JesseM said:
if anyone at the trial understands physics they can show that because of the speed of the signals and the movement of the device at the center, then even though the strikes were non-simultaneous, they were timed just right so that the signals would reach the device simultaneously. So why did the jury conclude that you and Dr. Mad were innocent? Are you just assuming that the jury isn't capable of basic physics calculations, and none of the physicists who testified bothered to correct them?
You also seem to be using this thought-experiment to support the idea that the strikes really were simultaneous in some objective sense. Why? Even if one believes in some sort of Lorentz ether theory where one frame's measurements are objectively correct and all other frames are distorted by the fact that their rulers are objectively shrunk and their clocks objectively slowed down and objectively out-of-sync, it is still perfectly possible that the observers on the ground were the ones at rest in this preferred frame while the train was moving relative to it, and thus the strikes really did happen at different times in an objective sense.
I fully agree, but still think that althonhare has some valid points.
As I said in an earlier post, relative simultaneity is relative and absolute simultaneity is absolute and each concept has its own purpose and hence should have its own niche in language. The problems (the paradoxes) only arise if you use one for the purpose of the other or vice versa. But please don’t quote this clumsy paragraph in helpless isolation. I’ll try to explain myself.
Absolute simultaneity of two events is an idea, an intellectual construction, an invention of the mind. Nobody can forbid me to imagine and define that concept as such: an abstract notion, valid for discussion purposes. It means the following: if two events are “absolutely simultaneously”, that entails that they both have “happened” and hence it is logically impossible that one of them is prevented from happening. For example, if a witness from event 1 (located in a frame where that event has happened “earlier”) traveled towards the location of event 2 faster than the speed of light (that is impossible, but even if it were possible), she would not be able to avoid that event 2 happens, because it has already happened and it has not happened in isolation, it has immediately created a myriad of interactions with its surroundings (remember the butterfly effect) that cannot be blurred out, at least in this universe (leaving aside the funny idea of parallel universes). Thus this concept plays a useful role. For example, you don’t follow the threads where people talk about tricky ways to overcome the speed limit, time-travel and kill your dear grandmother before she gives birth to your father. This saves you a lot of time to study relativity.
However, and here I loosely follow Einstein himself, for practical reasons, we may have to leave aside the chimera of measuring absolute simultaneity and content ourselves with relative simultaneity. The practical reasons are the fact that our measurements are inherently relative, since they are made from a certain position and state of motion, with physical instruments affected by a physical environment and so on. In principle, one should not discard that, in spite of all that, those measurements yield homogeneous effects, at least in some respects, since there often arises the helpful phenomenon of “compensation of effects”. In fact, you would not be able to apply transformations between different relative values if you couldn’t rely on some common or homogeneous ground (absolute spacetime in SR?).
In particular, the specific measurement of simultaneity, as of today, with our current measurement technology, yields relative values. Thus the simultaneity measurements carried out in the thought-experiment from the train and from the embankment gave off frame-dependent values. Does it mean that they are not equally trustable? Yes, they are! For their purpose, they are! If you combine the RS with TD and LC, you get a coherent system where all observers make the right predictions. Hence, as long as you do not ask them to do a different thing, we cannot prefer one measurement of simultaneity over the other, we cannot say that one was wrong and the other was right: in fact, both types of measurements helped the respective measurers to predict adequately the single event, the simultaneous arrival of the two light signals at the centre of the chair. Each served the purpose for which it had been made, so it was right… in that sense, for that purpose! Of course, if someone comes to you and says that, just because in her frame one event happened earlier, your grandmother was killed before your father was born, you dismiss her immediately, because the purpose of a relative measurement of simultaneity is not to predict nonsense.
Thus the two concepts of simultaneity can live together peacefully, like good brothers, each serving its own purpose in life. This paradigm should protect us against two types of mistakes:
a) The mistake of some critiques of SR = thinking that one of the two relative measurements must be absolute for the wrong reason, just because it serves its purpose. I am sorry, but both measurements serve their purpose, the one from the train and the one from the embankment. As JesseM points out, if one thinks (for discussion purposes!) that there is an aether, a synch operation carried out with the Einstein convention at rest in the aether frame would yield a measurement of absolute simultaneity, in the above sense. But it might perfectly happen that the frame at rest in the aether is the embankment and then your criterion, althonhare (really simultaneous is what is simultaneous in the “local” frame), is not valid. Events do not belong to any frame in particular, they take place in all frames. In your trial, what makes you guilty is not the fact that the bolts are absolutely simultaneous in the train (most probably they are not), but the fact that the device had been designed so as to kill if it captured relative simultaneity as measured on the train or, if you prefer, a certain relative non-simultaneity as measured from the embankment.
b) The mistake of some SR defenders = But I am too tired now and probably little prepared for that…
Criticism for this part is welcome.
Althonhare, would you consent? Otherwise I would initiate another thread, some day.
