Calculating kinetic energy of all matter

[jimjohnson]

Have there been estimates for the kinetic energy of all matter in the universe? For example, the Virgo supercluster moving at 700 km/sec though space has a kinetic energy of e62 erg. And of course, there is considerable movement of stars and matter within the cluster, just about everything has a velocity. The result has to be a large number. How close would it be to the energy equivalent of mass?

 

[zhermes]

I'm not aware of any published material (and I kind of doubt there is any), but many cosmologists and high energy physicists are starting to think that the total energy of the universe is just about zero---i.e. all positive energy (e.g. kinetic, mass, etc) is balanced by negative (potential).

One thing to keep in mind is that your question doesn't have a trivial solution: (1) kinetic energy is reference-frame dependent (but it should be roughly equivalent for all inertial reference frames), (2) the way to treat kinetic energy from cosmological velocities (i.e. the Hubble flow) isn't entirely clear, and (3) the velocity distribution of dark matter (which dominated mass by almost a factor of 10) isn't well constrained.

 

[jimjohnson]

I assume the negative energy is gravity which can be unlimited, right? Also,I was thinking in trivial terms, using assumptions to simlify the calculation but there was no overall purpose in mind. Thanks for the specific response.

 

[Haroldingo]

What wouldbethe point?

 

[zhermes]

I assume the negative energy is gravity which can be unlimited, right?

Sure, it just depends on what region you're looking at. If the universe is infinite and you calculate all of the (negative) gravitational potential energy it will be infinite as-well; but any finite region should have a finite value.

Also,I was thinking in trivial terms, using assumptions to simlify the calculation but there was no overall purpose in mind. Thanks for the specific response.

You could do a simple estimate by integrating the mass function of galaxies (how many galaxies there are of a given mass) times the square of the Hubble constant times the distance, over distance to estimate the kinetic energy... i.e.
$KE = \frac{1}{2} m v^2$ and for cosmological Hubble flow $v = H_0 x$ for the Hubble constant $H_0$ and a distance x. Therefore:
$$KE \approx \int M(x) (H_0 x)^2 dx$$
where M(x) is the mass function in terms of distance.

... Its definitely a non-trivial calculation ;)

 

[Vanadium 50]

You're calculating a frame-dependent quantity. So there is no unique answer.

 

[jimjohnson]

What wouldbethe point?

I was curious about how the value would compare with the CMB energy (4 x 72 erg) or mass eqivalent energy (about e76 erg) as part of a macro view of the universe. Is it large enough to have an impact on total energy density of e-29 gm/cm3?

 

[jimjohnson]

Sure, it just depends on what region you're looking at. If the universe is infinite and you calculate all of the (negative) gravitational potential energy it will be infinite as-well; but any finite region should have a finite value.
You could do a simple estimate by integrating the mass function of galaxies (how many galaxies there are of a given mass) times the square of the Hubble constant times the distance, over distance to estimate the kinetic energy... i.e.
$KE = \frac{1}{2} m v^2$ and for cosmological Hubble flow $v = H_0 x$ for the Hubble constant $H_0$ and a distance x. Therefore:
$$KE \approx \int M(x) (H_0 x)^2 dx$$
where M(x) is the mass function in terms of distance.
... Its definitely a non-trivial calculation ;)

I was initially thinking of velocites independent of expansion, relative galaxy movement. Should the integration above equal the cosmological constant (7.12 x e-30 gm/cm3)?

 

[lpetrich]

Why not kinetic energy relative to the local cosmological rest frame? The frame where one is at rest with respect to the Cosmic Microwave Background.

This is because when we talk about motion, we usually talk about motion with respect to the local environment. When it is ambiguous, we then specify which environment it is relative to, like airspeed vs. groundspeed.