Constant gravity exists only as an approximation that does well enough in small regions of space. And on this small scale the only case where Einstein's theory gives a detectably different prediction from Newton's is that of §§23.14–16. For further tests we have to consider vast spaces in which gravity obviously varies from place to place. And to cope with these more complex conditions we shall have to modify two of our most basic assumptions.

Our most fundamental assumption of all–Einstein's Principle of Relativity (§5.11)–involves the explicit condition ‘In the absence of gravity …’. In constant gravity conditions would it still be true that all inertial observers are equivalent?

Yes–since the inertial observers in this case are exactly like those of the no-gravity case, but observed by an accelerated observer (§§23.6, 23.12).

If, on the other hand, gravity varies from place to place, then this Principle is no longer true. For simplicity imagine that the Earth is the only massive body in the Universe. Then (ii) and (iv) of §23.5 are inertial observers, one at the Earth's surface, the other very very far away in space. Our demonstration (§23.6) that these have identical experiences only worked because we confined our observers to small rooms. If we let them watch things moving inertially a few thousand miles away, will their experiences be the same?

No. As (ii) sees it, such things will have accelerations of different sizes in different directions (depending on position relative to the Earth's centre). But (iv) will detect no deviation from motion in a straight line at constant speed.

It's time to attempt some sort of summing up. We've left the Special Theory so far behind that I'm not going to return to it now. Anyhow, since it's so generally acknowledged as a well-established theory that lies at the roots of so much of today's scientific thought, what is there to discuss? The General Theory is a more interesting topic–still subject to active controversy.

Let's begin with a limitation. It never lived up to its title, with the suggestion of a great all-round generalisation of the Special Theory. It turns out, as I said in the Introduction, to be only a theory of gravitation, and as such we must judge it. So let's start by comparing Einstein's theory of gravitation with Newton's at a philosophical level. You'll know by this time where my preference lies.

Please reread §§26.46–7. There we have one reason for preferring Einstein's outlook: at the most basic level it involves one assumption fewer than Newton's. And so (although technically more complicated) it is simpler in principle. And most of us would agree (though it's hard to say precisely why) that simple explanations are philosophically preferable to complicated ones.

We can't, of course, blame Newton for being more complicated–the Einstein approach was inconceivable in his time. But we can note what caused him to be so. And that is simply that his theory begins by saying, in essence, ‘If there were no gravity’, things would behave in such and such a way. That's unsatisfactory, because you can never find true no-gravity conditions in which to test its truth.

Another book on Relativity for the layman! Why? What's different about it?

There have been many books on Einstein's theory, written by authors who are highly expert in this field and who have gone to an immense amount of trouble to explain it with great logical clarity, yet in simple terms that should be comprehensible to any reasonably intelligent person even if he has had no scientific education. And still these books have left most of their readers bewildered. Why? After discussions with dozens of students I think I can answer that question. The difficulties that really trouble the layman are not those which you would logically expect. The Relativity expert, no matter how diligent and sympathetic, is unlikely to discover these difficulties, even more unlikely to know how to cope with them.

I am definitely not one of these Relativity experts. What I know of the subject has been learnt laboriously from their works. But I think I can claim to be an expert in something different–in the art of teaching science to the non-scientist. That has been my job since 1950.

I introduced Relativity amongst my courses in 1958. And since then I have been teaching it to carpenters and clerks, housewives, miners and insurance agents–to all sorts of people who have no special qualifications for learning the subject (and others like teachers and professional engineers who have limited qualifications). At first I taught it badly. But the customs of the Adult Education world enabled me to learn by my mistakes.

Suppose that W–the observer of the previous chapter moving with constant acceleration – watches any inertial observers that may be around. How will their motion appear to him?

Think, for example, about several cars moving at various steady speeds along a straight road, and about what their motion would look like when observed from another car that has constant acceleration. I think you'll conclude that the distance between W and any inertial observer E is changing in a constantly accelerated manner, and that therefore

(A possible worry: maybe it won't work out quite like that–because E and W don't agree about times and distances. Actually if you do the calculations, based on our Chapter 22 near-equations, you discover that the statement is only strictly true if E is near to W and moving slowly relatively to him–both conditions to be interpreted in an asaccurately-as-we-wish sense. But that's good enough for us, since we'll only want to use this proposition in nearby, slow-speed conditions.)

Maybe you protested that W knows (by the particle test) that he is accelerated, and so he can't regard himself as stationary. But do you know of any circumstances in which an observer's test particle runs away and yet he insists that he's at rest?

Your test particle accelerates rapidly away from you (cf. §5.4). Yet you have no difficulty in thinking of yourself as stationary.

Twice before we've discussed the so-called Clock Paradox (Space-twin Paradox). Please revise §§4.14-20 and 14.22–4. After that, if you've not already tackled the problem at the end of §4.18, please do so now. Figure 14.22 should help. Action!

You are being asked to compare the stories told by different versions of Figure 14.22 in which the curves near P, O and Q remain always the same in shape and length, but the two intervening straight portions of D's world line may be of any length we wish. If the accelerations do have the effect (suggested in §§4.18 and 14.24) of increasing the time that passes for D, then (with the same accelerations used in every case) the amount of this increase is fixed. But on the inertial parts of D's journey the dilation of time (§§3.10, 13.7) is always operating to diminish his total time measurement compared with A's; and the longer the inertial portions of the journey, the bigger this effect will be. So, even if there is an ‘acceleration effect’, it could only compensate for the dilation of time on a journey of one particular length. On longer journeys less time would pass for D than for A; on shorter ones it would be the other way round.

With a theory based on the assumptions we've used so far (all inertial observers equivalent, etc.) we can't definitely decide whether accelerations do or do not have some effect on the traveller's time. To make progress we must introduce a new assumption on this question, work out its consequences, and test them as usual against experiment.

When you're in a train, you can't say whether it is really moving or not–that's an everyday experience from which our theory begins.

You can, of course, see the telephone poles flashing by. The naive interpretation of what you see would be that the poles are moving and you are not. Actually, all you can justifiably assert is the relative motion of the poles and yourself. And for further confirmation, think about all those films showing the inside of a railway compartment travelling at high speed – think about how the illusion of motion is actually produced (Remember: bold type means work for you–page 5).

From this sort of experience we've learnt that watching objects around us merely gives information about relative motion. It can never tell us whether they are moving or we are (or both).

Well then, would some test done inside the train tell us whether it is moving or not? For the present let's stick to trains in steady motion-at constant speed on a straight bit of track. I suggest that everything in this moving train happens in exactly the same way as if it were stationary. For example, the steady motion of the train doesn't make any difference to the problem of keeping your balance. You stand upright just as you would in a stationary train. What happens if you drop something?

It falls straight down as you see it, and lands right beside your feetjust as it would do if the train were motionless.