Space, experience and perception

Darkness… cold… silence. Complete and perfect silence. In all directions: dark… cold… empty space. In the distance: the blue and vibrant glow of the Earth. Around it: dark, empty space. The Earth’s closest neighbour, Venus, is 40 million km away in the direction of the Sun. The second closest planet, Mars, is 70 million km away in the opposite direction. Our Sun, our life-giving Sun, is 150 million km away from us. The closest star, Proxima Centauri, is 4.37 light years or 40 000 billion km away. 40 000 billion km. Inconceivably far, and yet so close in comparison to the distance to the centre of our own home galaxy, from which it takes 26 000 years for light to reach us. This centre, this core, this heart around which everything revolves—every star, every dust grain, every molecule—and towards which everything falls without ever turning back, is a very unusual place indeed.

gb1244704496(image credit: NASA, Apollo 8 mission, taken by astronaut William A. Anders on December 24, 1968)

What is near, what is far? Is your house near or far from your office? Is India near or far from your city? Is the Moon near or far from the Earth? Is the Galactic centre near or far from the Solar system?

What is small, what is large? Is a virus small and a spider large? Is your hand small and your house large? Is your neighbourhood small and your country large? Is Pluto small and the Earth large? Is the Sun small or large?

What is vast and how vast is vast? Is our solar system vast? Is our Galaxy vast? Is our local group vast? Is the sky vast? Is the space of our lives vast? The space of seeing and hearing, the space of tasting and touching, the space of feeling, the space of our thoughts? Are these vast?

The Milky Way contains approximately two hundred billion stars. How many have solar systems? All these stars add up to a mass of about 100 billion solar masses. But we know from their orbits that the total mass of the Galaxy is around 1000 billion solar masses. This implies that all the stars, together with all the dust and molecular gas floating around make up approximately one tenth of the mass of the Galaxy. Where is the rest of it? What is the rest of it?

When a particle orbits a massive object, its velocity along the orbit depends on its distance from the central object: when it is closer it moves faster, and when it is farther it moves more slowly. If the orbit is circular, the orbital velocity is constant and depends only on the mass of the central object, and the distance from it. In the Solar system, where the planets move in circular orbits around the Sun, Mercury, the closest to it, moves at about 50 km/s, Venus moves at 35 km/s, Earth at 30 km/s, Mars at 25 km/s, and so on out to Uranus that moves at about 7 km/s and Neptune at 5.5 km/s. But all the stars in the Galaxy for which we have a measure of proper motion with respect to the centre, are moving at the same speed: they are all orbiting the Galactic centre with a velocity between 220 and 240 km/s. This does indeed seem odd. It is as if they were held in place by something, as if they were embedded in an invisible but massive, collision-less but gravity-binding cosmic gel. Even more surprising is that this binding cosmic gel, this Dark Matter (as it is called), accounts for 90% of the mass of the Galaxy, and therefore dictates the global dynamics of its contents. So, what appears as this all pervasive dark, cold, empty space is not so empty after all.

We move further and further away from our solar system, further and further away from the plane of the Galaxy. Its structure reveals itself as a gracefully shaped spiral with brightly illuminated arms, sprinkled with numberless point-like stars, and rotating majestically in a sea of subtly glowing red. This vast and expansive spiral extends over 100 000 light years. On average, 1 to 2 stars are born in our Galaxy every year, typically with about half the mass of the Sun, but sometimes much more massive, reaching 100 solar masses and more. They come to life in the depths of molecular clouds: the cloud collapses under its own gravity, and through this collapse dense cores appear and provide the ideal environment for star formation.

Winding inwards, the spiral arms merge with the Galaxy’s central stellar bar: millions of old, reddish stars that rotate coherently about the Galactic centre as an elongated structure 27 000 light years in length. The bar sweeps through space, sets in motion the gas and dust, and defines the molecular dynamics. From its edges to the very heart of the Galaxy, we think that the gas moves either in large elliptical orbits aligned with the bar, or on smaller orbits perpendicular to it, and contained within the larger ones. Turbulence in the flow makes the gas fall from the outer to the inner orbits, and then from those towards the central gravitational well.

