## Recap: May Dinner with Dr. Claudia de Rham

A busy week for geekery in the Region, so we were most pleased to see so many faces out, including some new ones. But then, Perimeter Institute’s public lectures sell out in minutes, so physics is a proven popular topic in this town.

We were back at the Centre in the Square Members’ Lounge (thanks as always to them for the fine hospitality), with catering by crowd favourite, Little Mushroom.

Dr. de Rham kicked things off by inviting us to Enter the World of Extra Dimensions. She presented her talk in three parts, beginning with some background on where scientists are in the study of cosmology, an overview of what’s in the vacuum of “empty” space, and a primer on particle physics. This will be a laywoman’s overview, as I’m no physicist, but I’ll do my best to get things right. ðŸ™‚

The basic premise we’re working from is that there isn’t really any such thing as “empty”. Take all the furniture, art, carpet, people, and everything else out of a room, and it’s still not really empty. Even if you shield the room against light, radiation, etc., and there are no more molecules in the room, there’s still energy. Space is the same; it’s a vacuum, but still filled with energy. The big question is what or what kind(s) of energy, and what could account for discrepancies in our calculations of how much energy there should be.

Particle physics works with tiny units of things: atoms, protons, electrons, quarks, and such. These particles bond together to form molecules, and form the building blocks of everything we can build, everything we are, and everything that holds us together.

In nature there are four fundamental interactions (most fundamentally among particles, which create bigger things, like us). These are strong interactions (bonds), weak interactions, electromagnetic force, and gravitation. Light is electromagnetic radiation, emitted and absorbed as photons, and is also a particle (though it also exhibits wave properties).

Taking particles and interactions further, pairs of virtual particles can be created (very briefly), out of nothing. This is what we build and use particle accelerators (used as colliders) like the Large Hadron Collider at CERN for. Particles get created and annihilated (again, very quickly and seemingly from out of the blue). Creating these particles isn’t limited to places like CERN. The probability of creating them is the same anywhere in the universe.

Moving along to where we get into calculations, energy density in a vacuum is constant, what we know as the cosmological constant (usually denoted by lambda: ÃŽâ€º), first proposed by Einstein as a way of keeping the universe static. (He kinda screwed up here…)

Additionally, energy and mass affect spacetime (they curve it), which is something that is well proven by this point. And the problem with the universe supposedly being static is that there was proof that it was changing and evolving. This is know as Einstein’s greatest blunder (in 1928), because the universe *isn’t* static.

The cosmological constant actually shows that the universe is not only changing (expanding), that expansion is accelerating, driven by vacuum energy.

To measure this accelerating expansion, we use supernovae, as they have a characteristic peak and specific frequency of energy. If a supernova is moving with respect to us, with the Doppler effect the frequency of the peak (redshift) changes. The peak position tells us the supernova’s velocity. Graphing this redshift shows the accelerating expansion. We’ve measured that supernovae are moving faster the farther away from us they are.

And that was the first of the three parts of our presentation to lay the foundations of where we’re going, which is the intersection of the standard model in particle physics and the standard model in cosmology.

Next Dr. de Rham talked a bit about the Higgs boson, media darling that it’s been for the last few years (discovery announced in July 2012). The Higgs is actually a fairly massive particle, relatively speaking (no inaccurate physics pun intended). By “massive” in this case we mean that it’s high in electron volts. Electron volts are the amount of energy gained or lost by the charge of a single electron moved across an electric potential difference of one volt. (The Higgs is 125.3GeV – GeV being giga electron volts.)

We expect the vacuum to be filled with energy to a density at least proportional to its mass to the fourth power (10^{8}GeV^{4}). So how does that expected measurement compare with the density based on the observed acceleration of the universe? The theory of general relativity tells us that we need 10^{-48}GeV^{4} energy for that acceleration.

Except that that’s a difference of **56 orders of magnitude** compared to what we thought should be there. Hmm… This is the biggest discrepancy in physics, and therefore ripe for much consternation and speculation.

To make an earthly comparison, this is like the difference between having a box that’s 10,000km^{3} and having one ant in it (expected energy density) compared to having a box that’s 1cm^{3} and stuffing the moon into it (observed density).

Did we *really* not understand gravity? Or could this problem be the first sign of the existence of extra dimensions or dark matter and energy? According to the standard model of cosmology, the make-up of the unverse is 68.3% dark energy, 26.8% dark matter, and 4.9% ordinary matter (that last one includes everything from the aforementioned individual particles to entire planets).

