Fantasy or Reality?...

(First development : October 1st, 1999 (in Spanish)
Last Update: September 22th, 2003)

I expect that readers arriving this point have dedicated a lot of time analyzing developments and consequences of the Special Theory of Relativity. Therefore, it is really probable they have wondered (more than once) how far it is certain and how far is speculation on this Theory.

Also, it is very probable that, if they are really interested in this question, they have found varied and contradictory answers during the clarification process. Still, it is also probable that many readers have more doubts after trying to solve this query than before thinking about it.

Almost with certainty, Einstein is the most famous scientist in the humanity's history and it is very difficulty somebody has not listen about the Theory of Relativity. It is also listen frequently that many of Einstein predictions have been confirmed. Then, it is astonishing that some people could put in doubt some aspects of his theories or, still worse, that Relativity is a theory conceptually difficult to explain.

While the Atomic Theory, the Theory of Evolution, the Theory of Chaos, etc., are explained and teached with certain easiness, around the Theory of Relativity remains a kind of mystery, reaching the point where, many times, discussions between detractors and defenders of Relativity become involved on dialogues similar to those used with religious credos.

Next, I include some typical expressions use in these discussions among those who accept or reject the results of Special Relativity:

Well, just as I have attempted in other pages I will try to put some order in this apparent puzzle. From my own point of view, the truth (as usually happens) rests in a kind of intermediate point between extreme postures.

Note: At Lorentz1.htm a deeper analysis is developed, supported by more mathematics and the same concepts here discussed.

Trying to reach the goal I will use a detailed numeric example and, when appears to be reasonable, I will introduce the conceptual discussion. To help the reader, periodically I will outline questions hoping to represent the equivalent doubts you could ask during the reading. At the end of the process I will request to the reader to decide for one of the words entitling this page. And of course, I am interested on the comments you could send me.

In our developing, we imagine we live in 1904 (before Einstein developing of Special Theory of Relativity), but we request to Einstein a lend of some of his brilliant ideas.

We will study the behavior of systems in motion using a series of suppositions and experimental data until we were able to make compatible the things we know as real with the answers the Nature want to show us. The situation could be summarized in the following way:

  1. We assume light (same than sound) could travel at different speeds in relation with motion systems. To simplify we will use different denominations for each speed: 
  2. We assume that an absolute frame of reference exists. Only in this frame of reference really happens that w = z = c. We are using a Newtonian model for space.
  3. We choose a system (named A), at rest in relation with the absolute reference frame.
  4. We choose a second system (B) that moves at speed = 259,808 km/s in relation with A.
  5. It is an experimental fact that c is always has the same value (300,000 km/s) independently from the measuring system.
  6. We accept that if a system leaves from rest and acquires an inertial motion (not subjected to accelerations), its internal measuring does not differ from those that are obtained when it was at rest.
  7. All descriptions we do are made from a kind of magic observatory that allows seeing the events without being limited by the speed of light.

Well, with this entire package of suppositions and models (in where I mix what we could call classic common sense and experimental results) let's go to try to understand how could our real Universe works.

At Fig. 1 we can see (thanks to our magic observation system) the instant when observer B, from the moving axis, see how observer A, from the axis at rest, sends a luminous signal toward another observer (X) in the same resting axis. In that moment A and B read 10:00:00 hours in their respective clocks.

The outline doesn't honor (it cannot) the real proportions of systems. The distance that separates A from X is 3,000,000 km (something like 8 times the distance from Earth to Moon) and the distance AB is assumed as a few meters or kilometers (a worthless value in relation with the longitude of systems) A and B can mutually be seen almost "face to face" without significant delay of electromagnetic signals. For that reason they agree that both clocks read 10:00:00 at the moment in which the luminous ray departs from A to X.

Fig.1 - T = 0 s. A sends a luminous signal toward X

A time later (Fig. 2) our privileged observation system allows observing how things are going . The luminous ray has covered a significant part of A-X distance at 300,000 km/s, while observer B has also advanced toward X, although at less speed (259,808 km/s)

Notice: We are using this speed because it leads to a value of 0.5 for Lorentz coefficient making easier the following calculations with times and distances. Of course the example is valid for any other speed value.

Fig.2 -T = 7 s.  The luminous signal is near X. B moves at speed " v "..

When 10 s elapses for the A chronometer, the ray reaches observer X (Fig. 3) At that moment, a casual observer, at rest in axis B, observes the ray reaching the position X. This observer, from axis B just coinciding with position X when the ray reaches it, will be called X´.

Fig.3 - T = 10 s. The luminous signal ")" reaches the position X. In the moving axis, the observer X´ verifies this phenomenon happening exactly in front of him.

Next, A and B wants to know how the experiment came out.

The observer A has a clock perfectly synchronized with the clock of observer X. So, he asks X what time was when he received the signal. X answer: "My own clock was reading 10:00:10 at that moment".

