## Just a minute! Is space really expanding?

Posted in Astrohype, The Universe and Stuff with tags , , , on August 2, 2013 by telescoper

Now then. I’m sure this little video will get a few cosmologists’ hackles rising:

The video was produced by minutephysics, so presumably the expansion of time accounts for the fact that lasts more than two minutes. More importantly, though, is the content. Here’s an old  discussion of mine on this question. Let me know what you think via the comments box!

## To “boldly” go…

Posted in Biographical, The Universe and Stuff with tags , , , on July 15, 2012 by telescoper

I thought anyone reading my rather gloomy recent posts could probably do with a laugh so I thought I’d put this up. It’s something I posted a while ago, in fact, but the video links on that have long since evaporated; a newer version appeared recently on Youtube so I thought I’d update it and re-post the piece.

This clip contains a short item  I did about twelve years ago for the BBC series Space, which was presented by Sam Neill. It was subsequently screened outside the UK with an alternative title, Universe. Originally we were going to demonstrate wormholes using a snooker table, clever editing and reversed video. However, the producer, Jeremy,  decided that wouldn’t look spectacular enough so instead we went to St Anton in Austria: I was flown over the Alps in a helicopter and then driven through the Arlberg tunnel in an impressively fast car. Well worth the cost to license fee payers, I’m sure, even if the three-day trip to Austria by me and a crew of six as well as the hire of the helicopter ended up as a mere three minutes of screen time…

The episode I was in, the last of 6 in the series, was called To Boldly Go. I remember suggesting to the producer that the only way to travel faster than light in the manner required was with a split infinitive drive, but they didn’t use that in the final script.

The segment I’m in starts at about 18:00 on the video. Notice how, in the helicopter sequence, I give the appearance of being completely terrified. A fine piece of acting by me, I thought. *Cough*

The item is daft, I know, and I don’t really believe any of that stuff about wormholes, but it was great fun doing it and I have to say the camera guys took some amazing footage of the mountains from the helicopter.

P.S. The next sequence, after mine, explains how the Anglo-Australian 2dF Galaxy Redshift Survey was done in order to provide a map for future generations of intergalactic space travellers. Really?

## Is Space Expanding?

Posted in The Universe and Stuff with tags , , , , , , , , , on August 19, 2011 by telescoper

I think I’ve just got time for a quick post this lunchtime, so I’ll pick up on a topic that rose from a series of interchanges on Twitter this morning. As is the case with any interesting exchange of views, this conversation ended up quite some distance from its starting point, and I won’t have time to go all the way back to the beginning, but it was all to do with the “expansion of space“, a phrase one finds all over the place in books articles and web pages about cosmology at both popular and advanced levels.

What kicked the discussion off was an off-the-cuff humorous remark about the rate at which the Moon is receding from the Earth according to Hubble’s Law; the answer to which is “very slowly indeed”. Hubble’s law is $v=H_0 d$ where $v$ is the apparent recession velocity and $d$ the distance, so for very small distance the speed of expansion is tiny. Strictly speaking, however, the velocity isn’t really observable – what we measure is the redshift, which we then interpret as being due to a velocity.

I chipped in with a comment to the effect that Hubble’s law didn’t apply to the Earth-Moon system (or to the whole Solar System, or for that matter to the Milky Way Galaxy or to the Local Group either) as these are held together by local gravitational effects and do not participate in the cosmic expansion.

To that came the rejoinder that surely these structures are expanding, just very slowly because they are small and that effect is counteracted by motions associated with local structures which “fight against” the “underlying expansion” of space.

But this also makes me uncomfortable, hence this post. It’s not that I think this is necessarily a misconception. The “expansion of space” can be a useful thing to discuss in a pedagogical context. However, as someone once said, teaching physics involves ever-decreasing circles of deception, and the more you think about the language of expanding space the less comfortable you should feel about it, and the more careful you should be in using it as anything other than a metaphor. I’d say it probably belongs to the category of things that Wolfgang Pauli would have described as “not even wrong”, in the sense that it’s more meaningless than incorrect.

