![general relativity curved space general relativity curved space](https://pitp.phas.ubc.ca/quant_lect/2014/GR100/pic/c6.png)
Tidal effects become even more drastic when an observer considers falling bodies on opposite sides of the earth. (Why tidal? Just such a difference in the moon’s gravitational attraction on the earth and on the earth’s oceans is responsible for the tides.)
![general relativity curved space general relativity curved space](http://www.astronomynotes.com/evolutn/grwarp.gif)
![general relativity curved space general relativity curved space](https://www.school-for-champions.com/science/images/gravitation_relatviity_curved_space.gif)
It is this difference in directions that’s responsible for the two sphere’s decreasing distance, a force difference that physicists call a tidal force. The reason for the shrinking distance? The gravitational force pulls the left sphere into a slightly different direction than the right – simply because both spheres get pulled towards the earth’s center. But she does notice the fact that the distance between the two spheres is shrinking steadily, little by little, over time. That is why even an observer inside the falling elevator will see some residual of the earth’s gravitational force at work: She doesn’t notice the downward pull – after all, she is falling alongside all other objects within the elevator. Under these circumstances, it becomes important to note that bodies falling towards the earth do not all move in the same direction (“down”) – they move towards one and the same point in space, namely towards the earth’s center of gravity. The following animation shows the elevator falling towards the earth, following our planet’s gravitational pull: To see why, have a look at this freely falling elevator of gigantic size, with two freely floating gigantic spheres inside. In fact, earth’s gravity does not vanish completely even in a free-falling reference frame (it cannot be “transformed away”, as physicists would say). Is the same true for gravity here on earth? Is it an artefact of the unnatural, accelerated reference frame from which we observe the world – and does it vanish as soon as we change to a freely falling reference frame? The remains of gravity All the observers in freely drifting spaceships (rocket engines shut off) are in agreement: The fact that the accelerated observer sees objects “fall” is merely an artefact, brought about by his spaceship’s acceleration – it vanishes as soon as you leave the accelerated reference frame and change to a free-falling one. But there is no gravity in this situation. “Upwards” is the direction in which his spaceship is accelerating. Our accelerated observer has a clear notion of “up” and “down” – when he looks up, he sees all freely drifting observers and their space stations “fall downwards”, in the direction of his own spaceship’s floor. This accelerated observer feels as heavy as we would feel on earth, since the gravitational acceleration with which an object on earth falls to the ground has that exact same value. Now imagine that there is another observer in a spaceship, shown on the left: The rocket engine of that observer’s spaceship is firing and produces an acceleration of 9.8 metres (32 feet) per square second. We, the crew of the spaceship shown on the right, are floating freely in space, far away from all major sources of gravity. Michael Foale aboard the ISS, together with two floating grapefruits: As an example, the following picture shows the astronaut-scientist C.
#GENERAL RELATIVITY CURVED SPACE FREE#
Those astronauts haven’t escaped the earth’s gravity – they’re experiencing a very special kind of free fall, a free-falling orbit around the earth. Most readers will have seen footage showing situations like this, involving, for instance, astronauts aboard the international space station ISS. In both situation, she would float, weightlessly, in the elevator, as would all objects around her.
![general relativity curved space general relativity curved space](http://i.ytimg.com/vi/xvZfx7iwq94/hqdefault.jpg)
Imagine a scientist in a small elevator more precisely, in a small, windowless compartment that looks like an elevator cabin) That scientist has great difficulty to tell whether she is in free space, far from all sources of gravity, or in free fall in a gravitational field. This seemingly harmless property has far-reaching consequences. At least in a vacuum (where there’s no air resistance), objects you place at the same location fall with the same acceleration – the mouse or the elephant, the feather or the cannonball. One central feature of gravity is that it makes no distinctions. Overall, gravity is intimately connected with the geometry of space and time. In part, it is associated with a quantity called “curvature”. What is gravity? Einstein’s general theory of relativity has an unusual answer to that question which will be explored in this spotlight text.