The equivalence principle is a fundamental law of physics which states that the forces of gravity and inertia are of a similar nature and are often indistinguishable.

The equivalence principle in the theory of general relativity is the equivalence of gravitational and inertial mass, and Albert Einstein’s finding that the gravitational “force” encountered locally when standing on a massive body (such as the Earth) is the same as the pseudo-force felt by an observer in a non-inertial (accelerated) reference frame.

EQUIVALENCE PRINCIPLE

To understand this further, lets first start with Newtons Law of Gravitation, which states that,

“Any two masses attract each other with a force equal to a constant (constant of gravitation) multiplied by the product of the two masses and divided by the square of the distance between them.”

When we stand on earth, the gravitational pull experienced is mostly constant(considering the earth is almost smooth and perfectly spherical).

constant gravity

This means we experience a force which is mass times the gravitational acceleration “g”.

Then why don’t we fall through the earth?

That’s simply because the molecular structure of the earth’s surface is much stronger and it can stop from falling through. Here the electrostatic force comes into action, which is way more stronger than the force of gravitation.

This is what eventually led Einstein to consider the Equivalence Principle.

He said that, if you are in a box and that box was in free fall, falling towards the Earth under gravity “g” then inside the box, you would feel weightless and start floating.

On the other hand, if you were in outer space well away from any other masses(in the same box) you would feel weightless too.

Einstein said these two situations were equivalent :

  1. A person in free fall inside a gravitational field.
  2. And a person in outer space where there is no gravity.

Equivalence Principle

Einstein went further,

He said if you were in a box on the earth subjected to the gravitational attraction(“g”), it would be entirely equivalent to you being in a rocket that is accelerating upwards with an acceleration “g”.

Equivalence Principle

There is no experiment that could distinguish these two situations separately.

Why did Einstein think that someone standing stationary in a box on the earth subjected to the gravitational attraction was in the same equivalent position as a person in outer space in a rocket which was accelerating at “g”?

Let’s consider a person who drops a ball.

Well, on the earth if you drop something it will fall under the gravity that is pulling it down.

ball falling under gravity

What happens if you are in outer space in a rocket accelerating at “g”?

If you drop something you might say, well since there is no gravity, it will stay where it is.

Yes, that’s true.

The ball will stay in its place but the rocket will move forward since it is accelerating upwards.

Therefore after some time, it will appear that the ball has touched the ground.


Equivalence Principle

How does gravity affect light? (Light and General Relativity)

Light always travels in a straight line which is famously called as the Rectilinear propagation of Light. However, in the presence of a gravitational field, the light follows an already bend space-time fabric and hence appears to have bent.

Let us see how

light bend

 

light in straight line

Consider a rocket which is accelerating with acceleration “g” having a beam of light, which we are going to shoot across the rocket.

What will happen to that beam of light?

  Equivalence Principle  

As you can see the light starts normally but as it travels across, the rocket has also moved upwards.

So by the time, it gets to the other end, it has come pretty close to the floor. (Although in reality, this effect will be very minute to be visible)

Hence the net effect to an observer would be as if the light is bending downwards as a consequence of the rocket moving.

Equivalence Principle

Well that may seem pretty logical and you might say that’s bound to happen, but here comes the problem.

We just established the principle of equivalence, that someone who is in a box on the earth and someone who is in a rocket accelerating at “g” will see the same thing.

So, if a person in a rocket accelerating at “g” experiences the light to curve, it must also follow, that a person on the earth who sees light coming through that box will see it curve too.

This led Einstein to the conclusion that light appears to bend in the presence of a gravitational field.

Now at first sight that seems rather surprising since light consists of photons and photons don’t have any mass, then how can massless photons be affected by a gravitational field?

During the total solar eclipse of the sun, where the sun had effectively been blocked out by the moon it was noticed that people on Earth could see a star which according to the calculations shouldn’t have been there.

light bendGeneral Relativity Verification

What is happening is that the light from the star is being bent as it goes around the sun.

Therefore it appears to be in a different position.

This was the first experimental evidence that light bends in the presence of a gravitational field.

The speed of light is of course invariant. Its a constant throughout the universe.

speed of light is constant

So the influence of the gravitational field doesn’t change the speed as it bends, but it does change the direction.

We might argue,

Well, what happens if the light is coming towards a massive gravitational object? will that cause it to speed up?

The answer is no, but it will change its wavelength and frequency and that’s called the doppler effect.

It is very similar to the effect you hear when an ambulance goes past you.

As it comes towards you it has a very high pitched tone. As it goes away from you it has a very low pitched tone. This is because the frequency of the sound is greater when it is coming towards you and is lower when it is moving away from you.

Let’s consider our rocket again,

Equivalence Principle

Inside it, we emit a beam of light from the top of the rocket.

Now, will that light reach the floor of the rocket?

Well, not quite in the way you would think because by the time the light has reached the floor, the rocket will have moved up.

So inside of the rocket, the waves get scrunched up, in other words, they get a shorter wavelength and the frequency increases to maintain the constant speed(of light).

blueshifted

 

This phenomenon is called the blueshift.

 

 

 

 

 

On the other hand, if we place the source of the light on the floor of the rocket and shoot the light beam towards it ceiling then it would take a little bit longer to get to the top since the rocket itself is also accelerating upwards.

redshifted

 

Therefore its wavelength is stretched out and the frequency decreases to maintain the speed of light.

 

This phenomenon is called redshift.

 

So Einstein concluded that if the rocket is accelerating with acceleration “g” then according to the equivalence principle it must be the same if the box were on the surface of the earth subject to the same gravitational acceleration “g”.

Thus we should get the same effects.

doppler effect

 

Therefore Einstein concluded that gravitational forces will either cause the light to increase or decrease its wavelength and we, therefore, get either a redshift or a blueshift.

Now lets analyse the position(x) VS time(t) graphs,

If it were a constant velocity body, then the graph would be a straight line.

constant velocity

The rate of change of distance with time would be constant because you were travelling at a constant velocity.

 

 

 

 

But if you were accelerating then the graph would be a curved line.

accelerating body

As you accelerate you get faster, and as you get faster you cover more distance in a similar amount of time.

 

 

 

 

When you accelerate you travel through space-time in a curve and therefore according to the equivalence principle if you are accelerating with an acceleration “g” or, you are under the gravitational acceleration in both cases your passage through space-time is curved.

This gave Einstein the idea of curved space-time.

We will further go deeper into this, in the upcoming series on Relativity.

Equivalence Principle FAQ

What is equivalent in the principle of equivalence?

Equivalence Principle, a fundamental law of physics which states that the forces of gravity and inertia are of a similar nature and are often indistinguishable. ... All dynamic experiments produce the same results as in an inertial state of constant motion that is not influenced by gravity.

Why is the equivalence principle important?

equivalence principle states that the inertial mass and the gravitational mass should be the same.

What is the principle of general relativity?

For physics, the principle of relativity is the requirement that in all admissible frames of reference, the equations representing the laws of physics have the same form. For example, in all inertial frames of reference, the Maxwell equations have the same shape in the sense of special relativity. The Maxwell equations or the Einstein field equations have the general relativity

Is gravity indistinguishable from acceleration?

You can't tell if the force you experience is due to gravity or something else just by doing local measurements (i.e. measurements of your immediate surroundings).


Mayukh

I am Mayukh Bagchi. 4th year Undergraduate Engineering student at SRM University , physics and in general Astrophysics is my passion and I want to pursue the same. This blog is dedicated to serve the community with honest and clear insights to the cosmos.