# Chapter 3.3 Interpreting symmetry

Both the majority and minority interpretations agree that measure- ments show that one ship is longer and shorter than the other, or that the car is longer and shorter than the garage, depending on which set of rulers and clocks is used. That is, they agree that appearances are symmetric. They also agree that there is no contradiction because different times are involved.

Symmetry is, however, a key test case for the two interpretations.

When we push beneath observations and measurements and ask what is really happening behind the appearances the two interpretations dramatically diverge. For many physicists, symmetry shows just how unappealing and unwieldy the minority interpretation can be.

The majority interpretation can explain symmetry quite briefly.

Recall that there is a democracy among sets of rulers and clocks that are moving inertially (principle of relativity). Therefore, when one set finds that objects moving past are shorter than when at rest, then other sets will also find that objects moving past are shorter. Different sets of rulers and clocks are governed by the same laws and should see the same effects – even when two spaceships are measuring each other. This is a beautifully simple and clear account of a very perplex- ing phenomenon. At once, the outrageous surprise of Einstein’s symmetry seems to dissipate. Symmetry seems natural: it is just a consequence of the principle of relativity. Moreover, the majority interpretation adds, there could be no contradiction in saying that one ship is shorter and longer than the other. Since lengths are not real properties, the ship does not have two opposite properties at once. Lengths are relations, and a ship can have two lengths in the same way a person can be a brother and cousin.

For advocates of the minority interpretation, this is all deeply unsatisfying. They assert that lengths are properties, and that there is a fact of the matter about which of two objects is shorter and which is longer. Explaining the symmetry is a serious challenge for the minority interpretation. According to this interpretation, the ether is at rest and other objects have definite speeds relative to it. Thus, for example, someone might say that the garage is really at rest and the Jaguar is moving towards it. This means that their real speeds relative to the ether are different or “asymmetric” (there is no sameness across difference). Usually, an asymmetry cannot explain a symmetry; usually, different causes have different effects. Thus explaining Einstein’s symmetries is difficult for the minority interpretation.

It succeeds because there is a second asymmetry. According to the minority interpretation, the lengths are really different. The moving Jaguar is really contracted. Thus both the lengths and the speeds are asymmetric. Roughly put, these two asymmetries cancel each other out: the effects of two compensating asymmetries can be symmetric.

To see this, consider the moving Jaguar. According to the minority interpretation the Jaguar is really contracted, but measurements made by the driver perversely indicate instead that the garage is shorter.

How can this be? Suppose the driver uses the car itself as a ruler. To measure the length of moving objects, the driver must determine when it is the same time at opposite ends of the car. For that purpose, the driver briefly turns on a dashboard light at the mid-point of the car; the moments when the flash reaches the front and rear end of the car are “simultaneous”. Unbeknown to the driver, however, the minority interpretation insists that the car is really moving as the light is travelling.

This shortens the time required for the light to reach the oncoming rear. But the front of the car is racing away from the flash.

If the car is travelling at nearly light speed, it will take a very long time for the flash to catch up with the car’s front. Crucially, the fact that the car is moving means that the two events in which the light reaches its end-points are actually very far apart in space: much farther than the real length of the car.

But the driver thinks the length of the car is unchanged. The driver thinks that the very large distance between the two events is just the ordinary length of the car. By comparison, stationary objects seem shorter than the Jaguar because the method of measurement makes the distance between the moving ends of the car seem much larger.

Thus, the driver grossly under-reports the lengths of bodies passed by the Jaguar. Measurements made from the car will show that the garage is contracted.

According to the minority interpretation, the symmetry of length contraction is partly an illusion. The moving car is really contracted, as measurements made by stationary rulers and clocks in the garage correctly show. But measurements made by rulers and clocks moving with the contracted car are fooled by the motion, and underestimate the lengths of passing bodies.

Miraculously, this mixture of real contraction and illusory measurements produces exactly the symmetry predicted by Einstein (details in Appendix B). In the end, the two interpretations are exactly equivalent.

Although both the mainstream and minority interpretations predict the symmetry of relativistic effects, the issue has been a tremendous psychological boost for the mainstream view. Where the minority interpretation seems a mad conspiracy of inelegant compli- cations, the mainstream interpretation is sweet and clear.

Both interpretations agree that appearances are symmetric. The majority interpretation says lengths are real relations, and these relations are really symmetric. The minority interpretation denies there is any real symmetry: the moving spaceship is really shorter than a resting spaceship. In one case appearances reflect reality; in the other, there are compensating real asymmetries that deceptively produce symmetric appearances.