The physics of empty space,explained from the ground up.
03All-directions field
Every arrow points inward. There is no universal down.
Touch the physics
Compare a trajectory and a distribution
Study 1 of 7: The ground state
A stationary spread, not a fast jitter
Scroll sideways if needed. Keyboard: focus the diagram frame, then use the arrow keys.
Show me the trajectory picture
Energy, in units of ħω
Show me the state
Energy, in units of ħω
Two pictures of the same ground state, side by side. Switch between them and watch the clocks. One picture has a bead swinging in a bowl and a clock counting periods; it is the intuition most readers arrive with, and this chapter teaches against it. The other is the state as it actually is — a spread over position that holds half a quantum and does not change with time at all. Its clock is greyed out because there is nothing for it to count.
Show me the trajectory picture
The picture this chapter is teaching against
Here is the bead in the bowl. It has a position at every instant, it swings out to a turning point and back, and a clock underneath it counts the periods. This is a fair intuition for one thing only: an energy you cannot remove, because nothing you do brings this bead to rest. It is worth looking at carefully, and it is worth knowing what it is not: there is no hidden classical path underneath the quantum ground state for this bead to be tracing.
Clock: 0.00 periods
Show me the state
Nothing here changes with time, so this clock is stopped.
Here is the state. The spread over position is the whole of it — measure many independently prepared oscillators and this is how the results are distributed. Nothing in this panel changes with time, so the clock beneath it has nothing to count. The uncertainty principle forbids a definite position together with a definite momentum; it does not hide a trajectory under a blur. The spread is the state.
Clock: —
- Ground-state energy
- half a quantum, ½ħω
- Share of measurements landing inside the shaded band
- 52%
OpenStax, University Physics volume 3, §7.5, the quantum harmonic oscillator — the stationary ground state and ½ħω, as taught
The state: a stationary spread over position holding half a quantum. The clock is stopped because nothing in this panel changes with time. Nothing here changes with time, so this clock is stopped.
Start here
A circling charge radiates, so the Bohr atom should pour out its energy and collapse into the nucleus in about ten picoseconds. It does not.
Hal Puthoff's 1987 paper gives the mechanism: the power the orbiting electron radiates away and the power it absorbs from the zero-point field of the vacuum balance, and the radius where they balance is exactly the Bohr radius.
The Pons–Fleischmann Palladium Cell
What did a palladium rod, heavy water, and a careful heat ledger show?
Pons and Fleischmann turned a tiny metal cell into a question with an energy ledger: where did the extra heat come from?