90% of gray matter remains invisible!
March 10, 2004
Astrophysics might be a science too serious to be entrusted to astrophysicists.
An unexpected response.
Eleven, Place Marcellin Berthelot. The Collège de France has been completely renovated. It’s as beautiful as the Louvre.
Narlikar, an Indian and president of the IAU, a longtime friend of Jean-Claude Pecker, is very pleasant. We’re the same age. He was a student of Fred Hoyle. I know that at one time they proposed the idea that the constants of physics might vary from one region of the universe to another. They wanted to use this to explain “abnormal redshifts,” the fact that there are deviations from the Hubble law. I know they were right, but at the time they lacked the theoretical tools to tackle this problem—through “joint fluctuations of metrics.”
Pecker knows that during this conference I intend to discuss this with my friend.
The conversation is very pleasant. Narlikar is a refined man, full of humor. We speak in English. I imagine for a moment the meeting between Souriau and him a few weeks earlier. Jean-Marie doesn’t speak English; not a single word. As for Narlikar, he probably knows only a few key phrases: how to give an address to a taxi driver, how to say three words to a secretary. Fortunately, I manage to get by using Shakespeare’s language. We talk for two hours. Narlikar is interested. At the end, I give it a try.
“I’ve thought about... the ideas you and Fred Hoyle once discussed regarding variations in the constants of physics.”
“Oh, that was purely speculative...”
“No, you were right. I know how to proceed. Perhaps we could collaborate, publish together.”
Narlikar smiles (I translate his reply into English):
“My dear colleague, I too am on the blacklist. I recently submitted a paper to a peer-reviewed journal. I received forty-three questions. The letter containing those questions was longer than the paper itself. So, I gave up.”
“Then, there’s no hope anymore...”
I must admit I’m somewhat stunned. I’d anticipated every possible reply except this one. I know my life has a somewhat “novelistic” character, but now an entirely unexpected chapter has begun. Even the president of the IAU, the International Astronomical Union, faces difficulties publishing; meanwhile, kilometers of nonsense get published every day. But Souriau faces the same problems. The public has no idea that since the post-war era, science has come under the control of anonymous groups. How can one identify these mysterious referees, protected by their sacred anonymity? It’s quite easy: they’re the ones who publish a lot. For them, everything seems easy. Same goes for members of their research teams or “clientele.” There’s also a sure sign: these people constantly cite each other. Reciprocal favoritism: “I cite you and you cite me.” Scientific papers have been online for ages now, and specialized search engines keep track of every author citation. CNRS and other bodies rely heavily on these citation counts; they’ve become a reference point. An important paper is one cited many times. Thus, groups form. The “Hawking Gang” is one example. In this vein, see Greene’s book, The Elegant Universe; it’s pretty good too. The superstring folks have formed a fantastic “community.” This is unprecedented: they’ve managed to give substance to a totally nonexistent discipline, since this “Theory of Everything” predicts nothing, explains no phenomena, models nothing. But as Larousserie wrote in Sciences et Avenir, “it’s a global theory.” If you’re “global,” you’re “in”; it’s that simple.
I know dozens of researchers who are hugely cited yet whose papers are pure fluff. Want a picture of contemporary astrophysics, cosmology, and theoretical physics? Take hundreds of cans of shaving foam and empty them all at once. Remember the movie Brazil? There’s a character—I’ve forgotten his name—who saves the hero several times using spectacular gadgets. He escapes by sliding along a steel wire. But one day he passes near a ventilation shaft and gets a form plastered to his face. He tries to tear it off, but soon finds himself buried under paperwork, stamped documents. He dies, suffocated by administrative emissions. Our modern-day Don Quixotes no longer charge at windmills; they plunge headfirst into anonymous mountains of shaving foam and perish there.
Tomorrow is the conference. I’ve prepared nothing. I haven’t even made any slides.
“Still... your friend Pecker... you should...”
I know, but the spring has broken since Larousserie’s article in Sciences et Avenir back in &&&. More recently, Dunod published a book by Magueijo titled Faster Than Light; it was a big hit. It’s somewhat similar to Greene’s book. In ’97, Magueijo, a young researcher at Cambridge, managed to publish a paper in Physical Review. He suggested that imagining a scenario where light speed was higher in the past would allow particles to “converse” in ancient times, thus ensuring the universe’s homogeneity. But immediately after, a Canadian named Moffat spoke up; he’d published similar things in ’93. Moffat protested vigorously.
Actually, I’m the true pioneer in this field; I’ll discuss this shortly. In ’88–’89 I published three papers in Modern Physics Letters A [1, 2, 3]. When I discovered Magueijo’s and then Moffat’s work in ’99, I emailed them both. No reply. The first was probably writing his book; it wasn’t the time to bother him. And really, what does it matter? There are so many battles I ought to fight, starting with MHD.
The next morning, Narlikar starts with the standard Big Bang scenario, including Linde’s inflation and all that. Pecker warned us:
“Narlikar will describe what others think, not what he personally believes.”
