Fri, 9. March 2012
My Future Light Cone
I had one of those "light bulb" moments when I saw a graph (Figure 2, below) for, the first time, on Geraint Lewis's blog Cosmic Horizons. It explained, in a flash, some of the obscure cosmological misgivings I had about the evolution of the Universe.
Figure 1 is a Light Cone diagram, using two spatial dimensions (horizontal) mapped against the time dimension (vertical). The cone appears 'straight' and the "absolute past" cone contains everything in the Universe that we can possibly see, looking backwards into it's past. The "absolute future" shows everywhere in the Universe which could see our emitted signals, getting larger as time passes. Put differently, the future light cone is the boundary of the causal future of any point in space-time and the past light cone is the boundary of its causal past. The cone appears the way it does, only because it does not go back far enough in time.
Figure 1: A Light Cone Diagram
(From "Relativity & Common Sense" by Hermann Bondi p.143).
Because of drawings like this, I always interpreted the 'Past Cone' as a literal cone, with its straight edges forever widening; but that obviously has problems as you reverse far backwards in time. As you reverse, the straight-edged light cone would get forever bigger and I had great difficulty in reconciling this backward cone expansion with a Universe which is known to shrink as you go back in time.
I easily understood that the extremely far distant universe can appear to break Einstein's light barrier as it expands. As Geraint explained, "We know the Universe is expanding, and that expansion is measured in terms of the Hubble Constant, which is about 72 km/s/Mpc. What this means is objects 1Mpc away are moving away from us at 72km/s, those at 10Mpc are moving at 720km/s, 100Mpc at 7200km/s etc etc. So, if you go far enough, objects will be traveling at the speed of light, and then even further go faster than the speed of light."
Objects such as galaxies, or clusters of galaxies, which have an apparent speed of greater than 299,792 kilometres per second, due mainly to the expansion of the Universe, will be invisible to us, because their light rays will not reach us.
The Hubble Sphere is the outer boundary of the volume surrounding us, beyond which objects are receding at a speed greater than the speed of light, due to the expansion of the Universe. We cannot see beyond the radius of the Hubble Sphere and as the expansion of the Universe accelerates, more objects will disappear. However, the "Observable Universe is apparently larger than the Hubble Sphere.
Now the graph, which is too important to squeeze down to my blog-width:
Figure 2: A Time - Distance Graph
(From 'Cosmic Horizons' - Geraint attributed the graph to Tamara Davis.)
This is the first time I have seen such a simple graph showing the Hubble Sphere and and the Light Cone going back to t=0 (the Big Bang) like that. It is the Universe in a nutshell. It changed my understanding of a light cone and gave me an immediate insight into the meaning of the visible Universe and why there is an invisible Universe (although it has left me with a few outstanding questions).
Space-time is curved and expanding. The cone still gets bigger in space as you go back in time but only within spacial 'dimensions' which are shrinking. In figure 2, the past light cone is contained to the left of the red light cone curve. To see the cone as a breast-shaped curve allowed me to reconcile what was going on. The Universe shrinks as you look back in time. As space itself shrinks so the cone shrinks with it. Simple. Geraint points out that the "light rays change directions from moving away from us to be moving towards us at the Hubble Sphere."
The Hubble Sphere is the outer boundary of the volume surrounding us, beyond which objects are receding at a speed greater than the speed of light, due to the expansion of the Universe. We cannot see beyond the radius of the Hubble Sphere and as the expansion of the Universe accelerates, more objects will disappear. However, the "Observable Universe" is larger than the Hubble Sphere. The Universe is 13.7 Billion years old and the Hubble sphere is very slightly larger, at 13.9 billion light years diameter, for reasons that I have yet to clearly understand.
The Observable Universe consists of the galaxies and other matter that humans can in principle observe from Earth in the present day, because light from those objects has had time to reach us since the beginning of the cosmological expansion. The word observable used in this sense indicates that it is possible in principle for light from the object to reach an observer on Earth.
The current comoving distance to the particles which emitted the CMBR, representing the radius of the visible universe, is calculated to be about about 45.7 billion light years, while the current comoving distance to the edge of the observable universe is calculated to be about 46.6 billion light years - about 2% larger.
An Event Horizon is a boundary in space-time beyond which events cannot affect an outside observer.The Cosmological Event Horizon is the boundary separating events visible at some time (past, present or future) and those that can never be visible. So in Figure 2, some events which occurred in the early Universe and were once visible are no longer visible.
The Particle Horizon of the observable universe is the boundary that represents the maximum distance at which events can currently be observed. For events beyond that distance, light has not had time to reach our location, even if it were emitted at the time the universe began.
The particle horizon is the maximum distance from which particles could have traveled to the observer in the age of the universe. It represents the boundary between the observable and the unobservable regions of the universe, so its distance at the present epoch defines the size of the observable universe.
It is still not totally clear to me why the event horizon does not coincide with the Hubble Sphere nor indeed, exactly where the boundary of the 'Visible Universe' lies and what exactly is meant by Particle Horizon.
Hopefully another light bulb will illuminate the misgivings I still harbour, at some point in space-time within my future light cone.
2. Prof. Geraint Lewis (Sydney Univ.) is a regular speaker at the Macarthur Astronomy Forum.
3. Further Reading:
Cosmic Horizons: How does the Hubble Sphere limit our view of the Universe? Geraint Lewis's Blog article which sparked my interest.
Universe? - paper by Prof. Geraint Lewis;
Universe and Cosmic Horizons thesis by Dr. Tamara Davis; and
common misconceptions of cosmological horizons
and the superluminal expansion of the universe
4. Wikipedia definitions: