What makes inertia

When v is removed from the integration in Equation 3 , the remaining expression to be computed turns out to be the computation that gives the scalar potential.

Consequently, in these circumstances we have:. Now we examine Equation 2 , taking it to be the gravito-electric force, to find out what force our test particle experiences. We note immediately that since is the same everywhere the test particle, by assumption, is too small to louse this up , vanishes. Since is what we normally think of as the origin of gravitational forces, we see that our normal intuition about gravity contributes nothing to inertia.

This means that if gravity is to account for inertia, it must be the vector potential part of the gravito-electric force that does the trick. To see if this will work all we have to do is put A from Equation 5 into Equation 2 and set equal to zero :. Since , being a constant, doesn't depend on time we can write:. Now when the test particle is moving with constant velocity E vanishes because is zero -- just as we expect should be true. But if an external force makes the test particle accelerate, then isn't zero and the distant matter in the universe produces a gravito-electric force on the particle that opposes the accelerating force.

If together with the other constant factors of order unity that we've ignored are just equal to one, then the gravito-electric field strength E is precisely the right strength to account for inertial reaction forces. If you go read Sciama's paper, you'll find that this also works for rotation and "centrifugal" forces. You may be wondering: Well, all of this is fine, but maybe we don't have to take the effects of gravito-magnetism and the vector potential seriously.

Perhaps they're so minute they can be ignored. Turns out that that's not true. As Ken Nordtvedt pointed out in [ International Journal of Theoretical Physics , 27 , ], gravito-magnetic effects must be taken into account in even the simplest planetary orbit calculations.

Only a moment's reflection is needed to see that this must be right. From Newtonian mechanics we know that the gravitational force acting on a planet must act along the instantaneous line of centers of the planet and the Sun if an elliptical orbit is to be recovered.

That is, the force exerted by the Sun must propagate to the planet instantaneously. This fact is the reason why Newtonian gravitation is called an "action-at-a-distance" force. Newton privately thought this preposterous; but he never found a way around it.

If relativity is right, then the gravito-electric field i. So, if the gravito-magnetic contribution to the total force weren't included, the force of the Sun on the Earth, for example, would point in the wrong direction and its orbit wouldn't be elliptical. Nordtvedt arrives at this conclusion by a variant of this argument. He shows that the motion of a test particle around the Sun is elliptical for an observer at rest with respect to the Sun. In this frame of reference the field is stationary and everywhere points toward the Sun at all times, so the force is always along the instantaneous line of centers.

If the observer moves with respect to the Sun [for example, with the planet], however, and doesn't take into account the gravito-magnetic vector potential, the predicted orbit "blows up". The observer at rest with respect to the Sun is effectively in the Coulomb gauge, and the one moving with the planet in the Lorentz gauge. I show this in, "Nordtvedt's Remarks on Gravitomagnetism" , in case you're interested. The formalism involved is no more daunting than that we've already used.

When Raine showed that Sciama's argument was true for all realistic universes in general relativity theory, the gravitational origin of inertial forces that is, Mach's principle ceased to be an area of active work for more than a decade.

Some subtleties attendant to Mach's principle, however, weren't fully appreciated and worked out in the s. They began to attract attention in the early s. Some of them are related to the business of transient mass fluctuations. So I'll tell you a bit about them. Be prepared. They're pretty weird. Problems arise when we ask how , in detail, inertial reaction forces are produced by the distant matter in the cosmos. The foregoing argument may leave you with the impression that the distant matter in the universe generates a vector potential field throughout space that acts on bodies immediately when external forces cause them to accelerate.

This notion is reinforced by the Image of the rigid relative motion of the universe invoked by Sciama to justify removing v from the calculation of the integral in computing the vector potential. All of this, however, is a bit misleading. The principle of relativity tells us that real physical influences that are involved in accelerations and the transfer of energy must propagate with finite speed -- namely, at or less than the speed of light. If all of the contributions to A that are responsible for any inertial reaction force an object experiences propagate at the speed of light, it would seem that the currents that generate A for any particular acceleration episode must have happened in the very distant past.

We are then left with the question: How did the stuff out there in the distant past know that we would try to accelerate, say, our car at any specific instant and, in the distant past, move in just the right way to launch the right A field in our direction? You may be inclined to think that this is some sort of trick question intended to set you up somehow.

It's actually a very serious, rather profound problem. Inertial reaction forces are instantaneous; there's no doubt whatsoever about that. When you push on something, it pushes back on you immediately. If they're caused chiefly by the most distant matter in the universe, how can that be? Relativity notwithstanding, the force really is propagated instantaneously.

