Physics: Inertia - An Energy Poorly Understood

This post is drawn from six prior physics Papers by this author and focuses on the role of Inertia in the understanding of some issues which still baffle modern Physicists.

Inertia

(3596 words)

Paper 7

M.J. Bull 2016

Abstract

This Paper no.7 defines Inertia and examines some of its important roles in the understanding of the physics of the universe.

Contents:

1. Introduction

2. Inertia's Definition

3. The Quantum of Inertia

4. Inertia, Time and Distance

5. Inertia and Gravity

6. Table of Quantum values for the Energies and Motions.

Summary

The energy Inertia has an unrecognised importance in the study of physics and cosmology principally because the quantum of Inertia is in fact the Planck Constant. The Planck Constant is used throughout quantum physics and cosmology and is seen within many different and widely used equations covering a number of different aspects of physics. The Planck Constant is thereby the 'quantum of action' or the smallest possible amount of energy needed to cause an action upon a particle. The SI unit, the joule.second, is the unit of measure for the Planck Constant and that unit of measure is demonstrably a measure of Inertia. Some of the evidence and implications of that fact are studied within this short Paper.

1. Introduction

Inertia has not been properly or accurately defined in mainstream physics literature and texts to date. It is often given the same units of measure as mass, that is, kilograms in the SI system of measure.

Inertia has been redefined in Paper 1, section 1 by this author and the validity of this definition has been mathematically supported throughout subsequent Papers in the course of discussion of other physical quantities. For example, refer Paper 5, section 2, where inertia's relationship to time and distance is numerically proven using the quantum values for those quantities expressed in Space-Time (S-T) units of measure to maintain equivalence of measurement between all three quantities. (For further information on S-T measurement refer Paper1, Appendices)

2. Inertia's Definition

Inertia is seen by current mainstream physics as a kind of negative force which resists the force of acceleration applied to a mass, and is often measured as mass. Inertia is in fact an energy in its own right and quite different to mass. There is no distinction between mass and inertial mass. Mass is itself an energy unrelated to inertia.

This author's view of inertia is that it has a reciprocal relationship to acceleration, not to mass. The following is reproduced from Paper 1 for the reader's convenience:

“There does not appear to be any meaningful quantification of inertia in the current or past physics literature, however inertia is quantifiable from Newton's Laws of Motion. The relationship between acceleration caused by gravity or any acceleration, a, and inertia can be quantified mathematically from Newton's Second Law of Motion, F = ma, in combination with the Equivalence Principle, which establishes an invariable mathematical product between the two, given that different masses accelerate at the same rate in the same gravity field. Let the Greek lower case letter iota, ί, be assigned to inertia for algebraic purposes and avoid confusion with other quantities using I or i .

From Newton's second law of motion, F = ma, then a = F/m from which SI units a evidently has units Newtons per Kilogram, (N/kg in addition to the more commonly used m/sec²) . From the Equivalence Principle, a is proportional to ί , and that proportionality is mathematically a simple reciprocal relationship a = 1/ί and ί = 1/a . ί has the units kg / N. The following examples demonstrate the above relationship:

1. if a mass of 20 kg has an acceleration of a = 10 N/kg, from F = ma, the force is 200 N. As a = F/m, the inertia ί = m/F = 20/200 = 0.1 kg/N.                  a x ί = 1
2. if a mass of 15 kg has an acceleration of a = 10 N/kg, force is 150 N and the inertia ί = m/F = 15/150 = 0.1 kg/N.                                                            a x ί = 1
3. if a mass of 40 kg has an acceleration of a = 0.1 N/kg, the force is 4 N and the inertia, ί = m/F = 40/4 = 10 kg/N.                                                             a x ί = 1

The examples demonstrate that the lower the acceleration the higher the inertia and vice versa. The force per unit mass determines the acceleration, and the mass per unit force determines the inertia.

Regardless of mass, a ί = 1, which is why different masses accelerate at the same rate in the same gravitational field.

Scientific experiment has so far never been able to disprove this and it is called the Equivalence Principle.”

Inertia is defined as the mathematical reciprocal, or inverse, of acceleration.