Let me briefly try to explain why. In cosmology we assume that the Universe is homogeneous and isotropic and consequently that the space-time is described by the Friedmann-Lemaître-Robertson-Walker metric, which can be written

$ds^{2} = c^{2} dt^{2}-a^{2}(t) d\sigma^{2}$

in which $d\sigma^2$ describes the (fixed) geometry of a three-dimensional homogeneous space; this spatial part does not depend on time. The imposition of spatial homogeneity selects a preferred time coordinate $t$, defined such that observers can synchronize watches according to the local density of matter – points in space-time at which the matter density is the same are defined to be at the same time.

The presence of the scale factor $a(t)$ in front of the spatial 3-metric allows the overall 4-metric to change with time, but only in such a way that preserves the spatial geometry, in other words the spatial sections can have different scales at different times, but always have the same shape. It’s a consequence of Einstein’s equations of General Relativity that a Universe described by the FLRW metric must evolve with time (at least in the absence of a cosmological constant). In an expanding universe $a(t)$ increases with $t$ and this increase naturally accounts for Hubble’s law, with  $H(t)=\dot{a}/a$ but only if you define velocities and distances in the particular way suggested by the coordinates used.

So how do we interpret this?

Well, there are (at least) two different interpretations depending on your choice of coordinates.  One way to do it is to pick spatial coordinates such that the positions of galaxies change with time; in this choice the redshift of galaxy observed from another is due to their relative motion. Another way to do it is to use coordinates in which the galaxy positions are  fixed; these are called comoving coordinates.  In general relativity we can switch between one view and the other and the observable effect (i.e. the redshift) is the same in either.

Most cosmologists use comoving coordinates (because it’s generally a lot easier that way), and it’s this second interpretation that encourages one to think not about things moving but about space itself expanding. The danger with that is that it sometimes leads one to endow “space” (whatever that means) with physical attributes that it doesn’t really possess. This is most often seen in the analogy of galaxies being the raisins in a pudding, with “space” being the dough that expands as the pudding cooks taking the raisins away from each other. This analogy conveys some idea of the effect of homogeneous expansion, but isn’t really right. Raisins and dough are both made of, you know, stuff. Space isn’t.

In support of my criticism I quote:

Many semi-popular accounts of cosmology contain statements to the effect that “space itself is swelling up” in causing the galaxies to separate. This seems to imply that all objects are being stretched by some mysterious force: are we to infer that humans who survived for a Hubble time [the age of the universe] would find themselves to be roughly four metres tall? Certainly not….In the common elementary demonstration of the expansion by means of inflating a balloon, galaxies should be represented by glued-on coins, not ink drawings (which will spuriously expand with the universe).

(John Peacock, Cosmological Physics, p. 87-8). A lengthier discussion of this point, which echoes some of the points I make below, can be found here.

To get back to the original point of the question let me add another quote:

A real galaxy is held together by its own gravity and is not free to expand with the universe. Similarly, if [we talk about] the Solar System, Earth, [an] atom, or almost anything, the result would be misleading because most systems are held together by various forces in some sort of equilibrium and cannot partake in cosmic expansion. If we [talk about] clusters of galaxies…most clusters are bound together and cannot expand. Superclusters are vast sprawling systems of numerous clusters that are weakly bound and can expand almost freely with the universe.

(Edward Harrison, Cosmology, p. 278).

I’d put this a different way. The “Hubble expansion” describes the motion of test particles in a the coordinate system I described above, i.e one  which applies to a perfectly homogeneous and isotropic universe. This metric simply doesn’t apply on the scale of the solar system, our own galaxy and even up to the scale of groups or clusters of galaxies. The Andromeda Galaxy (M31),  for example, is not receding from the Milky Way at all – it has a blueshift.  I’d argue that the space-time geometry in such systems is simply nothing like the FLRW form, so one can’t expect to make physical sense trying to to interpret particle motions within them in terms of the usual cosmological coordinate system. Losing the symmetry of the FLRW case  makes the choice of appropriate coordinates much more challenging.

There is cosmic inhomogeneity on even larger scales, of course, but in such cases the “peculiar velocities” generated by the lumpiness can be treated as a (linear) correction to the pure Hubble flow associated with the background cosmology.  In my view, however, in highly concentrated objects that decomposition into an “underlying expansion” and a “local effect” isn’t useful. I’d prefer simply to say that there is no Hubble flow in such objects. To take this to an extreme, what about a black hole? Do you think there’s a Hubble flow inside one of those, struggling to blow it up?

