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SIMULTANEITY

M

any SR/GR hypotheses have been matters of deep discussion. Today, in 1999, we are close to experimentally testing the final GR fantasy: Space dragging (See Chapter 9). But none of these hypotheses was studied so deeply and for so long a time as the SR failure relating to simultaneity. Many recognized physicists worldwide lost a lot of time, in a period spanning 30 to 40 years, trying to explain the problem of simultaneity.
                        Fig. 1

Of course, though SR accepted the Lorentz transformation wholesale with no criticism, the failure lies in the results of this transformation.  First at all, we will explain the issue as simply as possible.  When one event occurs at point x at time t and another event occurs at point x1 at the same time t, we find, applying SR's equation, that time t' and t'1 differ by an amount equal to

 

                                       (1)

 

This circumstance is called the "failure of simultaneity at-a-distance." Of course, this is an elegant expression to hide the guilty party: SR.  Really, we hide the guilty party at the outset, because to obtain equation (1) we use the Lorentz equation, which is the foundation of SR.  To tell the complete truth, we need to express the statement as the "SR failure of simultaneity at-a-distance."

Am I justified in pointing to SR as the guilty party?  Should I accuse Lorentz-Einstein?  I believe that it is SR, because though it is true that the equation and concept derive from Lorentz, it was Einstein who introduced it into SR with no discussion.

Many readers - laymen, Physics students and professionals - know that SR is a magic science. We will show to those who only know algebra, or less, where equation (1) comes from.

As the left side of equation (4) shows, the equation is only the subtraction of two fractions with equal denominator, equation (2) and (3).


          (2)                                     (3)

 


                                        (4)

t positive and t negative are eliminated in the equation's right hand side, and since v is a common factor, we have

                         (5)

 

Equation (5) is equivalent to equation (1) where u = v, and the conclusion is the same. SRs failure of Simultaneity at-a-distance.

The classical examples given in textbooks, i.e., a train in motion or two emitters in two parallel systems in relative motion - introducing time dilation or length contraction - and especially the example given by Feynman [1] , are mistaken because the proposition involves the same error.

Now we will show the mistaken concept introduced by Feynman, and later we will analyze one of the two others.

Feyman's example describes the synchronization of two clocks inside a space ship: one in front and the other in the rear. A light signal is emitted in the middle and the clocks are synchronous because the "distance" that the light "travels" is the "same." The Observer, the Astronaut, believes this because he doesn't know that the space ship is in motion.

 

This is, evidently, false.  He perfectly knows that he is moving with respect to the origin from where the space ship was launched. If he is actually "at rest," to stop his motion a force should have been introduced and this would create a "negative" acceleration that could be detected by an accelerometer.  Also, it will be shown that he can measure the relative velocity at which the space ship is actually moving with respect to the origin.

 

Before the space ship was launched, the relative two clocks "at rest" are automatically synchronized. After traveling for a while, the "distance" to the front clock is longer than the "distance" to the rear clock. (See Fig 2). They are in motion. When the light emitter emits the light in the space ship's center, it emits the light at velocity c in all directions and, precisely at this instant, it is possible to say that the emitter is "at rest." This is due to the Michelson and Morley discovery.

 

As the rear clock continues to move in the emitter direction, its arrival time will be shorter and longer for the front clock because it is traveling away from the emitter. (The zero instant when the light was emitted). For an external Observer, the light doesn't arrive simultaneously at the clocks.

 

This is the Feynman's conclusion, which is really the SR or Lorentz conclusion.

 

We mentioned before that the astronaut knows that he is in motion with respect to his departure's point. Now we will show that he can know the space ship's velocity if the two clocks are synchronized. This was done before the launch.

We will also show that the length contraction hypothesis is totally irrelevant.

Suppose, as normally happens with all NASA spacecraft that a signal is sent to the space ship. The signal will arrive first to the rear clock (1) in the space ship and later to the front clock (2) in Fig 2.

                                                                                                                                                           

 

 

Fig 2 [2] .  

 

Nevertheless it is correct in the explanation to suppose that the Earth is at rest.

