Dr. Strange said:if I know the total volume of space in the universe
What you are asking about is the energy density of the cosmic microwave background radiation. A box full of light at a certain temp represents how much energy per unit volume. It's a good question, although it does not give you a way to calculate the energy density of the universe because the universe contains other forms of energy besides the CMB radiation.Dr. Strange said:If I have a 1 km cube of empty space at a constant temperature of 2.7 K, how much energy do I have?...
Yes. I am basically asking how much energy a box full of CMB light would contain. In other words, if you knew what the total cubic volume of the universe was, could you use the temperature of space to calculate the total energy of the universe?marcus said:What you are asking about is the energy density of the cosmic microwave background radiation. A box full of light at a certain temp represents how much energy per unit volume. It's a good question, although it does not give you a way to calculate the energy density of the universe because the universe contains other forms of energy besides the CMB radiation.
Dr. Strange said:Yes. I am basically asking how much energy a box full of CMB light would contain. ...
Don't forget to add something like 0.6*10^15 eV per km^3 of intristic quantum vacuum energy.marcus said:There's the Stefan Boltzmann constant sigma and the related energy density constant a
σ =5.67 x 10-8 W m-2 K-4
a = 4σ/c = 7.566 x 10-16 J m-3 K-4
I think to get the energy density of radiation at a given temp you just multiply a by T4
This would get you the energy density in a box of thermal radiation at a given temperature but I don't see how you conclude from that the energy density of the universe because the universe has other stuff in addition to the CMB---for example the energy equivalent of the matter it contains. Maybe you are proposing to view all that other stuff as negligible.
There is an energy INVENTORY that the astronomer Peebles published a few years back. You might be interested. I'll see if I can find a link.
http://arxiv.org/abs/astro-ph/0406095
The Cosmic Energy Inventory
Masataka Fukugita, P. J. E. Peebles
(Submitted on 3 Jun 2004)
We present an inventory of the cosmic mean densities of energy associated with all the known states of matter and radiation at the present epoch. The observational and theoretical bases for the inventory have become rich enough to allow estimates with observational support for the densities of energy in some 40 forms. The result is a global portrait of the effects of the physical processes of cosmic evolution.
42 pages. Astrophys.J.616:643-668,2004
http://inspirehep.net/record/651635?ln=en
This would give an estimate of the energy density of the CMB among other things.
In this context, "empty space" refers to the vacuum of space that exists between celestial bodies, such as planets, stars, and galaxies.
Yes, according to quantum mechanics, even in a vacuum, there is a constant fluctuation of particles and fields that create energy. This is known as zero-point energy or vacuum energy.
The exact value of energy in a cubic km of empty space is still a topic of debate among scientists. Some calculations estimate it to be around 10^−9 Joules, while others suggest it could be much higher.
This energy has important implications in understanding the fundamental nature of the universe and the behavior of particles at a subatomic level. It also plays a role in the expansion of the universe and the presence of dark energy.
Measuring or detecting the energy in empty space is a challenging task due to its small magnitude. Scientists use various methods, such as the Casimir effect, to indirectly observe and measure the effects of this energy. Advanced technologies and experiments are continuously being developed to better understand this phenomenon.