Dear Sabine,
Very timely and topical essay! I agree with your introductory statement that it is ultimately impossible to determine what is ultimately possible in physics. I think your essay then becomes perhaps more about how we can *maximise* our potential to discover all that it *is* possible for us to know, given that your I1) and I2) conditions may ultimately apply.
You quite rightly and refreshingly raised the issue of the possibly fundamental limit imposed by our brain processes. I believe this is at the core of many of the problems you encapsulate in D3). Our brains can only ever give us a subjective "anthropocentric" perception of the external objective reality that we are trying to understand, even when aided by clever devices like telescopes and Tevatrons. This has often been called the "Prime Reality Interface". It is understandable then that we have evolved mathematics from it's humble beginnings of just being a way to make practical sense of the world for survival, to be our "Platonic" way of modelling that "external" reality. Some have even gone as far as to say reality *is* mathematics (eg Tegmark). Unfortunately, due to some of the resulting D1) no-go theorems, consistency requirements and, I might add, "elegance" requirements, we find ouselves in the situation you describe in D3).
One of the main barriers I see as coming out of all the above relates to time. We consciously sense "duration" and perceive "time" as a continuum in which all change happens. To organise our lives we must then quantify this evolving continuum for which we use clocks and we say that they measure "time". Obviously they only measure change, relative spatial displacements, *not* some abstract background entity we call time. Yet this very same procedure is applied to all of our physical laws, from QM and QFT to GR. What barriers might be removed and what progress might be made if we try to re-formulate our theories only in terms of what we can actually observe, mass/energy in evolving, relational configurations?
It seems there are two main areas of objection to even contemplating this, both of which could be placed under your D1):
1. Occam's Razor - there is nothing to be gained by way of simplification, or in fact a given theory would become more complicated if time is removed or replaced.
To this I would ask, should a theory (eg QM or GR), which is struggling for a consistent physically real interpretation and is known to be incomplete, let alone making any real progress, be persevered with as it is, only because something else may be, at least initially, more difficult? Einstein gave us a much more difficult theory than Newton when he tossed out what was considered to be the "complete explanation" of nature, because he saw that the Newtonian laws were at best incomplete. This resulted in one of the greatest leaps of progress in scientific history!
2. Time (operators, coordinates etc) will always be needed for "ordering" or describing events.
Whilst it has been an indespensible tool in the application of our theories *as they are formulated*, will it ultimately lead to our understanding of reality? Are we being hamstrung by our clocks and our need for quantifying "intervals" of some completely unobservable "continuum" entity? The laws we have now are considered symmetric in "time" (CPT violations may ironically be a symptom of our insistance on "time" as a symmetry?), yet we talk about arrows of time, eg "thermodynamic arrow". Can't thermodynamics be just that, ie entropy, as statistical mechanics, friction, kinematics etc, physical processes that we would still perceive to be "happening" in the usual "forward moving" durational progression we sense, whether they were reversed or even became totally static.
I just think that this "atemporal" way of looking at things may open up ways (for better minds than mine) to maximise our chances of gaining all of the knowledge of reality that we can, at least in principle, possibly comprehend.
By the way, I am not a subscriber to Julian Barbour's "no motion" quantum cosmology model as, for one thing, I don't see how Darwinian laws could operate?!
Anyway, just some thoughts I have had after reading some of the other essays (last years' are very relevant too!)and the various discussion threads. Your essay seemed to provide a nice context to put them in! Many of the authors are describing excellent attempts at this kind of fundamental re-formulation and it is a great credit to the concept and forum provided by FQXi.
Thanks for the essay and good luck!
Cheers,
Roy
