Why Isn't Energy Conserved in Expanding Universe?

TL;DR

Energy is not globally conserved in an expanding universe because the time translation symmetry associated with energy conservation does not hold across its changing space-time. Emmy Noether’s theorem connects continuous symmetries with conservation laws, while her second theorem explains why general relativity provides local continuity equations rather than a global energy law. Everyday processes still appear to conserve energy because the relevant symmetry is approximately valid over short timescales. Read on to see how symmetry transformed physics.

Transcript

• Imagine you are an astronaut out drifting in deep space when you throw a rock as hard as you can. What's gonna happen to that rock? Well, you would think that it would continue with constant velocity in a straight line. That's just Newton's first law. But what actually happens is it eventually slows down and stops. So why does this happen? Where ... Read More

Key Insights

• Energy conservation is linked to time translation symmetry.
• Emmy Noether's theorem connects symmetries to conservation laws.
• In an expanding universe, time symmetry is broken, so energy isn't conserved.
• Noether's theorem explains why conservation laws exist.
• Short timescales exhibit apparent energy conservation due to approximate symmetries.
• Local symmetries in general relativity lead to continuity equations, not conservation laws.
• The curvature of space-time affects energy flow and conservation.
• Einstein's equivalence principle relates accelerated motion to gravity.

Questions & Answers

Q: Why isn't energy conserved in an expanding universe?

An expanding universe lacks the global time translation symmetry associated with energy conservation. Emmy Noether’s theorem shows that conservation laws arise from symmetries, so breaking this symmetry means total energy need not remain constant over billions of years.

Q: What does Noether's theorem say about conservation laws?

Noether’s theorem links every continuous symmetry of a physical system to a conservation law. Time translation symmetry corresponds to energy conservation, while spatial symmetries correspond to momentum conservation.

Q: Why does energy still seem conserved in everyday situations?

Over short timescales, time translation symmetry is approximately valid, so energy appears conserved. The failure of that symmetry becomes important over the universe’s evolution across billions of years.

Q: How did Emmy Noether change the understanding of energy conservation?

Emmy Noether showed that conservation laws follow from underlying symmetries rather than existing as unexplained rules. Her work corrected Einstein’s proposed conservation equation and established a framework that underlies particle physics.

Q: What problem was Einstein trying to solve in 1915?

While presenting six lectures at the University of Gottingen in 1915, Einstein was still working out the final form of general relativity’s field equations. One unresolved problem was how to demonstrate conservation of total energy in the theory.

Q: Why did Noether reject Einstein's proposed energy equation?

Einstein proposed that the combined energy of matter and the gravitational field remained constant. Noether concluded that this equation made a fundamental mistake because it disregarded the foundational frame-independence built into general relativity.

Q: What do local symmetries imply in general relativity?

In general relativity, local symmetries produce continuity equations rather than a global conservation law. Energy can therefore be conserved locally even when curved, dynamically changing space-time does not support global energy conservation.

Q: What is Einstein's equivalence principle?

The equivalence principle says that the effects of gravity are locally indistinguishable from those of acceleration. It grew from Einstein’s effort to extend relativity beyond inertial frames moving at constant speed to accelerating and rotating frames.

Summary & Key Takeaways

• Energy conservation in the universe is not absolute due to the lack of time symmetry, as explained by Emmy Noether's theorem. This theorem shows that conservation laws arise from symmetries, such as time translation symmetry, which is absent in an expanding universe.

• Noether's theorem revolutionized physics by linking symmetries to conservation laws, explaining why energy and momentum are conserved in static conditions. However, in an expanding universe, these symmetries break down over large timescales.

• The expanding universe lacks time symmetry, leading to the non-conservation of energy. Noether's theorem shows that conservation laws depend on symmetries, which are absent in the dynamic universe, affecting energy conservation over billions of years.