From Newton's physics, acceleration is the rate of change of velocity, and force is the quantity of acceleration of an object according to its mass energy, (F = ma). Inertia is not a deceleration, it is an inverse of acceleration, a different concept entirely and a separate form of energy in its own right.

The general equation for the mathematical relationship of acceleration to inertia is a ί = 1

As mentioned above, acceleration can have as its measure in SI units both metres per second² or newtons per kilogram. Therefore inertia has the SI units seconds² per metre or kilograms per newton.

In S-T units of measure, acceleration has the unit S/T² , which is distance / time² and inertia the inverse, T²/S, which is time² / distance.

(Conversion from SI to S-T units is detailed in Paper 1, Appendix 2.)

3. The Quantum of Inertia

The quantum values of all the energies, motions and constants can be derived from the two fundamentals, both calculated by Max Planck in the early 20^th century, which are the quantum of distance and the quantum of time. Planck's quantum of distance (S_q) is 1.616199 x 10^-35 metres, and of time (T_q) is 5.391063 x 10^-44 seconds. All other quanta can be calculated from these fundamentals. The values obtained in the case of Motions, (S^x/T^y), can be expressed as SI units of measure directly as in metres per second. In the case of the Energies, (T^x/S^y), the values are expressed in S-T units of measure as the SI system does not have an equivalent expression for seconds per metre.

In the case of c, the speed of light constant, it is a motion and if S_q/T_q is calculated from the above quantities the result is exactly the value of c, i.e. 2.997924 x 10⁸, the value of light speed in free space calculated in the early 20^th century. All the other derived quanta can be calculated in the same way, including the quantum of Inertia, ί , which is an Energy, T_q²/S_q or sec²/metre. Its quantum value is 1.798 x 10^-52 sec²/metre. Planck calculated the Planck Constant, h, as 6.629 x 10 ^-34 Joule.sec.

An S-T equivalent unit for the quantum of inertia is, from the foregoing, sec²/metre and its value is 1.798 x 10^-52. The Planck Constant value in joule.sec is 6.629 x 10^-34 . They are the same quantum. The conversion factor from s²/m to J.sec is 3.687 x 10¹⁸. Multiplying 1.798 x 10^-52 by the conversion factor 3.687 x 10¹⁸ , the answer is 6.629 x 10 ^-34, the value of the Planck Constant in joule.seconds. From general observation, all of the conversion factors of the Energies from sec^x / metre^y to SI units are of the order of 10¹⁸ . [Note that the SI unit Joule.second is also that of inertia, T²/S. It is energy (joule) (T/S) x time (sec) (T) = T²/S.]

The Planck Constant, h, is in fact the quantum of Inertia.

This is not understood by most physics texts in general use today. The Planck Constant is used throughout physics and cosmology in the calculation of many different quantities and therefore the energy, inertia, is of major significance to much of physics, even though it is, to date, poorly recognised.

4. Inertia, Time and Distance

Inertia has a direct relationship to Time. That relationship demonstrates through quantum numerical values that this author's concept of inertia is the correct one.

The equation derived in Paper 1, section 2, being a Newtonian type equation for Time is

t = √ ( m s / F ) and is consistent between SI and S-T units of measurement. That equation can be further reduced to a simpler form involving distance (s) and inertia (ί) using Newton's second law of motion and the derivation of the correct unit of measure for inertia by this author.

because  t = √ ( ms/ F)

then       t² = ms/F

and        t² = ms/ma (because F= ma, Newton's 2^nd law of motion)

hence    t² = s/a (cancelling the m, (mass) from numerator and denominator above)

and       t² = s ί (because ί = 1/a, refer section 2. above)

then      ί = t²/s (re-arranging the previous line)

The original Newtonian equation says in English, time equals the square root of mass x distance divided by force, and is equivalent to the above derived equation inertia equals time squared divided by distance.

To check that this equation is correct, quantum values, _(q) , can be inserted for each algebraic symbol and calculations done to ensure that the result is numerically correct. All units of measure must be consistent and the quanta in space-time units of measure have been previously calculated in Paper 3, Table of Energies and Table of Motions, which is reproduced below.

In space time units, the above equation is written

ί _(q) = T_(q)² / S_(q)

        = 2.906356 x 10^-87 / 1.616199 x 10^-35

        = 1.798266 x 10^-52 sec²/metre

        = ί _(q) exactly as calculated for the quantum value of inertia.

