I would like to refer back to my post of Sep. 22, 2009 where I talked about the lack of proofs of the impossibility of time travel and perhaps state more strongly why Mr Smith's main essay premise is important. The statement that "a particular time is identically equivalent to, and is completely defined by, and only by, a particular configuration of the universe" *does* supply a potential proof and falsifiability, as Mr Smith has mentioned. The essential point is the fundamental difference between this model, with the equally important additional condition that any "particular configuration" only exists *once*, and the "block spacetime" model of General Relativity. In GR, the configurations (objects/sub-systems) are considered to be moving through a "pre-existing" spacetime with evolving 4 vectors, one coordinate of which is "time". The Einstein equations can then allow a metric solution which enables an object's trajectory F(x,y,z,t) to "transform" to a "past" coordinate frame. In Mr Smith's model, this cannot happen as there is no "pre-existing "spacetime".
The GR timeloop, wormhole etc solutions of course rely on there being a "time" coordinate. Remove this and you are just left eg, with a space-like loop, which can make sense in the context of some known relativistic effects. There seems no doubt however that, as I stated very early on in this comment thread, the world cannot be described with only 3 dimensions. The question is, what exactly is the nature of the 4th dimensional quantity? This relates directly to Paul Valetta's questions.. "can you travel anywhere without Time? can anything in the Universe, move from one location to another, without the concept of Time". I think it is very telling that he uses the word "concept" in his second question. We seem to be trapped in the confines of our own use of the word TIME, a la John Wheeler! I think we are also trapped by the "ingrained" concept of "time" that our reliance on clocks has imparted, so that we believe clocks are actually measuring something we *call* time. Clocks are just physical systems we have designed with reference to cyclical processes (Earth's rotation, Caesium atom oscillations), to give us information about those same *spatial* cyclical processes, ie spatial displacement.
In response to Paul I would say that, yes, we need to be able to define what it is that "allows" motion and that can fully describe an "event", to use conventional terminology. All I am saying is that it should be defined in terms of the only things we have, space, motion and mass/energy. Motion from place to place can be described as simply a re-distribution of energy. If the motion is inertial it will be symmetric with any other inertial frame with the usual effects caused by relative motion, but no "time dilation" effects. If the motion is accelerated or spatially asymmetric, an asymmetry results in the subsequent frames which results in the effect called time dilation, but which I think should be reinterpreted only in terms of the space/length "contraction" which is also an implicit effect, but one which tends to be overlooked in most explanations.
Mr Smith has quoted Feynman's belief that time quantities probably should be spatial.."time is space". There have been other prominent physicists who have also hinted at this. Stephen Hawking in "A Brief History Of Time" (I think?) also talks about converting time to space (using Wick rotations in the complex plane), to simplify equations. These solutions can then be converted back to time *if convenient*. As previously discussed here, an "evolving configuration space"(ECS) model could use some differential between vectors in a configuration space where the 4th vector may represent relative motion/velocity? Think of it firstly in conventional terms where motion along a particular spatial dimension, say X axis, is inversely proportional to motion along the Y or YZ axes and motion in "time" seems to be inversely proportional to motion in the 3D "bulk" vector space. So that being static equates to maximum "motion" in time (at c?) and maximum motion in space and/or velocity at or near c equates to being static in time. In the "ECS", the 4th vector could be considered to be orthogonal to the usual 3D's when maximal, with an angle "measuring" the relative motion at other velocity differentials?
Buzz's question..."What is the duration of Present Time?" is absolutely a good one! It goes to the heart of our perception of the world and how our consciousness shapes our understanding of reality. We have evolved to "sense"
time durationally and as a continuum. This is somewhat incongruent with the physical laws we use which are based on the world being *discontinuous*, ie quantum in nature. We quantise everything, the very nature of measurement implies that it is quantised. I would agree with Mr Smith that these "senses" are an evolutionary trait, presumably to aid in our survival. In the absence of any sensory input or in the absence of any motion in the world, I believe we would still have the sense of duration, so I don't think we can trust that sense to develop any description of reality. Attempts have been made to also "quantise time", so far, to my knowledge, without success. Peter Lynds may have developed a kind of proof that it can't be done, even in principle! What does this tell us? If we are to believe that nature is inherently discrete (again quantum gravity pending) and that time cannot be quantised, where is time??
Cheers all
