How fundamental is the holographic principle?

Really really… really fundamental… it is the most fundamental discovery since the discovery of socks… and maybe doughnuts…

Well, it is in some sense fundamental because it is based on much common sense. In principle, in its better form it says that a volume of space can communicate with the outside world via its boundary and not otherwise. It also imposes a limit on the degrees of freedom accessible in a volume, mainly related to the area around that volume… sure, there might be a problem if the topology is not that of a sphere, which most likely it is not but hey, we don’t like problems here, in string theory… But then, let’s go to the applications. One of these applications is well known to everyone who went to a high-school course of general physics… What? did you never compute the electrostatic forces acting on an object? Ya’ know, the old F_{e}=1/4pi*epsilon (q1*q2)/r^2 ? Well, where do you think comes the r^2 or the 4*Pi factor? Never bothered asking? Well, it’s because of the holographic principle of course: the interaction between domains happens to occur through the area that encompasses the charge… Ok, now, now, don’t look that surprised… you will see that Gauss’ theorem can be rewritten in a nice and complete way in the form of antisymmetric differential forms and that Stokes theorem invented in a primitive form by Lord Kelvin is a generalization of Gauss-Ostrograsky theorem and in the end the generalization of all these in a currently fashionable form is given by the oh so acclaimed “Holographic principle”…

Thing is, this is not completely correct… Why? Because space-time is not what we used to believe… many properties of a normal (meaning not so crazy) space must be abandoned in order to even hope to construct a correct theory for quantum gravity and among the properties that shake quite a bit are also these theorems all implying orientable stable manifolds…

So, don’t get too excited about the holographic principle or the AdS/CFT conjecture… They are cute but rather trivial…


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