Inertia Equals Gravity

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Much of modern physics is more tenuous than generally realised. Forces that can only be explained by imperfect analogies and crude models hold the world of the very small and very large together. Invariably, this means a distorted understanding of the thing being examined. Gravity is the least understood of the fundamental forces, which must mean that our model of it is most deficient, and that allows for a bit of 'tweaking' in order to get things right... or at least somewhat righter. Centrifugal force is a good place to start.

Centrifugal Force or Inertia

Megan is riding in a roller coaster car as it ascends one of its peaks. It's a good thing that she is securely locked in her seat, for as the car rounds the top and starts downward, she feels herself being lifted from the car, and only the safety restraint prevents her from becoming airborne. Besides momentarily feeling weightless, she is firmly pressed upward against the restraint.

If asked to explain what is the cause of her sensations, some people will say it is centrifugal force, but if someone blamed it on inertia, they would be just as, if not more, correct.

Let's consider a situation where the roller coaster is going in a straight line with some fair amount of speed. If the car she is riding in suddenly stops, she would be thrown forward, and it would be obvious to anyone that inertia was the cause.

Sir Isaac Newton's first law of motion states that a body in motion (Megan) will continue in that same motion unless acted upon by some force (deceleration) to either stop it, slow it, or change its direction. The First Law is a statement about inertia, and is directly applicable to Megan's situation in the roller coaster.

As the roller coaster tops a crest and begins to change direction from up to down, the car's passengers are also being forced to change direction from their straight-line travel, which would be a tangent to the rounded peak of the track support. At this point, Newton's first law 'kicks in', and they feel inertia.

Inertia Masquerading as Centrifugal Force

When it results from circular motion, inertia is called centrifugal force. Here, the roller coaster crest is only a section of a circle, but the same forces are fully at work until the track stops curving. Centrifugal force is considered a fictitious, or pseudo, force because it has no existence apart from inertia, and is only a convenient expression when the context is a rotating frame of reference.

According to Newton's third law of motion, forces are always produced in pairs with opposite directions and equal magnitudes. Most persons are more familiar with the Law stated as, 'every action has an equal and opposite reaction'.

When a breaking action is applied to a roller coaster, for example, the cars and their occupants react involuntarily by straining to continue going in the direction they had been travelling. One force, the breaking action, pulls to the rear while another force (inertia) reacts by pulling everything forward with an equal effort.

A slight problem becomes evident here because inertia, apparently not having any object as its source, is not considered a force at all, but rather just a 'tendency to obey Newton's laws'. Force is said to be a push or a pull exerted by one object against another object, so inertia cannot be a force by such a criterion. This uncertainty reflects the broader fact that science hasn't a clue as to where inertia comes from. Much the same can be said for gravity.

One Mysterious Force is Enough

Is it justifiable then, to speak of inertia as one of the pair of forces acting on a body? Newton spoke of forces in a real sense - not as abstract reactions. If it is said that one of his pair of forces is 'just the tendency to obey Newton's laws', the resulting circularity casts his third law into incoherence. To deny that inertia is one of the paired forces, would require the creation of yet another mysterious and unknown force to stand in its place.

If a man in a rowboat pushes with his hand against an ocean liner, the inertia of the liner conveys an equal force back against the man's hand, and forces him and his boat backwards. There is just no way to say that this reacting force is something other than the inertia of the much larger boat. The dilemma about whether to muck up the Third Law by denying to inertia the status of a force, and having to rely on some other mysterious force can be avoided by accepting inertia as a real force whose origin has yet to be discovered.

Like Two Evenly Matched Opponents

As the Moon revolves around the Earth, gravity provides a centripetal (centre-seeking) force causing it to curve away from what would be its normal straight-line path, resulting in an orbit. Circular motion puts the Moon in a constant state of acceleration1 directed toward the orbit's centre. Acceleration always produces inertia, and as stated earlier, inertia is called centrifugal force for a body in circular motion.

The centrifugal force (centre-fleeing force) affecting the Moon is equal in magnitude, and opposite in direction, from the centre-seeking force, gravity, just as required by the third law of motion when it speaks of action and reaction. It is gravity and inertia that are acting and reacting on each other - the centre-seeking force against the centre-fleeing force.

Galileo astounded his contemporaries by demonstrating that all objects fall to earth at the same rate regardless of their weight. The reason was that gravity and inertia are always working simultaneously against each other, and in proportion to an object's mass. Why this proportionality exists is one of the deep mysteries of physics, and points to a profound connection between the two forces.

What Really Excited Einstein

Einstein reinforced the relationship between gravity and inertia by declaring their equivalence. In his mind at least, they were the same force. Einstein made this point in 1921 when he lectured on relativity at Princeton University. 'The possibility,' he said, 'of explaining the numerical equality of inertia and gravitation by the unity of their nature gives to the general theory of relativity, according to my conviction, such a superiority over the conceptions of classical mechanics, that all the difficulties encountered must be considered as small in comparison2.'

