Copyright 2004 - 2013 David V Connell.

Key words :- Relativity principles, Relativity beliefs, Einstein, Time dilation, Transverse Doppler Effect, Local constants, Restricted motion, Natural Relativity.

    The Principle of Relativity has had many definitions over the years. Briefly, it means (at least, for the purpose herein), that the laws of physics should have the same form in all inertial systems [1], that speeds are always relative to a chosen frame of reference (FoR), (whereas relative velocity is that between two points, relative to a particular direction); masses, lengths and time units are relative to chosen standards of mass, length and time, respectively, in the chosen FoR, so that there are no absolute units for any of these items.
    In this article, the equivalence of mass and energy (E = Mc²) is assumed to be true (see Frames of Reference), this website), SR and GR refer to Einstein's Special and General Theories of Relativity, familiarity by the reader with the Lorentz/Einstein mass-velocity equation and frames of reference is assumed. Since it has been found that knowledge of the latter is often inadequate for the purposes herein, a separate (short) article on this subject is included (see Frames of Reference).
    The total energy of an object is defined as the sum of its apparent mass (potential energy), its kinetic energy and any other form of energy associated with the object.
    The fundamental principle of Conservation of Total Energy (CTE) ensures that when force is applied to an object such that energy is transferred, its relative speed and/or potential energy (mass) must change. When the mass of such an object (an atomic clock, say) is changed by the application of energy, the laws of physics dictate that its natural emitted frequencies of radiation and its size must also change. The relations between energy, mass, speed, gravity and those changes, is taken herein to be the Subject of Relativity.
    CTE also means that when an object is observed from different FoRs at the same instant, its total energy must be the same. That is, when no energy has been added, an object's total energy cannot have been changed by merely observing it. Therefore, when the observer has been accelerated relative to the object, in the observer's FoR the object is apparently moving, has kinetic energy and so must have a reduced (apparent) mass making up the same total energy. (e.g. Trees etc. seem to be moving when a person looks out of the window of a moving vehicle). For a more detailed discussion of this, see Frames of Reference.

    If an author has accepted any of the following beliefs as true in a theory, the prediction is that it will surely fail or come to false conclusions, such as requiring an aether or a preferred FoR etc., that do not comply with principles of relativity - because they are all wrong! The explanations of why they are wrong are given below.

    It is popularly believed that
1. relativistic effects are due to the velocity of an object (see also 11.),
2. moving objects cause distortions of Time and Space,
3. constants of proportionality in physics equations have the same value in all FoRs,
4. the SR mass-velocity equation is applicable to unrestricted inertial motion,
5. relativistic gains in mass occur in all FoRs, always,
6. the SR mass-velocity equation predicts a universal limiting velocity equal to the speed of
7. the limiting velocity found in experiments is a relativity phenomenon,
8. the Transverse Doppler Effect is caused by centrifugal force simulating gravity,
9. relativistic effects are not caused by acceleration,
10. all experimental evidence confirms SR, even at high relativistic speeds,
11. gravitational fields cause relativistic changes,
12. gravitational mass is the source of gravity,
13. gravitational mass and inertial mass are equivalent,
14. the Planck Units are useful absolute values.

    These beliefs are now examined with simple mathematics and common sense logic, rather than with complicated mathematics.

1. (Relativistic effects are due to the velocity of the object).
    This common belief is clearly due to Einstein's "relativity" equation being derived by considering the effects in an inertial FoR moving relative to a "stationary" (inertial) FoR [2].
    But, consider the following facts:-
a. The principle of CTE requires that, in its own FoR, energy applied to an object is adsorbed by that object, with or without resulting motion in external FoRs.
b. The equivalence of mass and energy is accepted, so applied energy can be adsorbed as mass. An increase in mass is added energy.
c. Relativistic changes to mass are always accompanied by changes to resonant frequencies and lengths [3], and only occur in an object's own FoR where relative motion of an observer can have no effect. (In external FoRs measurements of kinetic energy (KE) and potential energy (PE) are affected by the relative motion of an observer).
    From these facts, logic dictates that relativistic changes to an object must be due to applied energy, and are not due to its velocity (velocity can often be a measure of the energy supplied, when it occurs). SR omits to consider how the moving frame came to be moving!
    The famous Two Clocks contradiction arose because SR is based on velocity, not energy. According to SR when two standard atomic clocks are moving relative to each other, each must be running slower than the other. Impossible. It is known from observations [4] that a clock accelerated by applied energy runs slower than one at rest. It is therefore obvious that the accelerated clock runs at the slower rate.
    This contradiction and many other anomalous situations in SR are clearly due to this widespread belief. If this belief is an accepted fact of SR, then SR is invalid.

