Introducing Time E-Book

Craig Callender

• Herausgeber: Icon Books
• Kategorie: Wissenschaft und neue Technologien
• Serie: Graphic Guides
• Sprache: Englisch

Seitenzahl: 121

Veröffentlichungsjahr: 2014

Beschreibung

What is time? The 5th-century philosopher St Augustine famously said that he knew what time was, so long as no one asked him. Is time a fourth dimension similar to space or does it flow in some sense? And if it flows, does it make sense to say how fast? Does the future exist? Is time travel possible? Why does time seem to pass in only one direction? These questions and others are among the deepest and most subtle that one can ask, but Introducing Time presents them - many for the first time - in an easily accessible, lucid and engaging manner, wittily illustrated by Ralph Edney.

Leseprobe

Published by Icon Books Ltd, Omnibus Business Centre, 39-41 North Road, London N7 9DP email: [email protected]

ISBN: 978-184831-772-7

Text copyright © 2001 Craig Callender Illustrations copyright © 2012 Icon Books Ltd

The author has asserted his moral rights.

Originating editor: Richard Appignanesi

No part of this book may be reproduced in any form, or by any means, without prior permission in writing from the publisher.

Contents

Cover

Title Page

Copyright

What is Time?

All Kinds of Clocks

Biological Clocks

Psychological Time

Is Time Merely in the Head?

Clocks and Time

How Long is an Interval of Time?

The Most Reliable Clocks

The Atomic Clock

Absolute, True and Mathematical Time

True Time

Opponents of Newtonian Time: Relationalism

A Scenario of Time without Change

Can Relationalism replace Absolute Time?

Conventionalism

A Universe Out of Sync?

The Nature of Time: Relative and Non-Relative

Tenseless and Tensed Theories of Time

Tensed Time

Tenseless Time

Representing Dimensions

The Fourth or Time Dimension

Diagrams of Space and Time

Picture of a “Tenseless” Life

The Now and the Here

The Problem of Motion and Change

McTaggart’s Argument

Avoiding McTaggart’s Trap

How Fast Does Time Flow?

Galilean Relativity

Frames of Reference

Einstein’s Relativity

Simultaneity is Relative to the Observer

The Spacetime Event

Lightcones

Time and Observer Dependency

Relativity and Tenses

Does Logic Allow Time Travel?

The Logic of Impossibility

The Book That No One Wrote

The Causal Loop

A Logical Contradiction of Time Travel

Logical Contradictions Cannot Occur

Personal Time

Dying at a Time Earlier Than Your Birth

Future Compatibility

Can We Change the Past?

Can We Affect the Past?

Two Sorts of Time Travel Stories

Does Physics Allow Time Travel?

Moving Clocks Run Slower

Small Savings in Time

General Relativity and Four-dimensional Curvature

Why We Don’t Need a Fifth Dimension

Spacetime Curvature

General Relativity and Time Travel

Gödel’s Rotating Universe

Spacetime in a Rotating Universe

The Effect of Spacetime Curvature

Taub-NUT-Misner Spacetime

Gödel’s Complete Spacetime Travel

Is Gödelian Time Travel Possible?

Gödel Against Tenses

Another Problem for the Tensed Theory

Was Gödel Wrong?

Cosmic String Theory

Wormholes in Spacetime

Wormholes May Not Allow Travel

Exotic Possibilities For Time

Möbius Twist in Space

Möbius Twist in Time

Branching Time

Does Space “Run Out”?

Finite Space Without Limit

Geroch’s Theorem

Eternal Recurrence

Travelling to Big Bang

A Philosophical Objection

Closed and Open Time

To Sum Up, So Far …

The Direction of Time

“Irreversible” Processes

Time Reversal Invariance

Seeing in Terms of Particles

The Science of Heat

Spontaneous Processes

The Law of Entropy

The Problem of Newtonian Particles, Again

Statistical Mechanics

A Statistical Asymmetry

Is Reversal Probable?

The Most Probable State of Entropy

The Loschmidt Paradox

In What Direction Does Entropy Increase?

The Universe’s Statistical Development

The Boundary Conditions of the Universe

An Unlikely Hypothesis

Why Does Entropy Really Increase?

The “Temporal Double Standard”

A Reversal of Time’s Arrow

Communication with the Time Reversed?

Time-reversed Communication

Quantum Gravity: The End of Time?

The Wheeler-DeWitt Equation

Rounding-up of Positions

The Perfect or “Master” Clock

The Inexistence of Time

A Better-known Mystery

Further Reading

About the Authors

Acknowledgements

Index

What is Time?

The great theologian and philosopher, St Augustine (AD 354-430), famously wrote of his puzzlement in The Confessions.