 

As will be proved, this permits us to calculate at what velocity the space ship is traveling. As the clocks are synchronized at the launch point, the difference in time gives the space ship velocity.

We will suppose that the distance between both clocks is 1000 meters. We know that distance is equal to velocity times time.

 (6)

Why do we use c? Because c is a Universal velocity, it is constant, and is independent of the Observer and Emitter velocity. The light velocity is 3 * 10^8 meter/second.

Knowing c and d, we can calculate t.  t is the time that light needs to reach a distance d. This is equation (6) and from there

         (7)

 

Now the space ship receives a signal from Earth, Fig 2. Of course, this signal is traveling at c because it is an electromagnetic signal. This signal enters the rear clock first, position 1, and later the front clock, position 2, in Fig 2A. The time difference, i. e. is td = 0.000 003 344 333 second. Applying the rule of proportionality this time difference represents a distance

                   

 

                                                        (8)             

 

Of course it is the same to say that the signal traveling at c during 0.000 003 344 333 seconds will travel a distance equal to

        (9)

 

The time difference represents the time that the signal travels between the two clocks, 1000 meters, plus 3.3 meters. Consequently the net distance traveled by the space ship is ds = 3.3 meters.

To see this clearly, it is the same to get the time difference between the total time td and the time t related to 1000 meters, multiplying this by the light velocity.

 

                                                                                                      (10)

Spacecrafts velocity.

 

Fig 3.    

 

When the signal arrives at R, Fig 3D, the rear clock registers the time. The signal and the space ship continue in motion and the clocks in Fig 3 move to position E. When the signal arrives at the front clock F, Fig 3F, this registers the time, giving a time difference that is equal to td.

The 3.3 meters were traveled in 0.000 003 344 333 second that is the difference between the two clocks. The space ship velocity is

     (11)

Equal to 986.743 Kilometer/second.

 

If td = 0.000 003 333 773 33 the velocity v = 39.6 Kilometer/second.

 

 

The same order of magnitude that the Earth orbital velocity around the Sun.

 

If the time difference is td = 0.000 003 333 3 the space ship is at rest with respect to Earth, Fig 2B, and if td is smaller than 0.000 003 333 3 the space ship is traveling in the Earth direction, Fig 2C.

 

This overwhelmingly shows that the example for Simultaneity is a fallacy and the example given by Feynman is totally mistaken.

 

For an Observer at Earth, according to Lorentz and SR the distance between the two clocks in the space ship needs to be shorter, that is, this contraction is a real physical phenomenon.

 

To the Observer in the space ship the two clocks are at rest and repeating the experiment when the two clocks were at rest in Earth he will find the time difference equal to t = 000 003 333 3. Simultaneously he could send two signals from each clock to Earth to control the arrival time difference there. As the distance between clocks is shorter for the Observer on Earth, he should detect an arrival time difference shorter than t = 000 003 333 3. The contradiction is evident between the two Observers, one on Earth and the other on the space ship.

 

Regarding this conclusion it is not true that in SR all inertial systems are equivalent or the length contraction is non-existent.

 

We will discus now the classical experiment mentioned in many textbooks.

 

The classical textbook example is the following [3]

 

                  

Fig. 4

B is in motion with respect to A at 30 000 Km/s.

After 1 s, a pulse of light has spread out from A's lamp a distance 300 000 km and has reached point X. However, after 1 s the light from B has moved to B' during the second, the light has reached y', which is 330 000 km from A.

This conclusion is absolutely mistaken! The light emitted at point B will NOT reach point Y'. As the light velocity is independent of the emitter's state of motion, the light emitted at B, at rest or in motion, will reach point Y and the emitter (B) will reach point B' that is 30 000 km from B. The light emitted from this point (B) will reach Y but it is irrelevant to the problem

We will show that the fallacy of the argument is hidden in the common statement: "From A's point of view.......... " (The same reference) To get a "point-of-view", the Observer at point A needs to receive a signal from X, and if this signal is also a light beam, the Observer at A will measure a time of 2 seconds in his clock.