The one central point around which everything turns is the location of the most massive object in the Galaxy. A single object with a mass equal to that of four millions Suns, it moulds space-time of the central region, and yet it is invisible. Everything we know about it has been deduced or inferred by observing its surrounding and immediate neighbourhood. That, at the very centre of our Galaxy, is a supermassive black hole, is conceptually ungraspable, and yet it is inescapable.

A black hole: a state of matter for which we hold no description, and where gravity has overcome all forces (first compressing all electrons into a single shell around the protons, then compressing the electrons and protons together into neutrons, and finally overcoming the strong force, and compressing the neutrons into something beyond what we can describe or imagine, a state of matter beyond our theories and ideas). It is indeed difficult to conceptualize. A supermassive black hole of millions, and in some galaxies, billions, of solar masses, is something entirely foreign. So far removed this is from what is conceivable to us, that it is most naturally perceived as science fiction. But we know that it is not fiction. We know that at the centre of our Galaxy there is a concentration of dark mass of four million Suns. We know precisely where its centre is—exactly at the dynamical centre of the central star cluster. We know its maximum spatial extent—it must be contained within the tightest and most eccentric orbit of any star orbiting around it. And we know that with respect to the Galaxy, it is perfectly still.

We know this from observations of the brightest stars around it, but also from the motion of molecular gas. In fact, it was close to thirty years ago that we found that the best explanation for the motion of the gas in the central part of the Galaxy was a mass distribution composed of an extended star cluster of about three million solar masses, and a compact source of about the same mass right at its centre. It was hypothesised that a supermassive black hole would appear as a very bright, compact radio source. A few years later, it was discovered.

The supermassive black hole at the heart of the Galaxy is known as Sagittarius A*.

A black hole is black: it does not emit any light. Newton published the Principia Mathematica in 1687 and since then we have had the notion of escape velocity: the speed at which an object must travel in order to overcome gravity and escape its hold. Interestingly, this velocity is independent of the mass of the escaping particle, and is determined by the mass to size ratio of the more massive object. It was pointed out long before Einstein published his Theories of Special and General Relativity in 1905 and 1916, respectively, that as this ratio increases by making the mass larger, the radius smaller or both, the escape velocity eventually surpasses the speed of light at the surface. The event horizon, the distance from a point-mass where light is unable to escape, the only place in the universe where light stands still, is known as the Schwarzschild radius: Rs=2GM/c2.

For an object of one solar mass, the Schwarzschild radius is 3 km. For a typical black hole of 10 solar masses it is 30 km. If you recall that the distance between us and the sun is 150 million km—a mere 8 light minutes, then can we ever dream of seeing this for even the closest stellar mass black hole in our Galaxy, V4641 Sagittarii (or SAX J1819.3-2525), about 1600 light years away? Not really. For Sgr A*, the Schwartzschild diameter is about 20 million km. Observing it from here, this size corresponds to an angular scale of 19 microarcseconds. (An arcminute is a sixtieth of a degree, an arcsecond is a sixtieth of an arcminute, and a microarcsecond is a millionth of an arcsecond.) Believe it or not, we can currently distinguish features on scales of 30 microarcseconds. This is done with a technique called Very Long Baseline Interferometry (or VLBI) that makes use of a network of radio telescopes all over the globe. VLBI has recently been used to observe Sgr A*, and revealed the intrinsic size of the emitting region at wavelengths of a few millimetres to be around 1 Astronomical Unit. This is as if 4 million solar masses were contained in the space between the Earth and the Sun. Within about 5 years, we will be able to distinguish the shadow of the black hole, the dark depression inside the event horizon, the well in the curvature of space-time produced by this massive object, against the background of the bright hot gas surrounding it.

