THE INTERLOCKING PRINCIPLES OF THE SPECIAL THEORY OF

INTERLOCKING OF THE PRINCIPLES OF THE SPECIAL THEORY OF RELATIVITY (STR)

By:Clarence L. Dulaney

2226 Fairgreen Drive

Missouri City, TX 77489

Abstract: One cannot be a partial relativist. Any of the tenets of STR can be derived from any other tenet.

Can one believe only one or two of the tenets of STR and reject the other portions of the theory? For example, most of the dissidents I know believe in mass increase with speed, ( although the establishment relativists^1,2 have decided that mass is invariant with speed). Many of the other dissidents believe, (usually also) in clock retardation, (but Sachs³ does not believe in asymmetric aging). Greenberger⁴ says that if asymmetric aging does not occur, (in the "Twins" Paradox) that STR would be destroyed. Some dissidents do not believe in length change with speed. Many believe there can be speeds higher than "c". None believe in charge decrease with speed, but Carmichael⁵ and Bush⁶ say it might. Carmichael says that if charge is a direct function of g, then STR would be destroyed. (It is believed that Carmichael was more concerned that decrease of charge would indicate that mass did not change with speed.) (It is also noted that charge change with speed is not actually a tenet of STR.)

It is shown below that there is no physically tenable derivations of any of the Lorentz Transformations (LTs), and that if any LT actually exists, all do, since they interlock and any one can be derived from any other.

KITTEL ET AL’S⁷ DERIVATION OF THE LORENTZ TRANSFORMATIONS (LT) OF LENGTH, TIME, VELOCITY AND MASS WITH SPEED

This derivation, patterned directly after Einstein (but considerably clearer) is considered in some detail to indicate how these LTs interlock.

First, consider two inertial frames, with x’, y, z, t’ moving in the x direction with respect to (wrt) the frame x, y, z, t frame. We note that x’ = x -vt. …………………………………………………….(1)

If t’ = t one has the Galilean (classical) transform. If t’ ¹ t, then you have the situation for STR.

Secondly, take the two inertial frames, and pass a spherical wave with speed c outward from the origin. The equations of the wave in the two frames given by Einstein, assuming t’¹ t are:

x² + y² + z² = c²t² (2)

x’² + y²+ z² = c²t’² (3)

(See reference 17 for the reason that these equations do not describe a spherical wave travellling with speed c from the origin)

Following Kittel, p-327ff, we set x’= ax + et……………………………….…(4)

and t’ = dx +ht (5)

After some algebra, Kittel arrives at a = h (6)

Substituting from (4), (5) and (6) into (3) Kittel gets:

a²x² + 2aext + e²t² + y² + z² = c²(d²x²t² + 2adxt + a²t²) (7)

Comparing coefficients from (2) and (7), Kitel arrives at::

x’ = (x - vt)g and t’ = g(t - (vx/c²)) where g = (1 -(v/c)²)^-½……………..(7a)

But: remember (1) and compare it with (4). If we do this, we see a = 1, and e = -v. How does this effect equation (7)? Making the above substitutions, we get:

x² -2vt +v²t² + y² + z² = c²(d²x² + 2dxt + t²). (8)

Comparing (8) with (2) we obtain for coefficients of x², 1 = 1 - c²d², or d = 0. Remembering a = h =1, and substituting in (5), we get t’ = t, or there is no "time dilation", even though we allowed t’ ¹ t to start with. Even with Kittel’s derivation, we have ended up with the Galilean Transform. Neither the LT for length nor time can be derived from Einstein’s "c-spheres", nor in any other manner that I know of.

VELOCITY TRANSFORMS

Back on Kittel’s trail, he next develops LTs for velocities. In his original pair of inertial frames he lets a particle move with velocity components v_x, v_yand v_z.With a little calculus Kittel gets: v_x’ = (v_x - bc)/(1 - (v_xb/c)), v_y’ = dy/dt’ and v_z’ = dv_z/dt’, remembering that t’ from (7a) is g(t - (vx/c²)), this makes dt’ = g(dt - (bdx/c).

But: we remember that really t’ = t, so dt’ = dt. Thus, actually v_x’= v_x- V, v_y’ = v_y, and v_z’ = v_z. Here V is the speed of the moving frame (in the x direction).

MASS VS SPEED

Even the establishment relativists^1,2 are coming round to the idea that mass is invariant with speed. However, let us plod on down the path with Kittel. p-350ff to develop the STR mass increase with speed. The Gedanken Experiment (GEX) he cites has two rockets moving at near light speed in a vacuum. They proceed to throw balls at each other at a set time, the balls meeeting in an elastic collision. The fancy v_y transforms derived earlier are necessary to show that the mass of the balls must vary with g for the momentum of the two to be the same before and after the collision. With the "correct" transform, no effect is noted. See the paper "Mass vs Speed"⁸ for a more complete discussion of this GEX and several others, some involving inelastic collisions. It should be noted that these "mass" GEX violate one or more of the Laws of Thermodynamics. Even STR must obey the Laws of Thermodynamics.

