Origin of Newton’s Law of Inertia

June 21st, 2009 by Milo Wolff

and Geoff Haselhurst

This article has been written for special edition of GED (Galilean Electrodynamics)

Introduction

Inertia is experienced by everyone when, for example, we move, turn a corner, spin on a piano stool, or throw a stone. To produce an acceleration of massive objects by applying a moving force, energy is required. But what happens to the energy? The mechanism of this energy transfer has been elusive. Both Galileo and Newton commented on this mysterious fact. Newton recognized that the distant planets-stars were involved but he could not understand how. He wrote:

Anyone who believes that energy can travel instantly to the planets and back is a fool.

The physical origin of inertia could not be known without the introduction of the quantum Wave Structure of Matter (WSM) that replaces the ancient notion of matter as discrete “particles”. They do not exist. This is because inertia and other phenomena, especially gravity and spin, are entirely quantum wave behavior. Waves and their quantum space medium is the key to explaining their origins (See Wolff, 1995).

The origin lies in the behavior of the quantum space that is the medium of energy transfer. Understanding inertia begins with the wave structure of the electron, involves the philosophy of Ernst Mach, and requires a calculation of the entire Hubble Universe. The calculation of inertia below will predict Einstein’s General Relativity - in a simple form that everyone can understand (See Wolff, 1990).

1. The paradox of Inertia

Newton’s Paradox and quantum space

Newton first published inertia in Philosophiae Naturalis Principia Mathematica (1687) as three laws of motion. Galileo introduced the inertia concept about 1605, before Newton. Newton's Laws of Motion are the branch of physics now termed classical mechanics that begins with the equation $F = ma$ . It concerns the energy transferred by the force F when mass m is given acceleration a. This is often regarded as the beginning of modern physics. But no one knew what produces this equation, a basic natural law.

Newton saw inertia as an action-at-a-distance paradox because he expected that a distant planetary body (visible as a star) was the recipient of the inertial energy transfer. At that time he could not know the energy transfer role of quantum space - the wave medium of the WSM; it was unknown in his time. This difficulty of Newton, and much of the physics community today, is illustrated by the words of Sir Oliver Lodge:

A fish probably cannot understand the existence of water; he is too deeply immersed in it.

The Universe and all scientists – everyone, everything - are totally immersed in quantum space, the medium of energy transfer.

Mach’s Principle

Ernst Mach (1883) stated that inertia was caused by the fixed stars. This was regarded as a paradox too, despite its obvious truth. He asserted:

Every local inertial frame is determined by the composite matter of the universe.

His deduction arose from two different methods of measuring rotation. First, without looking at the sky one can measure the centrifugal force on a rotating mass m and use the inertia law $F = ma = \frac{mv^{2}}{r}$ to find circumferential speed v, as in a gyroscope. The second method is to compare the object’s angular position with the fixed (distant) stars. Surprisingly, both measurements give the same result. Thus he concluded that the inertia law depends on the fixed stars.

Quantum space to the rescue

Both Principle I and Principle II of the WSM (See preceding articles in this journal) completely describe the quantum-space wave medium of the Universe. The paradoxes are resolved because the energy-transfer mechanism of inertia is a property of space. The $F=ma$ Law occurs because an accelerated particle m, exchanges energy with Space in proportion to acceleration a. Mach’s observation is true because Principle II of the WSM establishes the density of space as proportional to the sum of the waves from all observable matter in the Hubble universe. Thus the energy exchange with space ‘appeared’ to Galileo, to Newton and Mach as an exchange with the distant masses in all space. Einstein’s General Relativity calculates motion due to energy transfer on an astronomical scale.

2. History of motion

Prior to Galileo, the generally accepted theory of motion was proposed by Aristotle (about 335 BC to 322 BC), which stated that in the absence of an external motive force, all objects would naturally come to rest, and that moving objects only move so long as there is a power inducing them. Aristotle's concept of motion was believed for nearly two millennia.

The Aristotelian concept of motion became increasingly dubious in the face of the conclusions of Nicolaus Copernicus in the 16th century, who argued that the Earth was never "at rest", but was in constant motion around the sun. Galileo, using the Copernican model, restated Aristotle's motion as a principle:

A body moving on a level surface will continue in the same direction at a constant speed unless disturbed.

Galileo later concluded, based on his principle, that it is impossible to distinguish between a moving and a stationary object without an outside reference to compare them. This became the Einstein’s basis for the theory of Special Relativity.

