A Leap in Energy

The discovery by BICEP2 of the signature of gravitational waves in the cosmic microwave background — if it holds up! — is not only good evidence for inflation in the very early universe, it’s a fairly precise indication that inflation occurred at a very high energy scale. I thought of a vivid way to emphasize just how high that energy is.

Particle physicists like to keep things simple by characterizing all physical quantities in terms of a single kind of unit — typically energy, and typically measured in electron volts. That’s part of the magic of natural units. We live in a world governed by relativity, so the speed of light c provides a natural unit of velocity. We also live in a world governed by quantum mechanics, so Planck’s constant ℏ provides a natural unit of action. And we live in a world governed by statistical mechanics, so Boltzmann’s constant k provides a natural conversion between energy and temperature. We therefore set these quantities equal to unity, ℏ = c = k = 1. Once that’s done, mass and temperature have the same units as energy. Time and distance have units of 1/energy. Energy density is energy per unit spatial volume, which works out to (energy)4. This kind of reasoning makes particle physicists happy, since they like to think of everything in terms of energy scales.

So, thinking about everything in terms of energy scales, what’s the energy of everyday life? It makes sense to choose room temperature, about 295 Kelvin. That works out to about 0.02 electron volts, which we can call the temperature of everyday life:

      E_{\rm everyday} = 2 \times 10^{-2}\, {\rm eV}.

One way of thinking about the progress of fundamental physics is to track the progress of our understanding to higher and higher energy scales. The highest energies we’ve ever probed in experiments here on Earth are those at the Large Hadron Collider. The last run of the LHC reached energies of 8 TeV, or 8×1012 eV. But it would be an exaggeration to say that we really understand those energies; when protons collide at the LHC, their energies are distributed among a number of particles in each event. That’s why the heaviest particles we’ve ever found are the Higgs boson and the top quark, both with masses a bit under 0.2 TeV. So let’s call that the highest energy we’ve understood through experiments here on Earth:

      E_{\rm understanding} = 2 \times 10^{11}\, {\rm eV}.

Thus, the progress of science has extended our understanding a factor of 1013, thirteen orders of magnitude, above our everyday experience:

      E_{\rm understanding}/E_{\rm everyday} = 10^{13}.

Not too shabby, for a species of jumped-up apes with only an intermittent dedication to the ideals of rationality and empiricism.

Now let’s turn to inflation. The great thing about detecting gravitational waves in the CMB is that, in contrast with the density perturbations we’ve known about for some time, the gravitational wave amplitude depends solely on the expansion rate during inflation, not on any details about the scalar-field potential. And the expansion rate is directly related to the energy density (energy to the fourth power) by general relativity itself. So measuring the amplitude, as BICEP2 did, tells us the inflationary energy scale directly. And the answer is:

      E_{\rm inflation} = 2 \times 10^{25}\, {\rm eV}.

For comparison, the reduced Planck energy (where “reduced” means “including the factor of 8π where it should be”) is 2×1027 eV, a mere stone’s throw away.

So, you can do the math yourself. Inflation was going on at energy scales that exceed those we explore here on Earth by a factor of about

      E_{\rm inflation}/E_{\rm understanding} =  10^{14}.

In other words, BICEP2 has extended our experimental reach, as measured by energy scale, by an amount (1014) slightly larger than the total previous progress of all of science (1013).

We don’t, of course, understand everything between LHC energies and inflationary energies, not even close. But we (the royal “we”) have been able to make an enormous extrapolation, using scientific reasoning, and get the right answer. It’s a big deal.

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12 Responses to A Leap in Energy

  1. Mike Nelson says:

    I’m looking forward to the first due diligence experiments for verification the BICEP2 results. Then we can really pop open the champagne for inflationary cosmology…

    Nice job relating LHC energies to everyday scales.

  2. Merle Riley says:

    An unnoted detail on inflation (money for nothing, chicks for free) is that a zero-sum energy for particle pair creation separated at a radius in which negative gravitational energy balances rest energy for the pair is that mass/radius is about 3x10E27 kg/m. This is close to the Planck unit ratio, suggesting another fundamental reason for Planck units to have physical significance.

  3. Nice comparison. Also worth noting that with the discovery of nuclear fission we were able to suddenly improve on everyday energy by a factor of 10^6 virtually overnight.

  4. John D says:

    I’ve been feeling a bit sceptical about BICEP2 Sean. You’ll have seen blogs by Peter Coles and Sesh Nadathur plus other things like this. And it’s got me thinking. So much so that now I’m feeling sceptical about inflation. Yep. The more I think about it the more unnecessary it seems to be. Not big bang cosmology, that’s a cert. Just inflation.

    Thought I’d mention it.

  5. I think that the most natural and elementary unit is G=E (Gravity and Energy each travelling at C²).

  6. Michael K Murray says:

    Nice comparison. It would be good to also have the energies of a few things we know about and have some sort of feel for. Like energy of a car driving fast, energy of a space shuttle taking off, energy of Hiroshima bomb ? I’m trying to get a feel for how big the jump of 13 orders of magnitude is.

    EDIT: Ah just saw Curious Wavefunction’s post. So nuclear fission is around 6 orders of magnitude increase. That’s helpful thanks.

  7. Good article. Makes you think. It’s important to note (especially for those not conversant with these energy levels) that these energies should be viewed in the context of the very tiny areas of space in which they manifest themselves. Two protons crashing at close to light speed release an energy that is immense (several TeV’s) only when considering that it is released within the cross section of a proton. The energy, according to CERN, is about the energy of the flight of a mosquito (bigger mosquitoes as the TeV level goes up from 4 to 8, etc.)–but concentrated in the tiny, tiny area of the surface of two protons (which “look”–because of special relativity–like two infinitesimally small pancakes). Proof? (for the skeptics): the magnets of the LHC don’t melt from the heat. In fact, the heat from the crashing protons is not even measurable outside the calorimeter.

  8. Josh says:

    Sean (or anyone else who can explain for that matter),

    I often hear physicists excitement on this manner talking about high energies, but what about exceedingly small energies? Maybe I’ve been reading all the wrong articles, but I would think probing tinier and more accurate changes in energy would be cool too.


  9. After reading Mike Nelson’s comment I just wanted to point out that confirmation of this result will not mean it’s time to throw an inflation party. Inflationary gravitational waves should be red shifted, but these may be blue-shifted. I may be confused, but I understand one reason why these modes did not appear in other experiments tuned to other scales could be because the signal may be anomalously shifted toward the scale of the BICEP2 detector.

    Sean, you probably know all about that and should make a post about red and blue shifts. And then post it to /r/physics so I will see it 😉

  10. Chris says:

    Not that we have to worry about this anytime soon, but is there any danger with doing experiments where we collide particles with energies on the order of 10^25 – 10^27 eV? I’m not being a paranoid doomsday person, but I just wonder because last time that happened, the universe exploded!

  11. drgsrinivas says:

    As long as the ‘hi-tech’ physicists think ‘high’ and refuse to come ‘down’ to the basics, this saga of scientific ignorance continues.