Simultaneity and Time Dilation

By: Clarence L. Dulaney

2226 Fairgreen Drive

Missouri City, TX 77489

Abstract: Albert Einstein himself¹ said that clock synchronization and thus simultaneity is possible for "stationary clocks in a stationary system". However because of the constancy of the speed of light, and the resulting time dilation specified by the Special Theory of Relativity (STR), simultaneity cannot be specified between moving inertial frames,( according to STR).

All the principles of STR are interdependent². If it can be shown that time dilation does not occur, then there is no length dilation, light speed constancy, mass increase with speed, or restrictions on simultaneity.

This paper attempts to show that there are no experiments, real or "Gedanken"(GEX) that can prove time dilation occurs within the confines of STR.

INTRODUCTION

This is one of three papers^3,4 on the basic principles of STR. All three papers are summarized in "Interlocks of STR², which notes that any of the tenets of STR can be derived from any of the others. In the current paper, the principles of "Simultaneity" and of "Time Dilation" are discussed. "Simultaneity" is shown to be equivalent to the principle of "Constancy of the Speed of Light", which, in turn is a basic postulate of STR.

SIMULTANEITY

Simultaneity is a relatively unimportant aspect of STR upon which a lot of print has been spent. In reality, the important aspect involved is "the constancy of the speed of light", one of the cardinal pillars of STR.

Because of the interlocking of the concepts of STR², most of the derivations of formulas start with the derivation of the Lorentz Transform of length (and time) which has been discussed at length in that paper. Suffice it to say that for an "inertial Frame S, with another frame S’ moving in the +x direction at speed V with respect to (wrt) S, The time "t’" in frame S’ compared to the time "t" in frame S is: (with g = (1-(V²/c²))^-½ ), ……. t’ = g (t – (Vx/c²)). In the "Interlocks" paper², it is shown that the Einsteinean derivation¹ of the Lorentz Transforms is flawed, and that the Galilean Transform is correct. Thus, there is no "Time Transform", and t = t’.

BORN ON SIMULTANEITY

Born⁵ states onpage 226, " Simultaneity is a fallacy.....", and "But there is certainly no such time for the quantitative physicist. He sees no meaning in the statement that an event at A and an event at B are simultaneous, since he has no means of deciding the truth or falsity of this assertion. To be able to decide whether two events at different points are simultaneous we must have clocks at every point which we can be certain will go at the same rate or beat, "synchronously." Thus the question resolves into this: Can we define a means of testing the equal rate of two clocks situated at different points?" and further from page 227, "But even if the assumption is made that there are ideal clocks free from errors (such as the physicist is `convinced he has in the atomic vibrations that lead to the emission of light), it is logically inadmissable to base on them the definition of time in systems moving relative to each other; for the equal beating of two clocks, however good they may be, cannot be tested directly, that is, without the intervention of signals, unless they are close, and at rest relative to each other. It cannot be established without signals that they maintain the same rate when in relative motion. The contrary is the kind of pure hypothesis which we should avoid if we wish to adhere to the principles of physical research." What the latter quotation is essentially saying is that time dilation in moving inertial frames precludes simultaneity between these frames.

TIME DILATION

A. Kittel’s Time Dilation vs. Speed of Light GEX⁶

Kittel et al. Have the ordinary two "inertial frames", S, stationary, and S’ moving at speed V in the +x direction wrt S. They have "identical" clocks in each frame that are synchronized when they pass at the origin. As the clocks pass, a light beam is sent a distance L in the y-direction, and there reflected by a mirror back to the origin. The light beam thus takes 2L/c = t seconds to make the round trip (in frame S). This time is printed out for all to see.

However, the observer in frame S’ notes that he is moving in the x-direction while this is going on, so that the light beam takes an additional ½v/t’ in each direction, making a total distance of travel, which must equal ct’,

……..ct’ = 2[L² + (½Vt’)²]^½…………………….(1) (my numbering), Thus:

……..(ct’)² = 4L² + (Vt’)²……………………….(2) Solving for t’,

……..t’ = 2L/(c² - V²)^½ = (2L/c)g…………….…(3) Remember t = 2L/c, so:

…….t’ = gt...........................................................(4)

(4) means that the clock in S will seem to run slower than that in S’. (Note that this seems to be the exact opposite of what we started out to prove, that the moving frame caused time to pass more slowly. But. STR if nothing else is reciprocal, and the observer in S’ can consider his frame stationary and S moving (at speed –V). Note that there cannot be negative time.)

