What is a Vacuum?

A vacuum is not nothing.    It is only a region of three-dimensional space that is entirely devoid of matter, entirely devoid of particles.

The best laboratory vacuum contains about 25 particles (molecules, atoms) per cubic centimeter (cm3).

The atmosphere on the surface of the Moon (if you can call it that) contains a lot more particles than the best laboratory vacuum: about 40,000 particles per cm3.  This extremely tenuous lunar atmosphere is mostly made up of the “noble” gases argon, helium, and neon.

The vacuum of interplanetary space contains about 11 particles per cm3.

The vacuum of interstellar space contains about 1 particle per cm3.

The vacuum of intergalactic space contains about 10-6 particles per cm3.  That’s just 10 particles per cubic meter of space.

But what if we could remove all of the particles in a parcel of space?  And somehow shield that empty parcel of space from any external electromagnetic fields?  What would we have then?

It appears that even completely empty space has some inherent energy associated with it.  The vacuum is constantly “seething” with electromagnetic waves of all possible wavelengths, popping into and out of existence on unimaginably short time scales—allowed by Heisenberg’s energy-time uncertainly principle.  These “quantum flourishes” may be a intrinsic property of space—as is dark energy.  Dark matter, on the other hand, is some weird form of matter that exists within space, exerting gravitational influence but not interacting with normal matter or electromagnetic waves in any other way.

Is there any evidence of this vacuum energy, or is it all theoretical?  There are at least three phenomena that point to the intrinsic energy of empty space.  (1) The Casimir effect; (2) Spontaneous emission; and (3) The Lamb shift.

The Casimir effect
Take two uncharged conductive plates and put them very close to each other, just a few nanometers apart.  Only the shortest wavelengths will be able to exist between the plates, but all wavelengths will exist on the other side of the two plates.  Under normal circumstances, this will cause a net force or pressure that pushes the two plates towards one another.

Spontaneous emission
An example of spontaneous emission is an electron transitioning from an excited state to the ground state, emitting a photon.  What causes this transition to occur when it does?

The Lamb shift
The Lamb shift is a tiny shift in the energy levels of electrons in hydrogen and other atoms that can’t be explained without considering the interaction of the atom with “empty” space.

References
Reucroft, S. and Swain, J., “What is the Casimir effect?”, Scientific American, https://www.scientificamerican.com/article/what-is-the-casimir-effec/.  Accessed 20 Feb 2018.

Koks,D. and Gibbs, P., “What is the Casimir effect?”, http://math.ucr.edu/home/baez/physics/Quantum/casimir.html.  Accessed 20 Feb 2018.

 

Do Dark Matter and Dark Energy Exist?

Numerous searches for the particle or particles responsible for dark matter have so far come up empty.  What if dark matter doesn’t really exist?  Could there be alternative explanation for the phenomena attributed to dark matter?

In the November 10, 2017 issue of the Astrophysical Journal, Swiss astronomer André Maeder presents an intriguing hypothesis that non-baryonic dark matter need not exist, nor dark energy either.  In “Dynamical Effects of the Scale Invariance of the Empty Space: The Fall of Dark Matter?” he suggests that scale invariance of empty space (i.e. very low density) over time could be causing the phenomena we attribute to dark matter and dark energy.

What is scale invariance?  In the cosmological context, it means that empty space and its properties do not change following an expansion or contraction.  Scales of length, time, mass, energy, and so on are defined by the presence of matter.  In the presence of matter, space is not scale invariant.  But take the matter away, and empty space may have some non-intuitive properties.  The expanding universe may require adding a small acceleration term that opposes the force of gravity.  In the earlier denser universe, this acceleration term was tiny in comparison to the rate at which the expansion was slowing down, but in the later emptier universe, the acceleration term dominates.  Sound like dark energy, doesn’t it?  But maybe it is an inherent property of empty space itself.

The existence of dark matter is primarily suggested by two  observed dynamical anomalies:

  1. Flat outer rotation curve of spiral galaxies (including the Milky Way)
  2. Motions of galaxies within galaxy clusters

Many spiral galaxies have a well-known property that  beyond a certain distance from their centers, their rotation rate (the orbital velocity of stars at that distance) stays nearly constant rather than decreasing as one would expect from Keplerian motion / Newtonian dynamics (think planets orbiting the Sun in our own solar system— the farther the planet is from the Sun, the slower it orbits).  Only there seems to be evidence that the rotation curves of galaxies when they are young (as seen in the high-redshift universe) do have a Keplerian gradient, but in the present-day universe the rotation curve is flat.  So, it appears, flat rotation curves could be an age effect.  In other words, in the outer regions of spiral galaxies, stars may be orbiting at the same velocity as they did in the past when they were closer to the galactic center.  Maeder writes:

…the relatively flat rotation curves of spiral galaxies is an age effect from the mechanical laws, which account for the scale invariant properties of the empty space at large scales.  These laws predict that the circular velocities remain the same, while a very low expansion rate not far from the Hubble rate progressively extends the outer layers, increasing the radius of the Galaxy and decreasing its surface density like 1/t.

We need to study the rotation curves (as a function of galactocentric radius all the way out to the outermost reaches of the galaxy) of many more galaxies at different redshifts (and thus ages) to help us test the validity of the scale invariant vs. dark matter hypotheses.  Maeder suggests a thorough rotation study of two massive and fast-rotating galaxies, UGC 2953 (a.k.a. IC 356; 50-68 Mly) and UGC 2487 (a.k.a. NGC 1167; 219-225 Mly), would be quite interesting.

The observed motions of galaxies within many galaxy clusters seems to indicate there is a substantial amount of unseen mass within these clusters, through application of the virial theorem.  However, the motions within some galaxy clusters such as Coma (336 Mly) and Abell 2029 (1.1 Gly) may be explainable without the need to resort to “exotic” dark matter.

Then there’s the AVR (Age-Velocity Dispersion Relation) problem which, incidentally, has nothing to do with dark matter.  But it may offer evidence for the scale invariant hypothesis.  It is convenient to specify the motion of a star in a spiral galaxy such as the Milky Way in a galactocentric coordinate system.

U = component of velocity towards the galaxy center

V = component of velocity in the direction of galactic rotation

W = component of velocity orthogonal to the galactic plane

Maeder writes:

The AVR problem is that of explaining why the velocity dispersion, in particular for the W-component, considerably increases with the age of the stars considered … Continuous processes, such as spiral waves, collisions with giant molecular clouds, etc… are active in the disk plane and may effectively influence the stellar velocity distributions.  However…vertical heating (the increase of the dispersion σW) is unexpected, since the stars spend most of their lifetime out of the galactic plane.

There may be more to “empty” space than meets the eye…

References
Maeder, A., 2017, ApJ, 849, 158
arXiv:1710.11425