Beyond the established symmetries of physics - Charge, Spin, Color, Time, etc. - is there any such thing as symmetry of Information?
Beyond the established symmetries of physics - Charge, Spin, Color, Time, etc. - is there any such thing as symmetry of Information?
In some sense, the asymmetry of information (entropy) is a defining feature of the universe. https://en.m.wikipedia.org/wiki/Arrow_of_time
But isn't entropy an emergent phenomenon, manifesting only at larger, relativistic (by which I mean non-quantum) levels?
Entropy doesn't affect the fundamental symmetries I mentioned in the title. So information may not be fundamental, then?Man... information is such a weird concept when one stops to look at it, I wonder if a true definition of it is as difficult to pin down as time.
If your lifespan was an hour, every generation that witnessed a sunrise or sunset would freak the fuck out and think the world was ending.
I've always thought of entropy like that, it seems one direction, but only because we're on a comparativly tiny timescale.
Used to subscribe to the "big crunch" theory that it'll just all start over. But the more Penrose and Hawking I read, the more I think the Big Bang just isn't that unique.
There's a lot of signs that the vast majority of existence is dark matter, and with how it interacts with regular matter, I don't think we have sequential big bangs like a single light slowly flashing. I think it's more like fireworks in the sky.
There's probably not anyway to travel through the dark matter to get to another "bubble", and even if we did, that bubbles laws of physics could be drastically incompatible with us.
Like, if you remember the Narnia books it's like that "main world" where it was just an infinite number of ponds and jumping into one shoots you out to some world world everything works better. I think The Magicians kind of ripped off the idea, and by now more people may be familiar with that then one of the least popular (but underrated) books in a children's series from ww2.
Entropy is functionally persistent, but only because everything we can see and interact isnt all there is. There could be multiple other bubbles of matter happening right now, it's just about what frame of reference we have.
[In] the Narnia books it's like that "main world" where it was just an infinite number of ponds and jumping into one shoots you out to some world ... I think The Magicians kind of ripped off the idea.
Completely off-topic from symmetries and entropies, but I can't pass up the opportunity to mention that the specific Narnia installment where we see this "main world" and branches is The Magician's Nephew, the sixth out of seven books.
One clarification: electric charge, angular momentum, and color charge are conserved quantities, not symmetries. Time is a continuous symmetry though, and its associated conserved quantity is energy.
Similarly, information isn't a symmetry, but it is a conserved quantity. So I assume you're asking if there's an associated symmetry for it from Noether's theorem. This is an interesting question: while Noether's theorem ensures that any continuous symmetry will have a corresponding conserved quantity,
the reverse isn't necessarily true as far as I know.In the case of information conservation, this normally follows naturally from the fact that the laws of physics are deterministic and reversible (Newton's laws or the Schrodinger equation).If you insist on trying to find such a symmetry, then you can do so by equating conservation of information with the conservation of probability current in quantum mechanics. This then becomes a math problem: is there a transformation of the quantum mechanical wavefunction (psi) that leaves its action invariant? It turns there is: the transformation psi -> exp(i*theta)*psi. So it seems the symmetry of the wavefunction with respect to complex phase necessitates the conservation of probability current (i.e. information).
Edit: Looking into it a bit more, Noether's theorem does work both ways. Also, the Wikipedia page outlines this invariance of the wavefunction with complex phase. In that article, they use it to show conservation of electric current density by multiplying the wavefunction by the particle's charge, but it seems to me the first thing it shows is conservation of probability current density. If you're interested in other conserved quantities and their associated symmetries, there's a nice table on Wikipedia that summarizes them.
What would ur proposed symmetry of information look like? I think then we can see if there is evidence for it.
This falls a bit outside my wheelhouse but I believe the answer is no. The established symmetries in particle physics are all associated with the quantum mechanical state of a particle (charge, parity, etc) and to my knowledge there isn’t an “information” quantum number.
The closest you might get to this is quantum information theory, where information is encoded in other physical characteristics (spin, parity, energy, etc). In this sense information is more of an emergent phenomenon than a fundamental property.