Philosophers have searched since the beginning of time why a moving mass continues moving.

Aristotle claimed that it is in the nature of matter.
Newton said that it is because no force caused the matter's state of uniform motion to change.
Einstein asked Is the matter moving forward or the whole universe backwards?

I claim that it is due to the whole universe all the galaxies with all their stars, atomic hydrogen and molecular hydrogen, black holes, dark matter, dark energy, the sun, the moon all the planets, the interstellar dust and photons in all their wavelengths, neutrinos, bosons, leptons the earth and everyone on it where pushing the little particle in a straight line.

The whole universe is bound together and every acceleration here is felt by every other mass in the whole universe.

Einstein seemed to like Mach's principle but still said that inertia originates in a kind of interaction between bodies.
(Wikipedia describing Einsteins view of inertia recuperated the 18/02/2009)

Now when I was small my parents told me never to use "kind of". "Kind of" is what people use when they do not really know what they are talking about.

Now most scientists agree with Mach's principle but few have a simple explication of how it works.

Ok it does not agree too much with Einstein, Newton or Aristotle and it also has absolutely nothing to do with the string theory but still but it is simple, clear cut and straight forward.

One simple equation answers the age old question.

It can be shown that the force of one accelerating mass on another is ;

F_acc=-G/c^2*M*m/r*a^2
G is the the gravitational constant
c the speed of light
M a distant mass
m the mass before us
and a the acceleration of mass m

This is the basis of a consistent theory that takes Mach's principle on its face value.

This equation describes force of an accelerating mass on all other mass due to the acceleration and is what is responsible for inertia.

If we plug in some values we will see that the force in normal circumstances is virtually zero.

Example. if a car (5e3kg) braked suddenly and had an acceleration of 50m/s^2 backwards a car just at its side (at .1 m) would have a forward force of

f=G*M*m/r/c^2*a
=6.7e-11*5e3*5e3/.1/3e8/3e8*50

or about

1e-17 N

This force is virtually nothing.

But , if we add up all the forces from all the masses in the whole entire universe we get

m*sum(G*M(i)/r(i))/c^2 which would be exactly

m*a=5e3*50
=2.5 e5 N

The first thing to note is the equation has a 1/r and not a 1/r^2.As in general we will assume that the density is about equal in the whole universe far away masses will have a much larger effect than those near by. In order to understand this better one could look up any good explication of Olber's paradox which applies if effect = 1/r^2.

If we now consider the acceleration of a mass m there will be an equal and opposite force due to all the forces in the whole universe .

The sum of these forces is

f= m*integrate(G/c^2*(4*%pi*Density_Universe*r^2)/r,r,0,Radius_Of_Universe)*a

Taking

Radius of universe as 7e26m

and Density of universe as 9.9 e-27 kg/m^3

We get

G/c^2*integrate((4*%pi*Density_Universe*r^2)/r,r,0,Radius_Of_Universe)
==23

Using other values for the density and radius of the universe we get .78

The true value is exactly 1 so that

f=m*a

Thus

2*G/c^2*%pi*Density_Universe*Radius_Of_Universe^2==1

This gives us a correspondence between the radius of the universe and its density.

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Our equation is f=m*a as we chose our units that this would be so.

Thus Mach's inertia is not just a philosophical question but a real force that could be measured with extreme accelerations and very ,very accurate measurements.