of prof. ing. Giovanni Fraterno (Naples Italy: 6.08.2019)
My goal is to finally succeed in freeing up, after 114 years, the mental energies of so many young scholars to seek a new true and sensible physical theory of motion.
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Suppose that the stationmaster Bob is at the center of the station, and the conductor Alice is in turn at the center of the train.
Suppose that the stationmaster Bob and the conductor Alice are in uniform relative motion. They agree in having the parallel coordinated axes and starting their own clocks in the instant in which their reference systems coincide with the time t = t ’= 0.
From Bob's point of view, Alice moves with velocity V in the direction of increasing x, while for Alice, it is Bob who is moving with velocity V in the direction of negative x's.
In the instant t = t '= 0 when the 2 reference systems coincide in space, Bob and Alice are in the same place. Exactly in that instant Bob makes a spark strike in the origin, so that a light signal starts.
What will Bob be, the shape of the wavefront at time t ?
Well, for Bob, the shape of the wavefront is a spherical surface of radius R = ct, because the light propagates with the same speed in all directions. The center of the sphere is at the origin, where he, Bob, is. At the same time t, Alice is in position x = Vt. Well, for Alice the same thing happens, but this time it is she, Alice, who is still in the center of the sphere, while Bob has moved to the position x ’= -Vt’
That is: for each of the 2 observers, not only is the other one moved, but each of the 2 observers is also considered to be stationary in the center of the spherical wave.
How is it possible that Alice and Bob are still in the center of the single spherical wavefront, if they are in different positions ?
The answer follows.
We know that the set of events of the spherical wavefront of Bob, (ct, x, y, z), must satisfy the equation of a sphere of radius R = ct:
x^2 + y^2 + z^2 - (ct)^ 2 = 0
This set of events are obviously all simultaneous for Bob, because the events that take place all at time t are on the sphere.
The same wavefront is also observed by Alice, who uses her own coordinates (ct’, x’, y’, z’). Also for her it must be:
x’^ 2 + y’^2 + z’^2 - (ct’)^2 = 0
Having said this, let us consider the events A and B which belong to the wavefront in the center of which is the stationmaster Bob (who for the sake of brevity we will call from this moment: "Bob wavefront") and where:
- A is the event: the metric wheel placed at the entrance of the station is hit by the "Bob wavefront"
- B is the event: the metric wheel placed at the station exit is hit by the "Bob wavefront".
And therefore:
- given that event B is closer to Alice than event A, because in Bob's reference, Alice moves towards the station exit and then towards B
- then it means that even in Alice's reference event B must be closer to Alice than event A.
But, if A and B are for Alice at different distances, then for Alice the 2 events A and B CANNOT BE SIMULTANEOUS. That is: for Alice it must be t'B <t'A precisely because B is closer than A.
Generalizing: the events of the spherical wave that are simultaneous for Bob, are not however for Alice.
Or:
- while Bob's spacetime is traversed by the outgoing spherical wave, its simultaneous events are on an equation sphere:
x^2 + y^2 + z^2 - (ct)^2 = 0
- the simultaneous events of Bob vice versa happen for Alice not simultaneously, and in fact in times and positions such that those simultaneous for Alice are on a different sphere of equation:
x’^2 + y’^2 + z’^2 - (ct’)^2 = 0
By imposing that all this happens, at the end of a series of mathematical passages, we obtain the so-called Lorentz transformations, and that precisely allow us to transform the coordinates of an event (ct, x, y, z) of Bob into the coordinates (ct ', x ', y', z') of Alice.
I will use 2 metric wheels to arm the measure of which just after, so that what is lacking in what is literally in the stationmaster's hands Bob, literally finding himself in the hands of the conductor Alice, can only prove that simultaneity exists for both, and is therefore absolute and not relative. We will imagine that around each of the 2 metric wheels a tape is wrapped around 30 meters long.
But let's go with order.
Suppose that the stationmaster Bob, at the center of a 100-meter long station, and the conductor Alice, in turn at the center of a train 800 meters long, are in uniform relative motion.
From Bob's point of view, Alice moves with speed V to the right, while for Alice, it is Bob who is moving with speed V towards the left.
When Bob and Alice are in the same place, Bob fires a spark so that a light signal starts.
Having said this, let us consider the events A and B which belong to the wavefront in the center of which is the stationmaster Bob (who for the sake of brevity we will call from this moment: "Bob's wavefront") and where:
- A is the event: the metric wheel IN, located at the station entrance and then 50 meters to the left of the stationmaster Bob, is hit by the "Bob wavefront"
- B is the event: the metric wheel OUT, located at the station exit and then 50 meters to the right of the stationmaster Bob, is hit by the "Bob wavefront".
The aforementioned 2 metric rollers, precisely arranged: the first IN at the entrance of the station and the second OUT at the station exit, each one is also equipped with 2 independent (one from the other) electronic devices, identical to each other, and that are activated when they are hit by the "Bob wave front", and in the way they fire a long pin that sticks in the side wall of the moving train, a pivot to which the respective metric wheel is hooked.