I cheated a little with my connection between the escape velocity and the Schwartzschild radius. The escape velocity in classical physics is derived by equating the gravitational potential to the kinetic energy of an object with mass m. But light has no mass, and is therefore not subject to gravity, or is it? Although the concept of an astrophysical object whose escape velocity is greater than the speed of light has been around for quite some time, black holes are formally pure general relativistic objects, and it is only in the context of Einstein’s theory that we can treat them mathematically.

For Newton, as for most of us with perceptions based on our everyday experiences, there is space, and events occur at particular times within this space. Objects, either still or moving with respect to some given reference, are contained within the space, and do not have any kind of influence on it. Gravity is explained as a field that pervades all of space, acting everywhere simultaneously and instantaneously. Every mass, regardless of its magnitude, acts on every other mass everywhere and at once. Light is without mass and therefore does not feel gravity, moving freely at infinite speed, in infinite straight lines.

For Einstein, space, time, matter and energy, are so intimately interwoven that they cannot be treated as if they were separate from one another. The speed of light, accurately measured in 1885 by Michelson and Morley to be 300 000 km/s, is the ultimate velocity for everything in the universe: nothing—no information of any kind—can travel faster than light. Matter, radiation and energy are simply different facets of the same thing, which is not really a thing, and the manner in which they are distributed defines  the shape of space-time. It is the shape or curvature of space-time, not gravity, that defines the trajectories of particles and bodies. Consider the subtlety of this: the disposition of the total sum of energy—matter and radiation—shapes space-time and defines the rules of motion. But this energy that moves within this space-time follows its shape that it simultaneously defines. And since nothing can ever be still, and every particle is always moving with respect to something else, all space-times are always shifting and changing, continuously remodeled and reshaped by the matter and radiation moving within, and as them.

Everything is so interlaced, so intermingled. Space and time, light and matter, black holes and dust grains; the space between planets, the space between stars, the space between the spiral arms; the space of our world: delicate and tender, bright, green leaves, a single bird sitting on the bare branch of an old, withered tree in the morning sun, a poplar seed floating in the air, swaying gently up and down, and back and forth in the warm summer breeze; the space of our lives: the space of our thoughts and feelings, sometimes so vast and sometimes so small, the space of seeing and hearing, sometimes so bright and sometimes so dull, the space of tasting and touching, sometimes so sensitive and sometimes so numb; the space of the bodies and minds: the space all around the body, the space between our fingers and toes, the space inside our nostrils, in our mouth, in our throat, in our lungs and belly. Where do any one of these spaces begin and where do they end? Where can we find any border, any separation? What do we really know? What do we really understand? Everything is so interlaced and so intermingled.

We look up at the skies at night, and we see Orion the hunter with his bright belt of three stars in a line, his dagger pointing down, and his arms and legs outstretched in all four directions. How far is Orion? How far is each star drawing out the constellation on the sky? Are they close together or far from one another? What else is there that we do not see behind and around the stars? What about the Great Bear, the Big Dipper? What about the winged horse, Pegasus? What about Aquila the eagle, and the Cygnus the swan? How much more is there than we can see? What about a cloudless, clear blue sky of a sunny summer day, where are the stars? Are they behind the blue of the sky, are they hidden within it? What about your thoughts, are they inside your head? Are they behind your eyes? Is everything that we say just a way of speaking about things, just descriptions and conventions that we use to communicate? When we say “it is hot”, what do we mean? When we say “I am cold”, what do we mean? When we say “stars” and “planets”, “galaxies” and “universes”, what do we mean? Do we know what anything is? When we see blue, when we see green, what is that? Is it the pigment, the impinging light, the combination of the absorbed and reflected wavelengths on the surface? Where is this blue, this green? Is it on an object, on its surface, inside of it? Is it in the eyes, in the cones and rods of the eye? Is it in the brain? And every day, a hundred, a thousand times a day, when you say “I”, out loud or to yourself, what do you mean?

(This essay was commissioned and originally published here for the “beam me up” project.)

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