Getting the Measure of Space

Astronomy is one of the oldest scientific disciplines. Human beings have certainly been fascinated by goings-on in the night sky since prehistoric times, so perhaps astronomy is evidence that the urge to make sense of the Universe around us, and our own relationship to it, is an essential part of what it means to be human. Part of the motivation for astronomy in more recent times is practical. The regular motions of the stars across the celestial sphere help us to orient ourselves on the Earth’s surface, and to navigate the oceans. But there are deeper reasons too. Our brains seem to be made for problem-solving. We like to ask questions and to try to answer them, even if this leads us into difficult and confusing conceptual territory. And the deepest questions of all concern the Cosmos as a whole. How big is the Universe? What is it made of? How did it begin? How will it end? How can we hope to answer these questions? Do these questions even make sense?

The last century has witnessed a revolution in our understanding of the nature of the Universe of space and time. Huge improvements in the technology of astronomical instrumentation have played a fundamental role in these advances. Light travels extremely quickly (around 300,000 km per second) but we can now see objects so far away that the light we gather from them has taken billions of years to reach our telescopes and detectors. Using such observations we can tell that the Universe was very different in the past from what it looks like in the here and now. In particular, we know that the vast agglomerations of stars known as galaxies are rushing apart from one another; the Universe is expanding. Turning the clock back on this expansion leads us to the conclusion that everything was much denser in the past than it is now, and that there existed a time, before galaxies were born, when all the matter that existed was hotter than the Sun.

This picture of the origin and evolution is what we call the Big Bang, and it is now so firmly established that its name has passed into popular usage. But how did we arrive at this description? Not by observation alone, for observations are nothing without a conceptual framework within which to interpret them, but through a complex interplay between data and theoretical conjectures that has taken us on a journey with many false starts and dead ends and which has only slowly led us to a scheme that makes conceptual sense to our own minds as well as providing a satisfactory fit to the available measurements.

A particularly relevant aspect of this process is the establishment of the scale of astronomical distances. The basic problem here is that even the nearest stars are too remote for us to reach them physically. Indeed most stars can’t even be resolved by a telescope and are thus indistinguishable from points of light. The intensity of light received falls off as the inverse-square of the distance of the source, so if we knew the luminosity of each star we could work out its distance from us by measuring how much light we detect. Unfortunately, however, stars vary considerably in luminosity from one to another. So how can we tell the difference between a dim star that’s relatively nearby and a more luminous object much further away?

Over the centuries, astronomers have developed a battery of techniques to resolve this tricky conundrum. The first step involves the fact that terrestrial telescopes share the Earth’s motion around the Sun, so we’re not actually observing stars in the sky from the same vantage point all year round. Observed from opposite extremes of the Earth’s orbit (i.e. at an interval of six months) a star appears to change position in the sky, an effect known as parallax. If the size of the Earth’s orbit is known, which it is, an accurate measurement of the change of angular position of the star can yield its distance.

The problem is that this effect is tiny, even for nearby stars, and it is immeasurably small for distant ones. Nevertheless, this method has successfully established the first “rung” on a cosmic distance ladder. Sufficiently many stellar distances have been measured this way to enable astronomers to understand and classify different types of star by their intrinsic properties. A particular type of variable star called a Cepheid variable emerged from these studies as a form of “standard candle”; such a star pulsates with a well-defined period that depends on its intrinsic brightness so by measuring the time-variation of its apparent brightness we can tell how bright it actually is, and hence its distance. Since these stars are typically very luminous they can be observed at great distances, which can be accurately calibrated using measured parallaxes of more nearby examples.

Cepheid variables are not the only distance indicators available to astronomers, but they have proved particularly important in establishing the scale of our Universe. For centuries astronomers have known that our own star, the Sun, is just one of billions arranged in an enormous disk-like structure, our Galaxy, called the Milky Way. But dotted around the sky are curious objects known as nebulae. These do not look at all like stars; they are extended, fuzzy, objects similar in shape to the Milky Way. Could they be other galaxies, seen at enormous distances, or are they much smaller objects inside our own Galaxy?

Only a century ago nobody really knew the answer to that question. Eventually, after the construction of more powerful telescopes, astronomers spotted Cepheid variables in these nebulae and established that they were far too distant to be within the Milky Way but were in fact structures like our own Galaxy. This realization revealed the Cosmos to be much larger than most astronomers had previously imagined; conceptually speaking, the Universe had expanded. Soon, measurements of the spectra of light coming from extragalactic nebulae demonstrated that the Universe was actually expanding physically too. The evidence suggested that all distant galaxies were rushing away from our own with speed proportional to their distance from us, an effect now known as Hubble’s Law, after the astronomer Edwin Hubble who played a major role in its discovery.