This energy density discrepancy lies between the quantum world of particle physics and gravity and cosmology (so of interest and research to a wide variety of scientists). The existence of extra dimensions would change gravity and could help explain the discrepancy. (Plus: really, really interesting to contemplate!)

Theories of extra dimensions have been around for a long time, and are used in other areas of physics like string theory. How many extra dimensions could there be? Well, that kind of depends on who you’re talking to, what they’re researching, and what they’re trying to prove. For the purposes of this presentation the possibility was limited to just one extra dimension.

Which moves us into the third part of the presentation, the idea of the existence of extra dimensions and what that would mean in the study of cosmology.

The first question that comes up is that if there are extra dimensions, why aren’t we observing them? There are a few possibilities.

- They could be extremely small, too small for us to see and covering distances too small for us to currently measure.
- They could be extremely large, but we’re not able to travel through them.
- We could be basically “flat” and unable to propagate into them.
- We could be confined to the surface of them, like sitting on the surface of a soap bubble. Or moving along the strands of a spider web but not able to move in the spaces between strands.

Gravity, on the other hand, would be free to spread along the dimensions. To understand the physics on the surface we’d need to understand how gravity behaves along these extra dimensions. (We know the rules of gravity in our world, but who knows how the rules could be different there?) An interesting visual is to think of ourselves like water strider bugs, and think of the water we’re on as gravity.

How does the idea of extra dimensions help our understanding of the universe and the discrepancies in expected energy density? Gravity could be weaker because it “leaks” into the extra dimension. Vacuum energy could be affecting the extra dimension rather than ours. (Sends “garbage” we don’t want or can’t explain into that other dimension.)

Within three-dimensional space (what we’re used to moving around in) the force of gravity gets diluted at r_{-2}. This is the origin of Newton’s Inverse-Square Law.

Within four-dimensional space the force of gravity gets diluted within the extra dimension as r_{-3} Ã¢â‚¬â€œ this would have been “Newton’s Inverse-Cube Law”.

A star in two-dimensional space would create a “deficit angle”. The 360 degrees the star inhabited would affect the extra dimension. (The space wouldn’t be evenly spread out, like having to cut a section out of a circle to fold it into a smooth cone.) Vacuum energy in our dimensions could create a deficit angle in the extra dimensions.

Extra dimensions would also affect Einstein’s theory model. Observation signatures would slightly modify Newton’s Inverse-Square Law. This would also slightly affect the motion of planets and satellites in our solar system. (We can measure this by shooting a laser at a mirror we left on the moon. Did you know we left a mirror on the moon? Or that we shoot lasers at it? Cool!)

This slightly modifies the way mass attracts itself and the way clusters of galaxies are formed. (We have modelled this, and the differences are quite noticeable.) The structure of these clusters is different depending on regular gravity of the presence of extra dimensions.

Gravitational waves would have more polarizations (general relativity accounts for only two polarizations). There’s distortion of the vertical (“stretching”), then the horizontal. Displacement along the gravitational wave would be possible. There could be 12 other polarizations (a lot of different distortions). Changes in gravity can be observed and measured on earth, but ideally we’d be able to do so in space.

Even if we can’t observe extra dimensions now, they could help explain problems in particle physics, like tackling the vacuum energy discrepancy. We could just be on the edge of testing observations signatures. As noted, extra dimensions are of interest in various areas of physics. String theory currently postulates six small extra dimensions and one large dimension.

The potential of this is bigger than the Higgs discovery. With the Higgs, we pretty much knew it was there, and just had to figure out how to prove it. With extra dimensions, we don’t even know for sure if they’re there, so proving it is much harder. Even if we solved it next year, it would take probably 20 years to test and vet the proof, so there won’t be a Higgs-like announcement for this any time soon.

And that brought us to the end of our presentation. Minds were expanded, creativity was catalyzed, and there were plenty of questions covering *“What if…?”* and *“So how…?”* I think I can say with authority that we all went home with lots to think about and a new appreciation of not only our place in the universe, but the make-up of our universe itself.

If you’d like to check out another talk by Dr. de Rham, take a look at Questioning Newton and Einstein as well.

Stay tuned as well for our announcement and registration opening for our June Dinner, the final one of this season, which will be at the newly re-opened Kitchener Public Library!