As regards simultaneity: in Einstein’s 1917 book, his attempt to justify the relativity of time rests on the analysis of the concept of simultaneity. Einstein begins this book by questioning the traditional concepts of time and space, and asserting that these traditional ideas are in conflict with the idea that light propagates at a constant speed. He maintains that it is the relativity of “simultaneity” which leads us to a different view of reality, and to the concept of the relativity of time and space, as opposed to the absolute nature of time and space.
But, as is clear, Einstein does not realize that there are two distinct and independent types of “simultaneity.” One type occurs when a single observer is aware of two distinct signals simultaneously, for example, hearing a doorbell and a siren at the same time. We can call this e-simultaneity, i.e. one observer, two events. The other type occurs when two observers become aware of one event at the same time, such as an explosion or an earthquake. We can call this o-simultaneity – two observers, one event.
Einstein confuses these two types of simultaneity, and so comes up with the bold assertion that simultaneity is relative. What he needs is for o-simultaneity to be relative, but borrowing the idea from e-simultaneity is not legitimate.
In addition, Einstein is unclear when he refers to the simultaneity of events. Sometimes he means the origin of signals, and sometimes he means the signals as received by one or two observers.
We can use a bolt of lightning and an exploding balloon or dirigible as an illustration of the difference between e-simultaneity and o-simultaneity. In the limiting case, which we could call true simultaneity, the bolt of lightning strikes the dirigible and it “simultaneously” explodes. Now all observers, wherever they are, or however fast they are moving, will see these two events “at essentially the same time.” They originate at about the same time from the same place, and therefore take the same time to reach any given observer (e-simultaneity).
However, observers may be at different distances from this double event, so they will not experience it “at the same time.” We are using the phrase “at the same time” in two different ways. It can mean “concurrently,” if it relates to the two events, but it also can refer to the clock time when we compare the time at which the signal reaches different observers (o-simultaneity).
By not keeping track of the different meanings, we can easily draw false conclusions. e-simultaneity does not imply o-simultaneity and the relativity of one does not imply the relativity of the other.
For Einstein’s theory, it is o-simultaneity that is the real issue, whether two observers in relative motion can compare experiences in a time frame common to both. He needs the relativity of e-simultaneity, but it does not apply to o-simultaneity, We see that Einstein’s attempt to justify the consequences of SRT by appealing to the concepts of simultaneity and synchronization, relies on ambiguities and contradictions in language and logic.
We can, and need to, be more precise with respect to the idea of “synchronization.” As with other concepts that Einstein uses, or misuses, this one also has two or more parts that we can call I-synchronization, B-synchronization, and T-synchronization.
The first, I-synchronization, relates to having equal intervals, or, say, seconds of equal duration; the third type, T-synchronization, refers to setting two clocks to the same point, or position, as we do when we adjust our wristwatch to another reference clock. That is what we are concerned with in the case of two points A and B that are stationary, or fixed to a body or platform. The first, I-synchronization, is the issue when it comes to bodies in motion. That is the question of time dilation. B- synchronization occurs when the points, indicating the beats between intervals, are simultaneous. It is important in music, such as drumming, or synchronizing all the violins in an orchestra when they are plucked. A good dictionary often gives several definitions of “synchronization,” corresponding to those above.
If the clocks are fully synchronized and the distance between them at locations A and B is fixed, the differences between tA and tB will correspond to the time it takes for a pulse of light to move from A to B and similarly for the return path from B to A. In that case, the differences tB – tA and tA’- tB will be equal.
The converse of this then becomes:
If the differences tB – tA and tA’- tB are not equal, then either there is motion during the time of travel of the light from A to B and back, or, alternatively, the clocks are not fully synchronized. At most, you can use these differences to create or verify T-synchronization, not to establish, verify, or define I-synchronization, which is the issue for SRT.
That would have been the correct logical inference.
Einstein – June 30, 1905
On the Electrodynamics of Moving Bodies
End of section 2:
“So we see that we cannot attach any absolute signification to the concept of simultaneity, but that two events which, viewed from a system of co-ordinates, are simultaneous, can no longer be looked upon as simultaneous events when envisaged from a system which is in motion relatively to that system.”
This shows that Einstein had no clear idea about the meanings of ‘simultaneity’.