A convincing theoretical interpretation of this astonishing result was only found with the adoption of Einstein’s General Theory of Relativity, a radically new conception of how gravity manifests itself as an effect of the behaviour of space-time. Whereas previously space and time were regarded as separate and absolute notions, providing an unchanging and impassive stage upon which material bodies interact, after Einstein space-time became a participant in the action, both influencing, and being influenced, by matter in motion. The space that seemed to separate galaxies from one another, was now seen to bind them together.
Hubble’s Law emerges from this picture as a natural consequence an expanding Universe, considered not as a collection of galaxies moving through static space but embedded in a space which is itself evolving dynamically. Light rays get bent and distorted as they travel through, and are influenced by, the changing landscape of space-time the encounter along their journey.

Einstein’s theory provides the theoretical foundations needed to construct a coherent framework for the interpretation of observations of the most distant astronomical objects, but only at the cost of demanding a radical reformulation of some fundamental concepts. The idea of space as an entity, with its own geometry and dynamics, is so central to general relativity that one can hardly avoid asking what it is space in itself, i.e. what is its nature? Outside astronomy we tend to regard space as being the nothingness that lies in between the “things” (i.e. material bodies of one sort or another). Alternatively, when discussing a building (such as an art gallery) “a space” is usually described in terms of the boundaries enclosing it or by the way it is lit; it does not have attributes of its own other than those it derives from something else. But space is not simply an absence of things. If it has geometry and dynamics it has to be something rather than nothing, even if the nature of that something is extremely difficult to grasp.

Recent observations, for example, suggest that even a pure vacuum of “empty space” possesses “dark energy” energy of its own. This inference hinges on the type Ia supernova, a type of stellar explosion so luminous it can (briefly) outshine an entire galaxy before gradually fading away. These cataclysmic events can be used as distance indicators because their peak brightness correlates with the rate at which they fade. Type Ia supernovae can be detected at far greater distances than Cepheids, at such huge distances in fact that the Universe might be only about half its current size when light set out from them. The problem is that the more distant supernovae look fainter, and consequently at greater distances, than expected if the expansion of the Universe were gradually slowing down, as it should if there were no dark energy.

At present there is no theory that can fully account for the existence of vacuum energy, but it is possible that it might eventually be explained by the behaviour of the quantum fields that arise in the theory of elementary particles. This could lead to a unified description of the inner space of subatomic matter and the outer space of general relativity, which has been the goal of many physicists for a considerable time. That would be a spectacular achievement but, as with everything else in science, it will only work out if we have the correct conceptual framework.


23 Responses to “Getting the Measure of Space”

  1. Does this apply?

    The Universe Might Be A “Hologram,” Scientists Investigating

    By Sophie Weiner | August 29, 2014 – 05:00PM

    Some physicists now believe that on an incredibly tiny scale 100 billion billion times smaller than a proton, everything may be moving. If this is true, then no particle could ever truly be located, as it is constantly in more than one place on an infinitesimal level. This means that the universe could be made up of waves, not points. People have been referring to this possibility as that of “living in a hologram.”

  2. Could an inhomogeneous cosmological model explain the supernova results without requiring exotic new physics?

    • telescoper Says:

      This is a subject we debated yesterday at the meeting I’m at. The main difficulty is to construct a viable exact inhomogeneous cosmological model within which one can work everything out to the same accuracy we can with a FRW model. We interpret all cosmological data through in terms of observables defined in the framework of a perturbed FRW model so if the real universe is not like that then some inferences drawn this way, especially dark energy, may be false. There’s a nice paper by Chris Clarkson and Roy Maartens from a few years ago

    • A Lemaitre-Tolman-Bondi model can reproduce an arbitrary mz relation, but the cure is worse than the disease, since a) it is ad-hoc and b) requires us to be at the centre of an enormous structure.

      A fractal model a) is of no help and b) is ruled out on other grounds.

      • telescoper Says:

        Yes, but these are just two very specific examples. I think we should keep an open mind about other possibilities..

      • Indeed; no objection there. However, anyone who claims that the cosmological constant is not the reason needs to come up with a model which explains the SNIa observations and everything else which the concordance model explains. It is easy to come up with alternative explanations for one observation; it is much more difficult to come up with an alternative explanation for all or even most observations. The fact that the concordance model fits all or at least most observations is why it is called the concordance model.

        Also, the concordance model is not something into which observations are shoehorned; most cosmologists were probably surprised that this model fits the data best.

      • No definitive DM predictions.

        A very long string of WIMP/axion/sterile neutrinos/etc. No-Shows.

        Egregious under-abundance of DM “subhalos”.