2. (Moving objects cause distortions of time and space).
    Established physics equations [5] predict that when mass changes, frequencies and lengths change, but SR only allows a change in length to occur in the direction of motion [6], so objects are distorted and SR attributes this to a distortion of space. This would cause the distance between the ears of a traveler to change every time he turns to face a different direction, and at high relativistic speeds this is observable by fellow travelers, thus offending the principle of equivalence of inertial FoRs (and probably kills the traveler).
    Since, in 1. above, it is shown that it is applied energy (which is not directional) that causes relativistic changes, distortion does not occur, and any consequent movements of objects that may or may not accompany those changes, cannot cause them.
    Also, distortion of space would occur if the length of a rod calculated from its rectilinear coordinates is not the same as cot, which appears to happen because c is declared constant in SR.
    Considering that the frequency of an atomic clock actually changes in accelerated FoRs thus changing the size of a time unit, attributing that to a distortion of Time itself is also not necessary.

3. (Constants of proportionality in physics equations keep the same value in all FoRs).
    This popular misconception is most probably a misinterpretation of the Principle of Relativity, which requires the laws of physics to be universal. The laws of physics are proportional relationships. When the two parts of a proportional relationship differ dimensionally, a dimensioned constant of proportionality must exist in the equation, and be adjusted in size to compensate for differing relativistic changes in the two parts. For example, in moving frames, when the experimentally known relativistic changes for mass and frequency (gamma and 1/gamma, respectively) are applied to the energy equations E1 = Mc² and E2 = hf , it is seen that when h and c are held constant, E1 increases due to the increase in M, but E2 decreases due to the decrease in f   (where h is Planck's constant and f is the frequency of emitted radiation). For these two equations to produce the same result, as they should, c² or h (constants of proportionality), but probably both, must change in moving frames. If c must change, then SR is based on a fallacy and is invalid. They are "factors" of proportionality and are only local constants, constant in any particular inertial frame.
    The invariance of c is often quoted as being a consequence of the principle of Relativity, since c is a constant in Maxwell's equations and the laws of physics are required to be the same in all inertial frames of reference. The reality is that c has a different actual emitted value in frames moving relative to the home frame, but, because the measuring instruments in that frame have also changed in the same proportions they will always measure c the same as in the home frame. When measured within the moving frame nothing seems to have changed. The reduced frequency in moving frames is only discovered by measuring it with instuments in the home frame.
    For the laws of physics to hold true in moving frames, a unique set of changes to mass, length, time units, (and therefore c and h) must exist for physics equations to be coherent. These are properly derived in Natural Relativity (NR), a separate paper by this author [7] (which shows that h and c both change in moving frames such that the product hc does not change).

4. (The SR mass-velocity equation is applicable to unrestricted inertial motion)
    This belief is obviously wrong, the SR equation has a "built-in" restriction to a maximum speed of c. Therefore it cannot represent the effects of unrestricted motion or speeds greater than c. SR does not state that it is for motion restricted to a maximum speed of c, or provide an equation for unrestricted motion and so it has been widely assumed to apply to all conservative inertial motion, restricted or not.

5. (Relativistic gains in mass occur in all FoRs, always).
    The principle of CTE ensures that a mass gain always occurs in an object's own FoR when energy is added, but when its speed (in external FoRs) is unrestricted, all the applied energy is utilized to increase its speed and and there is no energy available to increase its mass from Mo . The mass-velocity equation for unrestricted speed is therefore M - Mo = Mo/2c². Therefore, in most relativistic situations, mass gain is NOT in all FoRs.
    When motion of an object is restricted, its speed is then less than the possible (unrestricted) speed for the same added energy, and only then, to comply with the principle of CTE, can the mass increase in the observer's/external FoR, but it is only a fraction of the change in its own frame (but SR assumes it is the whole change - see text books for relativistic momentum, where MV is assumed, which is a mixture of frames of reference!).

