Vacuum energy
Vacuum energy is the energy of empty space. In physics, the "vacuum" means the state of lowest energy, and the vacuum energy is the energy density of that state. Physicists cannot yet calculate it with any confidence.[1] It is closely tied to the cosmological constant, a term that Albert Einstein added to his equations of gravity;[2] the physicist Sean Carroll treats "vacuum energy" and "cosmological constant" as essentially the same thing.[3]
Zero-point energy
Even empty space is expected to hold some energy because of quantum mechanics. A simple example is a particle on a spring. In everyday physics its lowest-energy state is simply resting still at the bottom, with no energy. In quantum mechanics, however, the uncertainty principle means the particle cannot be both perfectly still and in one exact place, so even its lowest-energy state keeps a small amount of energy.[4] A quantum field behaves like a huge collection of such oscillators, so empty space should have this "zero-point" energy too.[5] Without gravity this energy would have no effect and is usually ignored, but because gravity responds to all energy, its real value matters.[6]
Effect on the universe
Unlike matter, vacuum energy does not thin out as the universe expands.[7] A positive cosmological constant speeds up the expansion of the universe.[8]
The cosmological constant problem
Simple estimates of the vacuum energy from particle physics are enormously larger than the value allowed by observations of the universe. In a 2001 review, Carroll described this as "the famous discrepancy of 120 orders of magnitude" between theory and observation,[9] and called the puzzle one of the most significant unsolved problems in fundamental physics.[10] Not everyone accepts the size of that gap: in a 2012 review, the physicist Jérôme Martin argued that a more careful calculation gives a value far from the often-quoted figure.[11]
The Casimir effect
The Casimir effect, a tiny force between closely spaced objects, is often discussed as evidence for vacuum energy. Carroll wrote that vacuum fluctuations are "very real, as evidenced by the Casimir effect",[12] and Martin wrote that the Casimir effect and a related effect in atoms seem to show that zero-point fluctuations are not just a feature of the mathematics.[13] The physicist Robert Jaffe disagreed, arguing in 2005 that Casimir forces can be calculated without any reference to zero-point energy, as forces between charges and currents.[14]
References
- ↑ Carroll, Sean M. (2001). "The Cosmological Constant". Living Reviews in Relativity. 4. doi:10.12942/lrr-2001-1. Retrieved 20 October 2026.
The cosmological constant turns out to be a measure of the energy density of the vacuum — the state of lowest energy — and although we cannot calculate the vacuum energy with any confidence
{{cite journal}}: CS1 maint: unflagged free DOI (link) - ↑ Carroll, Sean M. (2001). "The Cosmological Constant". Living Reviews in Relativity. 4. doi:10.12942/lrr-2001-1. Retrieved 20 October 2026.
Einstein therefore proposed a modification of his equations, to ... where Λ is a new free parameter, the cosmological constant.
{{cite journal}}: CS1 maint: unflagged free DOI (link) - ↑ Carroll, Sean M. (2001). "The Cosmological Constant". Living Reviews in Relativity. 4. doi:10.12942/lrr-2001-1. Retrieved 20 October 2026.
In what follows, I will use the terms "vacuum energy" and "cosmological constant" essentially interchangeably.
{{cite journal}}: CS1 maint: unflagged free DOI (link) - ↑ Carroll, Sean M. (2001). "The Cosmological Constant". Living Reviews in Relativity. 4. doi:10.12942/lrr-2001-1. Retrieved 20 October 2026.
Quantum-mechanically, however, the uncertainty principle forbids us from isolating the particle both in position and momentum, and we find that the lowest energy state has an energy
{{cite journal}}: CS1 maint: unflagged free DOI (link) - ↑ Carroll, Sean M. (2001). "The Cosmological Constant". Living Reviews in Relativity. 4. doi:10.12942/lrr-2001-1. Retrieved 20 October 2026.
A (free) quantum field can be thought of as a collection of an infinite number of harmonic oscillators in momentum space.
{{cite journal}}: CS1 maint: unflagged free DOI (link) - ↑ Carroll, Sean M. (2001). "The Cosmological Constant". Living Reviews in Relativity. 4. doi:10.12942/lrr-2001-1. Retrieved 20 October 2026.
Again, in the absence of gravity this energy has no effect, and is traditionally discarded (by a process known as "normal-ordering"). However, gravity does exist, and the actual value of the vacuum energy has important consequences.
{{cite journal}}: CS1 maint: unflagged free DOI (link) - ↑ Carroll, Sean M. (2001). "The Cosmological Constant". Living Reviews in Relativity. 4. doi:10.12942/lrr-2001-1. Retrieved 20 October 2026.
Vacuum energy does not change as the universe expands
{{cite journal}}: CS1 maint: unflagged free DOI (link) - ↑ Carroll, Sean M. (2001). "The Cosmological Constant". Living Reviews in Relativity. 4. doi:10.12942/lrr-2001-1. Retrieved 20 October 2026.
a positive cosmological constant accelerates the universal expansion
{{cite journal}}: CS1 maint: unflagged free DOI (link) - ↑ Carroll, Sean M. (2001). "The Cosmological Constant". Living Reviews in Relativity. 4. doi:10.12942/lrr-2001-1. Retrieved 20 October 2026.
The ratio of (19) to (20) is the origin of the famous discrepancy of 120 orders of magnitude between the theoretical and observational values of the cosmological constant.
{{cite journal}}: CS1 maint: unflagged free DOI (link) - ↑ Carroll, Sean M. (2001). "The Cosmological Constant". Living Reviews in Relativity. 4. doi:10.12942/lrr-2001-1. Retrieved 20 October 2026.
this conundrum is the "cosmological constant problem". In Section 4 we will discuss a number of issues related to this puzzle, which at this point remains one of the most significant unsolved problems in fundamental physics.
{{cite journal}}: CS1 maint: unflagged free DOI (link) - ↑ Martin, Jérôme (2012). "Everything You Always Wanted To Know About The Cosmological Constant Problem (But Were Afraid To Ask)". Comptes Rendus Physique. 13: 566–665. doi:10.1016/j.crhy.2012.04.008. Retrieved 20 October 2026.
the properly renormalized value of the zero-point energy density today (for a free theory) is in fact far from being 122 orders of magnitude larger than the critical energy density, as often quoted in the literature
- ↑ Carroll, Sean M. (2001). "The Cosmological Constant". Living Reviews in Relativity. 4. doi:10.12942/lrr-2001-1. Retrieved 20 October 2026.
(And the vacuum fluctuations themselves are very real, as evidenced by the Casimir effect [49].)
{{cite journal}}: CS1 maint: unflagged free DOI (link) - ↑ Martin, Jérôme (2012). "Everything You Always Wanted To Know About The Cosmological Constant Problem (But Were Afraid To Ask)". Comptes Rendus Physique. 13: 566–665. doi:10.1016/j.crhy.2012.04.008. Retrieved 20 October 2026.
the Lamb shift and the Casimir effect seem to indicate that the quantum zero-point fluctuations are not an artifact of the quantum field theory formalism
- ↑ Jaffe, R. L. (2005). "The Casimir Effect and the Quantum Vacuum". Physical Review D. 72: 021301. doi:10.1103/PhysRevD.72.021301. Retrieved 20 October 2026.
Casimir effects can be formulated and Casimir forces can be computed without reference to zero point energies. They are relativistic, quantum forces between charges and currents.
{{cite journal}}: CS1 maint: article number as page number (link)