The Horizon and Beyond

Today we move to the vast and wonderful field of cosmology. In cosmology a horizon is a dividing surface between regions that are in causal contact. If particles are in casual contact they can interact, which means particles in one region can influence particles in another. A horizon however divides such regions, such that anything on the other side of a particle’s horizon cannot cause any influence upon it.

Now in cosmology there are a fair few of these horizons which are all a bit subtly different. Here is a quick guide to the different types of horizons and what they really mean. But first we must appreciate two things. First the fact that the universe is expanding. In fact it is expanding at an accelerating rate! It is not expanding because there is space outside for it to expand into, the universe is all there is and the very fabric of spacetime is expanding. Please see it’s moving fast – apparently for more details on this. The point is all intergalactic objects are moving away from us with what we can ‘recession velocities’. Secondly, the fastest anything can communicate is at the speed of light. The fastest way to send a signal from A to B is to send a light beam. Nothing moves faster than a photon.

Now we’ve cleared that up onto to the horizons:

Number 1: The Particle Horizon

The Particle Horizon is like the radius of sphere, with the observer at the center. An observer can be anyone – you, me, your brother, your pet cat sitting somewhere in the universe. Now the sphere encompasses all the regions that could have sent a signal to the observer within the lifetime of the Universe. So it’s as though this observer has been sitting here since the beginning of the universe and the distance to the edge of the radius will therefore be the speed of light (since thats the fastest way to send a signal) x the age of the universe (distance = speed x time). So this is quite an easy one.

Number 2: The Hubble Radius

Now this is not technically a horizon as it does not divide regions of casual contact but it is still very commonly used in cosmology and is therefore worth mentioning. The Hubble Radius is again like the radius of a sphere which encompasses the region within which the recession velocities of objects are smaller than the speed of light. Now you may think  – how can anything recede faster than the speed of light anyway? Nothing can travel faster than the speed of light?! And you’re right, but here’s the subtlety which means i’m not contradicting myself. These objects are travelling faster than the speed of light but relative to us they are receding from us faster than the speed of light from our point of view, as of course we too are moving away from them. And as the universe is undergoing accelerated expansion these objects are receding faster and faster as time goes on. Why this Hubble Radius is of importance may not be as obvious as Number 1 but it allows us to understand at what rate the universe is accelerating.

Number 3: The Past Light Cone

The Past Lightcone is a region that encompasses all regions of space that have ever been in casual contact with an observer. Imagine an upside down cone with the observer sitting at the point. The boundaries of the cone are defined by the speed of light, and the region encompassed by the inside of the cone contains all regions of spacetime that could ever have been in casual contact with us. So to be able to receive a phone call, the person on the other end of the phone needs to be within your past light cone. Now this past light cone is very big – so no worries about not receiving a message because the person was outside your past light one when they sent this – this is never going to happen. Think about it this way – I’m sitting at the point of the cone at this very moment. Taking the subsection of the cone from now to two minutes ago the light cone has a certain size. The boundaries of the cone are located at the distance that a photon can travel in two minutes, considering considering it travels 3×10^8m/s this is very far!! If anything can reach me quicker than this it can fit inside my past light cone and considering this distance is very far, things can afford to be a lot slower if they are a closer. And most signals sent two minutes ago originate from a source a lot closer than 360×10^8m away!

lightcone-300x349

Number 4: The Event Horizon

Finally, the Event Horizon is a variation of the Past Light Cone. It is the past lightcone in the limit of the time running towards the maximum value, i.e. the end of the universe. Different cosmological models have different values for the maximum value of time, some call it infinity, some are more pessimistic… So the jist of it is, if an object is outside the event horizon (with an observer at sitting the point), that object will never ever be able to send a signal to the observer, as long as the universe may live. Must have been damn far away.

horizons

A spacetime diagram to show how the different horizons overlap. Fear not if can’t make heads nor tails of this. Spacetime diagrams are odd but very usual tools for the conceptualisation of ideas in cosmology and theoretical physics in general. I’ll do a post on the them soon! 

Number 5: The Visual Horizon

As far as our tiny eyes can see. Varies per human.

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