Let us look at this derivation more closely in the light of STR. Since we are measuring the time in the moving frame, we must also remember the length contraction also applies. In frame S’, length L is actually L/g, because of length dilation. Thus, in (3) above, t’ = (2L/cg)g, so that t’ = 2L/c = t and thus STR is hoisted on its own petard. BUT remember that t = t’ as was shown in the “Interlock” paper², so the entire argument is negated, and there is no time dilation.

B. Kittel’s Dig at Born (See D below)

On p-336, Kittel says, "We have seen that the time-dilation effect does not involve mysterious processes in the interior of atoms; the effect arises in the measurement process. The clock at rest in S reads the proper time t when viewed by an observer at rest in S. But when we view from S’ a time interval which is t in S, we see a longer time t’ because of the longer light path." But, as we have shown, Kittel conveniently forgets the length dilation.

C. The Twins Paradox, or Dingle’s Dilemma

One of the most frequently quoted Gedanken Experiments (GEX) concerning time dilation is that of the "Twins Paradox", concerning twins, one of which, A, remains on earth, while the other. B, goes off at high speed in a rocket for a long period of time. Then, B turns around and heads back to earth at the same rate of speed with which he was leaving earth earlier. Because of time dilation due to motion, it is alleged that B will have aged much less than his "stationary" twin. (It is wondered if due to length contraction B will be much shorter than A).

There is a possible discrepancy in the GEX concerning the acceleration required to turn the rocket around, but Born states on page 261, "For in the considerations above we made the assumption that for sufficiently long journeys the short periods of acceleration exert no influence on the beating of the clocks." Essen⁷ deals with the question of acceleration in his book, as does Sachs⁸in his paper. Both agree that asymmetric aging does not occur in inertial systems, but possibly may in accelerated systems. Greenberger⁹ notes that if Sachs is correct, all STR is obviated including the constancy of the speed of light.

H. C. Dingle¹⁰ notes that the above GEX really is a paradox. According to the first principle of STR, the exact same result should be obtained if A were moving and B stationary, making B older than A at the end. This obviously is impossible.

Another equally plausible formulation of the GEX would initially have A moving at v/2 in the -x direction, and B moving at v/2 in the +x direction, then both moving in the opposite directions at v/2 after the reversal. This latter formulation has the advantage that both are accelerated, and the philosophical dilemma faced by Essen and by Sachs (op.cit) would be essentially removed, provided the acceleration were short enough. The shortest possible time of acceleration would occur if both A and B underwent an elastic collision at the limit point. BUT...If they were going at an appreciable fraction of c, neither could survive the rapid change in direction. After all, even in GEX there should be no superhumans, and the rockets or whatever they were travelling in would also be destroyed. If the acceleration took long enough that the people survived, there would be so much time involved that the nature of the GEX would not fit in the first principle of STR. Thus, the "Twins Paradox" GEX cannot prove time dilation within the framework of STR;

D. BORN ON THE FAST LIFE

On page 257 Born states, speaking of the twins paradox, "All atomic vibrations--indeed, even the course of life itself -- must behave just like the clocks. · · · · · · "This is a truly a strange deduction, which can, however, be avoided by no twist of reasoning. We must put up with it just as, some centuries ago, it had to be accepted that our fellow creatures in the antipodes stood on their heads."

Suppose that we have a container of gas on our rocket, moving along with the moving observer. Since the pressure in the container, at constant temperature, varies directly with the average velocity of the gas molecules, the pressure of the gas riding on the rocket should be less than that of a similar container in the "stationary frame". This should be one way of testing STR It seems that the gas molecules would have to be prescient to know they were on a moving frame, and therefore to slow down. Remember that the energy of the molecules is a direct function of their average speed. If the energy decreases, according to STR the mass should decrease, whereas, also according to STR, the mass should increase with speed This definitely seems to lead to a paradox.

E. MESON LIFETIMES

1. Cosmic Rays

One other evidence for time dilation is based on the lifetime of the p-meson¹⁰, which is found as a "secondary" in cosmic radiation. By secondary is meant a particle that is not present in the cosmic ray stream reaching the upper atmosphere, but is produced there by collision of a "primary" such as a proton with an air molecule. If the meson is produced at the outer reaches of the atmosphere, and further if it travels at the speed of light to the earth, 30 km below, it would take 10^-4seconds to reach the earth.

