1. SCIENTIFIC CONCEPTS OF TIME AND SPACE

2. Time has played a central role in mathematics from its very beginnings, yet it remains one of the most mysterious aspects of the world in which we live. Time has played a central role in mathematics from its very beginnings, yet it remains one of the most mysterious aspects of the world in which we live.

3. Philosophers have tried to come to grips with the concept; some have argued that time is a basic property of the universe while others have argued that it is an illusion or a property of the human mind and not of the world.

4. 1. Time is divisible. (Zeno of Elea, 450 BC) 1. Time is divisible. (Zeno of Elea, 450 BC) Suppose an arrow is flying through the air. Before it can reach its target, it first had to cross at least half the distance between the archer and the target. ZENO s PARADOX

5. But after it has reached the midway point, it still has to cross half the remaining distance. And after crossing that, it must cross half of the yet remaining distance. In fact, this process goes on forever, because the distance between the arrow and its target can always be halved, and the first half always stands between the arrow and its destination. But after it has reached the midway point, it still has to cross half the remaining distance. And after crossing that, it must cross half of the yet remaining distance. In fact, this process goes on forever, because the distance between the arrow and its target can always be halved, and the first half always stands between the arrow and its destination.

6. So, there are infinitely many states the arrow must pass through before it can hit the target, and only a finite amount of time to do it in. The arrow can t possibly do infinitely many things in finite time, and so it can never reach the target.

7. If in an indivisible instant of time the arrow moved, then this instant of time would be divisible.

8. 2. Time is not composed of indivisible nows. Time is related to motion. (Aristotle)

9. 3. Time was created at the same instant as the same instant as the heavens. (Plato) heavens. (Plato)

10. The Creator sought to make the universe eternal, so far as might be. Now the nature of the ideal being was everlasting, but to bestow this attribute in its fullness upon a creature was impossible. The Creator sought to make the universe eternal, so far as might be. Now the nature of the ideal being was everlasting, but to bestow this attribute in its fullness upon a creature was impossible.

11. Wherefore he resolved to have a moving image of eternity, and when he set in order the heavens, he made this image eternal but moving, according to number, while eternity itself rests upon unity; and this image we call Time. (Plato)

12. 4.Time does not exist without an intelligent being who is able to think in the present about things: past, present and future. (St. Augustine) (St. Augustine)

13. ... a present of things past, a present of things present, and a present of things future.... The present of things past is memory, the present of things present is sight, and the present of things future is expectation.... a present of things past, a present of things present, and a present of things future.... The present of things past is memory, the present of things present is sight, and the present of things future is expectation.

14. Time Measurement - Clocks - Calendars

15. 5.Time is... absolute, true, mathematical time, [which] of itself, and from its own nature, flows equably without relation to anything external. (Newton)

16. 6. Time is change. (Mach, 1883) 6. Time is change. (Mach, 1883) It is utterly beyond our power to measure the changes of things by time. Quite the contrary, time is an abstraction, at which we arrive by means of the changes of things.

17. 7. Time is relative. (Poincare, 1898) 7. Time is relative. (Poincare, 1898) Is it meaningful to say that one second today is equal to one second tomorrow? Is it meaningful to say that two events which are separated in space occurred at the same time? What information is required to predict the future?

18. 8.Time was the whole key to understanding the universe. (Einstein) 8.Time was the whole key to understanding the universe. (Einstein)

19. My solution was really for the very concept of time, that is, that time is not absolutely defined but there is an inseparable connection between time and the velocity of light.

20. Postulates of Special Relativity 1. Equivalence of Physical Laws The laws of physics are the same in all inertial frames of references. Postulates of Special Relativity 1. Equivalence of Physical Laws The laws of physics are the same in all inertial frames of references.

21. 2. Constancy of the Speed of Light of Light The speed of light in a vacuum, c = 3.00 x 10 8 m/s, is the same in all inertial frames of reference, independent of the motion of the source or the receiver.

22. An event is a physical occurrence that happens at a specified location at a specified time. Proper time is the amount of time separating two events that occur at the same location.

23. Time and space are linked together. Minkowski (1908) The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical.

24. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.

25. Nobody has ever noticed a place except at a time, or a time except at a place.

26. Hawking (1983) presented ideas on imaginary and real time. The so-called imaginary time is really the real time, and that what we call real time is just a figment of our imaginations.

27. In real time, the universe has a beginning and an end in singularities that form a boundary to space-time and at which the laws of science break down.

28. But in imaginary time, there are no singularities or boundaries. So maybe what we call imaginary time is more basic, and what we call real time is just an idea we invent to help us describe what we think the universe is really like.

29. Time is a fascinating topic and new ideas are continually being put forward. It is still the most mysterious property of the universe. Time is a fascinating topic and new ideas are continually being put forward. It is still the most mysterious property of the universe.