Cosmology / Elementary Tour part 1: The expanding universe

Together, billions and billions of stars like our sun form gigantic star systems – galaxies like our own Milky Way galaxy, which probably doesn’t look all that different from the galaxy NGC 4414 shown here:

Hubble-Aufnahme der Spiralgalaxie NGC 4414
© Hubble Heritage Team (AURA/STScI/NASA)

The cosmological models of general relativity paint a rather simple picture of a universe filled with a collection of such galaxies freely drifting through space. These galaxies are evenly distributed, and they drift in an orderly way, following the expansion of space. This expansion is shown in the following animation. The animation depicts part of a two-dimensional slice of the universe, including a number of galaxies, and it is certainly not to scale; all distances and sizes are chosen for easy viewing, not for verisimilitude.

The animation shows 100 million years worth of the expansion of the universe, as seen from our own galaxy (shown in red) which, as our personal reference point, remains firmly in the centre. Time is shown in the upper left corner (where “My” stands for “million years”), and the galaxies visibly move away from our own. The distances from our galaxy to the blue and green galaxies (measured in light years, abbreviated ly) are shown at both the beginning and the end of the animation. At the end of the brief clip, we see that the distances to the blue and green galaxies have doubled, and so have all distances between all of the galaxies shown!

The expansion of the universe

For each galaxy, the average speed with which it recedes from our own red galaxy is the distance it covers, divided by the time it needs for its motion. To calculate the distance covered by the green galaxy, we compare its distance from the red galaxy at the beginning (1 million ly) to the distance at the end of the observation period (2 million ly). We thus find that during the 100 million years shown in the animation, its distance has increased by a million light years, corresponding to an average speed of

v = 1 million light years/100 million years

= 0.01 light years/year = 3000 kilometres/second

On the other hand, for the blue galaxy with its initial distance of two and its final distance of four million light years, corresponding to an increase by 4-2=2 light years, we obtain

v = 2 million light years/100 million years

= 0.02 light years/year = 6000 kilometres/second.

This illustrates a direct consequence of cosmic expansion: the speed with which a galaxy recedes from us is directly proportional to its initial distance – double distance, double speed, in our example. This is called the Hubble relation: the further a galaxy is away from us, the faster it recedes.

Finally, a caveat. There’s one aspect of cosmic expansion that the animation above cannot show: In this expansion, the points of view of all the galaxies are equally valid. Had we chosen a different galaxy to form the immobile center point of our animation, the animation would look just the same, all galaxies moving away from the observer, and their average speeds and distances following the same Hubble relation as above – double distance, double speed. The expansion has no center: all distances increase by the same factor, and every observer on a galaxy sees the same expanding cosmos.

Tour index

Next part: Reddening galaxies

Definitioner

time

It is a fact of life that not all events in our universe happen concurrently - instead, there is a certain order. Defining a time coordinate or defining time, the way physicists do it, is to define a prescription to associate with each event a number so as to reflect that order - if event B happens after event A, then the number associated with B should be larger than that associated with A. The first step of this definition is to construct a clock: Choose a simple process that repeats regularly. (What is "regular"? Luckily, in our universe, all elementary processes such as a swinging pendulum, the oscillations of atoms or of electronic circuits lead to the same concept of regularity.) As a second step, install a counter: A mechanism that, with every repetition of the chosen process, raises the count by one. With this definition, one can at least assign a time (the numerical value of the counter) to events happening at location of the clock. For events at different locations, an additional definition is necessary: One needs to define simultaneity. After all, the statement that some far-away event A happens at 12 o'clock is the same as saying that event A and "our clock counter shows 12:00:00" are simultaneous. The how and why of defining simultaneity - a centre-piece of Einstein's special theory of relativity - are described in the spotlight topic Defining "now". With all these preparations, physicists can, in principle, assign a time coordinate value ("a time") to any possible events, and describes how fast or how slow processes happen, compared to that time coordinate.

speed

An object's average speed is the distance it moves during a given period of time, divided by the length of the time interval. If you make the time interval infinitely small, the result is the object's speed at one particular moment in time. The notion of speed can be applied to waves in different ways; for instance, for a simple wave, the phase speed is the speed at which any given wave crest or wave propagates through space. See also the more general entry velocity.

space

In a strict sense: Space as we know it from everyday life: the totality of all locations in which objects can sit, with three dimensions. In a more general sense used by mathematicians, all kinds of sets of points are spaces - a line for instance, which has but a single dimension, or a two-dimensional surface, but also higher-dimensional spaces. Also, in such more general spaces, geometry can be different from the standard Euclidean geometry taught in high schools - such spaces can be curved.

second

In the International System of units: the basic unit of time. Defined as a certain multiple of the oscillation period of electromagnetic radiation set free in a certain transition within the electron shell of atoms of the type Cesium-133.

point

Elementary "building block" of geometrical entities such as surfaces or more general spaces. For instance, a surface is the set of all its points, of all possible locations on the surface, and all geometrical objects in that surface are defined by the points that belong to them - for instance, a line on the surface is the set of (infinitely many) points.

observer

In the context of relativity, "observer" can mean two different things. Often, observer is synonymous with reference frame or (spacetime-)coordinate system: An observer in this sense is someone who assigns coordinates to everything that happens around him. In particular, all events are assigned space coordinate values and a time coordinate value. In the context of special relativity, it is often the case that when one talks about an observer, what is really meant is an inertial observer, corresponding to a special type of reference frame. On other occasions, the term is used in a more narrow sense - in those cases, an observer is someone sitting at a certain point in space and using the light signals reaching that location to construct an image of his surroundings. In the context of optical effects in relativity, for instance gravitational lensing, observer is usually meant in this way.

NASA (National Aeronautics and Space Administration (NASA))

Part of the US government in charge not only of manned space missions, but also responsible for numerous highly successful satellite and probe missions. NASA is a partner in projects such as the Hubble space telescope or the gravitational wave detector LISA. NASA website

light

Light in the strict sense of the word is electromagnetic radiation the human eye can detect, with wave-lengths between 400 and 700 nano metres. In relativity theory and in astronomy, the word is often used in a more general sense, encompassing all kinds of electromagnetic radiation. For instance, astronomers might talk about "infrared light" or "gamma light"; in this context, light in the stricter sense is referred to as "visible light". Within classical physics, the properties of light are governed by Maxwell's equations; in quantum physics, it turns out that light is a stream of energy packets called light quanta or photons. In the context of relativistic physics, light is of great interest, and for a number of reasons. First of all, the speed of light plays a central role in both special and general relativity. Also, there are a number of interesting effects in general relativity which are associated with the propagation of light, namely deflection, the Shapiro effect and the gravitational redshift.

Hubble relation

See Hubble constant

general relativity (general theory of relativity)

Albert Einstein's theory of gravity; a generalization of his special theory of relativity. For information about the concepts and applications of this theory, we recommend the chapter general relativity of our introductory section Elementary Einstein. Further information about many different aspects of general relativity and its applications can be found in our section Spotlights on relativity.

galaxy

Stars are rarely found alone - usually, they congregate in conglomerates of millions, billions or even more stars called galaxies. A case in point is our sun, part of a galaxy we call the milky way. The life of a young galaxy can be very turbulent. Examples of such young, active galactic nuclei are radio galaxies and quasars.

Cosmology / Elementary Tour part 1: The expanding universe

Together, billions and billions of stars like our sun form gigantic star systems – galaxies like our own Milky Way galaxy, which probably doesn’t look all that different from the galaxy NGC 4414 shown here:

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