Chapter 3.2 The garage

An illustration will help bring these points home. According to Einstein, length contraction will permit us to house the six-metre Jaguar in a three-metre garage, as mentioned above. By driving at 85 per cent of the speed of light, the car will contract by some 50 per cent. We can drive the car into the garage and quickly slam the door.

Does this show that the contracted car is really shorter than the garage? How could there be symmetry here? Could the car also be longer than the garage? (The discussion below is repeated in Appendix A.) Since we do not have everyday experience of cars moving so fast, we have to be very careful when thinking about lengths. If measure- ments are made using rulers at rest inside the garage, they will indeed find the car shorter than the garage. That is, the front of the car and the rear of the car will both be within the garage at the same time.

Since the car is moving so quickly, however, it will almost instantly thereafter smash into the back wall of the garage and explode. The explosion will first consume the nose of the car, and then a shock wave will travel along the body of the fast-moving car as its rear end continues to slide towards the flames. Finally, the car, rulers and garage will all be vaporized.
In sum, five events have the following order, according to clocks and rulers at rest in the garage:

1. The front of the car enters the garage.

2. The rear of the car enters the garage.

3. The door is slammed shut.

4. The front of the car is consumed by the explosion.

5. The rear of the car is consumed by the explosion.

The car is entirely inside the garage (or what is left of the garage) from the second event onwards.

The driver of the car, however, uses rulers and other equipment within the car and reports a very different sequence of events.

According to the driver, the garage is approaching at 85 per cent of the speed of light, and therefore the garage is contracted to 50 per cent of its ordinary length. Thus the three-metre garage is only 1½ metres deep. Unable to stop the oncoming garage, the driver sees the nose of the six-metre Jaguar hit by the approaching back wall. At this same time, the rear of the car is still sticking 4½ metres out of the garage door. The resulting explosion at the nose creates a shock wave that travels down through the car as it crumples against the moving back wall. However, the garage is moving so quickly that it continues to slide past the car during the explosion. Just as the garage door passes the rear of the car, the garage door is slammed shut, and then the whole is consumed by the explosion. The door was indeed slammed after the rear of the car was in the garage but, according to the driver, the explosion had already started and destroyed the front of the six- metre car.
In sum, there are again five events, but the driver records them in a different order: 1. The front of the car enters the garage. 2. The front of the car is consumed by the explosion. 3. The rear of the car enters the garage. 4. The door is slammed shut.

5. The rear of the car is consumed by the explosion.

The car is longer than the garage but fits inside because the explosion consumes the front of the car before the rear enters.

According to Einstein, it is generally true that events in different places may have no definite order in time. For example, suppose there are two distant places and that three events happen in each place. Say events X, Y and Z happen on the left and events A, B and C happen on the right. According to one set of clocks, the events may happen in the order ABCXYZ, while another set of clocks may record the order AXBYCZ. Thus events separated in space may have different orders in time, depending on which set of rulers and clocks is used to measure them. This is just a consequence of time dilation: the relative stretching out of time intervals at high speeds.

Two events have a fixed and definite order only when one is the cause of the other. For Einstein, causes always precede their effects.

But when neither light nor any other causal process can travel fast enough to pass from one event to another, there is nothing to determine their order. Thus if, on the right, A causes B, which causes C, then no clock could record their order as BAC.

To summarize, time passes in different ways. When events are separated in space, different sets of clocks will find they occur in different orders. The order of events differs. The car is shorter than and longer than the garage, but not “at the same time”. There is symmetry of effects but no contradiction.

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