Then it’s my turn to speak. An astonishing phenomenon occurs, akin to a tide: our hall seats only a hundred people. From murmurs at the entrance, it seems there’s a problem. Pecker goes to check and turns to the audience:
“To accommodate everyone, we’ll move to the Grand Amphitheater.”
That hall fills instantly; some people even have to sit on the steps. Good heavens, I hadn’t anticipated this. How many are there? Three hundred? Four hundred?
Pecker introduces me and I begin:
“Apart from Narlikar and Pecker, are there any astrophysicists or cosmologists here?”
Silence.
“Are there any theoretical physicists?”
Nothing. This reminds me of what my Greek teacher, Barquissau, used to say when I was a student at Lycée Carnot: when he asked if anyone wanted to write on the board, our eyes dropped to our shoes or rose to the ceiling.
“So many hands went up the sky turned dark.”
I ask:
“Is there anyone here who’s a physicist?”
Hands rise. The audience is diverse, but there are plenty of “seniors,” aged forty to sixty. I have an hour to present my twin-universe vision.
Groups.
It all begins with an article by Andrei Sakharov from 1967, which went completely unnoticed and remains little known today. True, the Russian didn’t develop things much further, but the essentials are there. According to him, there wouldn’t be just one universe, but two, linked by this space-time structure called the Big Bang. Second point: the arrow of time in this “Twin Universe” (his term) runs opposite to ours.
This is hard to grasp. Imagine a universe whose spatial part has only one dimension and is closed upon itself. Its image is simply a circle. Add time. The following diagram shows such a universe whose perimeter grows—it’s expanding.
&&& 2D space-time diagram
Now let’s visualize Sakharov’s universe. It resembles an hourglass. Let t be cosmic time in our universe and t* that of the twin universe. These two temporal directions are opposite. What does this mean?
The answer emerges from mathematician Jean-Marie Souriau’s work from the late 1960s, published by Dunod in a now-out-of-print book titled Structure des Systèmes Dynamiques. In 1999 it was republished in English by Birkhäuser as Structure of Dynamical Systems; more than thirty years after its French release it still stands at the forefront of mathematical physics. In what follows I’ll conduct a dual discourse. On this webpage you’ll find the presentation rendered as simply as possible. Non-scientific readers shouldn’t be discouraged; there’s much to gain. By clicking links, scientific readers can access a somewhat more elaborate version.
For a layperson, a group is hard to understand. It’s a set of mathematical objects that “act” on other objects, “transporting” them. Take points on a plane. Draw geometric figures on it. We can “act” on them by rotating them around a fixed point.
&&& rotation group
These rotations around a point O form a group, obeying three axioms.
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There exists an operation allowing us to compose two rotations around O; the result is also a rotation around O.
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There exists a “neutral” element that changes nothing in the plane: “zero-angle rotation.” Combining a rotation of angle q with zero-angle rotation yields a rotation of angle q.
-
If I rotate an object by angle q, I can return it to its original position via an “inverse” or “opposite” rotation of angle –q. In other words: to any rotation q I can associate the inverse rotation –q.
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Successive rotations are equivalent to adding their angles: q1 + q2 + q3. This “rotation” operation is associative, like adding numbers; I may compute (q1 + q2) + q3 or q1 + (q2 + q3). This combination of two rotations satisfies the group axioms defined by Sophus Lie.
Incidentally, I could perform these rotations in any order; the result of (q1 + q2) equals that of (q2 + q1). The “rotation around a point” operation is commutative. This group is commutative (but not all are).
All this seems obvious, yet these four axioms represent some of humanity’s greatest discoveries in mathematics and physics. If you follow me without overthinking at first, you’ll see why.
We can consider another group: translations on a plane. The translation vector is (Δx, Δy). This also forms a group whose neutral element is the null translation: (0, 0). To any translation we can associate its opposite: (–Δx, –Δy). Combining both yields the null translation; the object returns to its original spot. We’re merely opening closed doors, stating truisms.
We can combine these two operations—rotation plus translation—to obtain the “plane displacement group.” Its neutral element means “no displacement”: neither translation nor rotation. The concept of inverse displacement is equally intuitive: we restore the object to its original position. We thus obtain a group whose rotations and translations constitute what we call its “subgroups.” Don’t panic; this is just terminology.
Species notions.
We can imagine infinite figures on a plane. Some can be brought into coincidence via displacement. Examples: squares of side a, circles of radius R, line segments of length L. We call these the “species ‘circles of radius R,’” “‘squares of side a,’” “‘segments of length L.’”
&&& diagram
Two segments of different lengths L1 and L2 cannot be superimposed; they belong to different species. This gives us a sort of geometric taxonomy. Clearly, though:
All points belong to the same species
Look at the following figure.
&&& right-angled triangles with unequal sides
Obviously I can’t superimpose these two triangles by combining a rotation and a translation. Something’s missing: symmetry. I need only add one more element to the group, say symmetry relative to a given line. By performing three successive operations:
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Symmetry relative to line D
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Rotation so that triangle sides become parallel
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Translation
I can now make both triangles coincide. I’ve thus formed what we call the “2D Euclidean group.” This group represents all possible actions on objects; these actions preserve size and angles. They maintain a circle’s radius, a square’s side, a triangle’s sides. Intuitively we can divide these elements into two categories:
-
Those that don’t reverse “right-left”
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Those that do.
