A tennis court appears to have a length (24 metres) and a tennis match appears to have a duration (say three hours). Likewise, a shoe appears to have a definite size, and the wink of an eye seems to take less than a second. The key question is about these distances and durations. Bodies appear to have lengths; events appear to have durations. Are these real properties of bodies and events, or are they mere appearances, like the flatness of the earth? Or are they something else altogether?
Of course, science has no pope. No one imposes uniform views on physicists, and every shade and variation of opinion on this issue has been asserted at one time or another. Nonetheless, there are two chief answers to these questions. The first is accepted – implicitly or explicitly – by most mainstream physicists. Therefore, for our purposes, call it the “mainstream interpretation”. This view denies the existence of real distances and durations. More precisely, a body does not have a real length and an event does not have a real duration that is independent of other things. Since, as experiment and observa- tion confirm, there appear to be no invariant distances and durations, these are not real properties of physical things. This is a radical claim but it is orthodox within the mainstream.
SPACE, TIME AND EINSTEIN
For comparison, consider the case of a controversial portrait hang- ing on the wall of an art museum that is variously thought to be beautiful, ugly or indifferent. Suppose that, over the centuries, judge- ments have always been mixed but tended to shift with the prevailing fashions. Some would conclude that beauty or ugliness is therefore not a property of the painting. Since the painting is the same but judgements of it vary, the judgements seem not to reflect any inner quality of the painting at all.
The mainstream interpretation relies on a similar argument.
When astronauts watch a video, it takes 90 minutes according to their watches, but earth-bound observers say it lasted two hours.
Since one drama cannot last both 90 minutes and two hours, these durations are not properties of the video. Physicists use a very short argument to buttress this conclusion. Recall that a property is invari- ant when all sets of rulers and clocks report the same measurement results:
Argument against distances and durations A. If a property is not invariant, then it is not real. (P) B. Distances and durations are not invariant. (P) C. Therefore, distances and durations are not real properties. (from A,B) That is, if measurements of distances and durations produce different results depending on which set of rulers and clocks is used, then distances and durations are not real properties of individual things (like beauty in the painting).
The first premise in the argument, A, is key. It moves from a claim about what we observe and measure to a claim about nature itself: from appearances to realities. This is a very big assumption and is, strictly speaking, not a part of Einstein’s theory of relativity. It is a part of the interpretation of that theory: the attempt to clarify what the theory says about our world. But the first premise seems reasonable. If a property really belongs to an object, then different measurements should all faithfully report the same result.
The second premise, B, is just the assumption that observations confirm the occurrence of length contraction and time dilation. That is, it assumes that Einstein’s predictions turn out to be true, which is widely accepted.
Together, the two premises produce a startling conclusion.
According to the argument, relativity theory implies that shoes do not
EINSTEIN IN A NUTSHELL
have sizes! A tennis court does not have a definite length; a tennis match in itself never lasts three hours.
Of course, the claim that distances and durations are not real properties is merely negative: it makes an assertion about what does not exist. But the mainstream interpretation also makes positive claims about what does exist instead of distances and durations. A comparison will help make this clear.
Suppose that, at a large family reunion, someone is variously introduced as a brother, son and cousin. Should we conclude, as in the case of the painting, that these various attributions are not all correct?
Since being a brother, being a son and being a cousin are not the same, should we conclude that the introductions were mistaken? Clearly not. The reason is that being a brother, and so on, depends on the kind of relation to other people. One person can be at once a brother to a sister, son to a father and cousin to a cousin because he enters into various relations with different people.
According to the mainstream interpretation, the relativity of distances and durations seems revolutionary only because of an error.
We thought that they were real properties of individual things, but actually they are each a kind of relation (technically, a “projection onto a coordinate system”). Lengths vary because they are like family relations to the surrounding bodies and measuring instruments. We mistakenly assumed that lengths are properties of individual things only because our ordinary experience involves objects moving far more slowly than the speed of light. Since we are also moving slowly, we all have the same low speeds relative to such objects. Since our relations are thus all the same, we overlooked their key role. A later chapter explains this strange world of relativity further, and explores this positive side of the mainstream interpretation.
In sum, the mainstream interpretation denies that real distances and durations are properties of individual bodies or events. It asserts, instead, that distances and durations are kinds of relations. A shoe has one length relative to one set of rulers and another length relative to a different set of rulers (like the brother who is a cousin), but no particular length of its own.
Properties belong to one thing, relations to two or more.
Although distances and durations are not real properties, they are also not mere appearances: they are real relations.