6. (the SR mass-velocity equation predicts a universal limiting velocity equal to the speed of light).
    The SR equation M = M0(1 - V²/c²)-1/2 is interpreted to mean "V must be less than c for any change in mass". In 1905 Einstein assumed the speed of light to be a universal constant in his derivation of the above equation. In relativity, if the speed of anything is restricted to a maximum value without a unique external reason, then all speeds must be restricted to the same maximum and this condition will appear in the derived equation. Hence, the limit was assumed rather than predicted, and from item 4 above, the equation is applicable only to motion restricted to a maximum speed of c.

7. (The limiting velocity found in experiments is a relativity phenomenon).
    The limiting velocity found in Bertozzi's experiment [8] and in cyclotron work , accelerating charged particles with an electric field, has been assumed to be a relativity phenomenon because the SR equation apparently predicted that limit. If that prediction did not exist, or was found to be false for unrestricted motion (as shown above), then some other explanation must exist and it is a logical conclusion that the limiting speed must be a property of the electric field, and is therefore not a relativity phenomenon.
    It is postulated that if an electric field was itself propagating at the speed of light, then it could not accelerate a charged particle beyond that speed. This explanation provides a real cause for the effect, which was lacking hitherto - relativity itself is a subject and cannot be the cause of any physical effects (as commonly assumed). The SR equation is therefore accepted as being correct for this type of acceleration.

8. (The Transverse Doppler Effect is caused by centrifugal force).
    This effect is explained in the literature (e.g. Kundig [9]) to result from the centrifugal force (of a rotating mass) simulating gravity and the distance between the source of e/m radiation (on the axis of rotation) and the detector (at a radius r), simulating a displacement r down a gravitational potential. If true, the accompanying energy change would produce a change in the detected frequency, as confirmed by experiment (e.g. Pound and Rebka [10]). The flaw is that there is no displacement of the source or detector along the direction of the centrifugal force, and force times a displacement of zero equals zero energy, thus no frequency change could result. The centrifugal force effect is always zero, and also has nothing to do with relative velocity (the basis of the Doppler Effect), yet was ill-named "The Transverse Doppler Effect".
    Actually, the frequency reduction effect must also take place (using the tangential speed in the calculation), producing the expected change in frequency, but this was ignored on the grounds that SR is only valid for inertial motion, so the simulation was invented. Therefore it is clear that the SR explanation of the frequency change is invalid, it is not caused by the centrifugal force (nor by Time Dilation!). If it was, the effect would be doubled.

9. (Relativistic effects are not caused by acceleration).
    Declarations that acceleration has no relativistic effects (so they must be due to velocity!) have been made (e.g. Bailey et al [11] ) after using enormous forces of acceleration (up to 18g or more) on suitable objects, but alas, just as above, there is no distance moved and no resulting speed in the direction of the force. Adding the fact that atomic clocks run at a constant lower rate when accelerated to a given speed, can only mean that the change in its 'tick rate' and other relativistic changes (in its own FoR) were caused by the acceleration for the time required to achieve that speed (see item 2 above). Reversing the effects, an expected facet of relativity, is therefore accomplished by reversing the acceleration (by subtractng energy).

10. (all experimental evidence confirms SR, even at high relativistic speeds).
    No published experiments utilizing low speeds were found accurate enough to detect the difference between SR and NR. For relativistic speeds, apart from accelerating charged particles by electric fields (where SR and NR are in agreement), extremely few experiments have been published. Of the two purporting to support SR that were examined in NR (see Curvilinear Motion Evidence), one [12] was shown to be invalid (the values of the two unknowns in the two equations are not expected to be the same in each equation) and the other [13], when corrected for an error in the expected gradient of the line on the chart, indicates a relation between mass and kinetic energy of Beta particles which does not agree with SR by a factor of 2, and their speeds (calculated much more recently in NR) were found to be greater than c. That is, both important experiments now fail to support SR.

