Mach's Principle And Reference Frames

Mach's Principle, Inertia, Gravity And The Importance Of Frame Of Reference

By: John K. Harms

Abstract:

This text discusses the relationship of inertia, gravity and frame of reference from the point of view of Mach's Principle. It is proposed that the matter on the Earth is in a fundamentally different reference frame than the gravitational field itself. An accelerating object is viewed as constantly changing its reference frame. This suggests that gravitational fields as accelerated frames via Mach's principle are tied to the "fixed stars", an absolute reference frame for accelerated frames. Hence, gravitational fields are pictured as related to each other. The probable consequences of this idea are discussed.

Key Words: Mach's Principle, Inertia, Gravity, Reference Frame, Matter Distribution, Fixed Stars

Introduction

Ernst Mach proposed that the matter distribution in the Universe (the so-called fixed stars) is the universal fixed-frame of reference for all inertial effects. As Mach visualized inertia, the cumulative gravitational effects of this matter distribution on other material bodies was to cause all bodies to resist acceleration. This remains true whether the body is bending around in a circle (lateral acceleration) or accelerating positively or negatively in a straight line. This is known as (and named by Einstein) "Mach's Principle".

Einstein was very influenced by Mach's ideas and tried to incorporate his ideas into the general theory of relativity. Einstein was later dissatisfied that the general theory did not explain inertia and, in fact, it is not actually clear that Mach's Principle (despite Einstein's efforts) is incorporated at all into Einstein's theory. Indeed, the relationship between Einsteinian gravity and inertia is only a weak union at best. A more successful integration of gravity and inertia via Mach's Principle is the purpose of this discussion here.

The model proposed here is based upon the idea of reference frame and its relationship with gravity and inertia. Frame of reference is defined here as one's present-state of uniform motion in a straight line. As we will see, when there is an acceleration of a body, the object's frame of reference is constantly changing.

It is proposed in the author's other work that inertia is caused by a forward-shift of the gravitational radiation void of a body in its direction of motion. This previous model and the model proposed by this text can peacefully coexist without major difficulties. They are, therefore, not incompatible with each other. See the "Inertia" link below for further details.

Uniform Motion And Frame Of Reference

The uniform motion of a body can only be considered linear and uniform if both the moving body and an observer watching the moving body are in exactly an identical frame of reference. That is, both bodies must be moving with the same uniform velocity in a straight-line.

If they are not, then the two bodies (observer and body being observed) are in somewhat different reference frames. This being the case, the observer can never observe from his or her vantage point, the other body traveling in exactly a straight-line. Thus, unless the two bodies are in an identical frame of reference, the observer will always observe the other bodies path to be curved, a curvature of which depends upon the observer's relative frame.

Frame Of Reference And Gravity

It should be noted that this is exactly the situation that one always observes in a gravitational field. In a gravitational field, one observes that one can throw a stone into the air and it traces out a curved-parabolic path until it finally impacts the ground. Therefore, it must be the case that the observer and the stone are actually in two different frames of reference. How can this be so?

From an observer's frame of reference on the ground, a thrown stone in the air first goes up and then comes back down. It is as if the observer is in one frame of reference and is accelerating upward on the Earth to meet the stone, giving the appearance of a downward force on the stone. In fact, the Earth, in its accelerated reference frame "came-up" and collided with the stone when the stone left the Earth's reference frame. Hence, gravity may actually be the effect of the stone temporarily leaving the Earth's frame of reference.

The same is true of a stone which is dropped to the ground. When the stone is left to its own devices and let go from a distance above the Earth, it temporarily leaves the accelerated frame of reference of the Earth. Because the stone cannot accelerate on its own, it falls out-of its accelerated reference frame. The stone, therefore, obeys Newtonian laws of motion (the first law); it travels in uniform motion only, unless given an impulse or force.

Since the frame of reference of the Earth is accelerated, the stone falls out of the accelerated frame once it is let go (the stone, therefore, changes reference frames) and falls to the ground. From the Earth's accelerated frame of reference the stone appears to be accelerating toward it, but actually the stone is constantly slowing down its speed relative to the Earth's accelerated frame. Once the stone has hit the ground, it is jolted and speeds-up rejoining the Earth's accelerated frame of reference once again.

