Time and Physical Geometry |
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Putnam (Hilary) |

Source: Putnam - Philosophical Papers 1 - Mathematics, Matter and Method |

Paper - Abstract |

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__Morals and Conclusions__

- What moral should we draw from all this? In the first part of this paper I showed that, if we couple the assumption
__III___{1}with the principle (__2___{2}), we must say that future things are real, even if they do not exist yet. Strictly speaking, I showed only that some future things are real, and that only on the assumption that the situation shown in figure__1___{3}obtains. But the argument can obviously be extended (bringing in certain further assumptions with which virtually no one would argue) to show that all future things are real ("things" here includes "events"), and likewise that all past things are real, even though they do not exist now. To spell this out: If I accept (2), then I must say that all those things are real (but not only those things, as we saw) which bear to me the following relation: the relation y bears to x just in case y is simultaneous with x in the coordinate system of x. I must describe the relation this way, and not as "the relation y bears to x just in case y is simultaneous with x in the coordinate system of me-now," because otherwise I would be committed to the view that the real things bear to me-now a relation which is not Lorentz-invariant and, hence, that they define an absolute simultaneity. But principle III then requires that I also count every thing and event which bears the transitive closure of R to me (i.e., which bears R to me, or which bears R to something that bears R to me, or which bears R to something that bears R to something that bears R to me, or....) as real. But every thing and event in space-time bears the transitive closure of the above relation R to me, at least if there are enough observers. And, if we allow all physical systems (even electromagnetic fields, etc.) as "observers" (as why should we not?) and allow observers to use coordinate systems in which they are not at rest, then there are certainly "enough observers." - In the second part of this paper I showed that contingent statements about future events already have a truth value. In consequence, the "tenseless" notion of existence (i.e., the notion that amounts to "will exist, or has existed, or exists right now") is perfectly well-defined. This is fortunate, since the upshot of the first part of the paper could also have been stated by saying that the notion of being "real" turns out to be coextensive with the tenseless notion of existence.
- I conclude that the problem of the reality and the determinateness of future events is now solved. Moreover, it is solved by physics and not by philosophy. We have learned that we live in a four-dimensional and not a three-dimensional world, and that space and time – or, better, space-like separations and time-like separations – are just two aspects of a single four-dimensional continuum with a peculiar metric which sometimes permits distance (y, x) = 0 even when x not= y. Indeed, I do not believe that there are any longer any
*philosophical*problems about Time; there is only the physical problem of determining the exact physical geometry of the four-dimensional continuum that we inhabit. - In this paper I have talked only about the relativistic aspects of the problem of physical time: there is, of course, also the problem of thermodynamics, and whether the Second Law does or does not explain the existence of "irreversible" processes (the so-called "problem of the direction of time"), and the problem of the existence or nonexistence of true irreversibilities in quantum mechanics
^{4}, which, I gather, is currently under hot discussion. I have not talked about these problems.

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