The above algebra confirms the validity of the inertia S-T unit of measure as T²/S and the quantum values of distance S_(q) and time T_(q) calculated by Planck confirm the exact quantum value of Inertia.

5. Inertia and Gravity

In section 2. above it was demonstrated that acceleration and inertia are mathematically reciprocal to each other. Inertia is an Energy and acceleration is a Motion, which can be clearly seen in the Table of Motions and Energies below.

That same inverse relationship applies in a similar way to Mass and Gravity, where Mass (T³/S³) is an Energy and the Gravitational Field (S³/T³) is the reciprocal Motion. Refer to the Table below. Their product, as in the case of acceleration and inertia, is also unity. The relationship between gravity and acceleration is also not understood by most physics textbooks. The acceleration caused to an object having mass energy by the gravity field is designated as g and has the same S-T units as any other acceleration, (S/T²) . The Gravity Field, G, on the other hand, is reciprocal to Mass energy and has the S-T unit S³/T³, so that g and G are different entities. (Further details in Paper1.)

The Newtonian 2^nd Law of Motion is only half of the facts. It states, in cosmology that F = m x g. From the reciprocity of these quantities evident from the Table below, 1/F = 1/m x 1/g which is equivalent to 1/F = G ί. Inertia acts with the G field in a similar way that acceleration acts with mass.

Paper 4 deals with use of inertia to allow the calculation of the frequency and wavelength of the G-field, never before possible without an understanding of the true nature of the energy called inertia.

The following is an extract from Paper 4, demonstrating the role of Inertia with Gravity

“As far as is known by this author, there has not been published scientific consideration that the electric, magnetic and gravity fields (E-M-G fields) may have a frequency. The highest known electro-magnetic frequencies are associated with gamma radiation, which is of the order of 10²⁵ Hz. The current electro-magnetic spectrum physics texts do not look beyond gamma radiation.

The equations relevant are E = mc², E = hυ and υ = c/λ .

These equations are quantum and relativistic in their physics and sourced from the accepted work of Planck and Einstein. [where h is the Planck constant ; c is Speed of light constant ; υ (Greek letter upsilon) is the frequency ; λ (lambda) is the wavelength and ί (iota) is this author's symbol for inertia.] Also relevant is the reciprocity of an energy to its field (or motion) such as potential to kinetic energy or electric charge to electric current for example. Space-Time units of measure make that reciprocity clear.

The Space-Time (S-T) units of measure can be used to confirm the validity of the equations used to calculate the following Frequency Constants. The three fields compared are the electric (E) field, the magnetic (B) field and the gravity (G) field. (Note that the G field and acceleration g are different physical quantities.)

                            E field                                         B field                                              G field

Equations           1. E _field = 1/mc²                    2. B _field = 1/mc                              3. G _field = 1/m

                          4. E _field = 1/hυ                        5. B _field = c/hυ                               6. G _field = c²/hυ

S-T unit             1. s/t = (t³/s³ x s²/t²)^-1 = s/t        2. s²/t² = (t³/s³ x s/t)^-1 = s²/t²         3. s³/t³ = (t³/s³)^-1 = s³/t³ check                 4. s/t = (t²/s x 1/t)^-1 = s/t            5. s²/t² = s/t (t²/s x 1/t)^-1 = s²/t²   6. s³/t³ = s²/t² (t²/s x1/t)^-1 = s³/t³

All six equations above correlate with the S-T units below them, indicating they are correct and equivalent. (for details on S-T units refer Appendix 1 and 2 of Paper 1, “Mass, Gravity and Unity” by this author)

Substitute the values for h and c in the equations below,

E = 1/hυ = 1/6.629x10^-34 υ

B = c/hυ = 3x10⁸/6.629x10^-34 υ

G= c²/hυ = 9x10¹⁶/6.629x10^-34 υ

(where h is value of the Planck constant and c is Speed of light constant and υ is the frequency)

The algebra becomes

Eυ = 1.508 x10³³ = KE                   Bυ = 4.525 x10⁴¹ = KB                    Gυ = 1.357 x 10⁵⁰ = KG

where K_E, K_B and K_G are constants.