Given the author's gravity models, one can see the relationship:

Excess Incoming Photon Pressure From Space = The Constant Loss Of Velocity (From That Of The Accelerated Velocity) Of A Piece Of Matter Dropped From A Height Above The Earth = The Constant Acceleration Of All Bodies Equal To - 9.8 meters/sec^2.

See the "Gravitation" link for further information about gravity as photon pressure, the attraction of background photons to the radiation void of the Earth.

The Fixed Stars And Gravity

It is notable that when there is a shift in one's reference frame to a new frame, there must be an acceleration. Newton described this as a force (F = ma). This can be pictured here as:

Equation 1): A Changing Reference Frame = An Equivalent Force = A Mass x An Acceleration

A force, therefore, changes one's frame of reference as does an acceleration times one's own mass. These statements must indeed all be valid. A body in circular motion, therefore, must be constantly changing not only its velocity (it is constantly accelerating), but also its frame of reference. A body in circular motion, therefore, is constantly changing its frame of reference.

Newton noticed that accelerated motion appears to be absolute. He believed in absolute space. Newton demonstrated this with a bucket filled with water that, when quickly rotated over a period of time (and suspended from a rope), the water eventually moves in-unison with the bucket's rotation.

Hence, the motion of the bucket is transmitted to the water, which starts to spin. The water then feels a centrifugal force and begins to rise-up the side of the bucket. The water in the bucket bulges at its outer edges with less water (a dip) toward its center. After a while, the water and bucket spin together without any relative motion, and the water surface reaches its greatest curvature. Newton asked what was it that caused the water's surface to curve? Was it the water's motion relative to the side of the bucket or motion relative to Newtonian absolute space (Barbour, 2000)?

When the relative motion is greatest, at the start, there is no curvature of the water's surface, but when the relative motion has stopped (and water and bucket spin together) the curvature is greatest (Barbour, 2000). While Newton did realize that accelerated motion is absolute and needed a frame of reference (Newton thought all motion needed a frame of reference), he did not consider that only accelerated motion acted in this way. As we will see, accelerated motion is relative to all other massive bodies in the Universe--Mach's Principle.

Thus, a centrifugal force was acting on the water, which as Mach subsequently deduced was relative to the "fixed stars". Mach's revolutionary suggestion was that it is not space, but all the matter in the Universe, exerting a genuine physical effect, that creates centrifugal force (Barbour, 2000). The "fixed stars", therefore, was the absolute frame of reference (and not space) for acceleration and inertial effects.

A gravitational field is a field of constant acceleration. If acceleration is absolute with respect to the other matter in the Universe, so this must also apply to the Earth's gravitational field. Small bodies in the Earth's gravitational field are constantly accelerating toward the ground.

Where there is a curve of an object in a gravitational field, the reference frame of that object must be constantly changing as described above. This gives the appearance that a force (or a mass x an acceleration) as defined by Newton was responsible for the changing frame of reference.

One might ask the question: If the gravitational field of the Earth's reference frame is constantly changing, it is changing with respect to what? The answer is Mach's Principle as alluded to earlier. The constantly changing reference frame of the acceleration due to gravity of the Earth, is changing with respect to all the matter and its distribution in the Universe. Hence, gravity and inertia both must have the same absolute reference frame, that of the "fixed stars" as envisioned by Ernst Mach.

This suggests that all gravitational fields are somehow related to each other. But how can this be? My other works below might yield some answers to this question. That wormholes may connect all massive bodies in the Universe in hyperspace is suggested by the "Inflation" text. See the link below for further details.

Conclusion

This model leads to the following probable consequences:

1) Objects in circular motion are constantly changing their frames of references.

2) Since acceleration is absolute relative to the particles of matter and their distribution in the Universe, so are all gravitational fields. All gravitational fields are, therefore, related to and must affect each other.

This suggests an additional important question: What is the precise relationship (besides their obvious gravitational attractions) of all these pieces of matter in the Universe with each other? My other works below suggest some possible answers to this question--wormholes in hyperspace!