John Archibald Wheeler, the physicist we owe the term "black hole" to, formulated in 1989 a principle that fits into three words: it from bit. Everything that exists comes from information. Matter, space and forces, if Wheeler is right, are all derivatives of a more fundamental layer in which bits live.
At the time it sounded like metaphor with ambition. Today it sounds like a research programme.
Landauer: information is physical
In 1961 Rolf Landauer showed that erasing one bit of information must release at least kT·ln 2 joules of heat; going below that threshold would break the second law of thermodynamics. In 2012 Bérut and colleagues (Nature) measured it in the lab. They held a single colloidal particle in a double-well trap and erased the information about its position, and the slower the erasure, the closer the heat released came to Landauer's limit.
The result is enough to close the question. Information has a thermodynamic cost. It is physical in the same sense energy is.
Delayed choice: the strangeness that stays strange
Delayed-choice experiments have been plentiful over the last twenty years. The basic scenario: a photon flies through an interferometer; the decision how to measure it (as a particle or as a wave) is made after it has already traversed the device. Classical intuition says this cannot work, because the outcome should already be fixed by what the photon has done.
The results agree with quantum mechanics: the photon behaves as the chosen measurement requires, even when the choice is made later. One interpretation: information travels backwards in time. Another: "what the photon did" before measurement has no meaning at all. Physicists prefer the second, but it too destroys the intuitive picture of time as a tape running left to right.
What this means for consciousness
Two facts have to be reckoned with.
- Information is a physical object with a thermodynamic cost (Landauer, Bérut).
- Quantum events have no well-defined "before measurement" (Wheeler's thought experiment; the experiment by Jacques, Aspect and colleagues, 2007).
Combine these and you get a picture in which time is the way local information processors (brains, for example) order their interactions with the universe. The arrow of time is the gradient of entropy increase for a given observer. Outside a specific computational process, "when" has no physical content.
The idea is not mine. Carlo Rovelli wrote a book about it (The Order of Time, 2017). Julian Barbour did so earlier still (The End of Time, 1999). Barbour in fact thinks there is no time at all, only a Platonic space of instantaneous configurations of the universe, with "flow" an illusion. I do not go that far, but physicists take the position seriously, and brushing it aside would be dishonest.
Where speculation starts
Not speculation: information is physical, time has been emergent in statistical mechanics since Boltzmann (1872), and quantum measurement has no "before".
Half-speculation: the brain is a local information processor, and its sense of time is a byproduct of its computations. Neuroscience supports this: perceived time stretches and shrinks depending on what the brain is busy with (Eagleman, Current Opinion in Neurobiology, 2008). Whether the subjective arrow of time matches the physical one is still unknown.
Speculation: "echo of consciousness", "déjà vu as information time-travel". The phrases are pretty, but no measurement yet separates them from the ordinary workings of memory.
I file this under "interesting to test"; "proven" is a long way off.
If Wheeler is right, consciousness is what produces time, locally, out of bits.