After pointing out all the things he is able to say about time without knowing what it is – for instance, that it takes time to say this – he admits that he really is in a “sorry state, for I do not even know what I do not know!”.

WHAT IS TIME? IF NO ONE ASKS ME, I KNOW BUT IF I WANTED TO EXPLAIN IT TO ONE WHO ASKS ME… … I PLAINLY DO NOT KNOW

Augustine is not alone in his bewilderment. The question of what time is and related puzzles – such as whether the past and future are real, whether time travel is possible, and the explanation of the direction of time – are among the most intractable yet fascinating questions asked.

All Kinds of Clocks

In everyday life, we are probably most familiar with time from two sources: clocks, and our inner psychological experience of time.

Clocks are everywhere. There are grandfather clocks, watches, alarm clocks, even incense clocks that let you tell the time through scent.

There are also natural clocks.

But clocks existed well before the modern invention of portable artificial ones.

Over four thousand years ago, the Egyptians used obelisk shadow clocks, sundials, and water clocks which measured time by the flow of water passing through a stone vessel.

By 1800 BC, the ancient Babylonians had divided the day into hours, the hour into sixty minutes, and the minute into sixty seconds.

All the great civilizations of the past used the positions of the sun or stars to tell the time.

These clocks were very accurate.

Looking at the stars with the naked eye, an ancient astronomer could tell the time to within fifteen minutes. And anyone can tell roughly the time merely by looking up at the sun.

Biological Clocks

We also carry within us our own biological clocks. The human heart beats 70 times on average each minute. Our moods, alertness, and appetites follow regular patterns, depending on the time of day, the lunar cycle or the season.

Our biological clock seems to be intimately associated with a group of nerve cells in our brain’s hypothalamus.

HYPOTHALAMUS

These cells are linked to the retina of our eyes and appear to regulate cycles of hormone secretion, our skin temperature and cycles of rest and wakefulness. The hormone melatonin is thought to play a significant role in controlling our daily (circadian) rhythm.

Biological clocks are not special to us. Every creature in nature seems to have them. Some are so good that they have been proposed for human use. The Swedish naturalist Carl Linnaeus (1707–78) thought we might use flowers as clocks.

Surprisingly, not every biological clock is based on the day, lunar cycle, season or year. The cicada is a remarkable chirping insect that remains underground for 17 years. Then 17 years after going underground, thousands of them emerge at the same time, climb the trees, mate and then die a few hours later, whereupon the 17-year cycle begins again.

Whether natural or artificial, clocks have helped order the patterns of life for as long as human beings have been around. In modern society, they also can cause a lot of stress.

Psychological Time

We also feel time pass. In addition to the physical time measured by various clocks, there is also psychological time. We have memories of the past and anticipations of the future. And we experience temporal durations of different sizes. We are personally, subjectively aware of time passing.

Everyone can guess roughly how much time has passed between two events.

Some people can do this surprisingly well, as if there were little inner clocks in our heads – related somehow to the biological clocks.

The interesting thing about these inner clocks is that they seem to speed up or slow down for a person in ways that disagree with other people’s inner clocks.

According to a watch, the trip on a super-fast roller coaster might take only 11 seconds.

11 seconds might seem an eternity to the person on the ride, whereas it may seem like almost nothing to someone waiting. A game of basketball might seem to pass in no time to the child playing it, but forever for the parent watching his twentieth such game in a month!

To begin our investigation into time, it’s important to see that time is more than merely clocks or the subjective experience of time. Time isn’t simply the alarm clock on your nightstand or something solely in your mind. Once we establish this, curious and deep questions will be right around the corner.

Is Time Merely in the Head?

After calming from his initial panic, Augustine argues that time doesn’t really exist outside the head.

WHEN WE MEASURE TIME WE MEASURE WHAT REMANINS FIXED IN MEMORY IT IS IN MY OWN MIND, THEN, THAT I MEASURE TIME. I MUST NOT ALLOW MY MIND TO INSIST THAT TIME IS SOMETHING OBJECTIVE

TIME IS MERELY A FEATURE OF OUR MEMORIES AND EXPECTATIONS

A NEWBORN BABY DOESN’T EXPERIENCE THE PASSAGE OF TIME

Can this be right? Although people disagree about their feelings of how much time has passed, they also enjoy remarkable agreement about the temporal ordering of events.

For example, the father and son returning home from the basketball game might not have looked at a clock since they left for the game – and maybe it was overcast, so they have no sense of where the sun is.

Suppose they guess what time it is before actually looking at a clock. Their guesses might disagree by as much as a couple of hours. They might even argue about who is right, but they typically won’t argue much about the ordering of events that took place.