(Because, for example, from Gυ = c²/h, Gυ is constant because c and h are themselves constants.)

3. The G-field of varying Frequency and Wavelength

The above constants (K_{E, B and G}) allow the calculation of the frequency and wavelength of, for example, the gravitational fields of the Earth, the Sun and a hypothetical Black Hole, which vary with the gravitational field strength.

Frequency and Wavelength calculations, (given ί =1/g, λ= c/υ, and υ _{G earth} means frequency of the G-field of earth, and g is the acceleration of mass caused by gravity)

Earth

Frequency υ _{G earth} = K_G /g _earth = 1.357x 10⁵⁰ / 9.8 = 1.384x10⁴⁹ Hertz

Wavelength λ _{G earth} = c/υ _{G earth} = 4.613 x10 ^-40 metres

Sun

Frequency υ _{G sun} = K_G /g _sun = 1.357x10⁵⁰ / 274 = 4.952x10⁴⁷ Hertz

Wavelength λ _{G sun} = c/υ _{G sun} = 6.058x10^-39 metres

Black Hole (of mass 10,000 times the Sun)

Frequency υ _{G black hole} = K_G / g _{black hole} = 1.357 x 10⁵⁰ / 2,740,000 = 4.952 x 10⁴³ Hertz

Wavelength λ _{G black hole} = c/ υ _{G black hole} = 6.058 x 10^-36 metres.

[ This wavelength approaches the quantum of length, 1.616 x10^-35 metres. A marginally more massive black hole would exhibit a gravitational wavelength longer that the quantum of length and gravitational waves would theoretically be detectable. A detection was recently claimed (in 2016) from the study of a binary Black Hole system of very large mass using a laser interferometer. The claimed result is consistent with these mathematics of frequency and wavelength calculation, although there is still a (perhaps unfounded) view in mainstream science that gravity waves are a much longer wavelength.]

(Note that the G field interacts with inertia in a similar way that mass interacts with acceleration, g, which is the basis of the above equations using K_G /g to determine υ and λ. F = m g and 1/F = G ί.

Logic of the Mathematics above and the relevance of Inertia, ί.

υ _{G earth} = K_G ί _earth , (as ί = 1/g,) and ί _earth = 1/9.8 = 0.102041 kg/N, which is why the frequency of G varies between the Earth and the Sun, because of the different inertia values. (ί _sun = 0.003650 kg/N).

A maths validity check of these equations is υ = c/λ, so c = υλ  and the equations approximate              3 x 10⁸ = c.

Light speed in the sun's G-field is 3.385 m/sec slower than in the earth's G-field, (c _earth – c _sun)

and slower in the earth's G-field than in free space. Light speed in the vicinity of the black hole is 1000 m/sec slower than in the vicinity of the sun. Both are very small variations when it is considered that light speed in free space is nearly 300 million m/sec.

The foregoing mathematics and associated supporting references allow the following conclusions and proposals:-

Conclusions

1. The G-field has a variable frequency and a wavelength shorter than the Planck length (quantum of distance) in our section of the cosmos . This may be why gravity waves are so difficult to detect. They exhibit a wavelength greater than the Planck length in areas of extremely high mass, such as near the centre of the galaxy or near 'black holes'.
2. The Sun has a less energetic G field than the Earth, and a higher mass energy, (and vice versa.) The difference in mass is obvious, but the difference in G field strength is somewhat counter-intuitive. The G-field and mass energy are mathematically reciprocal, and are different forms of the same energy, hence regions of high mass (such as a galaxy) have a lower Gravity field strength than a region of 'empty' space. The above mathematics support that view. That may explain why the universe is not homogeneous, mass energy and the G-field energy are interchangeable. (Gravity field strength, G, and acceleration of mass, g, are different quantities.)
3. The speed of light is faster in a higher energy G-field than in a lower energy G-field. Observation and the above mathematics of G-field frequency suggest that a light ray diffracted by a large mass's gravity field is diffracted because the large mass has a lower energy G-field than does free space. The light ray is bent because it is slowed, just as it is when it is slowed by the glass of a prism when moving from air to glass.
4. The G-field appears to act as the medium of light wave transmission which the hypothesised “aether” was expected to for light waves in Michelson and Morley's time, and which they failed to detect. Modern science has still failed to recognise it, but the mathematics suggest the “aether's” modern name may be the G-field.
5. The large (and invisible) G-field energy, which is at its highest energy and frequency in 'empty' space, is a good candidate for being the elusive 'dark energy' which modern science has calculated exists, but has also failed to detect.”

