There appears to be some confusion over my previous post on Relativity so I want to produce some further clarification. First, we know that Einstein’s version of the train was used to destroy the concept of “simultaneity” because what is observed on the moving train as being simultaneous was not observed as being simultaneous outside the train. In reality what this demonstrated is that time itself is fluid; there is no objective time. Time, apart from frame of reference, is meaningless. Far from being a defeater to my argument (as Paul C. seems to think), this was my point.
Brian Greene gives his own example of this experiment:
Imagine that the leaders of two warring nations, sitting at opposite ends of a long negotiation table, have just concluded an agreement for a ceasefire, but neither wants to sign the accord before the other. The secretary-general of the United Nations comes up with a brilliant resolution. A light bulb, initially turned off, will be placed midway between the two presidents. When it is turned on, the light it emits will reach each of the presidents simultaneously, since they are equidistant from the bulb. Each president agrees to sign a copy of the accord when he or she sees the light. The plan is carried out and the agreement is signed to the satisfaction of both sides.
Flushed with success, the secretary-general makes use of the same approach with two other embattled nations that have also reached a peace agreement. The only difference is that the presidents involved in this negotiation are sitting at opposite ends of a table inside a train travelling along at constant velocity. Fittingly, the president of Forwardland is facing in the direction of the train’s motion while the president of Backwardland is facing in the opposite direction. Familiar with the fact that the laws of physics takes precisely the same form regardless of one’s state of motion so long as this motion is unchanging, the secretary-general takes no heed of this difference, and carries out the light bulb-initiated signing ceremony as before. Both presidents sign the agreement, and along with their entourage of advisers, celebrate the end of hostilities.
Just then, word arrives that fighting has broken out between people from each country who had been watching the signing ceremony from the platform outside the moving train. All those on the negotiation train are dismayed to hear that the reason for the renewed hostilities is the claim by people of Forwardland that they have been duped, as their president signed the agreement before the president of Backwardland. As everyone on the train—from both sides—agrees that the accord was signed simultaneously, how can it be that the outside observers watching the ceremony think otherwise?
Let’s consider in more detail the perspective of an observer on the platform. Initially the bulb on the train is dark, and then at a particular moment it illuminates, sending beams of light speeding toward both presidents. From the perspective of a person on the platform, the president of Forwardland is heading toward the emitted light while the president of Backwardland is retreating. This means, to the platform observers, that the light beam does not have to travel as far to reach the president of Forwardland, who moves toward the approaching light, as it does to reach the president of Backwardland, who moves away from it. This is not a statement about the speed of the light as it travels toward the two presidents—we have already noted that regardless of the state of motion of the source or the observer, the speed of light is always the same. Instead, we are describing only how far, from the vantage point of the platform observers, the initial flash of light must travel to reach each of the presidents. Since this distance is less for the president of Forwardland than it is for the president of Backwardland, and since the speed of light toward each is the same, the light will reach the president of Forwardland first. This is why the citizens of Forwardland claim to have been duped.
When CNN broadcasts the eyewitness account, the secretary-general, the two presidents, and all their advisers can’t believe their ears. They all agree that the light bulb was secured firmly, exactly midway between the two presidents and that therefore, without further ado, the light it emitted travelled the same distance to reach each of them. Since the speed of the emitted light to the left and right is the same, they believe, and in fact observed, that the light clearly reached each president simultaneously.
Who is right, those on or off the train? The observations of each group and their supporting explanations are impeccable. The answer is that both are right. … The only sublety here is that the respective truths seem to be contradictory. An important political issue is at stake: Did the presidents sign the agreement simultaneously? The observations and reasoning above ineluctably lead us to the conclusion that according to those on the train they did while according to those on the platform they did not. In other words, things that are simultaneous from the viewpoint of some observers will not be simultaneous from the viewpoint of others, if the two groups are in relative motion.