        Everything Kroupa points out as falsifying the “standard” cosmological liturgy (irrespective of MOND bias).

        I’d say keeping an open mind would be a good idea for cosmologists. But those with a tenaciously conservative bent are free to double-down, triple-down, …

      • telescoper Says:

        It’s true that we haven’t identified the Dark Matter yet, but there’s a huge parameter space to explore and I don’t really think that’s all that surprising.

        Kroupa’s wild statements are very far from being justified on either theoretical or observational grounds.

        It’s Dark Energy that’s the really controversial topic. I think it’s highly possible we’re way of the mark on that one.

      • Agreed, and it is possible that an inhomogeneous model would offer a natural and elegant solution to the problem.

        Note that I say “possible”.

      • The burden of proof is on those who claim it is possible to come up with a quantitative inhomogeneous model which is, in the sense of Occam, better than any alternative.

        Note that the neutrino was a “no show” for a couple of decades.

      • The burden of scientists in general is not to get mentally locked into fixed ideas, but rather to keep an open mind towards new ideas, even if they conflict with cherished but poorly tested assumptions.

      • “It’s Dark Energy that’s the really controversial topic. I think it’s highly possible we’re way of the mark on that one.”

        If by dark energy you include the cosmological constant (and not just something with a different, perhaps time-dependent, equation of state), then I don’t quite follow you. A positive cosmological constant follows from three premises: 1) On large scales, the universe is described by a Friedmann-Lemaitre model, 2) Omega is less than 1 (together with George Ellis, you literally wrote the book on that), and 3) the universe is nearly flat (which is a quite robust result from studies of the CMB). So, own-up time: Which of these three assumptions do you doubt? Or do you think there is an additional one which I have left out?

        I don’t think any of these premises are assumptions in the narrow sense, but rather themselves have been well tested. (Of course, there is always some framework, such as we are not in a simulation, we are not being deceived by the Devil etc.).

      • telescoper Says:

        You also have to assume the Cosmological Principle and General Relativity…

      • OK, granted. However, if one assumes that GR holds (and we have no reason to believe it doesn’t), then the Cosmological Principle is actually no longer an assumption these days. First, it follows from the observed isotropy if we are not in a special place (and using that as an explanation is not much better than invoking fat angels* as CDM or saying that the Devil is deceiving us). Second, one can now actually observe homogeneity, e.g. by measuring the CMB temperature at another point in space. George Ellis, of course, has always been careful to remind us what are assumptions and what is secure knowledge. However, my impression, especially from his talk at the last Texas Symposium, is that he is happy that some things are no longer assumptions. In other words, unlike, say, Peebles in some contexts, he’s not really a Devil’s advocate as much as just careful.

        *Apologies to Jefferson Airplane; I saw Jefferson Starship last week!

    • Have you actually read what Sabine wrote? Her blog post basically disagrees with this claim.

      • The blog is linked to the paper. Do you think the editor and referees of PLB did not see it?

      • Did not see what?

      • The blog is linked to the paper. Do you think the editor and referees of PLB did not see blog?

      • No, the arXiv papers are linked to the blog. That is, there is a link from the blog to the papers.

        The papers are from 5 June and 5 September. The blog post is from 26 September, i.e. after the papers were put on arXiv (and, presumably, after they were submitted).

        I don’t think any editor searches the web to see if some blog post links to the arXiv version of a submitted paper.

        And how do you get from these papers or the blog post to “no big bang either”?

      • The author said that Black Hole as a mathematical singular solution does not exist in reality, and Big Bang as a mathematical singular solution does not exist either. According to my opinion, the total Einstein Field Equation is wrong. See:
        “Certainly GR is not directly applicable to galaxies. For example, the weak field approximation of GR is called gravitoelectromagnetism (GEM, see \cite{j12}) which maintains the Poisson’s equation. For a mass point, the Poisson’s equation reduces to Newton’s formula of universal gravity. Because the left side is linear with the gravitational potential and the right side is linear with the mass density, the Poisson’s equation in its general form is nothing but the linear summation of Newton’s universal gravity between mass points. That is, Poisson’s equation is a differential expression of the two-body interaction and the law of action at a distance. It is hard to imagine that the stars far away from the galaxy center suffer instant forces from the stars near the galaxy center. If gravity was consistent with a theory resembling Maxwell’s electromagnetism as suggested by GR, then gravitational waves would be ubiquitous because of omnipresent black holes. However, the waves have not been detected by now. Currently astrophysicists use Newton’s universal gravity and dark matter to explain the kinematic phenomena of galaxies. However, the purpose of the addition of dark matter is to make Poisson’s equation hold. This theory needs to be changed even though we assume dark matter would exist.”

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