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I am coming to this question in response to scepticism about emergentism as more than an overlay (eg. SEP article).

Entropy is well established as related to relative information about systems, and as the driver of temperature change. The position and momentum of all the particles isn't enough, you also need relative uncertainties, and the system as a whole will move to the more chaotic less pure state.

Causality doesn't make sense without an arrow of time, and that seems to arise from entropy. Causality then seems to be at root information flow.

It seems that modern science is property dualist, with energy + information. And information, everything as events, is increasingly thought to be fundamental and where all other properties will be unified (ie It From Bit).

So what is the get-out I am missing? Surely information has to be causal, and emergent order has real measurable impacts on the physics, separate to a purely reductionist account?

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    By the standard model time does not arise from entropy (I personally disagree) time is a dimension of space, and entropy increases across time due to the fluctuation theorem and the fact it is already flowing that direction. That keeps causation and information separate. Information measures causation and does not drive it. If we ignore time as a dimension of space, this gap disappears. [But then 1) you need another reason for spacetime to seem that way and 2) it forces you into a sort of idealism or duality with an idealist component, most physicists resist this stridently.] – jobermark Aug 8 '18 at 17:33
  • Get out of what? On the traditional account information only reflects observer's uncertainty and is essentially a "secondary quality". If it does indeed become a fundamental category then causality will be reworked to reflect the shift, it shouldn't be hard if indeed it arises from the thermodynamic arrow somehow. But what does this have to do with "emergent order" having measurable effects? Reshuffling categories will have no more measurable effects than the shift from Lagrangian to Hamiltonian dynamics, from forces to energy. – Conifold Aug 8 '18 at 22:38
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Mass, energy, and information are all interchangeable (https://www.technologyreview.com/s/420996/physicists-convert-information-into-energy/) and so can all be thought of as being made of the same essential building blocks. Look close enough, and any definition of either mass or energy is going to contain a time component. However, information is more fundamental than either mass or energy. I wouldn't necessarily say that information is causal, but it is certainly relative.

The Shannon entropy of... anything I guess... is a measure of the relative likelihood of... anything/something/nothing. So, where does that leave things?

It from bit. You nailed it.

But I think what's tripping you up is that true information requires more than just bits. You need a sender, a channel, and a receiver (though these may not necessarily have to be classical and conscious in nature). The channel can be any combination (perhaps ratio is closer to the essence...) of time AND space, but it must be both. The bits stored on a hard drive don't count as information if they are never read and a signal beamed into deep space is just noise if no one happens to be listening. Information is only information if it completes its journey and so, in that sense, it at least requires a relative ordering of local events. I suppose you could call that causal...

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