top of page

A Walk in the Park with Newton and Einstein


It’s a bright spring morning. The last drops of dew hang on the tips of the flower petals here in the park. With your latest invention, the super-deluxe time machine, you have rounded up two important guests, Sir Isaac Newton, and Professor Albert Einstein. You ask them to take a walk with you in the local park. They oblige.


“Sir Newton, will you please explain all of what you see here according to your principles of motion?”

Girl walking dog, explained by Newton, Einstein

He nods. “Let’s start over here with that girl walking her dog. The act of walking involves

forces and motion. As the girl walks, she pushes on the ground, and the ground pushes back on her with an equal and opposite force. Friction forces with the ground help her speed up and slow down. The reason she even has friction forces with the ground is the force of gravity pulling her down to the ground, giving her her weight. If it weren’t for gravity, when she pushed off the ground to move, she would just propel herself off Earth’s surface, and there would be nothing to stop her motion in space, except maybe for some air particles in her way.”


“Thanks,” you say, and, turning to Einstein, “Professor Einstein, would you be so kind?” motioning to the girl and the dog.


“Sure, well I agree that the act of walking involves forces and motion, and certainly the part about equal and opposite forces and even friction forces is correct. I beg to differ, however, with the cause of the friction. Gravity, in my theory, is not a force, but a change in the shape of spacetime, a bending around objects with mass. Therefore, the girl and her dog would tend to follow this shape of spacetime toward the center of Earth (in other words, they would fall), but the ground keeps getting in the way, causing a constant upward push on their bodies. This is what they feel as their “weight.” It is the ground pushing up on them with electromagnetic forces (the ground’s electrons repel their electrons). Their mass or inertia resists this push, giving them the sensation of weight. I partially agree with Newton in his last statement, but again, switching off gravity would not be turning off a force, but changing the very shape of spacetime. If it were flat instead of curved, then the girl and her dog would indeed keep moving in the direction the ground pushed them, and the air might slow them a bit.”


“Professor,” you say, addressing Einstein again, “you said the ground pushed them, but didn’t they push the ground?”


“Ah, well, you should have asked Newton this one, because it was his famous Third Law of Motion I am referring to. When they push on the ground one way, the ground pushes back on them the other way with equal force, pushing them in the direction they are going.”


At this, Newton nods and smiles. You then address him, “How about this then, Sir Newton?” pointing to a boy letting go of a ball on the top of a slide.

Motion of a ball on a slide explained by Newton, Einstein

“Ah yes, again, this has to do with the force of gravity. The Earth pulls straight downwards on the ball, but the slide gets in the way, causing the motion to be slanted instead of straight down. Still, you can see that the ball goes faster and faster as it rolls down the slide. This is gravity’s force acting on the ball, accelerating it toward the ground. It would move much faster if the slide weren’t slowing it down.”


“Thank you,” you say. Then, turning to Einstein, “Professor?”


“I agree that this has to do with gravity, and again, it is the curvature of spacetime which causes the ball to roll down the slide. The slide does indeed “get in the way” as Newton says, but it is getting in the way of the ball’s falling motion on what I would call a geodesic, a straight-line path in curved spacetime that leads to the center of the Earth’s mass. When the slide pushes on it, it falls with spacetime’s curvature less than it would if the slide were not there. This is why Newton says it would move faster if the slide weren’t slowing it down. However, I must insist we look at this from the perspective of the ball, in which it is the ground accelerating towards the ball. Let me show you something here."


At this point, Einstein scoops up a ball near the slide, retrieves the original ball as well, climbs to the top of the slide, and asks the boy if he may demonstrate something. The boy nods and moves to the side. Einstein releases both balls a the same time, one ball off to the side of the slide drops straight to the ground while the other, released on top of the slide, is still rolling down the slide. "As you can see, the ground accelerates at a slower speed toward the ball when the slide is in the way. The ground would accelerate faster if the slide were not there. This is, as I mentioned before, due to the fact that the slide puts forces on the ball, keeping it from following its natural freefall motion, keeping it from following its geodesic.”


“That sounds reasonable,” you say, “but why do you insist that it’s the ground accelerating toward the ball and not the other way around?”