“We agree that the free throws by Smith in the second half occurred sometime after his free throws in the first half…”

“And Joey broke his finger when Smith stepped on it. ”

Except in rare circumstances, everyone (who has the same information available) agrees – for the most part – on the time order of events. There is definitely something objective and independent of a particular person’s feelings about the time ordering. The objectivity of the ordering of events in time proves that there is more to time than just our psychological sense of its passage. There is the fact that events seem to be laid out in a unique and observer-independent succession in time.

Clocks and Time

Is this agreement merely agreement about what clocks will say? Maybe all there is to time is clocks. This is actually already a deep question. But, at least at first glance, it seems the answer is “no”, for we often talk about a clock being wrong. You might say my watch is ten minutes slow or even completely off. This may be your excuse for being late for an appointment. But is your watch an infallible guide to time? No, we know it will “lose” a few seconds per year, even if it’s pretty good.

WHAT DOES “LOSING SECONDS” MEAN? WHAT IS A CLOCK ANYWAY? A CLOCK IS A PHYSICAL OBJECT THAT EXHIBITS A REGULAR PERIODIC MOVEMENT …THAT IS, MOVEMENT THAT RETURNS BACK TO ITS ORIGINAL STATE

Between each “tick” of the clock, we want the same amount of time to pass. It should be no surprise that pendulums, which have regular periodic motion, can be used as clocks. But pendulums aren’t perfect. On a boat in high seas their motion will be disrupted, or in hot weather they may behave differently than in cold weather.

Consider a pendulum swinging back and forth twice. How do we know that the amount of time that passed on its first trip back and forth is the same as the amount of time that passed on its second trip? This question illustrates what the German philosopher Hans Reichenbach (1891–1953) called the “problem of the uniformity of time”.

YOU MIGHT ANSWER THAT THE FIRST TRIP SIMPLY FEELS AS LONG AS THE SECOND BUT THIS ANSWER ISN’T VERY SATISFACTORY FOR THREE REASONS

Firstly, your personal estimations of time won’t be precise enough for science. We need to know whether the first trip seemed exactly the same as the second trip. Secondly, your feeling as to the amount of time that passed is subjective. You might say the same amount of time went by, but your friend might not think so. Thirdly, and most importantly, you’re measuring the time that passed with your thoughts, but these are – plausibly – physical processes, and so this merely pushes our question back a step. That is, we would then ask how you know how long your thoughts last?

How Long is an Interval of Time?

We can’t directly measure durations of time passing. We never measure pure time. Is this minute the same length of time as the next minute? In one sense the answer is of course yes: minutes are defined to be the same length of time. But we mean something deeper.

IS THE AMOUNT OF TIME THAT PASSED WHEN THE MINUTE HAND WENT FROM 42 TO 43 THE SAME AS WHEN IT WENT FROM 43 TO 44? WE JUST DON’T KNOW… WE CAN’T PUT THE TWO INTERVALS SIDE BY SIDE TO SEE IF THEY ARE THE SAME LENGTH

Back to the swings of the pendulum. Despite our inability to directly measure time-lapse, we still think a pendulum can be wrong. Why? Well, suppose some troublemaker wanted to treat his pendulum as an infallible guide to time. What would be wrong with this?

Imagine that he decided to take it to the equator by boat. Even discounting the rocking of the boat, we can expect at least two other factors to affect the pendulum: air at the equator is more humid and provides greater resistance to the pendulum, and the gravitational field that attracts the pendulum is slightly weaker at the equator. By our standards, the pendulum slows down.

I MAINTAIN THAT EACH SWING STILL MEASURES THE SAME TEMPORAL DURATION THAT’S FINE AS FAR AS IT GOES BUT IF YOUR CLOCK ISN’T SLOWING DOWN THEN LOTS OF OTHER THINGS ARE SPEEDING UP

He is going to have to say his boat is moving faster than before, even though (let’s assume) it has the same-strength wind on its sails, same-strength current, etc. He must explain why all the clocks in the world are magically starting to speed up; why the speed of the sun has altered. Since he can’t provide an explanation for these changes, and yet we can, it seems we’re right and he’s wrong. Our hypothesis, that time can be given by the motion of the stars, for example, is a scientifically better claim than his pendulum hypothesis.

The Most Reliable Clocks

Let’s first pause to note that three clocks have proved to be very good. Historically the sun and the night sky have been most important.

The sun defines regular “ticks” of a clock, if we think of it as ticking each time it crosses the meridian. The stars in the night sky define “ticks” through a chosen star’s passing through due south. Both clocks are better than my wristwatch.

I can explain a discrepancy between the two by appealing to low batteries in my watch, whereas I cannot blame the discrepancy on the sun or stars slowing down or speeding up. Though these two clocks are amazingly accurate (the night sky being better than the sun), there are better still.

The Atomic Clock

The development of particle physics in the 20th century, and in particular ideas by the American physicist Isidor Rabi