Week 11 Session: What degeneracy pressure can and cannot hold up

Reasoning quantitatively about why squeezed electrons push back harder, and why that pushback runs into a ceiling gravity does not share.

28 October 2026

Week 11 gave you the rule and the number, but not the reasoning in between: squeeze electrons and their pressure rises, and above roughly 1.4 times the Sun’s mass, that rise is not enough to hold a white dwarf up. This session works through why, at the level the lecture already supports, without reaching for the full statistical machinery behind it.

Before the session#

Nothing to prepare. The reasoning uses only what Week 11 already gave you: that quantum mechanics does not let a confined electron shrink into arbitrarily little room without its momentum going up.

In the session#

Week 11 already told you the shape of the rule: squeeze something into less room, quantum mechanically, and it needs more momentum to be in there — that is why an atom has a size it cannot be pushed below. A white dwarf is the same rule at a much larger scale. Picture the Sun’s mass packed into a volume roughly the size of the Earth, and work out how crowded that makes the electrons. Halve the volume, the way gravity is trying to, and each electron is confined to less room than before, so by that same rule its momentum has to go up. Higher momentum means a harder outward push — that push is the pressure resisting gravity.

Now ask what happens if you keep halving the volume. Momentum keeps climbing. Speed does not climb forever, though: nothing goes faster than light, so past some point a further increase in momentum buys less and less additional speed, and the pressure stops rising as fast as it needs to. Gravity, meanwhile, gets stronger as you add mass, with no equivalent ceiling. Somewhere the two stop keeping pace with each other. That crossing is the number Week 11 gave you: above roughly 1.4 times the Sun’s mass, squeezing the electrons harder cannot supply enough pressure to win.

Afterwards#

You have not derived the actual mass limit — that takes more machinery than one session gives you, and nothing here required Fermi-Dirac statistics. What you should be able to say is why a limit has to exist at all: the pressure squeezing buys you runs into a ceiling set by the speed of light, and gravity’s demand does not.