Simultaneity

(First version (in Spanish): November 6^th, 1999
Last modification: September 3^rd, 2003.)

In this page I will try to arrive to the concept of simultaneity that allows settling down the relationship among distant events (with a significant spatial distance between them). Einstein began the development of the SR (Special Relativity) defining this concept through appropriately luminous signs. However, considering that the speed of light possesses a magnitude far away from our routine managed values, I will try to use situations closest to our daily experience.

Let us suppose that people in some city decide to scream simultaneously, maybe with the intention of greeting with a noisy "Good morning!" a neighboring city. To use a concrete case we could say that the educated city of this story is Buenos Aires and the surprised city, to be greeted, is La Plata (both cities in Argentina). The 3,000,000 people of Buenos Aires come to an agreement in screaming at 8:00:00 in the morning.

Let us also suppose, to simplify the reality, that people use good clocks and Buenos Aires is defined by a perfect circle of 10 Km diameter.

The sound travels 10 Km every 30 seconds and La Plata is located about 60 Km South from Buenos Aires. It makes the greeting arrives at 8:03:00 to La Plata.

FALSE!. People at La Plata could complain that since Buenos Aires decided to greet them, at least they could have do things appropriately with everybody screaming at the same time. According to people in La Plata, what they received was a confused murmur that lasted around half minute.

The reason is very simple. If all people at Buenos Aires screams at 8:00:00 and the greeting goes directed to La Plata, the scream of people North of Buenos Aires should first cross the own city before undertaking the journey 60 Km toward La Plata. And this internal journey takes thirty seconds (See Fig. 2).

When they realize the mistake, Buenos Aires decides to make things appropriately and synchronize the greetings keeping in mind the speed of sound. In this way, next day North Buenos Aires screams "Good morning!" at 8:00:00 and those of South at 8:00:30, while the rest makes the greeting in an intermediate moment, in accordance with the location.

Now yes!, people of La Plata are more satisfied, although they notice that in the East and West suburbs the greeting arrived again distorted. (Fig.3)

But when Buenos Aires decide to celebrate the improvement in greeting efficiency they receive a complaint from people at Lujan, also 60 Km from Buenos Aires but at North. The complaint is about the growing disorder of Buenos Aires. The previous day they had received a murmur of about 30 seconds of duration (the same as in La Plata) but today they received a noise of 1 minute.


*Fig. 1* - Advance of the sound wave	*Fig. 2* - Sounds generated "simultaneously" from distant centers

Confused the Buenos Aires inhabitants discover that they cannot carry out a simultaneous greeting from all surrounding cities. If they make the sound simultaneous in one direction, they cannot make it in another. In consequence the Buenos Aires inhabitants decided greet not more people in other cities, giving origin to this very well known Buenos Aires habit.

Fig. 3 - When sounds are emitted in order to obtain
a simultaneous advance towards South, they are
out of phase at all the other directions

Returning to the serious tone of this page, we could say that duration of thunder in rapport to the lightning is an example of this lack of absolute simultaneity. The physical phenomenon (the electric spark) lasts more or less what we see (the lightning) but the sound sign not only arrive later, but last much more. The reason of its biggest duration in thunder resides clearly in the different distance (until our hearing) from the different points of the lightning. The lightning is a phenomenon that embraces several km, as long as our hearing is a punctual receiver.

Arriving to this point the crucial question is: Does the lack of absolute simultaneity obey one problem that can be solved, or is an internal property of the system?

No matter how many times you turn around this question, we will finish with the convincing that it is impossible to make two distant sounds simultaneous for all observers.

I believe not falsify the reality if I affirm that the incredible genius of Einstein was manifested when he recognized this property of physical systems and the consequences that derive from it.

Frankly, we could try to solve the problem saying that there exists an absolute simultaneity, independent from the observers. So, if everybody screams at 8:00:00 o'clock the sound is simultaneous (by definition) and if, those that listen don't understand the message, it is their problems.

If you are one of those that have reached this conclusion you have to remember that Atomic Bomb works because there are people that decided to deep in the topic (and I am not saying that Atomic Bomb is good or bad, I only say that it exists).

Let us analyze the expression "...observers" I used in a previous paragraph. In that context I am referencing to people that is listening. However in Physics, we should equally the expression "observer" with "element that interacts with"

An atom that receives a luminous ray and exchange information with it, is the equivalent of an observer to this luminous sign. And here is where turns gigantic the Einstein conception. Einstein assumed that all matter interactions take place at maximum speed "c" (speed of light in vacuum = 300,000 Km/s).

Accepting this definition is accepting that there are not infinite speeds in the universe and therefore not absolute simultaneity exist in the universe. If somebody affirms that two distant events are simultaneous is accepting (implicit or explicitly) a definition of simultaneity.

At the naive solution of the sound problem, we used a much bigger speed to define in absolute form the simultaneity. Light is about 1,000,000 times faster than sound. In this way a separation of 60 Km is worthless using electromagnetic waves. For that reason we could synchronize the clocks but not the acoustic greetings.

So, if we use a system 1,000,000 times bigger, the light problem acquires the same magnitude than the sound problem just analyzed.

Let us suppose that now, the Solar System is the one who decides to greet with a luminous sign the neighboring planetary systems.

Again it is impossible to emit a sign that arrives simultaneous to all the stars. The lack of simultaneity between The Earth and Saturn signs can be several hours. And if we achieve the simultaneity in one direction the signals are not simultaneous in all other directions.

However we could appeal the same naive solution. Let us synchronize all clocks and send the sign at 8:00:00. I define this situation like a simultaneous sign and let those who receive the sign, to arrange themself with the problem!!!.

One moment! ..... Not so quick!. Because the question is now: How do I could synchronize the clocks?

Because, now, I don't have an infinite fast sign to put all clocks at the same hour. With sound, I used light as an infinite speed. But with light, what to use?

Let us suppose that although I don't have an infinite speed, I imagine that it exists and when I say: in Titan (city in a Saturn satellite) and in Buenos Aires it is 8:00:00 o'clock it is because these things happen simultaneously.

We will see that this is not as simple as it can seem. In what form do I control this "absolute" synchronism? In other words: How can I be sure that a clock in Buenos Aires mark 8:00:00 simultaneous with that of Titan? Remember that light takes more than one hour traveling the distance Earth-Titan and (one additional detail) this distance is varying continually as a result of planetary and satellites rotations and adjournments.

Synchronization implies the travel of signals (in both senses) for "verifying" that the readings of the clocks are consistent.

We finish here the problem outlining that synchronization of clocks are based on the sketched concept of simultaneity