Naturally, it depends on the objects acted upon. Circles, squares, isosceles or equilateral triangles, regular polygons remain unaffected by “right-left” reversal. Fundamentally, since a group element is a way of acting on an object, we can divide the group into two subsets:
&&& diagram
We call these subsets “components of the group.” The one containing the neutral element is called the “neutral component.”
It’s easy to extend this notion to three dimensions. We’d encounter rotations and translations. Considering 3D-oriented shapes like corkscrews, we realize we must add one more operation: symmetry relative to a plane, reversing “right-left.” By combining these three operations—possible “right-left symmetry,” rotation, translation—we create a set of transformations preserving angles and lengths; this constitutes the “3D Euclidean group.” It likewise has two components, depending on whether chosen transformations preserve or reverse object orientation (turning “right-handed” corkscrews into “left-handed” ones).
&&& diagram
Let’s call this “right-left” reversal “P-symmetry” (for “parity symmetry”).
I’ve laid this groundwork to introduce the concepts of “group” and “action of group elements on objects” (here, geometric figures). But physics isn’t static; the space we’ll consider is spacetime
(x, y, z, t)
What’s a “geometric figure” in this spacetime? Essentially it’s a directed straight-line trajectory (in time). To simplify, we’ll consider a three-dimensional spacetime:
(x, y, t)
In principle this space could contain infinite oriented lines, each representing a trajectory.
&&& diagram
This isn’t really physics; it’s a mere model illustrating concepts. Vertical trajectories correspond to stationary objects; horizontal lines indicate motion at infinite speed. Yet physics forbids such motions. Treat all this “with a grain of salt.” If we wanted to account for Special Relativity, we’d limit ourselves to lines situated “inside light cones,” forming a minimal angle with the xy plane corresponding to motion at light speed.
&&& diagram
The underlying idea is:
Tell me how you move and I’ll tell you what you are
This is a behavioral description of physical objects, “material points.”
Orthochrone and antichrone.
Return to our three-dimensional spacetime (x, y, t). Consider the trajectory shown below, moving from A to B. Looking at this figure, I see that path AB is orthochrone: from A to B time flows toward the future, not the past (as would be the case for BA).
I have this trajectory and imagine a group allowing me to shift this material point from one trajectory to another. For a non-mathematician, a group is like a magic bag symbolized by a circle. Inside are points, each representing an element g of group G. One of these elements, e, is the neutral element; it changes nothing, leaves the trajectory untouched. This seems silly, but according to Lie’s axioms I absolutely must include such an element for this to be a group.
&&& changing trajectories
With a group, basically anything can happen. When handling the 3D Euclidean group, I could easily imagine a cone pointing upward, toward the “z-axis,” and posit that group elements could flip this object upside down. But I could also weed out all elements that invert the cone’s orientation.
Similarly, given an infinite number of ways to act on a line segment—like the one depicted above—starting from this orthochrone trajectory I could find an element transforming it into another orthochrone path where points A and B shift to A' and B' such that time tA' occurs later than tB'. Thus I’d switch from one orthochrone trajectory oriented past-future to another orthochrone path at different spatial locations, different speeds, over a different time span.
I can also imagine that within this dynamic group creating all possible motions there exists an element reversing this fifth dimension z, the “Kaluza dimension.”
Earlier we saw that particles are tied to a set (space plus group). Suppose I consider a particle of mass m moving at velocity V along some trajectory. Using elements of the group (which I call a “dynamic group” since it governs particle dynamics), I can generate all trajectories of mass m moving at velocity V in any direction. I thus define “the species of all particles of mass m moving at velocity V.”
In practice this group is called the “Poincaré group.” It extends the “Lorentz group.” Choosing an element from this group lets me convert one trajectory, described by certain parameters (called energy, momentum, etc.), into another trajectory with different parameter values. But this group has special properties. We said trajectories are oriented in time; there are two subsets of elements:
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Those that don’t reverse time; Souriau calls these orthochrones
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Those that reverse time; he calls these antichrones
Like the Lorentz group, the Poincaré group derives from an “axiomatic definition.” Until now physicists have used only orthochrone elements; they assumed all existing objects move from past to future, that the universe contains only orthochrone entities. In this view
object = movement
There was no room for antichrone motions. Yet this is precisely what Sakharov suggested by reversing time’s arrow in his Twin Universe. But what could such a peculiar entity possibly signify?!?
Here lies a major discovery by Souriau: a movement is associated with a particular choice of parameters; this collection constitutes what Souriau terms the “moment” linked to that movement. The relativistic movement of a material point is tied to a moment comprising ten components. Only those with some theoretical physics background can delve into these details. For non-theoretical physicists we’ll state that the moment includes:
(E, plus other things)
where E is energy.