Why Isn't Energy Conserved in Expanding Universe?

TL;DR

Energy isn't conserved in our universe due to the lack of time symmetry, a concept explained by Emmy Noether's theorem. This theorem links symmetries in nature to conservation laws, showing that energy conservation depends on time translation symmetry, which doesn't hold in an expanding universe. Over short timescales, energy seems conserved, but over billions of years, this symmetry breaks down.

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?

Energy isn't conserved in an expanding universe because the universe lacks time translation symmetry. According to Emmy Noether's theorem, conservation laws arise from symmetries, and energy conservation is linked to time symmetry. In an expanding universe, this symmetry is broken, leading to the non-conservation of energy over large timescales.

Q: What is Noether's theorem?

Noether's theorem, formulated by mathematician Emmy Noether, establishes a profound link between symmetries and conservation laws in physics. It states that every continuous symmetry of a physical system corresponds to a conservation law. For instance, time translation symmetry leads to energy conservation, while spatial symmetries relate to momentum conservation.

Q: How does Noether's theorem relate to energy conservation?

Noether's theorem relates energy conservation to time translation symmetry. It shows that when the laws of physics are invariant over time, energy is conserved. However, in an expanding universe, time symmetry is broken, meaning energy isn't conserved over large timescales, although it appears conserved over short periods.

Q: What role did Emmy Noether play in physics?

Emmy Noether was a groundbreaking mathematician who developed Noether's theorem, linking symmetries to conservation laws. Her work provided a deeper understanding of why certain quantities are conserved in physics, profoundly influencing fields like general relativity and quantum mechanics. Noether's insights reshaped how physicists view symmetries and conservation.

Q: Why does energy seem conserved in everyday situations?

Energy seems conserved in everyday situations because, over short timescales, time translation symmetry approximately holds true. Noether's theorem shows that energy conservation arises from this symmetry. While the universe's expansion breaks this symmetry over billions of years, in the short term, the effects are negligible, making energy appear conserved.

Q: What is the significance of local symmetries in general relativity?

In general relativity, local symmetries lead to continuity equations rather than global conservation laws. Noether's second theorem shows that while energy isn't conserved globally in a curved space-time, it is conserved locally. This means energy conservation holds within small regions, but curvature allows for energy 'leakage' between regions.

Q: How does the curvature of space-time affect energy conservation?

The curvature of space-time, as described by general relativity, affects energy conservation by allowing energy to 'leak' between regions. Noether's theorem shows that while energy is locally conserved, the curvature introduces terms that account for changes in energy due to the universe's dynamic nature, impacting global conservation.

Q: What is the equivalence principle in general relativity?

Einstein's equivalence principle in general relativity states that the effects of gravity are indistinguishable from those of acceleration. This principle suggests that locally, the laws of physics in a freely falling frame are the same as in a gravity-free environment, forming a cornerstone of general relativity and influencing how we understand gravity.

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.