The same particle is produced in particle accelerators on earth, and is known to have a (low speed) half-life of about 10^-8seconds. Thus, the relativists reason that the lifetime of the meson must be increased by time dilation caused by its high velocity

Two comments may be made. 1. The half-life of the particle is the time required for half of those present to decompose. Many undecomposed particles may be present after a considerable number of half-lives have passed. 2. Nobody knows exactly at what level of the atmosphere the "meson" is made, or how many are made. It very well could have been made quite close to the point at which it was detected, since the primaries are known to penetrate the entire atmosphere. Thus, this theory cannot prove the validity of time dilation. See my paper "Charge vs. Speed"⁴ for a discussion that indicates that mesons may just be high speed electrons, with reduced charge, instead of increased mass.

2. Accelerated m Mesons

Bailey. et al¹¹ of CERN did an experiment involving acceleration of a "meson stream" in the CERN cyclotron. The "meson stream" was made in some fashion and introduced into the cyclotron, and not further identified. The particles were accelerated up to 0.9994c, and electron detectors were placed around and inside the cyclotron. According to the results, the particles were able to last on average about 29 times their "rest" lifetime, precisely the extension predicted by STR.

This is exactly the kind of experiment that illustrates "Anonymous’" "Law of Experimentation", that It is always easier to interpret an experiment when one knows the results to expect.".

First, you must take their word that what they were accelerating was only mesons, and that they measured only electron products, even though the mesons are supposed to have the same charge of the electron, and that all these measurements can be made in microseconds. Secondly, the fact that major particle acceleration is involved completely obviates interpreting the experiment as verification of STR (due to violation of the first principle of relativity, no acceleration). Thus, it must be concluded that this experiment does not verify time dilation in the context of STR. The author will provide a more detailed critique of the experiment for any interested party. One thought this author had concerning the experiment was that it was a knee-jerk reaction to Dingle and Sach’s arguments. Dingle, in particular, was at one time the explainer of STR for the Encyclopedia Brittanica, and had a high respect in the physics community.

Read the Bailey paper with particular attention to the dates the paper was submitted, accepted, and printed.

There are several other meson experiments mentioned in references 10 and 13 that lead to exactly the same conclusions. Critiques on request.

3. Other Experiments

There are other experiments such as those of Ives and Stillwell¹³, Pound and Rebka¹⁴, Vessot and Levine¹⁵ and Haefele and Keating¹⁶that deal indirectly with time dilation and are outside the scope of this paper. The author will provide a critique of these papers to any interested parties. Basically, these experimenters knew what answer to expect.

CONCLUSIONS

It is concluded that there is no experimental proof that time dilation occurs. If you can’t measure it, or show it by a reasonable GEX, you can’t prove it exists. The author will explain any time dilation experiment upon request. No math higher than differential equations, please, nor any experiment involving accelerations.

If there is no time dilation, there is no restriction on simultaneity between inertial frames..

REFERENCES

1. A. Einstein, "The Principle of Relativity", translated by W. Perrett and G. Jeffery, Dover, NY, 1952, p38-40.

2. C. Dulaney,, "Interlocks of STR".

3. C. Dulaney, "Mass vs Speed"

4. C. Dulaney,, "Charge vs. Speed"

5. M. Born, G. Leibfried and W. Biem, "Einstein’s Theory of Relativity", Dover, NY,1962, p225ff.

6. C. Kittel, W. Knight, and m. Rudderman, "Mechanics, Berkeley Physics Course, Volume I, 2^nd Ed",McGraw-Hill, NY, (1973)

7. L. Essen, "The Special Theory of Relativity, A Critical Analysis", Oxford, London, 1971

8. M. Sachs, Physics Today, September 1971, p23

9. D. Greenberger, Physics Today, January 1972, p13.

10. H. Dingle, "Science at the Crossroads", Martin Brian & O’Keefe, London, 1972, p228ff

11. T. Osgood, A. Ruark, and E. Hutchisson, "Atoms, Radiation and Nuclei", John Wiley, NY, (1955), page 410ff

12. J. Bailey and 11 Co-authors, Nature, 268, 301 (1977)

13. R. Durbin, H. Loar and W. Havens, Jr. .Physical Review, 88, 179,(1952)

14. H. Ives and G. Stilwell, J Opt. Soc. Am. 28, 215, (1938)

15. R. Pound and G. Rebka, Phys. Rev. Lett., 4, 274 (1960)

16. R. Vessot and M. Levine, Meterologia, 6, 116 (1970)

17. J. Haefele and R. Keating, Nature, 227, 270 (1970)

NOTE: My papers may be found at: http://mywebpage.netscape.com/clarencedulaney/index.html as of 12/12/01

Clarence L. Dulaney