Almost every pilot is taught, and may even believe, that the lift force must equal the force of gravity or weight in order to maintain flight. But if that was true, then aviation as we know it, wouldn’t be possible. Gravity is not a force in modern physics and its general relativity theory. And he thinks that is relevant for pilots.
Gravity is considered a force in Newtonian physics, which assumes time is constant and spacetime is flat. Since Albert Einstein published the theory of general relativity in 1915, we know that this assumption is not true.
Newtonian physics is still commonly taught and applied as it provides a reasonable approximation of reality where a straight line is a straight line, and a flat surface is flat. But neither is the case in the world of pilots.
A straight line from place A to place B is only a straight line on a chart. We cannot fly a straight line. In reality that straight line on the map is a geodesic or in other words, a curved line over the sphere of planet earth. That’s neither straight nor flat, and therefore Newtonian physics is not sufficiently accurate and consistent to understand the reality in which we fly. That is, if you care about reality. He does.
Gravity as the curvature of spacetime
Inertial frames of reference
In general relativity theory it is important to understand the concept of an “inertial frame of reference”. This is a reference frame with no acceleration in which Newton’s first law of motion holds. I.e no net force is exerted on an object within a reference frame. An object in space moves by inertia only and is then said to be in an inertial frame of reference.
If you as an observer are also moving by inertia only, then you are also in your own inertial reference frame. Any motion is relative to a specific reference frame. An object may be in motion relative to one frame, but at rest in relation to another. There is no absolute motion and no absolute rest.
To make this easier to grasp, imagine that you are jumping out of an aeroplane with a pen in one hand and a baseball in the other. When in freefall you will feel no weight. And when you let loose of the pen and the baseball, both will remain stationary relative to you. Relative to your frame of reference, the pen and baseball are at rest. Relative to someone who remained in the aeroplane both are in motion and so are you. He used to sky dive in the air force and can thus from first-hand experience confirm that this is true. Or better, real.
You might say: But if you jump out of an aeroplane you will fall to the ground together with your pen and baseball. In reality you don’t fall. We get later to why you will meet the ground. For now, remember that gravity is not a force, and therefore in “freefall” you are together with your pen and baseball in an inertial frame of reference with no acceleration.
Spacetime
Our humanly brains cannot really intuit spacetime. In essence it is the three dimensions of space with a fourth dimension of time. Important is that time is a dimension. We may be at rest in space, but not in time and every event occurs at a specific position in space and time.
Spacetime around large masses, such as the earth, is curved. That means, both space and time is curved. Yes, that is what it is. Time is curved too, which is referred to as time dilation. In the vicinity of a large mass, lines from A to B are no longer straight lines but geodesics, i.e. curved lines. Just like those along which pilots fly over earth. In the words of theoretical physicist John Wheeler “Matter tells spacetime how to curve, spacetime tells matter how to move.”
In general relativity theory, gravity is the curvature of spacetime. It is not a force that acts on an object, such as you jumping off an aeroplane. A gravitational field is the curved spacetime around a large mass in space.
Relativity of time
General relativity also states that the speed of light is constant in all frames of reference. That has an important implication on time. A straight line between two points is the shortest distance between these two points. The same applies to a geodesic along a curved line in curved spacetime. But the distance along a curved line is longer than the distance of a straight line through space. If the speed of light is constant, then time must vary between a straight line and a curved line. Consequently then, time in the vicinity of a large mass where spacetime is curved, flows slower than further away from that mass where it is less curved or straight.
That is a very important consequence to understand. Unlike in Newtonian physics, in general relativity theory, time is not a constant, and spacetime is not flat either. Time is relative to your frame of reference. Time flows faster further away from earth, and time flows slower in a moving reference frame relative to a stationary reference frame. That is an empirically verified fact, and a crucial part of the reality in which we live. Like it or don’t.
Combining it together
Imagine you and a fellow pilot start flying from the same latitude at the same altitude along two different longitudes straight north. You will both collide just over the north pole, without there being any external force applied which is moving you closer. You both fly a “straight” line, or geodesic along a curved surface.
That’s similar to what happens in curved spacetime. Spacetime geodesics define the deflection of light and the orbit of planets around the sun. Depending on the masses of a planet and the sun and their distance, spacetime is curved and that determines the motion of the two objects relative to one another. Path of motion means their different place in space due to time dilation. The exact same thing applies to any object in space, including you in “freefall”.
Let’s go back to that thought experiment again. As we now know, there is no force of gravity acting on you as you jump off that aeroplane. In “freefall” you are in your own inertial frame of reference, and in that reference frame there is no acceleration whatsoever. To be precise, you are not falling. But your future is on the ground, because of the curvature of the spacetime in which you are. If you had jumped off the plane further away from earth, then your future would be at a different place in space (may be still on the ground, may be not).
In essence then, in the perceived “freefall” in this thought experiment, you are merely on an inertial path to the center of the earth. So what happens then when we are on the ground?
Weight and lift
On the ground, you are no longer in your own inertial reference frame. You are part of earth’s frame of reference, and so is everything around you. Effectively, you are in a spaceship called earth.
What is important here, is that whilst there was no acceleration during your perceived “freefall”, there must be acceleration once you stand on the ground. If there wasn’t any acceleration you wouldn’t be able to stand at rest in space.
That is consistent with general relativity which states that: The second derivation of position relative to time, is equal to acceleration squared minus the curvature of spacetime multiplied by the velocity through time squared. That means that there must be acceleration to remain at rest in space. And that acceleration comes from a force exerted onto you by earth itself as you stand on it.
To understand this better, let’s extend the above thought experiment slightly. Imagine that you jump off that aeroplane in an upright position on top of a scale attached to your feet. Whilst you are in “freefall” the scale would show zero weight. It’s exactly the same as if you were in outer space. You are weightless. The only difference is that you are in curved spacetime and thus on an inertial path towards the center of earth.
But once you reach the ground, you will be in earth’s frame of reference, and at that moment that scale will indicate your weight. That means, now a force is exerted onto you by earth. There is no gravitational force pushing you on the scale! Consequently, weight is the force required to accelerate you out of your inertial path towards the center of earth.
And that is precisely why we need lift to fly. Lift force is required to enable us to fly along a geodesic of our choice as opposed to a geodesic determined by the curvature of spacetime. Because “spacetime tells matter how to move”.
Why it matters
Firstly, it matters because it is reality. The force of gravity is merely a perception or illusion. A good and competent pilot is conscious of many illusions which affect the performance and safety of flight. If these illusions matter, then so should those around the principles of flight itself.
Secondly, Newtonian physics works on the premise that time is constant. If you simply ignore the fact that time flows faster in the satellites in orbit compared to time on earth, you effectively render GPS navigation as useless. If the different time flows between satellite clocks and earth clocks wouldn’t be constantly corrected, the position error of the GPS system would exceed 11km within the first 24 hours of operation. That’s the error caused by time dilation.
And lastly, it is in general relativity where the speed of light is constant across all reference frames. Essential equipment in aviation from DME, radars, GNSS, satellite-based augmentation systems etc. all work on the principle of a constant speed of light. If it matters for all the handy stuff that makes flying safer and more efficient, well then it should matter for flight itself too.