The same 2 electronic devices are also able to cut the wrapped tape around the 2 respective metric rollers even when they are unrolling, and exactly, and always autonomously and automatically, when the train has traveled a preset distance D (depending on the train speed V).
I point out that the cutting of the 2 belts is autonomous and automatic because the 2 devices have in memory the distance D, and that they compare electronically with the distance that the train travels in real time, and when the latter passes in front of them.
The distance D is preset when the train is still stationary, and must take into account the speed of the train and obviously must have a value that allows the "Bob wavefront" to have all the time it needs to hit the 2 wheels metrics and even a little further.
We therefore determine D:
- before everything starts, let's imagine Alice stops in the middle of the train, I repeat 800 meters long, train in turn stopped for most of its length to the left of the station, and exactly with Alice distant 250 meters from the center of the station where it is the stationmaster Bob. For 200 meters the train is therefore stopped in the station and beyond, while for the remaining 600 meters the train is stopped outside and to the left of the station
- we also imagine that the train subsequently crosses the station at the speed V of 10 meters per second (V = 10 m/sec), and to simplify the calculations, we assume that this speed is reached instantaneously.
Alice, moving at a speed of 10 m/sec, therefore reaches Bob in 25 seconds, or Bob sparks 25 seconds after the train departs.
The "wavefront Bob" that is generated, reaches the metric wheels IN and OUT in DELTAt seconds, an obviously very small interval of time finding the 2 metric wheels just 50 meters from the center of the "Bob wavefront".
The distance D remains at this determined point, in fact a good value is D equal to 260 meters (D = 260 m), in this way, when the automatic cutting takes place, a tape will be unrolled from each of the 2 metric wheels long:
length of the cut tape = 10 meters - [ V * DELTAt ]
After the distance D, and therefore once the 2 belts have been cut independently and automatically:
- as the stationmaster Bob verifies that the tape surplus still wrapped around the OUT metric wheel is long:
20 meters + [ V * DELTAt ]
- as the stationmaster Bob also checks that the tape leftover wrapped around the IN metric wheel is long:
19 meters + [ V * DELTAt ]
consequently Bob understands that the two aforementioned events A and B were not simultaneous, ie he understands that the event A occurred before the event B.
The same conclusion also reaches Alice, and in fact:
- the conductor Alice verifies that the sheared tape remained fixed to the respective pin making little first part of the metric wheel OUT, (pin that finds fixture in the side wall of the train) turns out to be long:
10 meters - [ V * DELTAt ]
- the conductor Alice also verifies that the sheared tape remained fixed to the respective pin making little first part of the metric wheel IN (pin that is fixed in the side wall of the train) turns out to be instead long:
11 meters - [ V * DELTAt ]
Even Alice then understands that the two aforementioned events A and B were not simultaneous, that is, she understands that the event A occurred before the event B.
The stationmaster Bob obviously understands that to make the 2 events A and B simultaneous, he simply has to move the metric wheel IN enough to the left, and after vati attempts, at the end, exceeded the distance D, and therefore once autonomously and automatically are the 2 tapes were cut:
- as the stationmaster Bob verifies that the tape surplus still wrapped around the OUT metric wheel is long:
20 meters + [ V * DELTAt ]
- as stationmaster Bob also checks that the tape leftover wrapped around the IN metric wheel is long:
20 meters + [ V * DELTAt ]
consequently Bob understands that the two aforementioned ev
The same conclusion also reaches Alice, and in fact:
- the conductor Alice verifies that the sheared tape remained fixed to the respective pin making little first part of the metric wheel OUT, (pin that finds fixture in the side wall of the train) turns out to be long:
10 meters - [ V * DELTAt ]
- the conductor Alice also verifies that the sheared tape remained fixed to the respective pin making little first part of the metric wheel IN (pin that is fixed in the side wall of the train) turns out to be long:
10 meters - [ V * DELTAt ]
Alice also understands that the two aforementioned events A and B were simultaneous.
That is: the conductor Alice, regardless of the speed V, regardless of the watches, regardless of the light and its speed, regardless of the inertial references (allowed and not allowed that exist), regardless of how much the speed V is more or less high, regardless of the fact that event B is seen by Alice closer to herself than event A (and this because Alice moves towards the station exit and therefore towards B), the same conductor Alice verifies that the 2 sheared strips still attached to the 2 respective pins fixed in the side wall of the train are perfectly of the same length. The conductor Alice, I repeat, thus comes to the natural conclusion that the 2 events A and B are simultaneous.
Conclusion: unlike what the supporters of Special Relativity say, the so-called relative simultaneity of a specific event is brought into play and imposed as physically existing to mathematically derive the Lorentz transformations, as I have experimentally demonstrated, it is not true that it is relative, but vice versa it is completely absolute, thereby disavowing the Lorentz transformations.