In fact the mathematical task of embedding inhomogeneous structures in an asymptotically FLRW background is not at all straightforward to do exactly, but it is worth mentioning that, by virtue of Birkhoff’s theorem,  the interior of an exactly spherical cavity (i.e. void)  must be described by the (flat) Minkowski metric. In this case the external cosmic expansion has absolutely no effect on the motion of particles in the interior.

I’ll end with this quote from the Fount of All Wisdom, Ned Wright,in response to the question Why doesn’t the Solar System expand if the whole Universe is expanding?

This question is best answered in the coordinate system where the galaxies change their positions. The galaxies are receding from us because they started out receding from us, and the force of gravity just causes an acceleration that causes them to slow down, or speed up in the case of an accelerating expansion. Planets are going around the Sun in fixed size orbits because they are bound to the Sun. Everything is just moving under the influence of Newton’s laws (with very slight modifications due to relativity). [Illustration] For the technically minded, Cooperstock et al. computes that the influence of the cosmological expansion on the Earth’s orbit around the Sun amounts to a growth by only one part in a septillion over the age of the Solar System.

The paper cited in this passage is well worth reading because it demonstrates the importance of the point I was trying to make above about using an appropriate coordinate system:

In the non–spherical case, it is generally recognized that the expansion of the universe does not have observable effects on local physics, but few discussions of this problem in the literature have gone beyond qualitative statements. A serious problem is that these studies were carried out in coordinate systems that are not easily comparable with the frames used for astronomical observations and thus obscure the physical meaning of the computations.

Now I’ve waffled on far too long so  I’ll just finally  recommend this paper entitled Expanding Space: The Root of All Evil and get back to work…

## We have all the Time in the World

Posted in Music, The Universe and Stuff with tags , , on February 14, 2011 by telescoper

I came across this on Youtube a while ago, but I’ve been saving it up because I thought it might make a nice St Valentine’s Day gift for all lovers of astronomy (and/or someone special). Enjoy!

## Our Place in the Universe

Posted in Television, The Universe and Stuff with tags , , , on February 9, 2011 by telescoper

I suspect I’m not the only person working in astronomy who found inspiration in Carl Sagan‘s epic TV series Cosmos, which was broadcast on British television when I was at Secondary School. Although the graphics are a bit dated now, and the language perhaps a bit florid for modern tastes, it has lost nothing of its splendour or profundity which is largely due to the charisma (and beautiful writing) of the presenter. It’s also in stark contrast to the simple-minded stuff served up by modern so-called science programmes. Here’s a little taster, which brought back happy memories to me, and I hope will do the same for fellow astronomers-of-a-certain-age.

We live on an insignificant planet of a humdrum star lost in a galaxy tucked away in some forgotten corner of a Universe in which there are far more galaxies than people. We make our World significant by the courage of our questions, and by the depth of our answers.

## Space: The Final Frontier?

Posted in The Universe and Stuff with tags , , , , , , , on July 9, 2010 by telescoper

I found this on my laptop just now. Apparently I wrote it in 2003, but I can’t remember what it was for. Still, when you’ve got a hungry blog to feed, who cares about a little recycling?

It seems to be part of our nature for we humans to feel the urge  to understand our relationship to the Universe. In ancient times, attempts to cope with the vastness and complexity of the world were usually in terms of myth or legend, but even the most primitive civilizations knew the value of careful observation. Astronomy, the science of the heavens, began with attempts to understand the regular motions of the Sun, planets and stars across the sky. Astronomy also aided the first human explorations of own Earth, providing accurate clocks and navigation aids. But during this age the heavens remained remote and inaccessible, their nature far from understood, and the idea that they themselves could some day be explored was unthinkable. Difficult frontiers may have been crossed on Earth, but that of space seemed impassable.

The invention of the telescope ushered in a new era of cosmic discovery, during which we learned for the first time precisely how distant the heavenly bodies were and what they were made of.  Galileo saw that Jupiter had moons going around it, just like the Earth. Why, then, should the Earth be thought of as the centre of the Universe? The later discovery, made in the 19th Century using spectroscopy, that the Sun and planets were even made of the same type of material as commonly found on Earth made it entirely reasonable to speculate that there could be other worlds just like our own. Was there any theoretical reason why we might not be able to visit them?

