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GENERAL RELATIVITY

Special relativity included Newton's laws as a special case of low speeds. However, the Newton's law of gravity is not included in SR, in particular, according to the Newton's law, the gravitational force propagates with the infinite speed.

Also, the distance is not absolute but relative. Which distance to use in computing the gravity force?


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\framebox{\Huge\bf ?}On the orbit around the Earth, astronauts in the Space Shuttle feel no gravity: they float around, move objects many times their own mass with one finger, etc. Does it mean that there is no gravity in the outer space?

A
Yes.
B
No.

\framebox{\Huge\bf ?}When the Space Shuttle lifts up, astronauts often feel several ``g'', i.e. gravity several times larger than the gravity at the surface of the Earth. Does it mean that the gravity is stronger in the Space Shuttle than out side it?

A
Yes.
B
No.

We can get a clue to the ``weightlessness'' of the astronauts if we consider an object, thrown inside the Space Shuttle (an astronaut himself will also suffice). An object will fly in a straight line with constant speed (until it hits a wall or someone's head). Thus, the Space Shuttle orbiting the Earth is an inertial frame of reference!

Yes, even if the Shuttle itself does not go in a straight line! $\Uparrow$

(this is a clue to the General Relativity)

Since it is an inertial frame, there is no force acting on a freely moving object $\rightarrow$ weightlessness.

\framebox{\Huge\bf ?}What is so special about the Shuttle orbiting the Earth?

A
It moves really fast.
B
It made in the US.
C
It freely falls in the Earth gravity field.
D
It has a special shield, protecting it from the Earth gravity.

Equivalence principle

If a freely falling object is an inertial frame of reference, then an object that does not fall freely is not in the inertial (i.e. in accelerated frame of reference.


\begin{displaymath}\Downarrow\end{displaymath}

Gravitational and inertial forces produce effects that are indistinguishable. This is called the weak equivalence principle. It states that all objects will move in the gravity field the same way as in the accelerated frame of reference.

The gravity force that pulls us downward is equivalent to upward acceleration.

Einstein went one step further, and formulated the strong equivalence principle: all physical laws are precisely the same in all inertial and freely falling frames, there is no experiment that can distinguish them.

Can equivalence principles be tested experimentally? Of course yes.

The weak equivalence principle is, in fact, a result of Newton's law of gravity. All objects fall to the ground with the same acceleration, because the gravity force is proportional to the mass:

\begin{displaymath}m g = G{m M\over R^2}\ \ \ \Rightarrow\ \ \ g = G{M\over R^2}. \end{displaymath}

But who said that the above equation is right? We must make a distinction between the inertial and the gravitational masses.

Thus, the weak equivalence principle states that

\begin{displaymath}m_{\rm in} = m_{\rm gr}. \end{displaymath}

This was verified experimentally first by Baron Roland von Eötvös in 1889 to the level of 1 part in 109, and then later in our century by other to the level of 1 part in 1011.

This is fantastic accuracy! It is equivalent to noticing the size of an atom compared to the size of our classroom!


However, equality between the inertial and gravitational masses only means that all bodies fall with the same acceleration in the gravitational field. It says nothing about other laws of physics. Thus, Einstein's strong equivalence principle is not verified experimentally yet. It is, however, supported by observations in as much as GR is supported by the data.