One of the most interesting hypotheses about the nature of reality today is the so-called holographic principle, according to which our reality is a hologram.
In the late 1990s, theoretical physicists discovered a remarkable connection between two seemingly unrelated concepts in theoretical physics. This connection is fundamentally technical in nature, but it can have far-reaching implications for our understanding of gravity and even the entire universe.
To illustrate this connection, we'll start … with a black hole. The researchers found that when one bit of information hits a black hole, its surface area increases by a very precise value: the square of the Planck length (about 1.6 x 10-35 meter).
At first, the fact that a black hole grows as matter or energy falls into it may not seem particularly interesting. However, it is surprising here that in direct proportion to the information that has fallen into the black hole, it is its surface area that increases, and not its volume, which is fundamentally different from any other known object in the Universe. In the case of most objects known to us, it is fair to say that when one bit of information is "absorbed", the object's volume will grow by one unit, and its surface area will only grow by a fraction. But in the case of black holes, the situation is different. As if this information does not get inside a compact object, but remains on its surface.
Black hole hologram
A hologram is an image of a system obtained using fewer dimensions, capable of containing all the information from the original system. For example, we live in three (spatial) dimensions. When you take a selfie, the smartphone camera takes a 2D picture of your face, but it does not capture all the information, and when you later review your picture and select a filter, you cannot, for example, see the back of your head, no matter how you rotate the image.
A hologram recording would have retained all this information. Even if it were two-dimensional, you would still be able to explore it from all angles in three dimensions.
Describing a black hole as a hologram can provide a solution to the so-called information paradox of black holes - the problem related to where information goes when matter enters the event horizon. However, this is a separate topic, the article on which you can read here. The concept of a black hole as a hologram is also a good example to remember when considering the entire universe.
Life on the border
The connection between the seemingly unrelated branches of physics discussed at the beginning of this article is another application of holographic techniques known as the AdS / CFT correspondence.
AdS stands for "anti-dessitorial space" - a particular solution of the equations of Einstein's General Theory of Relativity, describing an absolutely empty universe with negative curvature of space. This is a rather boring universe: there is no matter or energy in it, and the parallel lines eventually diverge due to the geometry underlying it. Even if it does not describe the universe in which we live, for a start it is already some kind of universe. And this model has the necessary mathematical properties to make the connections that theorists need.
The other side of this correspondence is a system known as conformal field theory (CFT).Theoretical physics is not very accurate with field theories - these are the very hammers with which scientists hammer in the many quantum nails used to describe three of the four forces of nature. Electromagnetism, strong nuclear force, and weak nuclear force have field theory descriptions that have been used extensively over the past 50 years.
Now that we have sorted out all the definitions we need, let's look at why this relationship is so important.
Let's say you're trying to solve a very complex problem like quantum gravity with string theory, which is an attempt to explain all the fundamental interactions and particles in the universe in terms of small vibrating strings. In fact, it is such a difficult task that no one has yet found a solution to it, despite decades of trying. The AdS / CFT compliance tells us that a holographic technique can be used to avoid incredible headaches.
Rather than trying to solve the problem of quantum gravity in our 3D universe, the AdS / CFT correspondence allows us to switch to an equivalent problem at the border of the universe, where:
A) there are only two dimensions;
B) there is no gravity.
Namely, there is no gravity on the border. The mind-bogglingly complex mathematics of string theory is being replaced by a set of simply insanely complex field theory equations. Then you have the opportunity to solve your problems without gravity interfering with them, and transfer the result to the normal three-dimensional Universe and make predictions.
Not so fast
It all sounds like a wonderful idea: to deceive nature by bypassing gravitational machinations. Moreover, it can be a wonderful way to "solve" quantum gravity. However, there are several points here. First, you do not live in a universe with anti-dessitorial space. Our universe is full of matter, radiation and dark energy, and has an almost perfect flat geometry. Is there a similar correspondence that works in our real universe? Perhaps theorists are also working hard to find it.
Second, the "boundary" referred to in the AdS / CFT correspondence is the cosmological horizon, the boundary of what we can see in our observable universe. And all would be fine, but we live in a dynamic space-time with a constantly expanding space, where the border is constantly shifting. Modern theories are not yet very good at dealing with this point.
And third, when you move from a fully described anti-de Sitter universe to a simpler frontier model to which conformal field theory applies, the new sets of equations are only solvable in principle. And they may well remain incredibly difficult to solve. So just because you've cut a corner and bypassed gravity doesn't mean you've already figured it out. Otherwise, theorists working in this area would have long ago found a unified solution to this problem.
Life in a hologram?
So, are we living in a hologram? Even if the AdS / CFT correspondence relationship turns out to be fruitful for working with quantum gravity, and if scientists can find a way around the complexities and make this technique appropriate for the universe in which we live, it will not mean that we really live in a hologram. In other words, if the AdS / CFT correspondence provides a convenient way to solve gravity problems, this does not mean that our universe with gravity and three spatial dimensions is an illusion, and we actually live on a two-dimensional border without gravity.
Maths, as useful as they are, do not necessarily dictate exactly how we should perceive the fundamental nature of reality. If holographic principles are useful for solving problems, this does not mean that we live in a hologram.And even if we really lived in a hologram, we would still hardly be able to tell the difference.