Time Dilation

TIME literally is defined as the indefinite continued progress of existence and events in the past, present, and future regarded as a whole.

time dilation
time

On the other hand,

DILATION is defined as the action or condition of becoming or being made wider, larger, or more open.

time dilation
dilation

They both together literally mean, the phenomenon by which time is stretched or compressed.

More formally time dilation is a physics concept about changes in the passage of time, as related to relativity. It is a difference of elapsed time between two events as measured by observers.

time dilation
dilated time

This concept first originated from Einsteins Theory of Relativity.

In Albert Einstein’s theories of relativity, there are two types of time dilation:

Case #1: In special relativity, clocks that are moving run slower according to a stationary observer’s clock. This effect does not come from workings of the clocks, but from the nature of spacetime.

Case #2: the observers may be in positions with different gravitational masses. In general relativity, clocks that are near a strong gravitational field run slower than clocks in a weaker gravitational field.

Before we go any deeper into time dilation, we need to clear our concepts on Newtonian Relativity and Electromagnetism.

According to Newton , velocities are relative to one another. He stated that

“The laws of physics (mechanics) are the same for any observer moving at constant speed.”

Newton

In other words, we all play by the same physical rules, whether we are ‘moving’ or ‘standing still’.

Indirectly, this tells us that there is no such thing as absolute motion: if there is no physical experiment which can distinguish between an experimenter moving at (absolute) constant speed or sitting at (absolute) rest, the term ‘absolute motion’ has no meaning.

The only motion that matters is relative motion between objects.

time dilation
relative motion

And this is pretty much understandable. When we travel on an airplane we actually can’t tell whether we are moving at 700 kmph unless we look outside and see the clouds and the ground moving away.

And all the experiments we perform on the airplane will be agreed with the experiments performed on the ground. If you spill coffee on the airplane it will fall the same way on your lap like it would do on your sofa in your living room.

Provided!!!! there is no acceleration and the airplane travels at a constant velocity.

If you start accelerating than obviously, you can feel the effects of acceleration.

Now coming to electromagnetism.

Maxwell through the basic laws of electricity and magnetism derived the speed of the light. It was also concluded that whatever reference frame you are in, the speed of light is constant.

Which means, if you shine a beam of light from a car traveling at 50kmph then the speed of light will not be c+50kmph.

time dilation

But these two ideas are really conflicting.

This means that either Newton’s statements are incomplete or the speed of light may not just be a universal constant.

Soon Einstein realized that this dilemma could be fixed by just a small tweak with Newtons Laws of Motion.

To get rid of all the discrepancies, Einstein suggested that time must slow down to compensate both the theories.

Einstein called this time dilation.

Now in order to proceed further we need to consider a more simple and accurate clock.

For understanding time dilation we consider a simple light clock that has a photon source, and mirrors above and below to reflect the photon back.

time dilation

I can assure you that, whatever time you measure from this clock is same as you would measure from a pendulum clock or any other clocks for that matter.

Now lets picture the whole situation :

time dilation

Allen has planned a short interstellar trip this upcoming winter vacation. his friend Rick, however, decides to sit back and relax and enjoy the lazy winters back at home.

So Allen goes takes his specially made spaceship that can travel very close to the speed of light.

He also has the light clock which ticks away with time t. Now as he is at rest initially inside the spaceship, we can see that the proton goes straight up covering a distance ct.

Now as Allen starts his journey and crosses earth and reaches space, he stars moving ahead with a velocity v.

therefore if Rick were to observe Allen he would now see that the beam of the photon will have to travel a greater distance in order to reach the top mirror as the whole ship is moving ahead with some significant velocity.

This will eventually trace out a triangular path as shown.

Therefore now the time taken for the clock to tick once will change, and hence the new distance will be ct’.

Where t’ will be time measured by Rick at rest on back on earth.


time dilation

so as we can see, we clearly get a right angle triangle, from which we can apply the Pythagoras formula and calculate the relation between the time t (time experienced by Allen on the spaceship) and t'(time experienced by Rick on earth).

time dilation
time dilation
time dilation
time dilation graph

This clearly shows that as the velocity of Allen’s rocket increases his time will be slower by this factor of gamma compared to Rick’s time on earth.