Gravity Equals Centrifugal Force

Without the benefit of Einstein's intuition, it would still be only a small leap to make the assumption that gravity and inertia are somehow the same, and see where things may lead. First off, centrifugal force must then also be considered a gravitational force. Centrifugal force = inertia = gravity. To see how such a 'trick' might be accomplished, consider again, the Moon revolving around the Earth.

Centrifugal force is pulling the Moon away from the Earths centre of gravity (fleeing from the centre). If it does, in fact, have the nature of a gravitational force, it must also be a centre-seeking force, because that is what defines gravity. Even lacking a rotating frame of reference, gravity is always a centre-seeking force. Posing centrifugal force as a centre-seeking force suggests that it is acting to keep the Moon at the centre of its own gravitational field as Earths gravity tugs at it. That would mean two centre-seeking forces pulling on the Moon in opposite directions.

Turning Centrifugal Force Around

Here is the picture: the Moon is accelerating toward the Earth. The Moon's gravity field is experiencing a drag against space (more about this later) that causes the field to be swept back from the Moon, making it (the field) roughly egg-shaped instead of round. Consequently, the Moon finds itself slightly displaced, in the direction of Earth, from the centre of its now elliptical field. In other words, the Moon has been skewed from its natural resting position at the centre of its gravity field. This immediately sets up a counteracting, centre-seeking force - no longer to be mistaken for a fictitious centre-fleeing force - working to pull the Moon back into its fields centre, and re-establish the symmetry of a spherical mass at the centre of a spherical field.

Is it centrifugal force, inertia, or gravity which is represented by the centre-seeking force? Apparently, it's all three because of 'the unity of their nature'. Depending on an observer's perspective, the function being observed will determine which label is applied.

Drag is Key

The likely assumption that gravity and inertia are an identical force has allowed a chain of reasoning showing how this unification of forces may come about. The weakest link in this scenario has to be the purported drag of a gravity field against space to produce inertia - a truly fantastic proposition... Or is it?

As it happens, theoretical physics has postulated something called a Higgs Field to account for mass in the universe. This field, and its associated particle, the Higgs boson, is considered essential to completing the Standard Model of particle physics. According to the theory, particles having mass would be surrounded by a condensate, or 'clustering', of the Higgs field in their vicinity. The clustering would create a drag for any particle moving through the Higgs field. This drag is apparently triggered only by acceleration, since everything moves smoothly through space without any resistance, as long as it is in uniform motion.

The Higgs field exists as a well of energy permeating all of space and interacting by a sort of frictional, or viscous, force with particles. The greater the friction experienced by a given particle, the higher its mass. The friction can also be thought of as the cause of the inertia of massive bodies.
- James Glanz, 'Particle Physics Braces for the Next Big Thing', The New York Times, Tuesday 21 November, 2000

Time Out for Substitution

The theory quoted above, borrowed from a science article in The New York Times, supplies just the mechanism needed to explain why the gravitational field of the Moon, or any massive objects, could be swept back as it drags against space. One needs only to substitute 'gravitational field' for the 'clustering' of space energy that the Higgs theory speaks of, and the centre-seeking force becomes the only force needed to explain the action called gravity, and the reaction called inertia.

Stated more specifically, the centre-seeking force is called gravity when it seeks to draw an object into a gravity fields centre. It is called inertia when it seeks to retain a gravity field's source-object within its fields centre while an external force is acting on that object.

Both processes are simultaneously at work on any falling object, creating a balance that causes all objects to fall at the same rate. The proportionality of gravitational and inertial mass no longer needs to be considered 'just a very unlikely coincidence'.

What Would Sir Isaac Think?

Science progresses by unifying forces and making connections between what had seemed like unrelated elements. The concept of a centre-seeking force acting in concert with a cosmic drag becomes the mechanism which finally clarifies centrifugal force, exposes the source of inertia, and unifies both forces with gravity.

Because this 'Higgs mechanism'3 is derived from the Higgs field which is predicted by quantum mechanics, it establishes the elusive connection between gravity and the Standard Model of particle physics4. Now, almost too meagre to mention, it also removes the uncertainty about the nature of the reacting force in Newton's third law by confirming it to be inertia, a force at least as real as gravity.

Just how acceptable is all this speculation about equivalence, cosmic drag, and upside-down centrifugal force? It does seem to tie up a lot of loose ends, and as they say in the 'trade', 'anything that isn't prohibited, is allowed'... but, does Megan really care?

Related BBC Links

1 Gravity causes the Moon to fall along a trajectory that never allows it to strike the Earth. Its path merely follows the Earth's curvature resulting in an orbit. Because it is constantly falling, it is always in a state of acceleration toward the Earth's approximate centre.2Martin Gardner, The Relativity Explosion, New York: Vintage Books, 1976, p. 833 The construction and meaning of the Higgs mechanism remains unsettled in conventional physics.4 The inability to integrate gravity with quantum mechanics is considered indicative of a serious flaw in either the Standard Model or General Relativity. Finding a way to join the two theories is a major goal of physics.

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