Above we found a “reasonable point of view” on motion. True, the “reasonable” points of view, which we called inertial frames of reference, turned out to be infinite in number.

Now, armed with a knowledge of the laws of motion, we can become interested in what motion looks like from an “unreasonable” point of view. Our interest in how inhabitants of non-inertial frames of reference live is by no means idle, if only because we ourselves are dwelling in such a system.

Let us imagine that having grabbed our measuring instruments we settled down in an interplanetary space-ship and went travelling in the starry world.

Time flies quickly. The Sun already resembles a little star. The engine has been cut off and the ship is far away from gravitating bodies.

Let us now see what’s going on in our flying laboratory. Why does the thermometer that slid off its nail float in the air and not fall to the floor? In what a strange position deviating from the “vertical” has the pendulum hanging on the wall got stuck! We immediately find the solution: after all, the ship is not on the Earth but in interplanetary space. The objects have lost their weight.

Having feasted our eyes on this extraordinary scene, we decide to change our course. We turn on the jet engine by pressing a button, and suddenly … the objects surrounding us seemed to come to life. All bodies which hadn’t been made fast were brought into motion. The thermometer fell down, the pendulum began oscillating and gradually coming to rest assumed a vertical position, the pillow obediently sagged under the weight of the valise lying on it. Let us take a look at the instruments which indicate the direction in which our ship started accelerating. Upwards, of course! The instruments show that we chose a motion with an acceleration of \(9.8~\mathrm{m/s^2}\), not very great considering the possibilities of our ship. Our sensations are quite ordinary; we feel the way we did on Earth. But why so? As before, we are unimaginably far from gravitational masses, there is no gravity but objects have acquired weight.

Let us drop a marble and measure the acceleration with which it falls to the floor of the spaceship. It turns out that the acceleration is equal to \(9.8~\mathrm{m/s^2}\). This is the number we have just read on the instruments measuring the acceleration of the rocket. The ship is moving upwards with the same acceleration with which the bodies in our flying laboratory are falling downwards. But what is “up” or “down” in a flying ship? How simple things were when we lived on the Earth. There the sky was up and the Earth was down. And here? Our up has one unquestionable property—it is the direction of the acceleration of the rocket.

It isn’t difficult to understand the meaning of our observations: no forces were acting on the marble we dropped. It moves by inertia, whereas the rocket moves with an acceleration relative to the marble. To us who are inside the rocket it seems that the marble is falling in the direction opposite to that of the acceleration of the rocket. Naturally, the acceleration of this fall is equal in magnitude to the true acceleration of the rocket. It is also clear that all bodies in the rocket will “fall” with the same acceleration.

We may draw an interesting conclusion from all that has been said. Bodies start “weighing” when the rocket accelerates. Moreover, the “gravitational force” has a direction opposite to that of the acceleration of the rocket, and the acceleration of free “fall” is equal in magnitude to that of the motion of the jet ship. And what is most remarkable is the fact that in practice we are unable to distinguish the accelerated motion of a frame of reference from the corresponding gravitational force.¹ If we were inside a spaceship with closed windows, we could not tell whether we were at rest on the Earth or moving with an acceleration of \(9.8~\mathrm{m/s^2}\) This indistinguishability of an acceleration from the action of a gravitational force is called in physics the equivalence principle.

This principle, as we shall now see illustrated by a series of examples, permits one to quickly solve many problems by adding to real forces the fictitious gravitational force existing in an accelerating frame of reference.

The elevator can serve as our first example. Let us take along a spring balance with weights and go up in an elevator. We shall follow the behaviour of the pointer of the scale after placing a kilogram of vegetables on it (Figure 1). The ascent has begun; we see that the scale reading has increased, as though the weight weighed more than a kilogram. The equivalence principle will easily explain this fact. During the upward motion of the elevator with an acceleration \(a\), there arises an additional gravitational force directed downwards. Since the acceleration of this force is equal to \(a\), the additional weight is equal to \(ma\). Hence, the scale shows a weight of \(mg + ma\). The acceleration has ended, and the elevator is moving uniformly—the scale has returned to its initial position and shows a weight of 1 kg. We are getting close to the top. floor, and the motion of the elevator is slowing down. What will now happen to the spring balance?

Well, of course, the load now weighs less than one kilogram. When the motion is slowing down, the acceleration vector points downwards. Therefore, an additional fictitious gravitational force is directed upwards, opposite to the direction of the Earth’s gravitation. Now a is negative, and so the scale shows a quantity less than \(mg\). After the elevator comes to a halt, the scale returns to its initial position.

Let us begin the descent. The motion of the elevator speeds up; the acceleration vector is directed downwards; hence, an additional gravitational force is directed upwards. The load now weighs less than a kilogram. When the motion becomes uniform, the additional weight disappears, and towards the end of our trip on the elevator—when the downward motion is decelerating—the load will weigh more than a kilogram.

The unpleasant sensations experienced in rapidly accelerating and decelerating elevators are related to the change in weight under consideration.

If an elevator is falling with an acceleration, the bodies inside it seem to become lighter. The greater this acceleration, the greater will be the loss of weight. But what will happen when a frame of reference falls freely? The answer is clear: in this case, bodies stop pressing down on the scale—cease weighing: the Earth’s gravitation will be balanced by the additional gravitational force existing in such a freely falling frame of reference. Being in such an “elevator”, one can calmly place a ton on one’s shoulders.

At the beginning of this section, we described life at \(g\) zero in an interplanetary spaceship which has left the sphere of gravitation. There is no weight in such a spaceship during uniform rectilinear motion, but the same thing also takes place during the free fall of a frame of reference. Hence, there is no need to leave the sphere of gravitation. Weight is. absent in every interplanetary ship which is moving with its engine cut off. A free fall leads to the loss of weight in such systems. The equivalence principle brought us to the conclusion that a frame of reference moving rectilinearly and uniformly far from the action of gravitational forces is almost (see this this footnote) completely equivalent to a frame of reference falling freely under the action of its weight. In the first system there is no weight, and in the second the “downward weight” is balanced out by the “upward weight” We will not detect any difference between these systems.

Life at \(g\) zero begins in an artificial Earth satellite at the moment when the ship is orbited and begins moving without the aid of a rocket.

The first space traveller was the dog Laika, and soon afterwards a human being adapted to life at \(g\) zero in the cabin of the spaceship. The Soviet cosmonaut, Yuri Gagarin, was the first to do so.

Life in the cabin of a spaceship cannot be called ordinary. A great deal of inventiveness and ingenuity were needed in order to make objects so easily subordinated by gravity obedient. Is it possible, for example, to pour water from a bottle into a glass? For water pours “downwards” under the action of gravity. Is it possible to cook food if water cannot be heated on a stove? (Warm water will not mix with cold one.) How can one write with a pencil on paper if a slight push of the former against a table is enough to drive him aside? Neither a match nor a candle nor a gas burner will burn, since burned-up gases will not rise upwards (after all, there is no up!) to make room for oxygen. It was even necessary to think about how to guarantee a normal course for the natural processes occurring in the human organism, for these processes are “accustomed” to the Earth’s gravitation.