“history would become an experimental science.” carl sagan (1934-96)
Post on 19-Dec-2015
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TRANSCRIPT
The fundamental theory of physics that deals with time is Einstein’s theory of special relativity.
Albert Einstein (1879-1955)
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
Time is the fourth dimension– time exists as a block, quite unlike
our psychological perception of time
Time is relative– time slows down for moving particles
Travelling to the Future
Imagine Pooh is going off on a long space journey ...
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
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)
To explain the force of gravity in terms of curvature of space-time, Einstein cameup with the theory of general relativity.
In fact, there are many solutions with CTC’s in general relativity:
Gödel universe (1949)
Kerr black hole (1963)
Tipler’s rotating cylinder (1976)
Traversable wormholes (1988)
Gott’s cosmic string time machine (1991)
Paradoxes in Backward Time Travel
Grandfather paradox
Information creation in a causal loop
Hawking’s paradox:Where are all the time travellers from the future?
The only solutions to the laws of physicsthat can occur locally in the universe, arethose which are globally self-consistent.
The Principle of Self-Consistency
Consider playing billiards near the mouthsof a wormhole time machine...
(This is a version of the Grandfather paradox phrased in terms of a physics experiment)
Similarly, one could use causal loops to ...
Find out next week’s winning Toto numbers
Decide who to marry
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 blockof physics - quantum mechanics ?
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 traversablewormholes and other time machines.
Quantum mechanics allows negativeenergies
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 universeis created and branches off.