The Unbearable Lightness of Gravity

Well that's the moot point. Mr. Cooperstock might be right. Which is why we go out and ask this Universe via measurement these very questions, and then align our thinking accordingly. No biggie there. Welcome to scientific method.

However the statement "I’ve never seen anyone prove that information must carry energy" indicates that Mr Cooperstock is using a somewhat different definition of the concept of information than the usual. He's allowed to do that of course, but it ought be flagged as such or given a new word to indicate that variance.

Information is classically given as "any difference that makes a difference" ie. some distinct physical states which are assigned meaning. But different physical states are measurably so because there is an energy difference* between them : that difference is what we leverage in order to discover the state and interpret accordingly. In any event what others may or not prove theoretically is rather beside the point. The key issue is whether the Universe behaves in such a manner. Or not. If Mr Cooperstock wants to place information as the primary quantity but without energy implications then I'm not sure where that goes, probably to the realm of unmeasurable outcomes I say. Or equivalently all outcomes can be assigned meaning independent of actual energy state. Text messages do have an energy cost .... which is why we have batteries in mobile phones. These run flat during the processes of producing/maintaining the energy differentials that convey something to the daughter about the shopping. Bear in mind that ( unless you go for full solipsism ) it is our choice to assign meaning and in particular what physical states are given a 'signal' assignment versus a 'noise' assignment. A blank phone face carries no meaning other than perhaps 'recharge me'. Does Mr Cooperstock use a phone charger ? If so, why ?! :-)

The point of special interest with any energy discussion is where one places the zero of scale. This has been long considered as not absolute in that we can only measure energy differentials anyway. So we are at liberty to assign as we please. Gravitational waves are a tidal effect meaning that an observer - at say one end of a LIGO arm - is going to measure accelerations of the other end of the arm. Vice versa. So any energy differential is a statement spanning across the extents of the apparatus. In that regard gravitational energy - in the weak field limit at least - is far less localised than what we are accustomed to. For LIGO the particular energy statement is the photon number ( at the laser frequency ) being emitted at the dark port. What we seek to do is disambiguate all possible effects upon that photon count and see if wave behaviour as predicted by GR is displayed. Or not.

[ 'Tidal' in generality means differences in accelerations b/w points. For that matter one can invert this and state that gravity can be defined as that which is evident via tidal effects ( I thank Mr Bernard Schutz of AEI for that interpretation ). At it's core General Relativity is a differential theory in that at most it specifies how adjacent spacetime elements ought relate, and boundary conditions come from without the apparatus. Specifying a zero of energy at some particular time and place is an example of a boundary condition. ]

Cheers, Mike.

( edit ) There are physical states which have no measurable energy difference in some circumstance. These are typically called 'degenerate' in the sense that some underlying values - like a quantum number - may be distinct but we can't tell who has what. A good example of this is the spin of an electron within an atom. By and large chemistry proceeds and is explicable without this concern, but if put into a Stern-Gerlach type apparatus one can sort atoms using a magnetic field. That is, the SG gadget discloses that which would otherwise be labelled as identical in the absence of a magnetic field gradient. You can vary the field strength and vary the differential that you see.

* One can invert this logic if you please.

Q : What is the difference b/w your house's ground floor and it's roof line ?
A : Your speed when you reach them ! :-)

Meaning that with regard to position dependent energies ( potentials ) we may resort to energy interchanges to quantify them. So I can use an electric motor to raise a weight, then lower that weight against some friction device to produce heat. That heat boils an egg and in so doing the egg protein is denatured ..... etc.

( edit ) "that which would otherwise be labelled as identical" : some further musings. What follows is a quantum point of view. If one takes everyday human energy levels as the norm or ~ zero base on some large scale then some phenomena are quite absent. As I sit writing this at my desk with commonplace energy levels then one proton is as good as the next. Maybe a cosmic ray will fly through my office but otherwise nuclear transitions are uninteresting for the purpose of explaining what I immediately experience.
Not so in the main beam pipe at CERN with the LHC at full throttle. Typically proton energies are manifold it's rest mass equivalent. Proton internals now matter and the proton states prior to impact are highly important. The energy density of the situation now tickles mechanisms that were previously well below some quantum threshold. Transitions can take place that are almost never going to happen in my office.
You may hear of a 'unified force' at some high energy realm, and by implication some 'symmetry breaking' at lower energies. This hypothesis assumes that quantum levels ( as yet unmeasured ) of particles has extra degrees of freedom - more choices of energy states ultimately - at those higher levels. Now since we don't have a working quantum theory of gravity then we don't even conceptually know if the gravitational force will join in with the other forces in this characteristic. This is why 'energy per unit volume' is important in the discussion. Does gravity have a quantum nature ? Will that be evident at low energies or will discrete energy levels ( that's the quantum bit ) emerge only when we up the scale ?