Nevertheless, despite defining the concept so elegantly in his laws of motion, even Newton did not actually use the term "inertia" to refer to his First Law. In fact, Newton originally viewed the phenomenon he described in his First Law of Motion as being caused by "innate forces" inherent in matter, which resisted any acceleration. Given this perspective, and borrowing from Kepler, Newton attributed the term "inertia" to mean "the innate force possessed by an object which resists changes in motion"; thus Newton defined "inertia" to mean the cause of the phenomenon, rather than the phenomenon itself. However, Newton's original ideas of "innate resistive force" were problematic, and thus most physicists no longer think in these terms. As no alternate mechanism has been accepted, the term "inertia" has come to mean simply the phenomenon itself, rather than an inherent mechanism. Thus, "inertia" in modern classical physics has come to be a name for the same phenomenon described by Newton's First Law of Motion.

Relativistic motion

Albert Einstein's theory of Special Relativity (1905) "On the Electrodynamics of Moving Bodies," was built on the inertia of Galileo and Newton. Einstein's inertia concept in his later General Relativity (1916) provided a unified theory unchanged from Newton's original inertia. However, this limited Special Relativity so that it only applied when reference frames were inertial meaning that no acceleration was present. In his General Relativity Einstein found it necessary to redefine inertia and gravity, in terms of a new geodesic "curvature" of space-time, instead of the more traditional forces understood by Newton. The result is that according to General Relativity, if concerned with very large distances, the traditional Newtonian idea of "inertia" does not actually apply. Luckily, for sufficiently small regions of space-time, the Special Theory can still be used.

A profound conclusion of Special Relativity was that energy and mass are interchangeable, $E = mc^{2}$ . Thus if mass exhibits inertia, then inertia must also apply to energy as well.

3. Calculations

Shapes of the Universe

Einstein’s General Relativity calculates gravity and inertial forces by using a geometric model of the Universe where density changes with distance, measured by the Hubble constant H. The changes in space density cause space geometry to differ from Euclidean geometry. If the difference is zero, it is called a flat Universe. If it is flat, then the density is termed critical, that is, $d_{c} = \frac{3 H^{2}}{8 \pi G}$ , where G is the gravity constant. If the density change is positive or negative, it is termed a spherical or hyperbolic Universe. These shapes of the Universe have, until recently, been entirely theoretical since no data existed to choose one or the other. Recent measurements by Bernardis (2000) show that the Universe is flat with a 10% possible error.

The complete General Relativity calculations are very complex because the complete geometry of a varying Universe requires a six dimensional algebra, 6D. However if the Universe is flat then the inertial energy transfers are simple. They can be calculated with 3D methods as follows:

Assume that accelerating matter in space creates an ‘acceleration field’. This is a calculation analogous to the electric acceleration field E_a that produces a force on an accelerated charge e. The analogy calculates a matter acceleration field M_a in space that produces a force F on a mass m with acceleration a. In this situation, energy is transferred between the mass and the surrounding space created by the Universe. The force F is an equal and opposite interaction between the mass m and the Universe. The acceleration changes the frequency of the matter waves by the Doppler effect. The resulting energy transfers to space and the accompanying force are local. Thus they appear almost instantaneous in agreement with astronomical observations and space missions and explain Newton’s paradox.

Accelerated mass interacts with the Universe: Define the two masses involved: One is m and the other is M_u, the mass of the Hubble universe, that creates the field. Since we know the $R= \frac{c}{H}$ we can find its average mass and its density. The density is given by the General Theory of Relativity as the critical density d_c of a ‘flat’ universe,

Formula 1: $\mbox{Critical density} = d_{c} = \dfrac{3 H^{2}}{8 \pi G}$

Acceleration causes a change of the mass’s wavelengths in quantum space. This wavelength change disturbs the local amplitude balance with waves from other matter in the universe. The Minimum Amplitude Principle (a form of Principle II) corrects the imbalance by moving the accelerated mass with respect to the space medium. This produces the forces.

