Newton’s gravitational force & Einstein’s spacetime

Dr Irengbam Mohendra Singh
I was born in a family with guns. My father Gulamjat had a single-barrel shot gun. My eldest brother Gokulchandra had Webly & Scott .32 revolver, .22 rifle and 12-bore double barrel shotgun. During my student time, I practiced with them all. During my college holidays, I went to shoot wild pigeons with the .22 rifle at Langol Hill and at my friend Kh Dhiren’s rice research farm at Wangban.
While I was in Imphal last year (2016), I was talking with my grandson Aaryaman Lairenjam, when he showed me his latest German model target-shooting air-rifle. He’s very good at shooting and won a few trophies in national competitions while he was at a public school in Dehradun. He has just won a silver medal in Delhi. He is very talented, and with his dotting parents, who do not do things in halves, I’m hoping he might one day surprise us all with a shot at the Olympics.
I wasn’t good at any sport, including shooting, but I did represent Agra Medical College at regional NCC shooting competitions at Lucknow. I loved handguns. The feel of it in my pocket gave me the assurance when I needed one. As a doctor in Imphal, I went about with my own semi-automatic 0.28 pistol in my right hip-pocket, day and night. After I came to Britain I was a member of an indoor pistol shooting club In Bradford, and went out with friends for outdoor shooting on some Sunday mornings with a ‘James Bond’ Walther PPK, ending with a couple of pints at a nearby pub.
I was explaining to Aaryaman how does a bullet travels to its target and that, a bullet doesn’t travel in a straight line once it leaves the barrel, but in a parabolic arc because of gravity. In the study of mechanics at school, we were taught a parabolic arch is a parabola, the curved architecture you often see in bridges or, Hindu temples.
The reason why it appears for the bullet to go in a straight line is because of the high velocity (speed in a straight line) at which it is ejected from the gun. It makes the parabola extremely wide, giving the impression that the bullet is travelling in a straight line.
What we see when a gun is fired as the bullet travels to hit the target, is often small, and since the parabola is so wide, we perceive the bullet to move in straight line. Rifles with an open sight (Iron sight) need adjustments depending on the distance ie zero the distance to the target, depending on the range, by elevating slightly to compensate for the fall of the bullet in the parabola. Actually the path the bullet travels is not a true parabolic arc due to air resistance. It is referred to as ballistic arc.
In distance shooting, if the rifle is pointed perfectly horizontal, the bullet’s motion will all be downwards and will miss the target. So you need to compensate for the distance that the bullet drops by adding one or two degrees aim upwards first. The bullet will still travel in a parabolic arc.
According to Newton’s ‘universal law of gravitation’, a bullet or a large cannonball fired from the same point in space, with the same speed, will follow the exact same path and hit the ground at the exact same time and exact same place, provided no other forces, such as air resistance act on the object being fired.
While learning physics in college, Newton’s law of gravity has been superseded by Einstein’s theory of ‘general relativity’, but the mechanics are still quite consistent. Einstein dismissed Newton’s gravitational ‘force’ theory with an apology, and the force with which Newton’s apple fell in his garden with what Newton called the standard gravity of 32 ft per second every second (32ft/ s2) as Newton didn’t know the nature of that force. Einstein says mass does not attract mass over a distance. Instead, it’s the curving spacetime.
To understand Einstein’s theory, we really need to consider ‘spacetime’ rather than space as we perceive. Because all objects around us exist in spacetime. It’s the spacetime, which is matter like the Sun, that can bend, and the effect of that bending is to create a generalised kind of ‘force’ that was known as Newtonian ‘gravitational force’ (cf. author’s Einstein’s Theory of Relativity & Elementary Quantum Mechanics, Points to Ponder, pp 336-342).
General relativity says that energy in any form such as mass, light, and whatever, causes spacetime to bend, and the bending of spacetime causes the energy how to move ie the object falls along the bending of spacetime. That’s why a bullet moves in a parabolic arch or, Newton’s apple fell to the ground. The path that the object follows is called ‘geodesic’. A body undergoing geodesic motion feels no forces acting upon itself. It’s just following what it feels to be a ‘downward slope through spacetime’. It’s like a bead which rolls down on the curved wall of a funnel. There’s no force generated by the centre of the funnel; it is the curved nature of the funnel wall which guides the rotation of the bead.
That’s the reason why the Earth turns around the Sun, because spacetime around the Sun is curved. So does the Moon around the Earth. Things fall on to the ground because space around them is curved. As the sun’s mass is very big it contributes the biggest bending of our solar system.
Einstein published his second theory of general relativity that includes gravity, ten years after his first theory of Special Relativity that does not include gravity. He was thirty-five. General relativity explains Newtonian “gravitational force” that Newton himself didn’t know how the apple was pulled to Earth when there was “nothing” in between. Maxwell, and Faraday later, however discovered the existence of electro-magnetic “field”.
But the theories of Newton and of Maxwell contradict each other. Einstein found ‘special relativity’ in order to resolve the apparent conflict between Newton’s mechanics and Maxwell’s electromagnetism, and then ‘general relativity’ in order to resolve the resulting conflict between Newton’s mechanics and his own special relativity.
According to Democritus, bodies move in ‘space’. But what is space? Over the millennia there were many theories. Newton (religious) resuscitated Democritean idea of space. He simply called it God’s sensorium”, which nobody understood. Einstein, who gave little credit to the idea of God, found Newton’s idea of space utterly unconvincing. He worked out to find what is Newton’s mysterious space.
The theory of general relativity was conceived. Einstein discovered that unlike Newton’s space, which is flat and fixed with gravitational field, his space is ‘matter’, one of the components of the world. It fluctuates, undulates, bends and contorts like a flexible mollusc. To be precise, what curves is not space but “spacetime”. Matter bends spacetime and the object falls following its geodesic path through spacetime. Spacetime, we know is the mathematical/physical entity in which space is truly fused with time.
Einstein’s relativity theory says it isn’t only space that curves, time does too. Time is not universal, but fixed. It’s something which expands and shrinks according to the vicinity of the masses, such as the Earth. Einstein predicted time on Earth passes more quickly at higher altitudes, and more slowly at lower altitudes. For example: two twins spend their time, one at sea-level and the other in the mountains. When they meet up again, the twin who lived in the mountain is older. This is called the gravitational dilatation of time.
Carlo Rovelli, a very distinguished Italian theoretical physicist, explains why things fall. If you look at a map of the world and the route taken by an aeroplane flying from Rome to New York, it does not seem to be straight. The aeroplane makes an arc towards the north. It is because the Earth being curved, crossing northwards is shorter than keeping to the same parallel. It is the same why a ball thrown upwards falls downwards. It gains time moving higher up, because time passes at a different speed up there. In both cases, the aeroplane and the ball follow a straight trajectory in spacetime that is curved.
Coming to Newton’s apple falling from a branch of his tree, which at the beginning was momentarily at rest, and so had no geodesic path, the General Relativity says the apple “at rest” is actually moving through spacetime, because of its time component. The apple that is moving first only in time direction (ie at rest in space) starts accelerating when it is detached because of the spacetime curvature caused by the Earth. The apparent acceleration is because time passes slowly as it gets nearer the Earth than it does far away.
Einstein’s predictions are becoming true, such as the expansion of the universe and the existence of Black holes. We know the expansion of the universe after the Big Bang, and that Black holes are caused when big stars collapse under their own weight as their fuel hydrogen runs out. The strong weight of the squashed material causes the spacetime to curve so intensely as to plunge down into an actual hole.
It now seems that Einstein’s theory is not the last word in physics.
(The writer is Based in the UK. Email: [email protected] Website:

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