# What is the total mass-energy of the universe?

• Greg Bernhardt
In summary, conservation of energy does not apply to cosmology in general relativity. There is no standard way to define the total energy or mass-energy of the universe, and different definitions can result in different values. Some definitions, such as pseudo-tensors, are not desirable due to their coordinate-dependence. Estimates of quantities like the sum of rest masses of all hydrogen atoms in the observable universe do not represent the total mass-energy or energy measured by any observer, and are not conserved.
How does conservation of energy work in general relativity, and how does this apply to cosmology? What is the total mass-energy of the universe?

Conservation of energy doesn't apply to cosmology. General relativity doesn't have a conserved scalar mass-energy that can be defined in all spacetimes.[MTW] There is no standard way to define the total energy of the universe (regardless of whether the universe is spatially finite or infinite). There is not even any standard way to define the total mass-energy of the *observable* universe. There is no standard way to say whether or not mass-energy is conserved during cosmological expansion.

Note the repeated use of the word "standard" above. To amplify further on this point, there is a variety of possible ways to define mass-energy in general relativity. Some of these (Komar mass, ADM mass [Wald, p. 293], Bondi mass [Wald, p. 291]) are valid tensors, while others are things known as "pseudo-tensors" [Berman 1981]. Pseudo-tensors have various undesirable properties, such as coordinate-dependence.[Weiss] The tensorial definitions only apply to spacetimes that have certain special properties, such as asymptotic flatness or stationarity, and cosmological spacetimes don't have those properties. For certain pseudo-tensor definitions of mass-energy, the total energy of a closed universe can be calculated, and is zero.[Berman 2009] This does not mean that "the" energy of the universe is zero, especially since our universe may not be closed.

One can also estimate certain quantities such as the sum of the rest masses of all the hydrogen atoms in the observable universe, which is something like 10^54 kg. Such an estimate is not the same thing as the total mass-energy of the observable universe (which can't even be defined). It is not the mass-energy measured by any observer in any particular state of motion, and it is not conserved.

MTW: Misner, Thorne, and Wheeler, Gravitation, 1973. See p. 457.

Berman 1981: M. Berman, unpublished M.Sc. thesis, 1981.

Berman 2009: M. Berman, Int J Theor Phys, http://www.springerlink.com/content/357757q4g88144p0/

Weiss and Baez, "Is Energy Conserved in General Relativity?," http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

Wald, General Relativity, 1984The following forum members have contributed to this FAQ:
bcrowell
George Jones
jim mcnamara
marcus
PAllen
tiny-tim
vela

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Gannet, PWiz and (deleted member)
Thanks for sharing.

jbriggs444

## 1. What is mass-energy and how is it related to the universe?

Mass-energy is a concept in physics that combines the properties of mass and energy into a single quantity. In the context of the universe, mass-energy is the total amount of matter and energy contained within it. This includes all forms of matter, such as atoms, particles, and dark matter, as well as all forms of energy, such as light, heat, and gravitational potential energy.

## 2. How is the total mass-energy of the universe calculated?

The total mass-energy of the universe is estimated using a combination of observations and theoretical models. Scientists use measurements of the cosmic microwave background radiation, the distribution of galaxies, and the expansion of the universe to estimate the amount of matter and energy present. Additionally, Einstein's famous equation, E=mc^2, can be used to convert the total mass of matter into its equivalent energy.

## 3. Is the total mass-energy of the universe constant or does it change over time?

The total mass-energy of the universe is not constant and can change over time. According to the law of conservation of energy, energy cannot be created or destroyed, but it can be converted from one form to another. This means that as the universe expands and evolves, the amount of matter and energy may change, but the total mass-energy remains the same.

## 4. What is the significance of understanding the total mass-energy of the universe?

Understanding the total mass-energy of the universe is crucial for understanding the fundamental laws and principles that govern the universe. It also helps scientists to better understand the origins and evolution of the universe, as well as the role of dark matter and dark energy in the universe's expansion. Additionally, studying the mass-energy of the universe can provide insights into the nature of space and time.

## 5. How does the total mass-energy of the universe affect our daily lives?

The total mass-energy of the universe may seem like a concept that is far removed from our daily lives, but it actually has a significant impact on our existence. The laws of physics that govern the universe, including the conservation of energy, also apply to our everyday experiences. Additionally, the matter and energy in the universe are constantly interacting, leading to the formation of stars, galaxies, and other structures that ultimately make up our world.

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