Category Archives: physics

On Looking For Things That May Not Be There

The Flyer for the Series Mentioned Below

On Monday (4/14/08) I had occasion to attend an informal talk on dark matter and dark energy at the Picnic Café given by Alberto Nicolis as part of a continuing series called Café Science in collaboration with Columbia University. I think this sort of casual interaction between scientist and the general public is all to rare, and I was heartened by the lively discussion that resulted between the speaker and the capacity crowd of about 40 individuals spanning ages from 13 to 80. The talk itself lasted about 30 minutes, with Alberto taking sips of white wine from his stance in the middle of the room.

His talk was intended to provide, in broad strokes, a lay understanding of those mysterious terms I mentioned above, dark matter and dark energy. In general, the reason for their recent explosion of use in scientific literature and news media in general is a matter of length scales.

It goes like this: we have two ways of talking about gravity: Newton’s law of universal gravitation, and Einstein’s theory of general relativity. Within out solar system, they are essentially indistinguishable in they are both quite capable of explaining the orbits of the planets (although general relativitistic calculations are required for use of the global positioning system, GPS). When astronomers observe galaxies – where the effects of gravity occur over much larger distances – however, things are different.
Allow me a brief dalliance for the purpose of pedagogy: it is possible to estimate the mass of a galaxy by the number of stars and planets it contains. Even the presence (and indirectly the mass) of black holes can be inferred by watching more distant stars pass behind and become occluded by them, in this way we can calculate the approximate mass of all the matter that we can see. This is where we run into a problem. Based on these calculations, the stars in these galaxies are moving far too fast, there is not enough mass to explain their observed velocities. By rights, if these stars are moving this fast, their centrifugal acceleration should shoot them away from their galactic homes. This realization has led to the inference that there must be some additional mass in the galaxy that we cannot see; that simply doesn’t interact with light as all known matter does, to create enough force to bind these stellar conglomerations together. This is dark matter.

A graphical representation of dark matter

Another astronomical observation on a still larger length scale leads to further worries. It is believed that the universe is expanding because of the observation that individual galaxies appear to be moving away from one other. This wouldn’t be troubling at all if their relative velocities were constant, it could be explained as a remnant of the outward linear momentum created by the big bang, but it isn’t. In fact the rate of expansion seems to be increasing with time. Because all matter creates attractive gravitational force, one cannot here again invoke dark matter, this would only exacerbate the issue. To deal with this conundrum, we must instead postulate some other weird stuff that creates a repulsive gravitational force. This is where dark energy comes in. Because one well known feature of Einstein’s general relativity is the ultimate equivalence of matter and energy (E=mc2), it accommodates the existence of some form of energy that generates the requisite force to produce the acceleration of the universe.

These explanations are fairly tidy in the sense that they work well at patching up existing theories. However, in talking with Dr. Nicolis after the conclusion of his remarks and the Q&A session, a slightly different picture arose. I was questioning him about the recently raised possibility that the assumption of a homogeneous distribution of dark energy requires substantially different corrections to general relativity than some other, more exotic distributions might1. His sensible response to this was to point out that we have no reason, theoretical or otherwise, to favor any particular distribution of dark energy over any other (unlike dark matter, which must take on a very specific distribution in order for it to have the appropriate effect). In fact, his own work on gravitation goes even further, abandoning the concepts of dark matter and dark energy entirely in favor of a more fundamental reformulation of the laws of gravity which we hold so dear. This may sound radical, but it actually bears a resemblance to a similar sort of decision made by Einstein early in this century.

I am referring here to Einsteins rejection of the concept of æther. This enigmatic substance was originally proposed by Isaac Newton in order to explain what we now know to be the effects of gravity on light. He observed that light from distant sources was diffracted or bent in proximity to certain heavenly bodies, and proposed that there must be some all pervasive stuff collecting near heavy objects which was responsible for this effect. Further, and much later, it was suggested that the æther was needed to support the propagation of electromagnetic waves through space.

The short version of the story is that while some were performing painstaking and extremely sensitive experiments designed to distinguish between various theories of æther, Einstein was quietly developing his theory of special relativity, which did away with the need for such machinations entirely.

It is anybody’s guess what the outcome of all this dark matter & energy business will be, but one thing is sure, the most interesting science is born out of times like these; eras in which empirical observations challenge experimentalists and theoreticians alike to tinker with and explain things they don’t understand.


1. Ellis, G. (2008) Cosmology: Patchy solutions. Nature 452, 158-161 | doi:10.1038/452158a;

The Feel of Space

(left:eRiK, right:me)

That’s my friend eRiK. My mother emphatically titles him “eRiK the Dane.” eRiK and I studied Physics and Math together as undergraduates at The University of California at Berkeley. We share a great love of understanding, and whenever something’s puzzling me, from Set Theory to counting cards in BlackJack, I turn to him.

He’s been singing the praises of the show RadioLab on NPR lately and he was particularly stricken by a comment made by the well known Columbia University Physicist Brain Greene. Dr. Greene was discussing the expansion of the universe, and, this is hearsay now, he said that there is no center to the expansion. No origin, no point away from which things are expanding. This is, as eRiK said, unsettling. If you were blowing a bubble with chewing gum, bubble swelling from your mouth, the rate of expansion would be greatest at your lips where the mass of sticky stuff was being stretched into a sheet. If you were pulling a rubber band with your index fingers the rate of expansion would be highest near your digits and lower elsewhere. The point I’m trying to get across is that it’s difficult to think of examples of isotropic expansion of objects. This means spatially and directionally uniform expansion. A pizza pie made from a lump of dough is expanded into a sheet in a roughly constant spatial manner, but the spread is not directionally uniform, it is expanded radially, out from the center. Dr. Greene’s comment means that there is no direction or origin associated with the universes growth. As astrophysicists and astronomers watch stars getting farther away from eachother, it appears to be happening in the same way everywhere. At the very least this means that the universe itself must behave differently from every object in it.

There is one example that is a bit comforting : imagine that you lived on a line, confined to one dimension. Further, lets say this line was connected at the ends, an infinite hoop of 1D existence. If “something” caused this circle to grow radially out from the center (which wouldn’t be a part of the line itself of course), to those living on the line segment, it would appear as if everything was expanding isotropically. We could extend this idea to a 4 dimensional space-time as a hoop embedded in a higher dimensional space, but this is pure speculation.

This brings us to the topic that motivated the title of this post. What would it feel like to come to the edge of a universe? I don’t know that such a boundary exists or not, but we can certainly conceptualize a space like our own with well defined boundaries. This is not like being in a room with boundaries. The repulsive forces that we experience as a result of encountering walls are just that: fields of force. A boundary of space must be very different. There wouldn’t necessarily be any repulsive force, I imagine it more like asking a person to reach into the 14th dimension or backward in time. It doesn’t even make sense to try and conceptualize it. There is simply nothing to try or do or a direction to move in or a place to point to or anything. This is the closest thing I can imagine to arriving at a boundary to space. Not only would there be nothing there, our perceptual abilities would probably be quite stymied by such a thing. Again I have found myself in the slippery slope of speculation, and I invite others to weigh in on this. I’m not sure that anybody has the required personal experience to comment on this but I am sure that somebody could, in the great tradition of doing so in physics, suggest a thought experiment which would shed some light on the subject.