No theoretical reason, perhaps, but certainly practical ones. For a start, there’s the small matter of getting “up there”. Powered flying machines came on the scene about one hundred years ago, but conventional aircraft simply can’t travel fast enough to escape the pull of Earth’s gravity. This problem was eventually solved by adapting technology developed during World War II to produce rockets of increasingly large size and thrusting power. Cold-war rivalry between the USA and the USSR led to the space race of the 1960s culminating in the Apollo missions to the Moon in the late 60s and early 70s. These missions were enormously expensive and have never been repeated, although both NASA and the European Space Agency are currently attempting to gather sufficient funds to (eventually) send manned missions to Mars.

But manned spaceflights have been responsible for only a small fraction of the scientific exploration of space. Robotic probes have been dispatched all over the Solar System. Some have failed, but at tiny fraction of the cost of manned missions. Landings have been made on the solid surfaces of Venus, Mars and Titan and probes have flown past the beautiful gas giants Jupiter, Saturn, Uranus and Neptune taking beautiful images of these bizarre frozen worlds.

Space is also a superb vantage point for astronomical observation. Above the Earth’s atmosphere there is no twinkling of star images, so even a relatively small telescope like the Hubble Space Telescope (HST) can resolve details that are blurred when seen from the ground. Telescopes in space can also view the entire sky, which is not possible from a point on the Earth’s surface. From space we can see different kinds of light that do not reach the ground: from gamma rays and X-rays produced by very energetic objects such as black holes, down to the microwave background which bathes the Universe in a faint afterglow of its creation in the Big Bang. Recently the Wilkinson Microwave Anisotropy Probe (WMAP) charted the properties of this cosmic radiation across the entire sky, yielding precise measurements of the size and age of the Universe. Planck and Herschel are pushing back the cosmic frontier as I write, and many more missions are planned for the future.

Over the last decade, the use of dedicated space observatories, such as HST and WMAP, in tandem with conventional terrestrial facilities, has led to a revolution in our understanding of how the Universe works. We are now convinced that the Universe began with a Big Bang, about 14 billion years ago. We know that our galaxy, the Milky Way, is just one of billions of similar objects that condensed out of the cosmic fireball as it expanded and cooled. We know that most galaxies have a black hole in their centre which gobbles up everything falling into it, even light. We know that the Universe contains a great deal of mysterious dark matter and that empty space is filled with a form of dark energy, known in the trade as the cosmological constant. We know that our own star the Sun is a few billion years old and that the planets formed from a disk of dusty debris that accompanied the infant star during its birth. We also know that planets are by no means rare: nearly two hundred exoplanets (that is, planets outside our Solar System) have so far been discovered. Most of these are giants, some even larger than Jupiter which is itself about 300 times more massive than Earth, but this may simply because big objects are easier to find than small ones.

But there is still a lot we still don’t know, especially about the details. The formation of stars and planets is a process so complicated that it makes weather forecasting look simple. We simply have no way of knowing what determines how many stars have solid planets, how many have gas giants, how many have both and how many have neither. In order to support life, a planet must be in an orbit which is neither too close to its parent star (where it would be too hot for life to exist) nor too far aware (where it would be too cold). We also know very little about how life evolves from simple molecules or how robust it is to the extreme environments that might be found elsewhere in our Universe. It is safe to say that we have no absolutely idea how common life is within our own Galaxy or the Universe at large.

Within the next century it seems likely that we will whether there is life elsewhere in our Solar System. We will probably also be able to figure out how many earth-like exoplanets there are “out there”. But the unimaginable distances between stars in our galaxy make it very unlikely that crude rocket technology will ever enable us to physically explore anything beyond our own backyard for the foreseeable future.

So will space forever remain the final frontier? Will we ever explore our Galaxy in person, rather than through remote observation? The answer to these questions is that we don’t know for sure, but the laws of nature may have legal loopholes (called “wormholes”) that just might allow us to travel faster than light if we ever figure out how to exploit them. If we can do it then we could travel across our Galaxy in hours rather than aeons. This will require a revolution in our understanding not just of space, but also of time. The scientific advances of the past few years would have been unimaginable only a century ago, so who is to say that it will never happen?

