Holography

I said I am going to discuss today about why the holographic principle is wrong… then I started thinking about it and I observed this could become a rather interesting paper so I decided to keep it for me until it becomes public… ya’ know… being in business it’s not that everything should be public immediately and I do have this VERY bad habit to talk too much serious stuff… I have to train myself in saying nonsense so that a conversation can flow easily without saying anything too relevant… 

Anyways… 

The idea of holography has its origin in the physics of black holes (or at least in what is vaguely understood from the physics of black holes). There are several fundamental paradoxes that appear when putting together Hawking radiation and Einstein-Hilbert Black Holes… I use the name vaguely (you know Hawking and his radiation… maybe you don’t know Einstein and Hilbert but together they form the name for a pretty nice action functional you can write for gravity, although somehow out of fashion nowadays when only wormholes and black holes with alice and bob around are of any measurable sexyness)… However, the idea relates quantum field theories on one side, assumed to describe fields in space-time and to be compatible with special relativity (i.e. local lorentz invariance, LOCAL, ok?) and to derive the interactions between various particles and … no, not gravitation, or at least not directly… in fact it relates this with information, or entropy (lack of information, so to say). What means that? Essentially it means that QFT describes a system made up of some fictional fields that, after applying a specific formalism, can be used to calculate various cross sections and get measurable results… The fields in QFT are NOT observable, or not directly. What you observe in your detector is the result of an interaction of an outgoing particle with your detector… keep this in mind. So, what are the degrees of freedom of QFT? Well, infinity… we have fields… fields are continuous objects in space-time so they have a potentially infinite number of possible excitations… (but the quantum fields in QFT are NOT physical…) 

Now, let’s start exciting these fields and add energy in some region of space (I don’t care if the energy is in form of photons, electrons or whatever, as long as it is energy)… When you do this you may reach an energy in that region of space that ends up collapsing under its own gravity… if you continue exciting the quantum fields you get enough energy there so that a black hole appears… but, if Hawking is right, the entropy of the black hole scales like the area of its horizon. Area of horizon means R^2 and entropy means the logarithm of the number of microstates accessible to the system or the information “lost” or “unaccessible”… So, you get a horizon at the moment when you excite not all the possible states in a volume, but on an area that encompasses the region of space… First conclusion: the information is not encoded in the volume but on an area… 

Ok-ish… now, this is the “state of the art”, vaguely speaking… If you think now as I thought you to think you will see where the difficult spots are in this construction… I won’t say anything else…

 

 

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s