In this way, A and X are satisfied because they check that the luminous ray took 10 s traveling the 3,000,000 km separating both observers. As expected, the speed of light is 300,000 km/s for the observers at axis A.

Let us see, then, the situation in axis B.

First Analysis: Intuitive calculations

The distance B-X´ at Fig. 3 measured from axis A coincides with our privileged vision, which is showed at Figs 1 to 3.

For A, this distance may be easily calculated: The 3,000,000 km traveled by light at 300,000 km/s in 10 s, minus the distance covered by system B at 259,808 km/s in the same 10 s.

If clocks at B were running at the same rhythm than clocks at A, B would also accept the reading of X to calculate the time that light lasted during the trip. In that case B would accept too, that the time elapsed is 10 s during the whole experience.

If their local measurements were also indicating that distance B-X´ is equal to the distance calculated by observers at axis A, we would have the following result for the speed of the ray in relation with axis B.

This single result would allow the detection of their own absolute displacement at observers located in axis B. They could detect  that they are moving in relation with the stationary system. Conceptually this is what Michelson hoped measure with the luminous rays going and returning through a system moving at about 20 km/s (Earth speed during its displacement around Sun)

But point 6 of our outline says "We accept that if a system leaves from rest and acquires an inertial motion (not subjected to accelerations), its internal measuring does not differ from those that are obtained when it was at rest.". And if B had measured the speed of light at rest he had obtained a value of 300,000 km/s, just as the observers from axis A.

In consequence we have made something wrong in our analyses. Something like this was said by those who wanted to explain the flaw of the Michelson experiment for detecting the absolute movement.

Second Analysis: Improved calculations

At page Clocks.htm we made a development showing that it can be accepted as reasonable that clocks in movement slow down in relation with clocks remaining at rest. To do so, it is necessary that clocks internal structure be linked to the same phenomenon leading to a light speed, in vacuum, of about 300,000 km/s.

Applying for a first improvement in calculation, we will accept that clocks at B run at a speed proportional to the average speed of light in round trip journeys.

The operation is simple:

To travel 300,000 km in a round trip journey light uses 2 s in the stationary system.

In the mobile system (B) the light advances at 40,192 Km/s during the going (300,000 km/s - 259,808 km/s). In this way during the going itinerary it uses:

And during the turning back itinerary (at speed 300,000 + 259,808 = 559,808 km/s) it uses

With a total time of : 

for a complete round trip.

In consequence, as light takes 8 s in completing a total journey made in 2 s when the system was at rest, we assume that clocks at B run 4 times slower than those at A. Example: a 10 s lapse for clocks A, means a 2.5 s lapse for clocks in system B.

We are still accepting that distance B-X´ is 401,920 km. And, without too many analysis, we accept that clocks B and X´ are synchronized appropriately (it is not that easy as we will see) so in axis B the observers detects that the ray of light sent from A spends 2.5 s (10 s / 4) before reaching the position X´ (coinciding in time and space with the location of X)

In that case, when observers at B calculate the speed of the luminous ray they obtain:

Better than in the simple case, but still very far from the expected value.

But we are going in the right track!!!

Third Analysis. Let us speak about Synchronism and Distances.

In the previous analysis we accepted that if clocks at  B ran 4 times slower than clocks at A, it was enough for, when the observers in axis A register a lapse of 10 s, those of axis B affirms that 2.5 s elapsed. But things are not so simple. :-)

Observer B needs to trust the reading makes X´ of its clock, in the moment the ray reaches its position. Therefore, we will analyze in what way B and X´ came to an agreement as for their clocks run.

As observers of axis B ignores ("a priori") their absolute displacement speed, they suppose that light moves at 300,000 km/s in any direction (w = z = c = 300,000 km/s)

Let us suppose, additionally, that clocks at B, run at same rhythm than those of A. In that case, a ray of light leaving B toward X´ takes 10 s reaching the position X´.

And it takes 0.718 s returning to the observer B position.

Consuming a total of 10.718 s.

In that way B and X´ would be convinced that light traveled 3,215,388 km in the round trip itinerary.

And therefore the distance B-X´ would be 1,607,694 km (3,215,388 km / 2 = 1,607,694 km)

So, if their clocks run at the same rhythm than the clocks in system A, and they assume that the speed of light is always 300,000 km/s, the observers at axis B must conclude that their longitudes are 4 times bigger than those of the axis A.

First Summary.

Based on analyses and developments just made we face a situation that seems to be difficult to solve. After all, this is the type of problems faced by Physics on the final of XIX Century.

Let's see, then, what we can accept, reject or reformulate from what we have exposed.

The constancy of " c ".

