Rietdijk-Putnam argument

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If special relativity is true, then each observer will have their own plane of simultaneity, which contains a unique set of events that constitutes the observer's present moment. Observers moving at different relative velocities have different planes of simultaneity hence different sets of events that are present. Each observer considers their set of present events to be a three dimensional universe but even the slightest movement of the head or offset in distance between observers can cause the three dimensional universes to have differing content. If each three dimensional universe exists then the existence of multiple three dimensional universes suggests that the universe is four dimensional. The argument is named after the discussions by Rietdijk(1966)^[1] and Putnam(1967)^[2]. It is sometimes called the Rietdijk-Putnam-Penrose argument^[3]

Roger Penrose^[4] advanced a form of this argument that has been called the Andromeda Paradox in which he points out that two people walking past each other in the street could have very different present moments. If one of the people were walking towards the Andromeda Galaxy then events in this galaxy might be hours or even days advanced of the events on Andromeda for the person walking in the other direction. If this occurs, it would have dramatic effects on our understanding of time. Penrose highlighted the consequences by discussing a potential invasion of Earth by aliens living in the Andromeda galaxy. On Earth, one person might live in a universe where the Andromedeans have not yet decided to invade, whilst someone passing them in the street could live in a universe where alien spaceships are underway. As Penrose put it:

"Two people pass each other on the street; and according to one of the two people, an Andromedean space fleet has already set off on its journey, while to the other, the decision as to whether or not the journey will actually take place has not yet been made. How can there still be some uncertainty as to the outcome of that decision? If to either person the decision has already been made, then surely there cannot be any uncertainty. The launching of the space fleet is an inevitability."

The 'paradox' consists of two observers who are in the same place and at the same instant having different sets of events in their present moment.

Notice that neither observer can actually "see" what is happening on Andromeda at any given moment because light from Andromeda takes about two million years to reach earth. The argument is not about what can be "seen", it is purely about what different observers consider to be contained in their instantaneous present moment.

See Introduction to special relativity for an explanation of how and why the plane of simultaneity varies from one person to another.

[edit] References

^ Rietdijk, C.W. (1966) A Rigorous Proof of Determinism Derived from the Special Theory of Relativity, Philosophy of Science, 33 (1966) pp. 341-344
^ Putnam, H. (1967). Time and Physical Geometry, Journal of Philosophy, 64, (1967) pp.240-247
^ Being and Becoming in Modern Physics. Stanford Encyclopedia of Philosophy.
^ Penrose, R. 1989. The Emperor's New Mind: Concerning Computers, Minds, and Laws of Physics. New York and Oxford: Oxford University Press.