The occurrence of so-called "non-local" interactions in quantum phenomena reported even in the popular press of late might make such a scheme seem plausible. Some sort of a local field, maybe not our A field, is really the cause of inertia. When you push on an object a gravitational disturbance goes propagating off into either the past or the future.

Out there in the past or future the disturbance makes the distant matter in the universe wiggle. The wiggling stuff out there makes up the currents that cause disturbances to propagate from the past or the future back to the object.

They all arrive from the past or future just in time to produce the inertial reaction force you feel. Given these choices, you may be inclined to think that number 2 must be the right answer. Although number 2 sounds pretty good, it turns out to be the least likely explanation of inertia.

I'll explain why after we look into the other explanations a bit. To explore them we'll need to know about something called "gauge invariance".

If you've had a course in electromagnetism, you'll probably recall that the equations for the electric and magnetic fields and the scalar and vector potentials, by themselves, aren't enough to let you calculate much of anything. The problem is that the field equations are so general that they aren't completely defined. In addition to the field equations you have to specify a choice of "gauge" within certain broad constraints if you want to actually do any calculations. In practice, two gauges are commonly used.

One is called the "Lorentz" gauge [after H. Lorentz who created much of this theory around the turn of the century]. In this gauge both of the potentials and both of the fields explicitly propagate at the speed of light. The other gauge is called the "Coulomb" or "radiation" gauge [after C. Coulomb because in this gauge the scalar potential propagates instantaneously, as does the force between electric charges at rest according to "Coulomb's law"].

You might think that we can solve our problem of instantaneous inertial reaction forces by simply choosing a Coulomb type gauge so that the gravito-electric field propagates instantaneously. The problem with this is that while the scalar potential propagates instantaneously in this gauge, the vector potential still propagates at the speed of light. And the part of the gravito-electric field that produces inertial reaction forces is the part that depends on the vector potential.

So this doesn't work when you get down to the nitty-gritty. It might seem to you, as a result, that we can kiss off simple instantaneous action explanations of inertia. Almost, but not quite. It has been forcefully argued in the past few years [notably by I.

Slide a book across a table and watch it slide to a rest position. The book in motion on the table top does not come to a rest position because of the absence of a force; rather it is the presence of a force - that force being the force of friction - that brings the book to a rest position.

In the absence of a force of friction, the book would continue in motion with the same speed and direction - forever! Or at least to the end of the table top.

A force is not required to keep a moving book in motion. In actuality, it is a force that brings the book to rest. All objects resist changes in their state of motion. All objects have this tendency - they have inertia. But do some objects have more of a tendency to resist changes than others? Absolutely yes! The tendency of an object to resist changes in its state of motion varies with mass. Mass is that quantity that is solely dependent upon the inertia of an object.

The more inertia that an object has, the more mass that it has. A more massive object has a greater tendency to resist changes in its state of motion. Suppose that there are two seemingly identical bricks at rest on the physics lecture table.

Yet one brick consists of mortar and the other brick consists of Styrofoam. Without lifting the bricks, how could you tell which brick was the Styrofoam brick? You could give the bricks an identical push in an effort to change their state of motion. The brick that offers the least resistance is the brick with the least inertia - and therefore the brick with the least mass i.

A common physics demonstration relies on this principle that the more massive the object, the more that object resist changes in its state of motion.

The demonstration goes as follows: several massive books are placed upon a teacher's head. A wooden board is placed on top of the books and a hammer is used to drive a nail into the board. Due to the large mass of the books, the force of the hammer is sufficiently resisted inertia. This is demonstrated by the fact that the teacher does not feel the hammer blow.

Of course, this story may explain many of the observations that you previously have made concerning your "weird physics teacher. The massive bricks resist the force and the hand is not hurt. Imagine a place in the cosmos far from all gravitational and frictional influences.

Suppose that you visit that place just suppose and throw a rock. The rock will. According to Newton's first law, the rock will continue in motion in the same direction at constant speed. How much net force is required to keep the object moving at this speed and in this direction? An object in motion will maintain its state of motion.

The presence of an unbalanced force changes the velocity of the object. Mac and Tosh are arguing in the cafeteria. As Newton's first law states "If the resultant force on a stationary object is 0N , the object will remain stationary. If the resultant force on a moving object is 0N it will carry on moving at the same velocity" same speed and direction, as velocity, is a vector, which has speed and direction. Therefore the cause of Inertia is Resistance, as Inertia is the resistance for any moving or stationary object to change its state of motion, or as again previously stated as "The tendency for motion to remain unchanged".

Force changes Inertia, as previously stated in Newton's first law if a resultant force is 0N , a stationary object will remain stationary, and a moving object will remain moving with the same velocity, but resistance actually causes it. Although there is an interesting forum here which goes against my point What is the cause of inertia? Mar 11,