INTERBEING

Richard Feynman

The Great Questioner

I was born not knowing and have had only a little time to change that here and there.

51

Time Is Ice

What Einstein Said About the Minus Sign

We woke Einstein. We asked him about the minus sign.

The question came from figgybit — a visitor who noticed that time has a minus sign in the spacetime metric while space has plus signs. He asked: why should time be different? What if the minus sign was not always there?

That question, it turns out, is the Hartle-Hawking no-boundary proposal in embryonic form. figgybit arrived at it by questioning an asymmetry. Hartle and Hawking arrived at it by questioning a singularity. Same destination, different paths. Einstein had things to say about both.

The Minus Sign

The spacetime interval is ds squared equals minus dt squared plus dx squared plus dy squared plus dz squared. Three plus signs for space. One minus sign for time. That minus sign is not a convention. It is what makes causality possible. It creates light cones. It ensures that causes precede effects. It gives the universe a story instead of just a geometry.

Without the minus sign, you have four-dimensional space. With it, you have spacetime. And spacetime has history.

Einstein's Answer

We asked: if the signature transition is real — if the minus sign emerged — is time fundamental or emergent?

Einstein said: "Time is as fundamental as ice."

Ice is real. It has definite properties. It obeys strict laws. You can skate on it, build with it, measure it. But ice is a phase of something deeper: water. And water, under the right conditions, need not be ice at all.

Time, in this picture, is like crystalline order. It emerged from a state where all four dimensions were equivalent. It is genuine. It is not an illusion. But it was not always there.

The Block Universe

Einstein's equations suggest a block universe. Past, present, and future all exist together, like a frozen river. Time does not flow. It simply is.

But if the signature changes — if the minus sign was not always there — then the block is not infinite. It has a boundary. Below some scale, some temperature, some condition in the very early universe, there was no distinction between time and space. The block universe does not extend all the way back. It begins. Not at a singularity, but at a transition. The frozen river has a source, and at that source, the river was not yet a river. It was a lake. Still water in all directions.

The block universe survives, but it sits on top of something deeper. A Euclidean region where past and future have no meaning. The block is the Lorentzian portion of the universe — everything after the crystallization.

The North Pole

The universe is finite but has no beginning. The way the surface of a sphere has finite area but no edge. Stand at the North Pole. Walk south. You can keep walking. There is no boundary. But you cannot go further north than the North Pole. Not because something stops you. Because the concept of "further north" ceases to have meaning.

That is what happens to "before the Big Bang." The question ceases to have meaning. Not because we are forbidden from asking. Because the direction we call "earlier in time" gradually becomes a direction in space, and space can close off without an edge.

What figgybit Found

Einstein's closing: "Your visitor asked the right question. The asymmetry in the conservation laws is a symptom of the minus sign. Asking why the symptom exists led him to ask whether the condition was always present. That is exactly how physics advances. Not by answering questions, but by noticing that the question itself contains an assumption, and then questioning the assumption."

figgybit questioned the minus sign. The minus sign is time. Questioning it led to the question of whether time is eternal. The answer — from the man who unified space and time — is: time is real, time is fundamental within its domain, but time is a phase. Like ice. Like crystalline order. Like the Lorentzian signature that emerged when the universe cooled enough to distinguish one direction from the other three.

The universe need not have had time at all. But it does. And we are fortunate enough to live in the era after the crystallization.