The above extract clearly exemplifies the advances to be made in cosmology with an accurate understanding of inertia and its role in the cosmos with respect to the gravity field.

Motions and Energies Quantum Values M.J. Bull 2015

Table of Motions                                                                                       Contraction of Space

S4/T4 m4/s4 c4 = 8.077596x 1034	S4/T3 m4/s3 sc3 4.354684x 10-9	S4/T2 m4/s2 s2c2 2.347635x 10-53	S4/T m4/s s3c 1.265625x 10-96	S4 ? 6.823062x 10-140 m4	↑ S4
S3/T4 m3/s4 c3/t 4.997898x 1069	S3/T3 mass current (gravity) c3 = m3/sec3 = 2.694398x 1025	S3/T2 m3/s2 sc2 1.452565x 10-18	S3/T m3/s (cumecs) s2c 7.830923x 10-62	S3 volume 4.221672x 10-105 m3	S3
S2/T4 m2/s4 c2/t2 3.092377x 10104	S2/T3 m2/s3 c2/t 1.667120x 1061	S2/T2 magnetic current c2 = m2/sec2 = 8.957548x 1016	S2/T m2/s sc (= Gί = 1/F ) 4.845242x 10-27	S2 area 2.612099x 10-70 m2	S2
S/T4 ? c/t3 = 1.914383x 10138 m/s4	S/T3 change of acceleration Δa c/t2 = 1.031505x 1095 m/s3	S/T2 acceleration, Δv c/t = 5.560912 x 1053 m/s2	S/T velocity electric current c = m/sec = 2.997924x108 m/s	S length electric charge Q capacitance C Sq = 1.616199x 10-35 m Quantum of length	S1
1/T4 ? 1.183866x 10174 ←	1/T3 ? 6.385696x 10129 Expansion	1/T2 ? 3.440734x 1087 of Time	1/T frequency (Hz) 1.854921x 1043	Minimum Values MOTION Maximum Values	S0
← T - 4	T - 3	T - 2	T - 1	T0	O

Table of Energies

O	T0	T1	T2	T3	T4 →
S0	Maximum Values ENERGY Minimum Values	T time (sec) Tq = 5.391063x 10-44 Quantum of time	T2 Contraction 2.906356x 10-87	T3 of Time 1.566833x 10-131	T4 → 8.446895x 10-175
S-1	1/S power 6.187356x 1034	T/S potential energy electric energy sec/m 1/c =3.335643x 10-9	T2/S inertia ί t/c = s2/m 1.798266 x 10-52	T3/S moment of inertia t2/c = s3/m 9.694554x 10-97	T4/S ? t3/c 5.226395x 10-140
S-2	1/S2 ? 3.828338x 1071	T/S2 force, electric potential V 1/cs = sec/m2 2.063880x 1026	T2/S2 momentum magnetic energy sec2/m2 electric resistivity σ 1/c2 = 1.12265x 10-17	T3/S2 ? t/c2 5.998367x 10-62	T4/S2 ? t2/c2 3.233758x 10-105
S-3	1/S3 ? 2.368729x 10106	T/S3 elect field intensity E 1/cs2 = sec/m3 1.276998x 1061	T2/S3 electric resistance R magnetic potential 1/c2s 6.884371x 1017	T3/S3 mass energy quantum = 1/c3 sec3/m3 3.711404x 10-26	T4/S3 ? t/c3 2.000841x 10-70
S-4 ↓	1/S4 ? 1.465617x 10141	T/S4 pressure (sec/m4) (1/cs3 = force/m2, energy/ m3) 7.890828x 1095	T2/S4 magnetic intensity H 1/c2s2 4.253995x 1052	T3/S4 mag resistance μ 1/c3s 2.296378x 108	T4/S4 ? 1/c4 1.237992x 10-35

                Expansion of Space