Saturday, 17 January 2015

Black Holes: Event Horizons and The World As A Hologram - Part I


Luke Kristopher Davis

Newtonian Gravity

     We all know about gravity: the fact that two objects attract each other with a force proportional to the product of their masses and which gets weaker the further apart they are. This is what Newton essentially discovered. In the classical sense you can picture a tight-rope contest between the two masses and as they exert equal and opposite forces on each other, the lighter mass gets pulled in. If they are of the same mass they normally spin around the middle of the rope. If a mass comes from a long way away at a high speed the heavier mass at rest 'slingshots' the lighter mass, the lighter mass is moving so fast that the tight-rope slips from 'his hands' and continues to move on a new altered path. These little tight rope contests occur between all masses, from apples to stars. Mathematically instead of tight ropes we think of gravitational fields but the basic principle remains the same.

       The Einstein Fabric

      One of Einsteins greatest triumphs is the mass-equivalence principle, famously embodied as E=mc^2. This means you can think of a piece of mass as having an intrinsic energy in space and time. So if I completely destroy a piece of mass, say a kitkat chunky, I will get an energy equal to the mass of the kitkat multiplied by the speed of light squared. 
       In relation to our tight rope analogy, because mass can be thought of as some energy we can think of energy as some mass. Photons which are massless move at the speed of light so they actually have kinetic energy (energy due to motion) so Einstein says that this kinetic energy can be thought of as some mass. So if this energy can be thought of some mass it will be affected by gravity. So a photon actually takes part in tight rope contests with other masses, but they move so fast that in fact we hardly notice these contests. We only notice them when the heavy mass is really heavy which means the photons path through space is noticeably altered. This is called gravitational lensing. 

      Another step we must take is to ditch the tight-rope analogy. It can only go so far and as you may be familiar with gravitational forces now we can take the next step from Newtonian gravity, which is to introduce the notion of space-time. Time and space are normally thought as separate quantities, my time on my watch doesn't depend on where I am in space or my motion through space..surely?. Einstein showed the exact opposite,  that any time you read depends on how you are moving through space and as movement can only be recognized relatively to some other object, time is essentially relative. Every observer has a unique reading of time.

      This means that time and space are intrinsically linked, like two different threads being woven to form a fabric, and they form what is known as Minkowski space-time. This space-time has 4 dimensions which are time and the 3 dimensions of space. Instead of masses contesting with 'gravi-tight ropes' they curve this fabric (as in the picture above) and this curvature affects the motion of other objects. So think of an actual piece of fabric and an apple in the middle, the apple curves the fabric. If I place a grape on the fabric the grape falls inwards to the apple. This is gravity in the Einstein sense and it is the most accurate way to date in picturing what gravity is. Here is a really good video to show it.

Black Holes As Singularities

      So as mass curves space-time, you can start asking how much curvature occurs when a huge huge huge mass exists in the Einstein fabric. Well actually the curvature is so much that it forms a singularity. A point which is so dense that light spirals inwards and cannot escape due to the immense curvature of space-time. So as light cannot reflect off it we cannot see it hence the name black hole. 

      Black holes are formed when there is an object with a sufficient amount of mass, normally a heavy star, such that the object begins to collapse on itself due to the extremely strong gravitational pull. This can be anything, from a star to zillions of kitkats. The collapsing forms an infinitely dense black hole but with finite mass. 

       Let's imagine Marty and Doc doing a little experiment with a black hole. Crazy Doc wants to go in a spaceship so that he gets sucked into the black hole, merely following the curvature of space-time, and Marty is at a safe distance in another spaceship. Doc will send a photon to Marty to tell him he is alright every second or so. As Doc goes closer and closer to the black hole he will accelerate, he will get faster and faster. Doc still sends the photons and Marty picks them up knowing that Doc will be okay. But there comes a point where the curvature is so steep (gravity is so strong) that a photon cannot escape, this means that when Doc sends a photon he thinks Marty has got it but in fact Marty cannot receive it. So Marty does not know how Doc is or where he is. This point is known as the event horizon, a point of no return.

       So does Doc become completely obliterated ? Marty cannot know either way becomes he cannot retrieve any information about Doc beyond the event horizon. So the information Marty has about Doc seems to have completely gone. Is this a problem ? Yes. In part II we see why. 



  1. Dr. Preskill speculates that the information doesn't really vanish: it may be displayed somehow on the surface of the black hole, as on a cosmic movie screen.

  2. This will be explained in part II, hence the presentation of the hologram.