Gravity for the Not So Gifted

Anthony Fakineos

Description

Can someone who has no mathematical background understand gravity? I don''t think so. What about someone who has studied maths at high school level only? They can handle Special Relativity with the level of maths they already have, but when it comes to General Relativity, it isn''t enough. Either learn about tensors, or give up. A third option is offered in this book, which deals with gravity using Special Relativity only. This requires an unusual approach, and I would be surprised if the developmental procedures used in Parts 2, 3 and 4 can be found elsewhere.There is a remark attributed to the physicist Richard Feynman which made an impression on me when I first came across it many years ago. No exact quote is available, but the essence of what he said is this: If you can''t find a way to explain something without resorting to technical terms or concepts unfamiliar to the person you are explaining it to, then you don''t really understand it yourself.The challenge was to deal with this topic, bearing in mind the targeted reader, in a way that remains faithful to this view. So I sincerely hope that after reading this book, you understand something about gravity. Because if you still don''t get it, then I probably don''t get it.

Sujets

• Education

Informations

• Publié par: Austin Macauley Publishers Ltd
• Date de parution: 30 octobre 2019
• Nombre de lectures: 0
• EAN13: 9781528967372
• Langue: English

Extrait

Gravity for the Not So Gifted
Anthony Fakineos
Austin Macauley Publishers
2019-10-30
Gravity for the Not So Gifted About the Author About the Book Dedication Copyright Information © Introduction Part 1 The Newtonian View Versus Special Relativity The Newtonian Transformation Equations (Or “this is common sense”) The Relativistic Transformation Equations (Or “this is weird”) The Interval and Spacetime Part 2 Artificial Gravity The Accelerated Observer Two Accelerated Observers The Accelerated Reference Frame Part 3 Gravity The Spacetime of the Schwarzschild Metric The Spacetime of the Falling Observer Part 4 Two Dimensional Motion in Schwarzschild Spacetime Review Gravity Appendix
About the Author
Anthony Fakineos studied science at Melbourne University and obtained his BSc (Hons) degree in physics in 1977. He then found employment at a private school but decided that the public school system was more to his liking, and spent the major part of his many years of teaching there.
Now retired, he has more time to travel and to undertake “handy-man” type activities, things he has always enjoyed. And of course there is more time to think about his lifelong interest, Relativity.
Anthony lives in Melbourne, Australia.
About the Book
Can someone who has no mathematical background understand gravity? I don’t think so. What about someone who has studied maths at high school level only? They can handle Special Relativity with the level of maths they already have, but when it comes to General Relativity, it isn’t enough. Either learn about tensors, or give up. A third option is offered in this book, which deals with gravity using Special Relativity only. This requires an unusual approach, and I would be surprised if the developmental procedures used in Parts 2, 3 and 4 can be found elsewhere.
There is a remark attributed to the physicist Richard Feynman which made an impression on me when I first came across it many years ago. No exact quote is available, but the essence of what he said is this: If you can’t find a way to explain something without resorting to technical terms or concepts unfamiliar to the person you are explaining it to, then you don’t really understand it yourself.
The challenge was to deal with this topic, bearing in mind the targeted reader, in a way that remains faithful to this view. So I sincerely hope that after reading this book, you understand something about gravity. Because if you still don’t get it, then I probably don’t get it.
Dedication
This book is dedicated to those who like to think deeply but simply.
Copyright Information ©
Anthony Fakineos (2019)
The right of Anthony Fakineos to be identified as author of this work has been asserted by him in accordance with section 77 and 78 of the Copyright, Designs and Patents Act 1988.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of the publishers.
Any person who commits any unauthorised act in relation to this publication may be liable to criminal prosecution and civil claims for damages.
A CIP catalogue record for this title is available from the British Library.
ISBN 9781528967372 (ePub e-book)
www.austinmacauley.com
First Published (2019)
Austin Macauley Publishers Ltd
25 Canada Square
Canary Wharf
London
E14 5LQ
Introduction
You, the reader, have completed some study of physics and calculus at secondary school level and have achieved good results in these studies. You will need to call upon this knowledge to follow the material presented in this book. It is definitely not intended for those who have completed higher level studies in this field (though if you are one of these people, you are most welcome to read it anyway and provide some feedback.) How old you are is not important. Whether finishing high school is a recent event or an event in the distant past doesn’t matter, so long as your ability and desire to think has not been impaired. Don’t expect to understand everything quickly. It will take time and a lot of thinking.
