This day marking the passage from 2003 to 2004, it is fitting to again discuss the reality of space and time. Previously I presented arguments based on Loop Quantum Gravity (LQG) that space must exist because it can be derived from first principles in physics and can be quantized using the same theoretical approach that can derive quantim mechanics and the big bang. But I was uncertain about time. Now I have just read a article on the internet by Alex Green that claims that if space is real, then time must be real. The releveant portion of the article is copied below from the link:
The 'Reality' of Space-Time and its Role in Conscious Experience
It has been shown above that physical experiment supports the concept of the universe as a four dimensional space-time. The discussion was limited to simple space-time where the time and space directions are always linear and homogenous and it used Pythagoras' theorem to relate space and time intervals. The concept of space-time can also be generalised to cases where time and space are curved (General Relativity). The mathematics of this amendment is quite complicated because it involves the introduction of the actual intervals between events rather than the squares of the intervals.
The complexity arises because the expression for the intrinsic length of an object in 4D space time (r) involves a dimension, physical time, that has an opposite sign to the space dimensions ie:
r2 = x 2 + y2 + z2 - (ct)2
The most straightforward approach to this problem is to propose that time is an imaginary coordinate axis measured in units of the square root of minus one (i). This gets rid of the minus sign in Pythagoras' theorem:
r2 = x 2 + y2 + z2 + (ict)2
where i = Ö -1
Much of the physics of the early half of the twentieth century used this 'space-time formalism' either implicitly or explicitly. It has been said that many of the major advances in our physical knowledge in the twentieth century implicitly used this approach (Walter 1999).
However, the introduction of imaginary time has a major drawback because it does not account for causality; imaginary time has no in-built direction because it is much like a length in space. Modern physicists use 'real' time and a 'metric tensor' to explain the opposite sign of time in Pythagoras' theorem. This is equivalent to deriving - (ct)2 by multiplying -ct by +ct and, according to Zeeman(1964) is partially consistent with causality. See note 4 for a more complete treatment.
In Note 4 it can be seen that the metric tensor is a combination of differential coefficients each of which is a rate of change of one coordinate axis with another. These differential coefficients can be used to derive the values of a new set of coordinates in a new coordinate system from an existing coordinate system and are evaluated at the point under observation whose position is being calculated. This property is known as covariance. An important consequence of the way that points in space appear to be encoded with transformations from one coordinate system to another is that there no longer seems to be a requirement for space or time as extended entities. The impact of this was noticed by Einstein as early as 1916:
"That the requirement of general covariance, which takes away from space and time the last remnant of physical objectivity, is a natural one, will be seen from the following reflection. All our space-time verifications invariably amount to a determination of space-time coincidences. If, for example, events consisted merely in the motion of material points, then ultimately nothing would be observable but the meetings of two or more of these points. Moreover, the results of our measurings are nothing but verifications of such meetings of the material points of our measuring instruments with other material points, coincidences between the hands of the a clock and points on the clock dial, and observed point-events happening at the same place at the same time. The introduction of a system of reference serves no other purpose than to facilitate the description of the totality of such coincidences". (Einstein 1916a).
The simultaneity of the things in conscious experience contradicts Einstein's uneasy assertion that "If, for example, events consisted merely in the motion of material points, then ultimately nothing would be observable but the meetings of two or more of these points." We do indeed observe more than the meetings of material points. Clearly the description of space and time based on (3+1)D metric tensors may be incomplete, furthermore Einstein has focussed on precisely the problem that arises if conscious experience is modelled using processes (see chapter 1). Processes are sets of material points in motion and Einstein's insight could be reworded as: if, for example, conscious experience consisted merely in the motion of material points, then ultimately nothing would be observable but the meetings of two or more of these points.
If it is accepted that space has an objective existence then the discussion of invariance given above shows that time must also exist, as Einstein put it:
"With the discovery of the relativity of simultaneity, space and time were merged in a single continuum in a way similar to that in which the three dimensions of space had previously been merged into a single continuum. Physical space was thus extended to a four dimensional space which also included the dimension of time" Einstein (1934).
Or as Roger Penrose wrote in his introduction to Six Not So Easy Pieces by Richard Feynman: "It was the Russian/German geometer Hermann Minkowski, who had been a teacher of Einstein's at the Zurich Polytechnic, who first put forward the idea of four dimensional space-time in 1908, a few years after Poincare and Einstein had formulated special relativity theory. In a famous lecture in 1908 Minkowski asserted : 'Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of unity between the two will preserve an independent reality.'
Feynman's most influential discoveries, the ones that I have referred to above, stemmed from his own space-time approach to quantum mechanics. There is thus no question about the importance of space-time to Feynman's work and to modern physics generally. It is not surprising, therefore that Feynman is forceful in his promotion of space-time ideas, stressing their physical significance. Relativity is not airy-fairy philosophy, nor is space-time mere mathematical formalism. It is the foundational ingredient of the very universe in which we live." Penrose (1997)
People find it difficult to accept the reality of space-time despite the views of Einstein, Feynman and Penrose. This may be because we are taught in school science that we live at an instantaneous present and can neither observe the future nor the past except by prediction and recording and this apparent certainty then becomes used as an argument against the existence of coordinate time. This argument is dispatched as we read it because at the instantaneous present we could not know the argument. There can be no 'knowing' at an instant. This "Presentism", where only the durationless instant exists, is the conventional wisdom in many scientific disciplines even though it flies in the face of physical theory, experiment and personal observation. Every time we measure a length on earth anyone in orbit could look down and say that what we considered to be a length was actually a combination of space and time. Space and physical time are known to have no independent existence.
The interrelationship of space and time is critical to consciousness science because it is evident that our conscious experience is a 'view' that is a continuous field of simultaneous things that can change rapidly. Such a phenomenon is difficult if not impossible to describe using a three dimensional coordinate system. Furthermore the use of only three coordinates preempts the analysis because it only permits the consideration of a succession of stationary states viewed in some unknown way by an external observer. The inevitability of external observers when three coordinates are used to describe experience has long been known to philosophers and is summarised as the 'Homunculus Argument' (see chapter 1). It is only when four coordinates are used that our descriptions have a chance of being coordinate independent and independent of external observers.