Nowhere is the study of causality more relevant than in the study of time travel. Of the causality arguments by far the most familiar is that of the grandfather paradox. In the grandfather paradox a time traveler uses his time machine to go back in time and murder his grandfather. If we allow our time traveler to carry out this travesty what would become of him? would he cease to exist? If he did than wouldn't that mean that he never killed his grandfather and so is now capable of existing again? The loop is a vicious one and this argument alone has succeeded in convincing many people to disregard time travel as impossible. This argument is one of the most cogent and straight forward that can be built up on the subject of time travel. I find it irksome however that this refutal of time travel has existed so long under the guise of causality. The real culprit in this paradox is not causality but self reference. The fact is that effect can preceed cause without necessarily causing logical inconsistiencies. For those who deem time travel possible dismiss the grandfather paradox on equally logical grounds. The first argument is that a time traveler will not be able to kill his grandfather for the simple reason that he obviously never did. Time travelers they hold are not capable of changing the past because they had already traveled back in time and affected the time line before they ever built the time machine! This solution is mocked by many as either unstable because we cannot dictate what a time traveler would actually do if he came back in time. In order to make the argument work we must assume that anyone that would have killed their father before they were born given the opportunity cannot travel back in time. Despite the restrictive nature of this solution to the paradox it does demonstrate that time travel does not necessarily lead to logical fallacies. Self reference could with equal logic be deemed the culprit in the grandfather paradox. Anything that makes itself its own subject is guilty of self reference. For a separate treatment of the subject see my discussion on it here For this discussion it suffices to say that the only reason that the grandfather paradox leads to a logical fallacy is that it allows the time traveler to make any change (make any statement about) his past. which is just a more complicated version of the same logical fallacy that causes to the sentence "This statement is False"
There is a second solution to the grandfather paradox in which the time traveler is capable of killing his grandfather. This solution requires a belief in parralel universes. Quantum mechanics can be equally well explained by the standard model of quantum theory and a rival theory in which every time a particle must make a decision the universe splits. in one universe the particle made one choice in the other it made a different one. while this may seem crazy the theory has gained momentum over the past few decades and is now a main train of thought. In this kind of "multiverse" we find that the time traveler does not go back in time to his own time. in fact the time traveler is incapable of entering his own timeline because his mere presence indicates a split off point for a whole generation of new universes in which the time traveler now appears. if this is the case then the time traveler does not kill his grandfather but rather a parralel universe counterpart of his grand father. Causing a whole branch of universes in which the time traveler is never born.
so what is the answer to the question of what happens to our time traveling friend upon the murder of his grandfather? The answer is absolutely nothing! if the first scenario is true and time travel is not possible then the murder is averted. if the second scenario holds true then the time traveler will be foiled in his attempt and so again the murder is averted. If the third scenario holds true then the time traveler murders the person that would have been his grandfather but again the murder of his real grandfather is averted.
All this translates to all universes must be self consistient. Self consistient is a convienient term which means that no logical fallacies occur in the universe there are no loose ends and no contradictory statements. so in otherwords no time traveler can ever kill his grandfather because that would mean that an effect had no action to cause it. So although we cannot prove that cause always preceeds effect we can say that cause always is associated with an effect. So newtons third law of cause and effect may be all that can be said about the cause and effect relationship with any degree of absoluteness.
while the argument up to this point has been of a nearly logical nature in which we logically followed out arguments based on the premise of the existience or non existience of time travel. however causality is actually a physically measurable phenomenon. In the newtonian world causes seem to need to preceed effects. However in the quantum world not only do causes not "need" to preceed effects they often do not.
first it is important to understand that in the quantum world things happen only when they are forced to happen. schroedinger is famous for his thought experiment in which he places a cat in a box with some poison food. There is no way of telling what has happened in the box until we open it. Schroedinger then holds that the cat in the box neither has eaten the poison and died nor is it still alive untill someone opens the box to see which outcome prevailed. The cat in the box is in a superposition of states being both dead and alive at the same time. only when we open the box or measure the state of the cat does it actually become one or the other. Now this scenario could never really occur because we are incapable of constructing such a box that would cut of the cat from us completely. however the principle seems to hold on a subatomic scale. in the familiar slit experiment an electron beam is aimed at a wall with one or two slits in it. when we aim the jet at the wall with one slit we find that the electrons on the other side show a circular pattern with the most electrons directly across from the hole and a few strays scattered in a radial pattern around the center. in the experiement with two slits the electrons pass through the holes and display an interference pattern illustrating the wave/particle nature of the electron. IF we change the experiment to allow only one electron at a time through the slit we still get the same interference pattern. The electron is effectively going through both holes at once in order to interfere with itself and give the interference pattern. Now if you will please recall about what I said about the quantum world not making a decision unless it is forced to. in this case the electron has the choice of going through one of the two holes but since we do not force it to choose between them it never makes the decision and therefore goes through both holes. However just like with the cat in the box we can force the electron to make a choice between the holes by putting little detectors at each one of the slits to measure which one the electron goes through. in this case the electron is forced to make a decision and it goes through one hole or the other tripping the apropriate detector and instead of an interference pattern we get again the simple circular pattern concentrated at the center and fading away with distance.