Let’s calculate inertia

To compute inertia, find the force on the accelerated mass analogous to force on an accelerated charge (called radiation damping):

Formula 2: $\mbox{Electric Force} = e \times {\bf\sf E_{a}}\qquad ({\bf\sf E_{a}} = \mbox{electric field})$

In analogy,

Formula 3: $\mbox{Inertia force} = m \times {\bf\sf M_{a}}\qquad ({\bf\sf M_{a}} = \mbox{mass field})$

The E_a field of an accelerated charge e depends on the magnetic vector potential A:

Formula 4: $\mbox{Electric acceleration field} = {\bf\sf E_{a}} = \dfrac{\partial {\bf\sf A}}{\large \partial t} = \dfrac{(e)(\mbox{acceleration})}{4 \pi \varepsilon_{0} c^{2} r}$

Where r is the average distance to the matter sources of the space field.

For the analogous particle m, assume an analogous mass acceleration field:

Formula 5: $\mbox{Mass acceleration field} = {\bf\sf M_{a}} = \dfrac{m \: (\mbox{acceleration})\: G}{c^{2}\: r}$

Where the gravity constant G has replaced the electric constant $\frac{1}{4 \pi \varepsilon_{0}}$ .
This acceleration field M_a, due to acceleration of the mass m, acts upon the Universe. (More correctly it acts on the quantum space produced by the mass of the Universe)

The mass m_u of the Universe is

Formula 6: $m_{u} = (\mbox{density})(\mbox{volume}) = (d_{u})(\frac{4}{3} \pi R^{3})$

Where d_u is chosen equal to the density of a flat (critical) Universe $d_{u} = d_{c} = \frac{3 H^{2}}{8 \pi G}$ . Insert all relations into the force Equation:

Formula 7: $\mbox{Force} = m_{u} {\bf\sf M_{a}} = (\mbox{mass of Universe}) \times (\mbox{acceleration field}) = \\ \qquad = d_{c}(\frac{4}{3} \pi R^{3}) \times \dfrac{m a G}{c^{2} r} = \\ \qquad = \dfrac{3 H^{2}}{8 \pi G} \frac{4}{3} \pi R^{3} \times \dfrac{m a G}{c^{2} r}$

Where r is the average distance to the matter sources of the Universe that create the local space. This distance is taken as half of the Hubble distance $r = \frac{1}{2} \frac{c}{H} = \frac{c}{2H}$ . Then,

Formula 8: $\mbox{Force} = \dfrac{3 H^{2}}{8 \pi G} \dfrac{ \frac{4}{3} \pi R^{3} } \times \dfrac{m a G}{c^{2} \frac{c}{2H} }$

Inserting the radius of the Universe $= R= \frac{c}{H}$

Formula 9: $\mbox{Force} = F = \dfrac{3 H^{2}}{8 \pi G} \frac{4}{3} \pi (\frac{c}{H})^{3} \times \dfrac{m a G}{c^{2} \frac{c}{2H} }$

Surprisingly, every factor cancels in the equation leaving Newton's Law of inertia: $F=ma$ . This result confirms action-at-a-distance, shows that inertial mass equals gravitational mass as observed, and predicts a flat universe. It reaffirms Mach's Principle.

Summarizing, we have used Principle II (which yields Mach's principle) that the space medium is established by all masses of the Hubble Universe, and that the local space medium exchanges energy with any accelerated mass. As a result, we obtain Newton's Law and establish a mechanism for inertia.

Conclusions

Quantum space is the origin of Mach’s Principle and Inertia: Inertia exists because of the presence of the unseen space (the quantum-wave medium) around us and throughout the Universe. The density of this space is determined by waves from all the stars, galaxies and other mass in the Universe. In other words, the stars determine a frame of reference for rotational motion because the stars create the quantum space. So we see that Mach was really observing the presence of the quantum space around us, rather than the stars that produce it. There is no need to travel to the stars. For linear motion (The rock you threw across the river) space created by the stars, according to Principle II, is the frame of reference for acceleration.

It is important to realize that the quantum space is the heart of the Universe. It is the one thing that unites all of the Natural Laws, astronomy, cosmology, and our lives that are inter-connected with them. All that you need to know to find the complete origin of the laws of the Universe is the existence of quantum-space and its two properties: Principle I and Principle II. Nothing else.

References

P de Bernardis et al, Nature 404, 955 (2000).
Milo Wolff, Exploring the Physics of the Unknown Universe, Technotran Press (1990).
Ernst Mach (1883) German. English, The Science of Mechanics, (London, 1893).
Milo Wolff, Beyond the Point Particle – A Wave Structure for the Electron, Galilean Electrodynamics, Sept (1995).

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