## Ten Facts about Space Exploration

1. The human exploration of space began on October 4th 1957 when the Soviet Union launched Sputnik the first man-made satellite. The first man in space was also a Russian, Yuri Gagarin, who completed one orbit of the Earth in the Vostok spacecraft in 1961. Apparently he was violently sick during the entire flight.
2. The first man to set foot on the Moon was Neil Armstrong, on July 20th 1969. As he descended to the lunar surface, he said “That’s one small step for a man, one giant leap for mankind.”
3. In all, six manned missions landed on the Moon (Apollo 11, 12, 14, 15, 16 and 17; Apollo 13 aborted its landing and returned to Earth after an explosion seriously damaged the spacecraft). Apollo 17 landed on December 14th 1972, since when no human has set foot on the lunar surface.
4. The first reusable space vehicle was the Space Shuttle, four of which were originally built. Columbia was the first, launched in 1981, followed by Challenger in 1983, Discovery in 1984 and Atlantis in 1985.  Challenger was destroyed by an explosion shortly after takeoff in 1992, and was replaced by Endeavour. Columbia disintegrated over Texas while attempting to land in 2003.
5. Viking 1 and Viking 2 missions landed on surface of Mars in 1976; they sent back detailed information about the Martian soil. Tests for the presence of life proved inconclusive, but there is strong evidence that Mars once had running water on its surface.
6. The outer planets (Jupiter, Saturn, Uranus and Neptune) have been studied by numerous fly-by probes, starting with Pioneer 10 (1973) and Pioneer 11 (1974) . Voyager 1 and Voyager 2 flew past Jupiter in 1979;  Voyager 2 went on to visit Uranus (1986)  and Neptune (1989) after receiving a gravity assist from a close approach to Jupiter. These missions revealed, among other things, that all these planets have spectacular ring systems – not just Saturn. More recently, in 2004, the Cassini spacecraft launched the Huygens probe into the atmosphere of Titan. It survived the descent and sent back amazing images of the surface of Saturn’s largest moon.
7. Sending a vehicle into deep space requires enough energy to escape the gravitational pull of the Earth. This means exceeding the escape velocity of our planet, which is about 11 kilometres per second (nearly 40,000 kilometres per hour). Even travelling at this speed, a spacecraft will take many months to reach Mars, and years to escape the Solar System.
8. The nearest star to our Sun is Proxima Centauri, about 4.5 light years away. This means that, even travelling at the speed of light (300,000 kilometres per second) which is as fast as anything can do according to known physics, a spacecraft would take 4.5 years to get there. At the Earth’s escape velocity (11 kilometres per second), it would take over a hundred thousand years.
9. Our Sun orbits within our own galaxy – the Milky Way – at a distance of about 30,000 light years from the centre at a speed of about 200 kilometres per second, taking about a billion years to go around. The Milky Way contains about a hundred billion stars.
10. The observable Universe has a radius of about 14 billion light years, and it contains about as many galaxies as there are stars in the Milky Way. If every star in every galaxy has just one planet then there are approximately ten thousand million million million other places where life could exist.

## Space Time

Posted in Biographical, The Universe and Stuff with tags , , on April 30, 2009 by telescoper

I thought anyone reading my rather gloomy recent posts could probably do with a laugh so I thought I’d put this up.

These clips contain a short item  I did about nine or ten years ago for the BBC series Space, which was presented by Sam Neill. Originally we were going to demonstrate wormholes using a snooker table, clever editing and reversed video. The producer, Jeremy,  decided that wouldn’t look spectacular enough so instead we went to St Anton in Austria: I was flown over the Alps in a helicopter and then driven through the Arlberg tunnel in an impressively fast car. Well worth the cost to license fee payers, I’m sure, even if the three-day trip to Austria by me and a crew of six as well as the hire of the helicopter ended up as a mere three minutes of screen time…

The episode I was in, the last of 6 in the series, was called To Boldly Go. I remember suggesting to the producer that the only way to travel faster than light in the manner required was with a split infinitive drive, but they didn’t use that in the final script.

Notice how, in the helicopter sequence, I give the appearance of being completely terrified. A fine piece of acting by me, I thought. *Cough*

Unfortunately my bit is quite a long way into the first clip, so you need to wait until about 09.00, and it runs over the join into the second clip

The item is daft, I know, and I don’t really believe any of that stuff about wormholes… but it was great fun doing it.