TIME DILATION - CLOCK RETARDATION

One of the most famous of the clock retardation GEX is the "Twins Paradox". Dingle⁹ and Sachs op cit note that there is a reciprocal effect, and no asymmetric aging. Note also that Greenbergerop. cit. states that if Sachs is correct, all relativist effects would be eliminated. See the paper "Simultaneity and Time Dilation"¹⁰ for a more complete discussion of the twins, and why they may get shorter with travel, and other time GEX. Basically, there is no time dilation, or clock retardation, because there is no LT for time.

E/M EXPERIMENTS

Several experiments with high speed electrons are explained in some detail in the paper "Does Charge Decrease......"¹¹It is shown that charge is the only property of a body that is actually a function of g. Note that Carmichaelop cit. states that, (although the e/m experiments are not per se STR experiments), if e₀ = e/g then all of relativity would be destroyed. (Actually, he is probably more concerned about mass not varying with speed.) Remember Okun and Adler..

"C" AS LIMITING SPEED

Bertozzi^12.13 ran an experiment to show that a stream of electrons could not be accelerated to a higher speed than c. This experiment is shown to lead to the idea that charge decreases with speed

See also the paper "Why "C""¹⁴. Basically the speed of light on earth is c/n in any direction, where n is the refractive index of the medium. Light that comes from stars, at whatever speed, is very rapidly reduced to speed c, by the Ewald- Oseen Effect. Because of the Doppler Effect, the frequency of the stellar light is "red-shifted" if the stellar speed was less than c, and "blue-shifted" if the stellar speed was greater than c with respect to the earth.

Since the Michelson - Morley¹⁵ experiment, and other interferometric experiments are basically measuring the speed of light on earth in two different directions, there is no surprise that a null result is obtained. Exactly the same null result would have been obtained if the experiment had been run under water.

There is no reason that c cannot be exceeded⁷, simply that charged particles cannot be accelerated to a higher speed than c. Even if two particles happened to be accelerated in opposite directions each to higher than 0.5c, the relative speed would be higher than c.

MASS, ENERGY CONVERSION

See the paper "STR Experiment Critiques"¹⁶. None of the GEX listed can withstand the Laws of Thermodynamics. All physical processes must obey these laws.

G. Hull¹⁷ shows that in building up an electron from scratch by adding spherical layers of charge brought up from infinity gives rise to an energy of E = 10/11 mc². Thus, creation (or destruction) of a charged particle requires (or provides) roughly mc² in energy. Atomic energy is probably mostly due to annihilation of electrons by positrons.

CONCLUSIONS

It has been shown that all the principles of STR are interconnected. Each may be derived from any other, and cannot be disconnected from the chain of derivation. Thus one cannot be a "partial relativitist". In for a penny, in for a pound.

The speed of light on earth is c/n in any direction. "n" is the refractive index of the medium.

E » mc² applies to the creation or destruction of charged particles.

Charge decreases with speed in the ratio of 1/g. It is the only property of a body that changes with speed thereof.

There is no LT of length, time, velocity or mass. STR is nothing more than a mathematical exercise with no physical justification.

REFERENCES

1.L. Okun, ‘The Concept of Mass", Physics Today, June, 1989, p31-36

2.C. Adler, "Does Mass Really Depend on the Velocity, Dad?", Am. J. of Phys., 55,739,(1987)

3. M. Sachs, "A Resolution of the Clock Paradox" Physics Today, September 1971, p-23-29.

4. R. Carmichael, "The Theory of Relativity, 2nd Edition",p-70, (John Wiley &Sons, NY, 1920)

5. V. Bush, "The Force Between Moving Charges", Journal of Math and Physics, 5, 129-157 (1926)

6. D. Greenberger, "The Clock "Paradox" - Majority View", Physics Today, January 1972, p-13-14

7. C. Kittel, W. Knight, M. Ruderman, C. Helmholz, and B. Moyer, "Mechanics, Berkeley Physics Course, Vol. 1, 2nd Ed." (McGraw Hill, NY, 1973)

8. C. Dulaney, http://mywebpage.netscape.com/clarencedulaney/index.html "Mass vs Speed"

9. H. Dingle, "Science at the Crossroads", p-128ff, (Brian & O’Keefe, London, 1972)

10. C. Dulaney, http://mywebpage.netscape.com/clarencedulaney/index.html , "Simultaneity and Time Dilation"

11 C. Dulaney, http://mywebpage.netscape.com/clarencedulaney/index.html ."Charge vs Speed"

12. W. Bertozzi, "Speed and Kinetic Energy of Relativistic Electrons", Am. J. of Physics, 32, 551-555, (1964)

13. C. Dulaney, http://mywebpage.netscape.com/clarencedulaney/index.html "A Critique of the Bertozzi Experiment"

14. C. Dulaney, http://mywebpage.netscape.com/clarencedulaney/index.h ,"Why "C?""

15. C. Dulaney, http://mywebpage.netscape.com/clarencedulaney/index.html "The M-M Experiment and Einsteins LT"

16. C.Dulaney, http://mywebpage.netscape.com//clarencedulaney/index.html, "STR Experiment Critiques"

17. G. Hull, "Elementary Modern Physics", p-423, (MacMillan, NY, 1949) .

17. C. Dulaney, http://mywebpage.netscape.com/clarencedulaney/index.html , “Why STR?”

NOTE: All references http://sites.netscape.net/clarencedulaney/homepage have been changed to: http://mywebpage.netscape.com/clarencedulaney/index.html as of 12/12/01

Clarence L. Dulaney.