No it cannot. This is not an interpretation, nor a new theory, it is a misunderstanding. The papers are vacuous, and not in an interesting way.

### What time is it?

The basic idea is that we don't know what time it is, really. So we make a probability distribution for what time it is, and this changes the phase of the wavefunction by an amount proportional to however much we don't know the time. Then the authors claim that this uncertainty introduces a decoherence phenomenon into the Schrodinger equation, because the phases of energy eigenstates are shifted by an uncertain amount.

This is just plain wrong. The reason is that although we don't know what time it is, we know from the author's assumption that there is a consistent Schrodinger time (this is one of their axioms) that *whatever time it is*, it's the same time for any two things in the theory. So while there is an uncertainty in the phase of an isolated system from not knowing what time it is, there is no uncertainty introduced in the relative phase of two interacting systems, and there is no decoherence caused by this uncertainty, except through mistakes in analysis.

### Mistakes

These mistakes are subtly introduced by making a separation between "observer" and "system", and introducing the probability distribution for the clock reading only in those cases where the observer is interacting with the system, and when observers are interacting with each other, not when systems are interacting with systems.

For example, suppose you have a photon split by a beam splitter, with one part going through some glass, then through a double slit to measure interference. This will work, the beams stay coherent, because the photon that gets through doesn't excite any irreversible quantum in the glass. Notice that the glass is large and macroscopic, though.

Anyway, once the photons interfere, you get a pattern that doesn't give a hoot about what time it is, just on the relative phase-difference between the two photons, the path-difference in the optical system. So the photon didn't care that we don't know what time it is for the glass, because it just goes through the glass and not, and whatever time it is, it interferes with the other photon, which doesn't care what time it is either, because it's the same time as the other photon.

Note that the photon interacted with this enormous glass, and all the atomic absorption and emission events had to coherently come together even though for the glass, we don't know what time it is. The relative coherence is maintained throughout.

So when does the problem of time show up in these papers? It shows up when the observer entangles with the system, and at this point, the authors declare that the uncertainty in what time it is shows up as an uncertainty in the phase of the system that the observer measures.

If there is a second observer measuring something else, they introduce an uncertainty in the second observer's time. But then when the observers come to talk, the authors pretend that the two observers phase-shifts are uncorrelated, when in fact the uncertainty in what time it is is *exactly the same* for the two observers, because it is an uncertainty in the same global t variable that they both don't know.

So whatever the t-uncertainty for each observer, the coherence effects between the two observers are not washed out, unless you make the assumption that the actual global t is different for the two observers, an assumption that is at odds with the postulates of the theory, that there is a global time ticking down there underneath it all.

### There is no problem of time in S-matrix theory

Constrary to the authors' claims, string theory solves the problem of time definitively and for good, that's the whole point. The solution was the motivation for Heisenberg to introduce S-matrix theory in the first place, it allows you to make a theory in cases where space and time are unreliable.

An S-matrix theory doesn't give a detailed history of the events in the interior of spacetime, it only relates things on the boundary to other things on the boundary. It doesn't have a real local non-asymptotic time variable at all, so it can't describe time-dependent phenomenon, like the formation and evaporation of a quantum black hole in detail. This is why we are in the embarassing position of having essentially exact quantum description of forming and evaporating black holes while at the same time not being able to answer some of the simplest questions about this process.

So if you make a string scattering calculation, or an AdS/CFT calculation using boundary states, you don't have a problem of time on the interior, you can't, because time on the interior just doesn't appear in the description. It is at best reconstructed approximately from the quantum state on the boundary.

You might say "but then what about the problem of time on the boundary!", but the boundary theory is non-gravitational, and it doesn't have a time problem either. This is the miracle of string theory, and this is what makes it the only plausible candidate for quantum gravity--- the philosophical problems completely evaporate in S-matrix, it is as if they never existed.

You might object that there is a t-variable on the perturbative string world-sheet, but this is an artifact of the perturbative theory, of describing the string scattering process in detail using intermediate states, which you then interpret as localized in time. This interpretation is not completely good, you can't associate local operators to the string. If you do string field theory, you need to do it in light cone, and then the string story becomes more or less local along the light-front, but the light-front time variable is going diagonally in space time, and the string field is only telling a local story in the transverse coordinates to the light-cone pair. It stays nonlocal in the light-cone pair (time and one other coordinate).

If one were given the correct exact string S-matrix in our vacuum, there would be no t-variable in the S-matrix, only the S-matrix in and out state which does not reference any clocks at all. You might object that the S-matrix gives you phase shifts in outgoing waves, and to measure these phase shifts you might think you need a clock, but this is not so, since the relative phase between two states can be determined in principle by perfoming a second much-later scattering which can be approximated as two separate scatterings, and allowing the scattered products in different direction to interfere with each other to make fringes. The phase shifts of the original scattering now show up in the k-directions of the bragg diffraction of the two waves, and you can reconstruct the phase shift information from complicated scattering matrix data in principle without needing a clock on the interior, just by considering a more complicated in state.

This is exactly what you do for a photon--- you scatter it off a double slit to turn the difference in phase shift into a spatial diffraction pattern. This is not obscure at all, although it is hopeless to describe the appropriate s-matrix elements in detail for any realistic experiment.

This means that the problem of time cannot even be stated in S-matrix theory, and time is not treated differently from space, because neither is treated at all. This is the greatest virtues of string theory, and it is the reason that the S-matrix program was able to make such surprising progress in quantum gravity, which was not its original goal.

This post imported from StackExchange Physics at 2014-07-24 15:43 (UCT), posted by SE-user Ron Maimon