We will suppose for simplicity that the Observer at B' is now "at rest" after travelling the 30 000 km in a second. From his point of view at B' he will receive a light beam that will travel 300 000 km from B to Y and 270 000 km from Y to B'. This means that he will receive the signal in his clock in 1.9 second at his position at B'.

The calculation is a simple proportion. If 300 000 km means 1 second, 570 000 km (300 000 + 270 000) is equal to

t = (570 000 km * 1 s) / 300 000 km = 1.9 s    (12)

Everything works perfectly because we know that the light velocity is a Universal Constant independent of Observer or Emitter states of motion.

We will show now the Autodynamics solution regarding "failure of simultaneity at-a-distance."

From the theoretical point of view, AD can prove that simultaneity is a simple problem related to signal velocity that transmits information from one point in space to another.  From the practical point of view, the solution only involves a simple calculation, knowing the velocity of the signal that transmits information.

To show the conclusion in the first paragraph the following is conclusive.

Suppose that a body is traveling at a velocity equal to 0.8 of c and is traveling for 2 seconds

[4]

The distance X of the particle from its point Xo "at rest" is

X = 0.8 c * 2 s = 240 000 km/s * 2 s = 480 000 km     (13)

To know this, the Observer in Xo needs to receive a signal from X, that is to say, the signal needs to travel another 480 000 km. If the signal travels at light velocity, the time measured by the Observer at Xo is equal to 3.6 seconds. 2 seconds of this is the time that the particle traveling at 0.8 c needs to reach point X and 1.6 s is the time that the signal traveling at c needs to travel 480 000 km to reach Xo.

If the signal travels at 27 c, the time t is equal to 2.05925.

2 seconds, as before, is the time that the particle needs to reach point X and 0.05925 is the time that the signal traveling from X at 27 c needs to reach point Xo.

480 000 / 27 * 300 000 = 0.05925 s     (14)

Of course if v = infinite, the time that the signal needs to travel from X to reach Xo is equal zero and the time measured by Observer at Xo is only 2 seconds.

This clearly shows that "relativity" is given by c but, generalizing, "relativity and simultaneity" are given by the velocity to what information is transmitted.

Regarding only simultaneity, it is now clear that if the velocity of information is infinite, all Observers in the Universe will see simultaneously all phenomena at different locations happening at the same time.

If the transmission velocity is not infinite, the communication between any Systems in Relative Motion will restore simultaneity only because the transmission velocity is independent of the Observer or Emitter states of motion.

 

As conclusion, to AD, the failure of simultaneity is only the SR Failure of Simultaneity. For AD there is not any failure and truly the phenomenon simply doesnt exist.

 



[1] .- "The Feynman lecture on Physics," Feynman, Leighton and Sands.  Volume I, section 15.6 page 16-7. Fifth Edition 1975, Publisher Addison-Wesley Publishing Co., California, London, etc.

[2] .- In the example we suppose that Earth is "at rest" and this is not true. It is "at rest" for the spacecraft before launch. But, of course, after launch the spacecraft also possesses the Earth's motion, but later this also changes direction and velocity in its orbital motion. The Observer in the space ship needs to know the Earth motion to subtract or to add vectorial velocity from its own values. In practice, this is complicated, as happens with real spacecraft, but through the Doppler Effect, triangulation, etc. the theoretical explanation is valid because all references could be referred to the Sun, or more precisely to the Universal System of Coordinates used by Astronomers. NASA normally uses a system related to a far away Star that the spacecraft "can see."

[3] .-  Franklin Miller, Jr. College Physics Fifth Edition 1982, page 666, Harcourt Brace Jovanovich, Inc, New York, San Francisco, etc. This kind of conceptual mistakes are also teaches in Universities. The Associate Professor of Physics D. P. at University of Virginia gives the example. See Chapter 4 on Neutrino.

[4] .- As ADs conclusion the failure of Simultaneity is only the SRs failure of Simultaneity. For AD there is not any failure and truly the phenomenon for AD simply doesnt exist.