly symmetric universe would be uniform, massless, and essentially featureless.

Space Symmetry Conserves Momentum:Time Symmetry Conserves Energy:Space:Time

from Google AI:

Energy is fundamentally divided into kinetic (motion) and potential (stored) types, taking forms like mechanical, thermal, electrical, radiant, and nuclear. Potential energy includes gravitational, elastic, and chemical forms, while kinetic includes motion, sound, and electromagnetic waves. Energy converts between these types, obeying conservation laws.

Primary Types of Energy

Potential Energy (Stored Energy)- Time:

• Gravitational: Stored based on an object's position, such as a ball at the top of a hill or water in a dam.
• Chemical: Energy stored in molecular bonds, such as in food, gasoline, or batteries.
• Elastic: Stored by stretching or compressing, like in a rubber band or spring.
• Nuclear: Energy stored in the nucleus of an atom.

Kinetic Energy (Energy of Motion) - Space:

• Motion/Mechanical: Energy of moving objects, such as a car driving or wind.
• Thermal (Heat): The movement of atoms and molecules within substances.
• Radiant (Electromagnetic): Energy traveling in waves, such as light, X-rays, and radio waves.
• Sound: Movement of energy through substances in longitudinal waves.
• Electrical: The movement of electrons.

Momentum and Related Energy Concepts

• Momentum: While not a type of energy, momentum (p=mv) is directly related to kinetic energy (Ek=p^2/2m), representing the "quantity of motion" in an object.
• Mechanical Energy: The sum of an object's potential and kinetic energy.
• Internal Energy: The total energy contained within a thermodynamic system, often the sum of microscopic potential and kinetic energies.
• Rest Energy: The energy associated with an object's rest mass, described by E=mc^2

Forms of Energy Conversion

Energy is rarely found in only one form and frequently converts between potential and kinetic. For example, a falling ball converts potential energy into kinetic energy. Chemical energy in fuel is converted into thermal and kinetic energy to propel a car.

"Philosophy is the translation of Eros into Logos" 

- Byung-Chul Han

"...and the desire and pursuit of the whole is called, "Love"" 

- Plato "Symposium" (Aristophanes' Speech)

The Lacanian 'Real'

Isn't that Just SUPER?