11. (gravitational fields cause relativistic changes).
    When gravity is utilized to provide an opposing force such as when raising an object to a higher altitude, it is usually assumed that the relativistic effects are due to gravity. BUT, if the same opposing force is provided by other means, such as a spring, the relativistic effects would still occur because the same amount of energy would be applied. Therefore, in this example, it was the work done, not gravity, that caused the changes. Any change to mass in these circumstances is to inertial mass, not to gravitational mass. This is how inertial mass has been mistaken for gravitational mass!
    Applied energy has been shown to be the cause of relativistic changes, and gravity cannot supply any energy as it is not an energy field. Hence, an object in free fall (including orbital motion) does not suffer any relativistic changes due to speed or altitude changes in elliptic orbits.

12. (gravitational mass is the source of gravity).
    The term gravitational mass is assumed to mean that the attractive force emanates from mass.
    When the known relativistic effects due to adding energy to an object without resulting motion (as in moving an object a known distance against an opposing force) are applied to the dimensions of G (from Newton's equation), it is found that the value of G is reduced if the objects are inertial masses, but not changed if non-mass items replace the inertial masses (this fact has been overlooked or ignored for many decades). Since the value of G should, indubitably, not change in these circumstances, the attractive force must not emanate from mass, and the dimensions of G must change by M squared.
    Therefore, gravitational mass does not exist and cannot be the source of gravity, which is shown in Mass, Matter, and Real Gravity to emanate from the electric charges in the atoms comprising the objects.

13. (gravitational mass and inertial mass are equivalent).
    From 12 above, this cannot be true. See also No. 11 above.

14. From 12, the gravitational constant has altered dimensions, but its numerical value stays the same. The new dimensions are the same as for hc causing the Planck units to be invalid nonsense (also, such absolute values offend the principle of relativity).


    The Special Theory of Relativity should also be INVALID because:-

1. Einstein postulated the speed of light (c) to be measured the same in all FoRs, but this has been mistaken to mean that its actual speed was always the same in all FoRs (see 3. above). [1,4].
- Having a universal value for c offends the principle of Relativity. It demands a preferred frame of reference.
- That the Doppler Effect exists for light proves that it is not possible for the speed of light from a particular source to be the same in all frames of reference [14] as that effect is a function of relative velocity V and supposedly compensating frequency effects of relativity are a function of V², so they cannot nullify each other at all speeds.
- The Danish astronomer Ole Roemer [15] observed (in 1676) that light from the Jupiter satellite IO took longer to traverse the diameter of Jupiter when Earth was receding from Jupiter than when approaching it indicating that the light was travelling at different speeds relative to the Earth at those times, apparently violating Einstein's postulation.

2. SR does not comply with the principle of CTE for unrestricted motion, in that the total energy of an object should be the same in all FoRs, and therefore route-independent, when energy is added and subtracted.
- The calculated KE of an object for a given unrestricted speed relative to a stationary observer (Mo/2), is always less than the equivalent increase in mass predicted by the SR equation (in its own FoR) for the same speed. SR only complies with the principle of CTE if it is accepted that the equation is for motion limited to a maximum speed of c, when the mass in the KE is increased a little.
- When energy is applied to an object a given number of times in the same direction producing motion, the SR equation predicts that the sum of the increases in mass is less than when the object is accelerated to the same final speed in one step - it is route-dependent. To achieve the same final mass, the applied equation needs to be linear with energy, as is M = E/c² and the equation for unrestricted motion M - Mo = MoV ²/2c²  = KE/c².
    Hence SR fails to comply with ALL the principles of relativity, as shown below.

3. SR does not comply with the principle of Reversibility of Effects.
- The SR non-linear relation between mass and speed cannot provide this feature. As the speed of an object is reduced, the value of the mass subtracted can only be the same as the mass that was previously gained when the speed change has been reduced back to zero. As it does not follow the same path on a chart, at all intermediate speeds the mass is different.

4. SR does not comply with the principle of Invariance of the Laws of Physics.
- Allowing constants of proportionality to change in accelerated FoRs is necessary to comply with the correct meaning of this principle, but no examples of this have been found in the literature. SR does not allow them to change.
- SR predicts an increase of mass with speed, yet a free falling object must lose mass (potential energy) as it gains speed. SR is concerned with mass and motion, yet cannot solve this anomaly. The SR equation for mass change with inertial motion is of a different form compared to the corresponding equation for motion due to gravity. So it is proclaimed that SR does not deal with situations involving gravity and gives the problem to General Relativity. This does not avoid the fact that it is a failure of SR. Physical effects of acceleration due to gravity and applied energy belong to the same world and must obey the same fundamental laws of physics.

