I watched a video of Leonard Susskind the other day. He described the “rule” that information cannot ever be lost. He dropped a few drops of red coloring into a small dish of water and stirred it. You could see where the drops went in at first and after a while the water was solid red and you no longer could. The information is still there he insists. We can no longer see it, but it’s always there.
I don’t get it.
First off, lets perform a thought experiment. We make the dish very small. We put the coloring in. We spin the water. Let’s make the dish airtight so no particles can get in or out. At some point in time (I know it’s an unfathomably far time away), the particles will occupy the same position and spin state as at some time in the past. When this happens there would be no way to track the particles back to their starting point.
Next, what about the uncertainty principle? Specifically, some particle pair pops into existence and out again. It interacts somehow with the particles in the water. You can’t trace this back. Information is now lost - the information of where the food coloring was originally placed.
It also seems that if information is never lost that he believes the universe to be calculable. If we knew enough about the current state we could trace everything forward of backward and we’d know everything. But that would even encompass our own thought patterns so good bye free will.
Is he really talking about the actual information? As far as I can see, there is no way, short of magic, to retrieve it. Or is he talking about the (maximum) amount of information once present? I think you could make an estimation of that, even after blending, simply based on the total number of dye molecules.
Susskind posits that entropy can be considered and measured in bits of information. He also believes there’s an upper limit on this information by way of degrees of freedom of the original bit (or particle, really). This all works into his Holographic Principle. As an example, the information that falls into a black hole isn’t lost or irretrievable since the surface area of the event horizon is equally proportional to the sphere’s volume, so you could, theoretically, retrieve all the information of, say, a baseball that fell into a black hole by somehow analyzing or decoding the now smeared holographic information of the baseball on the surface of the event horizon.
In that, he suggests the cosmos to be holographic, and that all information (energy/matter) within the universe is really a 3D projection for this cosmological sphere surrounding the universe. And the upper limit to the density of information the universe can hold is subject to the diameter of this holographic sphere.
Entropy is certainly a measure of information, and the entropy of a black hole is proportional to its surface area. Many physicists believe that this means that the event horizon of a black hole somehow encodes information, but nobody really has any idea what form this encoding would take.
What I heard in the Susskind clip was that it is, in principle, possible to know everything about the system that distributes the color into the water. We could, in principle, know the position and energy state of every molecule. Ultimately, we could, in principle, with complete information, work the calculations backwards from the dispersed system to the more highly ordered original state. The information that would lead us through that transformation exists.
Now, we would not be able to do this. But, the reasons are practical rather than theoretical.
Leonard Susskind. Professor of Theoretical physics .His research interests include string theory, quantum field theory, quantum statistical mechanics and quantum cosmology.[1]
No suprise there. I didn’t think anyone outside of Theoretical physics would put there name to such an unlikely … someone what obviously disproved… theory.
These theoretical physicists are trying to work with the assumption that information is conserved in order to try to get some way to calibrate their theories. such as string theory. Or the theory of the contents of a black hole…
They jump from quantum theory to cosmology too easily.
its a wild leap of logic.
If information isn’t conserved, in any circumstances whatsoever, then everything we know of quantum mechanics comes tumbling to the ground. If black holes don’t somehow or another conserve information, it doesn’t just mean that we don’t understand the quantum mechanics of black holes (we already know that we don’t understand that); it means that we don’t understand the quantum mechanics of anything.
Right. This is why it seems physicists are so keen on saying that information is always conserved. But can any of them address my points in the OP? It seems that this information theory as well as the hologram theory (and for that matter almost everything I ever hear from Susskind) are all philosophical matters. These kinds of claims seem to me to be a belief (faith) of a physicist rather than actual science. None of it seems testable.
Holographic cosmology models are testable, though in some cases the tests might be very difficult. In fact, the simplest holographic cosmology models have already been tested and rejected, almost by accident: There was a gravitational wave detector in German that turned out not to be very good at detecting gravitational waves (no big surprise; like most gravitational wave detectors, it was considered mostly a proof of concept), but which coincidentally also turned out to be a great holographic-universe detector.
Thinking about this a bit more, I suspect the thought experiment fails in a manner similar to fallacies that try to reason about entropy in an open system. As a simple example - take my watch. In 12 hours the hands will display exactly the same time as they do now. Has the information inherent in the watch been lost? No, because the observing system is also 12 hours into the future, and it inherently has information about the passage of time. Information preservation isn’t a local phenomenon.
The only time when the entire universe will reproduce a previous state is if it ever endures a big-crunch. Something that is currently out of favour, but may still re-emerge as a possible end scenario. But that is a singularity and we tend not to try to predict what they mean.