But Why is Gravity? | Part-II
Introduction
To understand gravity, we need to know a little more about motion, light, and time. We know light moves very fast, around 3 lakh kilometres in a second. That’s equivalent to making 100 trips from Chandigarh to Kanyakumari in just a second! This speed is a constant, due to a fundamental law of physics as discovered by Maxwell, popularly known as Maxwell’s equation. We call this constant “c”, and it is fundamental to our universe. The value of c can only be different in another universe if it exists.
Spacetime Diagram
We have seen a lot of graphs, and they are very useful to represent a relationship between two quantities. Here is one below; between space and time. We know there are three axes in space, namely x, y, and z. Since our mind cannot easily visualize 4D graphs, we have only shown the x-axis. This graph is called a Space-Time diagram since it shows how time, space or the position of the object changes. Simple, isn’t it?
Now let’s consider assume a man and a goat are moving in the same line at different speeds. If we draw a spacetime diagram with respect to the man, he doesn’t move at all, while he will see the goat moving in the forward direction; being faster than man. Two light rays also move in forward and backward direction respectively represented by orange lines in the graph.
Relative Motion
Next, let’s change the perspective. We are now looking at what will the motion of man look to a goat. The goat will see that the man is moving backwards with some speed. So we have just done a rotation of the above graph to obtain spacetime diagram w.r.t. goat? No. We can easily figure out this will indeed cause the slope of the line representing light’s motion to change. Which means the speed of light will be perceived differently by the man and the goat. However, it raises a contradiction. Remember Maxwell’s law? Speed of light is always a constant, how it can be perceived as different by two bodies in the same universe?
Einstein was able to observe this anomaly in our intuition and Newtonian physics. Questioning existing understanding of physics and showing it is wrong is an act of bravery and ultra-smartness. So we have to redraw our graph. A rotation followed by a transformation will keep the speed of light the same. We also should ensure the angle between goat’s and man’s world line should remain the same. It will look like this:
Lorentz Transformation
This is called Lorentz transformation. It is the only way we can transform our graph correctly to represent how motion varies by changing the frame of references. Now again look at G1. Each snapshot image of the goat or man represents a tick in the clock attached to them. Something strange has happened now. In G1, the man observes the 4th tick of his and goat’s clock at the same time. However, the goat records the 4th man’s clock tick a few moments later(since the 4th tick of man is above the 4th tick of goat in the time axis).
Relative Time
Let’s digest what I have written earlier. For the man, both he and the goat stops at the same time, but the goat sees that the man stops a few moments after her. Is it possible that the same events can be perceived to be occurring at a different time for different observers? the answer is yes, as we can notice the same in the above graphs. This understanding has important inferences and consequences. We can conclude that time is not absolute, time is relative. Each moving body has its own clock, unlike a universal clock as we think intuitively. This is the gist of Special Relativity and the answer to many assumed paradoxes.
A Thought Experiment
Albert Einstein did a famous lightning train thought experiment. Thought experiments have been used by many scientists to do profound discoveries. The experiment is performed within your mind to check the validity of a proposition. They are nice methods to lead yourself towards proving a hypothesis, as you don’t need any resources.
Consider two lightning bolts strike a moving train on either of its ends. A person on the ground happens to see both of them occurring simultaneously as he is equidistant from both ends, thus light rays from both ends will reach his eyes at the same time. However, for a person inside the train, the events won’t be simultaneous. Since the train is moving towards the lightning bolt hitting the front end of the train, the person inside the train will observe it strikes first and later another bolt strikes the rear end as the rear beam has to travel more distance to catch up with the moving train.
A person inside the train reports that these two events are not simultaneous, however, the person on the ground claims them to occur at the same time. How we will decide that who is right and who is wrong?
As Einstein said, both are right. As we stated earlier, time is relative. The clock of a moving person ticks differently as compared to one who is stationary. In other words, simultaneity is relative. If you can accept this, everything in special relativity is just simple algebra.
Time Dilation
We have so far established two things:-
- Time is relative
- Speed of light is constant
You must be thinking about a lot of things now. We travel very frequently, why does our clock doesn’t need to be re-synchronized with the standard clock on earth if the time runs differently for an object in motion? The answer is, yes they get out of sync; however, the effect is very minute on such smaller speeds and durations. Scientists tested this phenomenon by keeping an atomic clock in a plane. Atomic clocks are very accurate and precise up to nanoseconds. It was found that there was a deviation of few nanoseconds in initially synchronized clocks. This phenomenon is called time dilation.
Look at the diagram below. Orange man is walking and his clock ticks every 2 seconds. A stationary blue man will perceive these ticking to happen at an interval of 2.12 seconds (depending upon the walking speed). The clock is dilated by an extra 0.12 seconds as a result of motion.
Further Readings
There are further interesting consequences of special relativity too. I would recommend you to read about length contraction and mass-energy equivalent. I haven’t covered them here since they aren’t very relevant to our discussion on general relativity. If you are more interested, you can look at the equations for Lorentz transformation and time dilation. They are simple and yet beautiful. Mathematical formulations of physical phenomena make our understanding more sound and strong.
Twin Paradox
I am ending this blog with a thought experiment for you. Twin Paradox is a great way to test your understanding of special relativity. Consider two identical twins, one of the twin journeys to space and returns back to earth. According to Special Relativity, we saw that time slows down for objects in motion. However, both twins perceive the other one moving. That means the twin who lived on earth will think he will be older, also the traveller will believe that he should be older as according to him his brother was travelling relative to him. It is not possible that both of them can be older, which means one of them is wrong. So who is wrong here? Let me know in the comments. Hope you can fix the paradox.