This constancy is an experimental fact verified beyond any reasonable doubt for round trip measurements of the luminous ray. It doesn't mean that " c " is really constant, but at least, it pretends to be so. It is necessary to remember that the value of " c " is obtained as quotient between lengths and times, so that the apparent constancy of " c " can be the result of an appropriate combination of altered longitudes and times.

Therefore, let us rewrite this postulate so it takes a wider content: "In any system where the value of the speed of light is measured in round trip experiences, a value of 300,000 km/s is obtained". This postulate agrees with the experience, and if we want a solid theory we should respect the experimental results.

And, what can we do with " w " and " z "?

Let us also accept that, when measured in any inertial system, " w " and " z " should give an identical value than " c ". For now it is a temporary hypothesis because the precise measurements of the speed of light have been made with light traveling round trips.

The rhythms of Clocks and Lengths.

Here we have a very serious problem. :-)

Therefore in the following scenario we will look for a reasonable balance that offers consistent answers with our common sense and with the experimental results.

Fourth Analysis: Let us do the things consistent.

In this case we will allow that clocks and longitudes be affected in systems which are in absolute motion in relation with the reference frame.

As a way to begin we accept the contraction of longitudes postulated by Lorentz to justify the negative result of the Michelson experience.

In this particular case (v = 259,808 km/s) we obtain a 0.5 coefficient of Lorentz.

So we postulate the longitudes in axis B are decreased in half as consequence of reaching a displacement speed of 259,808 km/s in relation with the system at rest.

This contraction should not be detectable for B, based on our outline (point 6). That means that ALL longitudes in the system have contracted and light takes the same time doing the journey as it took when the system was at rest. Otherwise the system B inhabitants would be able to check that its system was altered during the process of acceleration.

The above-mentioned means that, if once in movement, the longitude B-X´ is 401,920 km, when the system B was at rest, this longitude should be

And, also, with the system B at rest the light would use

in carrying out the round trip journey between B and X´.

This duration has to be conserved when B reaches the speed of the example, otherwise the observers of system B would be under conditions of determining that its system suffered alterations as a result of the change of speed.

But we already know that light really takes 10.718 s in covering the distance B-X´ in a round trip journey.

So, if observers of axis B must believe that light only takes 5.359 s in this process, it is necessary that their clocks go halfway the normal speed (The speed that their clocks had when system B was at rest).

Summarizing:

So, we are under conditions of re-making the calculations we made in previous scenarios, but taking consistent values for times and longitudes.

Just as we just said, we accept that clocks B run 2 times slower than those of system A.

Again we are in the case that the observer B needs to trust the reading made by X´ with its own clock, in the moment in which the ray reaches its position. Therefore, we will analyze in what way B and X´ arrive to an agreement, with this new outline, as for the readings of their clocks.

In that case, a ray of light that leaves B toward X´ takes 5 s (0.5 x the 10 s measured at A) in reaching the position X´.

And it takes (0.5 x 0.718 s = 0.359 s) in returning to the position of observer B, consuming, in total, 5.359 s in the round trip itinerary.

These values are consistent with the distance B-X and the constancy of " c ".

But we must still verify the synchronism between the system B clocks.

If the total round trip time is 5.359 s, B and X´, both agree in considering as adequate that the clock at X' must read (5.359 s / 2) more than the clock at B when it receives the signal indicating that clock B reads (for example) 10:00:00

Summarizing B settles down (in common agreement with X´) that clock X´ should read 10:00:026795 when it receives the signal that clock B reads 10:00:00.

The system A observers realize that in system B something wrong is happening but they can do nothing about it.

The signal arrives to X´ when clock B reads 10:00:05. The clock B was reading 10:00:00 when the ray was sent and the additional 5 s are the consequence of the10 s that light takes (ACTUALLY) in reaching X´ but at halfway rhythm than clocks at system A.

What happens in that moment (seen from the privileged frame) is that clock X´ reads 10:00:026795 when the ray departs from B.

Although in system A they realize that clocks at axis B have a not well-made synchronization, the observers in B are happy. All the calculations close appropriately for them .

In B, they only made the simple supposition that light has the same speed going and turning back (w = z = c = 300,000 km/s)

Now we can calculate the speed of light (w) for people resting at system B.

The same thing would happen for the turn. This is not surprising because they used the approach z = w = c = 300,000 km/s, when they synchronized clocks.

Although it was not said explicitly, in this reasoning we used the synchronization mechanism suggested by Einstein. And this mechanism reproduce the way as things happen in round trip interactions.

IMPORTANT: What is shown in this example is that could exist a privileged reference system and not to be detectable in simple way. 

Final summary.

We have developed a classical model conception, using a privileged reference frame, that allows developing the relativity equations without generating the well-known paradoxes characteristic of Special Relativity.

This model allows for accelerations and paradoxes disappear.

In systems in movement (According to this development)

But systems in absolute motion are not able to show this movement.

Discussion_1.htm carried out a critical discussion about the outlines develop in this page.

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