SCIENTIFIC CONCEPTS OF TIME AND SPACE. Time has played a central role in mathematics from its very beginnings, yet it remains one of the most mysterious.

SCIENTIFIC CONCEPTS OF

TIME AND SPACE

SCIENTIFIC CONCEPTS OF

TIME AND SPACE

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. 

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

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

  1. Time is divisible. 1. Time is divisible. (Zeno (Zeno of Elea, 450 BC) of Elea, 450 BC)

Suppose an arrow is flying Suppose an arrow is flying through the air. Before it through the air. Before it can reach its target, it can reach its target, it first had to cross at least first had to cross at least half the distance between half the distance between the archer and the target.the archer and the target.

ZENO’s PARADOX ZENO’s PARADOX

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

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

So, there are infinitely many So, there are infinitely many states the arrow must pass states the arrow must pass through before it can hit the through before it can hit the target, and only a finite target, and only a finite amount of time to do it in. amount of time to do it in. The arrow can’t possibly do The arrow can’t possibly do infinitely many things in finite infinitely many things in finite time, and so it can never time, and so it can never reach the target.reach the target.

So, there are infinitely many So, there are infinitely many states the arrow must pass states the arrow must pass through before it can hit the through before it can hit the target, and only a finite target, and only a finite amount of time to do it in. amount of time to do it in. The arrow can’t possibly do The arrow can’t possibly do infinitely many things in finite infinitely many things in finite time, and so it can never time, and so it can never reach the target.reach the target.

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

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

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

3.3. Time was created at Time was created at the the

same instant as the same instant as the heavens. (Plato)heavens. (Plato)

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

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

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

4.4.Time does not exist Time does not exist without an intelligent without an intelligent being who is able to being who is able to think in the present think in the present about things: past, about things: past, present and future. present and future.

(St. Augustine)(St. Augustine)

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

Time MeasurementTime Measurement  -         Clocks-         Clocks-         Calendars-         Calendars

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

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

7. Time is relative. 7. Time is relative. (Poincare, 1898) (Poincare, 1898)

Is it meaningful to say that Is it meaningful to say that one second today is equal to one second today is equal to one second tomorrow? Is it one second tomorrow? Is it meaningful to say that two meaningful to say that two events which are separated events which are separated in space occurred at the in space occurred at the same time? What same time? What information is required to information is required to predict the future?predict the future?

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

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

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

2.2. Constancy of the Constancy of the Speed Speed

of Lightof Light  The speed of light in a The speed of light in a

vacuum, c = 3.00 x 10vacuum, c = 3.00 x 1088 m/s, is the same in all m/s, is the same in all inertial frames of inertial frames of reference, independent of reference, independent of the motion of the source the motion of the source or the receiver.or the receiver.

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

Time and space are linked Time and space are linked together. Minkowski together. Minkowski (1908)(1908)

The views of space and The views of space and time which I wish to lay time which I wish to lay before you have sprung before you have sprung from the soil of from the soil of experimental physics, and experimental physics, and therein lies their strength. therein lies their strength. They are radical. They are radical.

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

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

Hawking (1983) presented Hawking (1983) presented ideas on imaginary and realideas on imaginary and realtime.time.

The so-called imaginary time The so-called imaginary time is really the real time, and is really the real time, and that what we call real time is that what we call real time is just a figment of our just a figment of our imaginations. imaginations.

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

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

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