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I watched a video featuring Leonard Susskind in which he took a small bowl of water and added three drops of food coloring. He swirled it around. At first you could tell where the drops must have entered the water, but after a while you could not tell anymore. He said that a cornerstone of physics is that information cannot ever be destroyed and that the information is always there -- we just cannot see it.

I see two issues here and I'm hoping for some clarification.

  1. The particles can never be traced back to their origin. The uncertainty principle says that other particles have popped in and out of existence. These may have interfered with the particles in the water and cannot be traced back. So information is in fact lost.

  2. Let's take the same type of experiment but narrow the scope. Instead of this, I put four protons into some sort of container that can hold them. Not sure what that is or if it's more of a field, but for this thought experiment, let's just say I have a box with four particles in it. At first you know where they originated by watching them (if you could watch them). But after a long enough time, the particles will occupy the same position and spin state that they did at some point in the past. So the first time they occupied this state they trace back to your initial placement. The second time they hit this state they trace back to the first state. So you cannot actually trace them back to see where they originated in the container.

Perhaps the second thought experiment has some flaws in it but I'm hoping you can see what I'm getting at. That a duplicated state must mean that the originating positions and information is lost, and given enough time you'll always get a duplicated state.

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marked as duplicate by Brandon Enright, John Rennie, Kyle Kanos, Kyle Oman, user10851 Sep 29 '14 at 18:50

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    $\begingroup$ This is a duplicate of physics.stackexchange.com/q/29175 and there is a absolutely fantastic answer by Johannes (one of my favorites on the whole site!). $\endgroup$ – Brandon Enright Sep 29 '14 at 16:26
  • $\begingroup$ @BrandonEnright: Unfortunately, Johannes' toy model is already wrong for a universe in which at least one degree of freedom is not finite and/or countable, i.e. it fails trivially for the Newtonian mechanics of a universe with three gravitating bodies. It is certainly wrong for a quantum mechanical universe (and he admits that in his introduction). $\endgroup$ – CuriousOne Sep 29 '14 at 19:26
  • $\begingroup$ Physics doesn't make such claims. Physicists like Susskind do, for all the wrong reasons, and I don't think these claims are very well thought trough. In practice the universe loses information extremely quickly and in an infinitely expanding universe model that can be proven rigorously on the mathematical level of the model. To get back from there to "information stays constant", one has to work a bunch of highly unphysical assumptions into the dough before that cake bakes. $\endgroup$ – CuriousOne Sep 29 '14 at 19:31