At some stage in your life, you have at least once encountered a statement something like “gravity is the manifestation of the curvature of space and time” and recognised that something deep and meaningful is being expressed in this statement despite your lack of understanding of its actual meaning. You know that the theory that deals with gravity is called General Relativity, and you assume (correctly) that this is a very demanding subject to study. Like most people, you have left it at that because, frankly, you have other more important things to do with your life. There are those gifted academics who have a deep understanding of General Relativity, who give lectures and write books on the subject, passing on their knowledge to other gifted individuals who can handle the advanced maths involved. The not so gifted, and those not so inclined to take on burdensome study, have to make do with documentaries and other non-mathematical presentations dealing with gravity. It seems there is no compromise available; it is either the heavy-handed mathematical versions, or versions geared more towards entertainment than understanding. However, you still remain curious and are prepared to make an effort to gain an understanding of gravity, provided it is explained at a mathematical and conceptual level that isn’t beyond you. But can gravity really be explained and understood using just high-school maths? You can render your own judgement, because this little book has been written for you.
After some more introductory remarks, we will embark on a course that will, in time, deal with gravity as described by General Relativity. The first step is to gain a basic understanding of Special Relativity, which is quite fascinating itself, and use it to examine “artificial” gravity—the simulated gravity experienced when in a state of acceleration. This will give us a remarkable insight into what to expect when we come to consider the real thing. Without this intermediate step dealing with artificial gravity, the real thing would be much harder to understand.
Of course none of this can be done without maths, no matter how much you wave your hands. Maths is the language of physics, and physics describes the natural world. Every equation or formula has a meaning, which needs to be appreciated. To that end, every effort will be made to translate maths language into English. So there will be plenty of mathematical work ahead, but it should not be beyond you, not if you are the person described in the introductory paragraphs. Depending on how long it’s been, you may need to hone your skills on algebraic manipulation and refresh your memory on the process of differentiating functions. If you don’t remember what that means, you definitely need to refresh your memory!
But not just yet. Let’s begin with some thought-provoking observations about gravity.
An argument that questions the reality of gravitational force, based on “feelings”.
In general, when a force acts on us we can feel it. We feel the sharp force when someone gives us a shove, or when we bump into a wall. We feel the more gentle force exerted by the seat on our body when we accelerate in a car.
Even if we haven’t personally experienced it, we have seen video of people floating about inside an airplane which is undergoing a carefully controlled dive, in order to give the occupants the experience of weightlessness. They feel no force acting on their body. Yet they are not in a gravity-free environment. They are falling, accelerating towards the ground under the action of the force of gravity. But the plane is falling with them, and so it is possible for their body to make no contact with any of the surfaces surrounding it. So having gone to all this trouble to create an environment where all contact forces have been eliminated, and even the force of air resistance that would normally accompany falling at high speed has been removed, it is only the force of gravity that is left to act on their body, and they feel nothing. If, instead of a plane, they were in a spacecraft in distant space where there is no gravity, they would feel exactly the same way as they do in the plane. The implication is that there is nothing to feel, that gravitational force doesn’t exist. (The existence of gravity is not being questioned here, just whether it is caused by the action of a force. There may be another explanation.)
It may be argued that gravitational force is different from the other forces we have so far mentioned. The forces exerted by shoves, bumps and car seats are all “contact” forces. Most forces are. But gravitational force acts at a distance, and perhaps that’s why we don’t feel it when it alone accelerates our body. Let’s look into this.
We know of other forces that act at a distance—electric and magnetic forces. It is difficult to come up with a realistic situation where our body would be accelerated by an electric or magnetic force, but a ridiculous one will serve our purpose just as well: put on a suit of armour and approach a powerful superconducting magnet (and then have someone ask in jest, ‘Did you feel that?’) Before the impact, would you feel it? A magnetic force, acting at a distance, is causing your body to accelerate. Yes, you will feel the sensation of being accelerated, just as you would in a car only more so, and nothing like the way you feel when accelerating to the ground under gravitational force alone. Gravitational force is not like other forces because it cannot be felt. Perhaps it isn’t there.
Why the previous argument is invalid
The “sensation of being accelerated” needs to be understood. When a force like a bump or a shove or a car seat acts on our body, it does so locally, meaning it only acts on part of our body. The suit of armour is no excepti