“In order to understand this, let’s go back to Newton’s Second Law of Motion. When we push on a ball, it accelerates. According to my gravity theory, called the General Theory of Relativity, falling objects experience no forces, and therefore do not accelerate. They simply follow the shape of spacetime. Any object which is not following the curvature of spacetime, is doing that because a force is acting on it. This applies to the ground and everything we see around us here. All of these objects, the trees, the grass, the people, the play equipment, all of these are not in freefall. And therefore, a force is acting on them, pushing them up, keeping them from falling; keeping them from following their geodesics, their natural course through curved spacetime. It is the same electromagnetic repulsion forces we spoke of earlier. The forces on the rolling ball are friction forces, supporting the ball and forcing the ball horizontally, as it tries to move vertically on its geodesic. So, we say, because of Newtonian physics, when forces act on the ball, it gets pushed in the direction of those forces, and as you can see, it does not land straight down below the top of the slide, but is pushed by the slide (electromagnetically) to follow its shape all the way to the bottom. From there, it is a small distance to the ground, but it experiences a bit of freefall, in which it follows a projectile motion, meaning it has a sideways movement, given to it by the slide, and a vertical movement, given to it by spacetime’s curvature. From an outsider’s perspective, the ball’s horizontal movement doesn’t change as it falls to the ground, but remains constant, since it is not really going fast and there’s not much air in the way. This is obeying Newton’s First Law of Motion. But vertically, if you had a good measuring device, you could see that the ball appears to speed up as it falls to the ground. But again, this is an illusion. It is the ground coming up to meet the ball. It is the ground with the forces on it, not the falling ball.”


“Wow,” you say, “that’s a lot to take in,” pausing a bit to ruminate. Then, you look to your left and see an open field where a girl and her mom are launching a model rocket. “Sir Newton,” you say, gesturing to the rocket, “would you like the first crack at this?”

Model rocket launch explained by Newton, Einstein

“Certainly,” he begins, “unless I am mistaken, it appears there is some kind of chemical propulsion at work here as evidenced by the white smoke. When the chemicals react, they are forced out of the bottom of the rocket at a high rate of speed. As the chemicals are pushed downward, they propel the rocket upward. And look, what is that? Something popped out of the top and is slowing the rocket’s descent. That’s ingenious. A great idea to catch air on the way down and slow the rocket as it falls back to the ground by the force of gravity. Back to when it was going up though. In order for it to rise, the upward forces on it, provided by the chemicals pushing it up, exceeded the rocket’s weight, allowing it to accelerate upward and move into the sky. When it hits the ground, it is at rest, meaning gravity’s downward force on it is then balanced by the ground supporting it.”


You look over at Einstein, who is ready, “A good summary, and you are correct about the chemical propulsion. But that line you see there on the ground contains copper wires which transfer electrical energy from a battery there, to the igniter, over there, which heats up and starts the chemical reaction. I agree with your idea of propulsion, but as usual, I will have to disagree on the gravity explanation. Before the rocket lifts off, it is being supported by the ground (and the same after it lands). This means that it is being pushed upwards, just as we discussed last time. This also means it is accelerating before it is launched. The difference is, upon ignition, the chemicals give it an even greater acceleration, allowing it to move into the sky. The falling is slowed by what we call a parachute, which indeed catches the air. This air pushes up on the parachute, causing the rocket to move away from its geodesic (think freefall motion here), slowing it down compared to the rate at which it would fall if the parachute were not present.”


You think about this explanation. Then a thought hits you, “Professor Einstein,” you begin, “if the ground is the object that is accelerating upwards toward the rocket, then how can air keep the rocket from hitting the ground as fast? I mean, if the ground isn’t changing its accelerated rate, then, wouldn’t the rocket hit at the same rate either way?”


Einstein smiles, “Now I’ve got you thinking!” He chuckles a bit, then, “But the air still has the last laugh. How do you think the air is moving? Is it following its geodesic (down toward the center of the Earth), or has it been influenced by the Earth below it?”


He pauses, waiting for your eyes to show your comprehension, then continues, “Indeed, it too is accelerating upward and has an effect on the parachute, which slows the rate of descent of the rocket, just as I said before.”


Newton looks over to Einstein, “It is fascinating, this Relativity theory of yours. I’d like to hear more about it.”


Just then, your alarm goes off. It’s time to return them to their respective centuries and locations. You respectfully interrupt their conversation and lead them to the time machine. As they walk, the last dewdrop hanging from a raspberry leaf catches everyone’s eye with a glimmer of colors. Newton smiles, knowing exactly where the colors come from. Einstein smiles too, thinking about different energies of photons. You smile because rainbows always make you smile.


Komentarze


bottom of page