5. SR does not comply with the principle of the Invariance of Properties of Matter.
- For objects accelerated by added energy, Time Dilation of SR states that the frequency of radiation reduces by the factor gamma and, for a constant value of c, lengths must increase by gamma. As volumes increase by length cubed and mass increases by gamma by definition, density of matter would be reduced by gamma squared. If the Lorentz contraction was accepted, density would increase by gamma4 and c (= fl) would not have the same value. In either case, at different speeds the change in density cannot result in the same properties of matter.

6. Velocity transformations had to be derived for SR so that the addition of speeds could not exceed c.
- This is necessary to make the data conform to the SR equation(!) and thereby offend the principle of Relativity. This reverses the normal accepted procedure of adjusting the theory to agree with the data!
    The speed of Beta particles is avoided in applying SR, some could be traveling faster than c. Their Kinetic energy values are used instead and are much easier to measure, their supposed speeds then being calculated from the SR equation (if ever required).

    SR is a mess. It is supposed to be a Theory of Relativity, yet does not conform to any Principles of Relativity, which, it should be said, are intended for unrestricted inertial motion only. SR fails that purpose, but has always been assumed to be suitable. In fact, postulating the invariance of c is, in effect, denying the possibility of unrestricted motion. In consequence, it has numerous problems and gives rise to many misconceptions and misinterpretations, as shown above, which exacerbate the situation. It appears to be only valid for motion restricted to a maximum speed of c, and its predicted relativistic changes are not coherent. It leads to a poor system of physics.
    Natural Relativity (Ref. 7) (the basis of this paper) is not a theory, but a system of physics. It is derived only from well known and long accepted physics principles and equations, producing all the information disclosed herein (and much more). Thus, it conforms to all principles of Relativity and Physics, agrees with all valid experiments and observations without recourse to fantasies, and has no known problems. It replaces SR and the gravitation parts of GR. The rest of GR is fantasy.
    When will it be officially recognized as a competent replacement for SR and a new basis for general relativity? When the current rulers of Physics policy have all died (and this author too), according to past history!
    P.S. Criticisms of the above (if any) should be based on physics and logic, not on theories or dubious assumptions.
    02Nov2011 - no criticisms have yet been received!

1.  Henry Semat, Introduction to Atomic and Nuclear Physics, 4th edition, p36, Chapman and Hall, London EC4 (1962).
2.  Idem, pp36-38.
3.  Idem, pp39-45.
4.  J.C.Haefele and R.E.Keating. Science vol. 177, 166-70 (1972).
5.  Henry Semat, Ref.1, p233.
6.  Idem, p39.
7.  D.V.Connell, "The Natural Effects of Applied Energy, Motion and Gravity on Mass", Phys. Essays, 22, 3, 402-412(2009).
8.  W.Bertozzi, "Speed and Kinetic Energy of Relativistic Electrons", Am.J.Phys.32, 551-5 (1964).
9.  W.Kundig, "Measurement of the Transverse Doppler Effect in an Accelerated System",
      Phys.Rev.129, 2371-5(1963).
10. R.V.Pound and G.A.Rebka, "Apparent Weight of Photons", Phys.Rev.Lett., 4, 337 (1964).
11. J.Bailey, K.Borer, K.Combley, H.Drumm, F.Krienen, F.Lange, E.Picasso, W.vonRuden, F.J.Farley, J.H.Field, and P.M.Hattersley, Nature 268, 301 (July 28, 1977)
12. M.M.Rogers, A.W.McReynolds and F.T.Rogers,Jnr, "A Determination of the Masses and Velocities of three Radium B Beta-Particles", Phys.Rev. 57, 379-83 (1940).
13. K.N. Geller and R. Kollarits, "Experiment to Measure the Increase in Electron Mass with Velocity", Am. J. Phys 40, 1125-30 (1972).
14. S.J.G.Gift, "The Invalidation of a Sacred Principle of Modern Physics",
     Phys.Essays 17.3, 338-341 (2004).
15. A.P.French, Special Relativity, Nelson, London (1968).

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