ARE TIME MACHINES POSSIBLE?
Time machines are topical, with articles in popular magazines suggesting that the Large Hadron Collider (LHC) may produce wormholes enabling time travellers from the future to reach back to the moment when that first happens. Well known paradoxes are raised by the possibility of physical time travel to the past, such as a man murdering his grandmother and so on. Fascinating science fiction stories have been written about the subject, beginning of course with H.G.Wells' The Time Machine. A nice twist is when the inventer of a time machine travels back to the moment when it is invented, and publishes the patent. Some physicists eagerly accept the possibility of time travel while others, such as Stephen Hawking, do not. So does physical time travel make sense? Two reasons will be suggested here why not:
A misunderstanding of time-dilation in Special Relatvity that goes back to Einstein himself;
Time is assumed to be a dimension, which is not necessarily true.
In his Special Theory of Relativity, Einstein sought to meet two objectives:
that physical laws are the same in all inertial reference systems;
that the velocity of light in a vacuum is constant regardless of the state of motion of an observer.
The first means that there is no absolute frame of reference for which physical laws are simplest, but rather they are the same in all reference systems that are in uniform rectilinear motion with respect to each other. The second means that the velocity of light will appear to be the same in all such reference systems i.e. the observer's velocity is not added to that of light. Three startling consequences of the equations of motion that solved this programme are:
Moving objects increase in mass, which becomes infinite at the speed of light;
Moving objects become shorter in their direction of motion, shrinking to zero at the speed of light;
Clocks on a moving object appear to tick more slowly as seen by outside observers, stopping altogether at the speed of light.
The third consequence is called time-dilation, and it should be appreciated that it does not only apply to clocks.
All cyclic or rhythmic processes will appear to slow down, including the beating of a human heart. Einstein concluded that time
itself slows down for the moving object relative to outside observers. The famous twins paradox is based on this, where one twin
(Fred) stays at home and the other (Jim) accelerates to a speed near that of light, travels for several years, reverses velocity
and travels back home again. Because Jim's heart appears to slow down he appears to be younger than Fred when they are reunited.
The paradox lies in the fact that the same argument can be applied to Fred as seen by Jim, so that Jim expects Fred to be younger.
However there is a flaw, as while Fred may well be in an inertial frame of reference, Jim most certainly is not because of the
accelerations he undergoes, and General Relativity may be invoked to show that Jim will in fact be younger than Fred because of that.
Einstein's (or Lorentz's) equations do not say that time itself slows down, only that time intervals will appear to be longer, for Einstein banished the notion of absolute time, so time as such is not involved, only intervals between events. An experimental confirmation of this idea is that particles called muons arising from cosmic rays entering the atmosphere reach the surface of the Earth in greater numbers than expected. That is because they decay quickly, having a definite half-life, which enables the expected number of arrivals to be calculated. The observed rate of arrivals suggests that the muon's "clocks" are ticking about 9 times more slowly as observed on Earth than those observed in the laboratory, and so they live long enough to reach the Earth. Now the half-life of their decay is based on internal physical processes, which time-dilation shows should slow down thus increasing the observed half-life. But this is a purely physical statement about process rates, and need not imply time itself goes more slowly for the muons. Denying that time itself is affected does not invalidate any of the experimental findings supporting Relativity, but it does suggest that no "time travel into the future" is involved. This is more fully explained in an article which may be downloaded (see below).
Time as a Dimension
Einstein also treated time as a fourth dimension alongside the three of space (ignoring for now the extra dimensions assumed by Superstring Theory). However it is argued in the accompanying article, which may be downloaded, that this leads either to a static universe with no genuine evolution or change, or else to an infinite regress as an extra time-like dimension would be required to measure changes occurring in four-dimensional space-time, etc, etc.. This dilemma is solved if time is not assumed to be an extra dimension alongside the three of space.
Physical observations can never distinguish between those two views.
Wormholes are supposed to be topological distortions of space-time predicted by General Relativity that enable "short cuts" to be
taken as in science fiction. However if time is not a dimension then the dramatic changes in the rates at which physical processes
proceed at either end of a wormhole are just that, but imply no time travel in the sense of H.G. Wells. Similarly the drastic
changes in process-rates supposed to occur in the vicinity of a black hole are again just that - changes in process rates - without
time itself being affected.
SO: if time itself does not slow down for moving observers, but only rates-of change of processes do so, and time is not itself a dimension, then the physical possibility of time travel does not arise.