“History would become an experimental science.” Carl Sagan ( )

The fundamental theory of physics that deals with time is Einstein’s theory of special relativity. Albert Einstein ( )

In this graph, time is vertical and space is horizontal. The z-axis has been suppressed. Time is the Fourth Dimension

Every particle traces out a worldline in space-time. If its velocity is constant, its worldline would be straight. Worldline of a Particle

By definition, light traces out a 45° worldline. The set of all light rays passing through the point forms the light cone. The Lightcone

The worldline of a particle lies within the lightcone, since no particle can travel faster than light. A Timelike Particle lies within the Lightcone

Summary of Time in Special Relativity n Time is the fourth dimension –time exists as a block, quite unlike our psychological perception of time n Time is relative –time slows down for moving particles

Travelling to the Future n Imagine Pooh is going off on a long space journey... n His spaceship accelerates at 1 g to the halfway point, and then decelerates at 1 g so that it comes to a rest at the destination n How does Pooh’s time compare to Earth time?

But the order of events (causality) is always preserved. If one sees A to happen before B, then everyone else would also see A to happen before B.

A CTC is a worldline that loops back onto itself. At some stage, the particle has to travel faster than light. A Closed Timelike Curve (CTC)

In special relativity, if one could travel faster than light, one could also go back in time.

To explain the force of gravity in terms of curvature of space-time, Einstein came up with the theory of general relativity.

… because of gravity or rotation of the space-time Light cones may tip over to form a CTC

In fact, there are many solutions with CTC’s in general relativity: n Gödel universe (1949) n Kerr black hole (1963) n Tipler’s rotating cylinder (1976) n Traversable wormholes (1988) n Gott’s cosmic string time machine (1991)

Kurt Gödel ( ) and Albert Einstein were good friends Gödel Universe

Tipler’s Rotating Cylinder

Kerr (Rotating) Black Hole

Kip S. Thorne (b1940) deve- loped the idea of traversable wormholes for the movie Contact Wormholes

Paradoxes in Backward Time Travel n Grandfather paradox n Information creation in a causal loop n Hawking’s paradox: Where are all the time travellers from the future?

Grandfather Paradox (in BTTF)

The only solutions to the laws of physics that can occur locally in the universe, are those which are globally self-consistent. The Principle of Self-Consistency

Consider playing billiards near the mouths of a wormhole time machine... (This is a version of the Grandfather paradox phrased in terms of a physics experiment)

A Self-Inconsistent Solution

A Self-Consistent Solution

Is there a conflict between self-consistency and free will??

“It has happened, it will happen…” Commander Data Star Trek: The Next Generation

Will history really become an experimental science?

A Causal Loop Creating Information (Where does the name “Marty” come from?)

Similarly, one could use causal loops to... n Find out next week’s winning Toto numbers n Decide who to marry n Discover a new theory, prove an unsolved theorem, compose music, create works of art, etc.

Why don’t we observe tourists, souvenir hunters, historians, archeologists, fugitives and criminals visiting us from the future? Hawking’s Paradox

So far we have only considered relativity. What about the other major building block of physics - quantum mechanics ?

“I think I can safely say that nobody understands quantum mechanics.” Richard P. Feynman ( )

The laws of physics do not allow time machines to be made Hawking’s Chronology Protection Conjecture (because calculations seem to imply that quantum fluctuations become infinite near a CTC) Stephen W. Hawking (b1942)

…which could be used to construct traversable wormholes and other time machines. Quantum mechanics allows negative energies However, they would be extremely small.

When every a quantum process occurs, the outcome is determined by probability. Many-universe Interpretation (Everett, Deutsch) For every possible outcome, a new universe is created and branches off.

Consider the Decay of a Neutron

What about time running backwards ?

Antiparticles can be regarded as particles going backwards in time. Antiparticles (Feynman)

Space-time diagram of antiparticle

Could the same happen for a person?

Further Reading n Paul J. Nahin, Time machines 2nd ed. (Springer-Verlag, New York) n Kip S. Thorne, Black holes and time warps (W.W. Norton, New York) n J. Al-Khalili, Black holes, wormholes & time machines (Institute of Physics Pub., Philadelphia)