This is pretty mind-blowing and crazy to think! but this is something that is accounted for every day by our GPS Systems which are calibrated accurately by this factor.  let us see a particular case,

let us now analyze a specific case,

time dilation

It’s Allen and Rick again. Like the last time, Allen decides to take a short trip to the moon and as usual, the lazy Rick decides to stay back at earth.

Allen proceeds towards the moon which is 384,400 km away from earth. He travels at 90% the speed of light which is approximately 270000000 m/s.

It takes him 2.846 secs to complete the round trip.

time dilation

Therefore if he leaves the earth at 5:00:00 pm he would again return back on earth at 5:00: 02.84, which will be time shown on his clock.

time dilation

But his time will not match with Rick’s clock back on earth!!!

lets see how,

Traveling at 90% the speed of light means,

time dilation

Allen’s clock on the rocket will be slower by a factor of 2.3, which would imply that the clock on the earth will show the time 5:00:06.54,

This fact just really blows my mind! I mean Allen would theoretically go on a time travel and come back to a future earth (3 seconds though!)

time dilation

It is thus well understood that for higher speeds and for longer distances the effects of time dilation will be significantly higher.

Now leaving all these hypothetical situations aside, there is real evidence for time dilation in reality.

It turns out that there are particles crashing into the earth’s atmosphere at 40-50km above the ground. When they crash into the atmosphere these cosmic rays, turn into muons.

time dilation

Now it turns out that muons are particles with a very short lifetime. These elementary particles(muons) decay so quickly that they don’t even get the time to reach at the ground level even traveling at speeds closer to the speed of light.

time dilation

So in the absence of Special Relativity, we would predict that the muons could never be detected as they would decay way before they even reach the earth’s surface where we would have the detectors.

However, since the muons are traveling close to the speed of light, that means their internal clocks are going slower with respect to the clocks on the ground. That means all their internal processes including the decay time will get slower.

The muons, therefore, decay much more slowly due to the effects of time dilation and therefore, in reality, we can actually detect them here on the ground.

This is a pragmatic example of time dilation in action.

So, we the faster we move through space the slower we move through time.

Due to its malleability time like space deserves its own dimension. In fact, Einstein claimed that the two were one. He called it the space-time fabric.

Einstein also suggested that massive objects like the sun bends this fabric of space-time due to its mass. He also stated that the sun doesn’t attract the planets with some mysterious force, rather it is due to the curvature of this space-time fabric.

time dilation

More massive the object the more they affect the space-time fabric around it.

This is also true for earth’s gravity. We are pinned on the earth because the distorted space by the the earth’s mass pushes us down from above.

Earths gravity thus intensifies as we move towards the center, where the curvature is maximum. An object that falls towards the earth accelerates towards its center.

time dilation

It falls faster just right above the surface than it does, say when it is above the atmosphere.

We just saw that according to Special Relativity the faster you move through space, the slower you move through time.

This literally means that time runs slower on Earths surface than it does around the atmosphere.

However if you measure time with a clock on the surface and on top of a mountain the effects will be really nugatory, in the order of nanoseconds.

Now because different planets have different mass and thus different gravitational strength, they also accelerate objects at different rates. This means a variable passage of time.

We see this effect in the movie Interstellar when they land at the watery planet close to the supermassive black hole.

time dilation

The gravity on the surface is so severe that 1 hr on the planet is 7 years on Earth!!!!!

I mean its an ideal place if you wish to complete your Ph.D. within an hour!!

Time dilation even affects the biological clocks! That’s right! Your head is slightly older than your feet!!

More articles will be coming soon on Time Dilation.

please leave a comment below or ask any question you want to regarding this article, “Time Dilation” .

I would highly recommend a few books that would really help you to know  in depth regarding the cosmos:

  1.  THE THEORY OF EVERYTHING
  2. A BRIEF HISTORY OF TIME
  3. GEORGE AND THE BIG BANG
  4. A Brief History of the Universe: From Ancient Babylon to the Big Bang (Brief Histories)
  5. The Physics Book: From the Big Bang to Quantum Resurrection, 250 Milestones in the History of Physics (Sterling Milestones)
  6. THE BIG BANG THEORY
  7. Cosmos
  8. Relativity: The Special and the General Theory (Routledge Classics)
  9. Black Holes: The Reith Lectures
  10. The Oxford Companion to Cosmology (Oxford Quick Reference)

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nature of vacuum


Mayukh

I am Mayukh Bagchi. 3rd 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.

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