now using this experiment we have a usefull tool for investigating quantum causality. we send an electron through the machine and while it is in transit we decide weather or not to activate the detectors. if we do activate the detectors we know that the electron will be shown to pass through one hole or the other, not both, and therefore show a simple radial concentration pattern. However if we do not activate the detectors it will pass through both holes and we will get an interference pattern. Looking at the causes and effects here we see that the cause comes after the effect. the effect is what path the electron travels whereas the cause is wheather or not we turn on the detectors. the electron is already on its way through the machine and could well be already through the hole and interfering with itself when we switch on the detectors. at which point the electron is detected and its pattern is again the simple radial one. this cause and effect relationship however does not have to happen on the small scales whith which we are so accustomed to doing things in the quantum world. we could put the wall with the slits in it a light year away from the electron jet and only after almost the full year decide wether or not to turn on the detectors. in which case the electrons must have been traveling towards one hole or the other for months before we even knew ourselves that we were going to turn on the detectors and force them through a hole. effect preceeding cause on a humanly appreciable scale.
Lets consider the multiple universes theory for a moment. admitting that there is more than one universe in existence running along paralel time lines we usually generalize to admit an infinite number of possible universes. This however is not necessary we might designate the number of universes as the cardinality of the set that contains all possible sets of states in a universe. for a finite discontinuous universe with a finite number of states over a finite period of time there will be only a finite number of possible paralel universes. this seems a ridiculus number of constraints to put on a universe to make a finite number of paralel universes but it may actually describe our own universe. First we must consider that because our universe was created in a big bang it must have a finite span of existience. second quantum mechanics implies that a particle does not change states until it reacts with another particle which "detects" its state. therefore because the state of the particle does not change continuously the number of different states needed for any transition between states is not infinite but only two. Next we consider that our universe is quantized which means that the only states possible are those described at intervals from one annother. given a finite amount of action in the system there is an extremely high but finite number of possible states that can be taken. However the last constraint that we live inside a finite universe does not have any support other than that the possibility does satisfy the relativistic field equations. However these conditions are not the only ones in which there are only a finite number of paralel universes. lets take the example of a universe without beginning or end. in this case all states possible within the system will occur eventually and will occur an infinite number of times. however the totlal number of possible states of the universe does not necessarily divirge. For any two universes with the same total possible states we can show that there is some moment in time in which the states of the two universes are the same. In fact we can show that there will exist an infinite number of such points. We can even show that there are an infinite number of places in the histories of the two universes that they had the same states successively. since there is no beginning and no end to the universes we can shift them relative to each other until we find a relative position at which all the states match exactly. in other words not only is there only a finite number of possible paralel universes for a universe with a finite number of possible states and equal probabilites but there is only one possible universe for each set of states and probabilites. so there are actually no paralel universes for such a system. this may not seem possible that a system with all finite parameters could have more possible paralel universes than one with an infinite paramater. But to illustrate lets consider for a moment a universe who has only two possible states 1 and 0 and it occupies either state with equal probability in unit time. in the universe with a unit time there are two possible universes one described by 1 and one by 0 if time increases to two units there are three possible univeres represented by the states 11, 10, and 00. however in the infinite universe case there can be only one possible universe with any set of states and probabilities. take for instance the infinite universe represented by the series of states ...1010101010101... this universe may seem to differ from one represented by the series of states ...010101010101010... but in reality if we shift every digit one place to the right we come out with the same set of states and so only one universe. This however is far from a complete description of the universes with possible states 1 and 0 what about the universe described by ...1001001001001001001001...? this universe is clearly different from the previous two universes and is therefore a separate paralel universe. However I stated that the universes contain the same possible states as each other. This is not true for the ...1001... universe because while the states of 1, 0, 10, 01, and 010 are all possible in both universes the state 1001 is not possible in the first and the state 101 is not possible in the second and therefore are universes governed by different basic principles and not elegible to be paralel universes. This solution for a universe with an infinite time parameter does not hold simply for the condition of infinite time but must also hold to the condition that it has neither a beginning nor an end. If there is a beginning or an end it breaks the symmetry which allowed us to make the shifts to bring any two universes with the same total number of states into agreement. so while the universes ...0101... and ...1010... are the same the universes 0101... and 1010... are not.
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