This is a startling conclusion. It is one of the deepest insights into the nature of reality ever discovered. Nevertheless, if long after you set down this book you remember nothing of the chapter except for the ill-fated attempt at détente, you will have retained the essence of Einstein’s discovery. Without highbrow mathematics or a convoluted chain of logic, this completely unexpected feature of time follows directly from the constancy of the speed of light, as the scenario illustrates. Notice that if the speed of light were not constant but behaved according to our intuition based on slow-moving baseballs and snowballs, the platform observers would agree with those on the train. …
The constancy of the speed of light requires that we give up the age-old notion that simultaneity is a universal concept that everyone, regardless of their state of motion, agrees upon. The universal clock previously envisioned to dispassionately tick off identical seconds here on earth and on Mars and on Jupiter and in the Andromeda galaxy and in each and every nook and cranny of the cosmos does not exist. On the contrary, observers in relative motion will not agree on which events occur at the same time. Once again, the reason that this conclusion—a bona fide characteristic of the world we inhabit—is so unfamiliar is that the effects are extremely small when the speeds involved are those commonly encountered in everyday experience. If the negotiating table were 100 feet long and the train were moving at 10 miles per hour, platform observers would “see” that the light reached the president of Forwardland about a millionth of a billionth of a second before it reached the president of Backwardland. Although this represents a genuine difference, it is so tiny that it cannot be detected directly by human senses. If the train were moving considerably faster, say at 600 million miles per hour, from the perspective of someone on the platform the light would take almost 20 times as long to reach the president of Backwardland compared with the time to reach the president of Forwardland. At high speeds, the starting effects of special relativity become increasingly pronounced.
Greene, Brian. (1999). The Elegant Universe. New York: Vintage Books. 34-37 (all italics in original)
Now we have three different examples (Einstein’s, my own, and now Greene’s), all of which really state the same thing. The sequence of events that one observes is dependent upon the relative motion between the observer and what is being observed. While Einstein and Greene both dealt strictly with concepts of simultaneity, it doesn’t take much thinking at all to change this into my own example where we have an event that occurs before another event according to one frame of reference occur after the other event in another frame of reference. In fact, in Greene’s second book (The Fabric of the Cosmos), he gave an illustration of this regarding cuts in the “space-time loaf.” Unfortunately, I’ve loaned that particular book out for the moment. But I will reproduce my own version of cutting the space-time loaf here.
In this picture, we have three events that occur separated by vast distances in space and time. For example, we could say that A is ten million light years from B, and likewise B from C (these are just arbitrary values for the sake of demonstration). We could also say that it takes 10 million years to go from “blue” to “red” to “green.” (Thus, time is going right to left.) Thus, the vertical axis of this diagram represents distance, the horizontal axis represents time.
Now from the perspective of one observer, all the “red” events at A, B, and C occur simultaneously. This observer has a “timeslice” that is directly perpendicular (in our graph). But from another perspective, the “green” event of A is simultaneous with the “red” event of B and the “blue” event of C. This “timeslice” is at a roughly 45 degree angle (both in space—that is distance—and in time—he is in the “future” if time is flowing from right to left).
Now let us give the graph some non-controversial meaning (although you must take note that the graph will not be to scale under these circumstances). Take line A as the life of a star that goes supernova (at green), line B is the life of a star that dwindles to a dwarf star (at green), and line C represents events that occur on Earth until Global Warming melts us (at green). Let’s further say that on Earth, the red dot represents the signing of the Declaration of Independence, and the blue dot represents the construction of the Great Pyramids. The red and the blue dots of the two stars are adjusted accordingly to be arbitrary events that occur at the correct time-scale.
Now obviously the observer that views perpendicularly sees that at the signing of the Declaration of Independence, both stars had the same amount of time left before reaching their ends. However, the observer at the 45 degree angle sees that the supernova star has actually gone supernova while the Great Pyramids are being built!
Now let us give it a little more controversial meaning (again, the graph is not to scale under these circumstances). Let us deal only with lines A and C. Let line A represent the bullet of a gun and let line C represent the finger that pulls the trigger. Line A is: “blue” = bullet loaded, “red” = bullet fired, “green” = bullet kills target. Line C is: “blue” = trigger finger in killer’s pocket, “red” = finger pulls trigger, “green” = finger rubbing killer’s nose. Now in this instance, the distance between line A and C is very, very short. But since a man’s finger and a bullet can never occupy the same space at the same time, there will always be some distance—even if it is only an atom’s length! As a result, the distance to the observer at the 45 degree angle (to both space AND time!) is going to be very, very far away. But the results are the same.
In one perspective, the trigger finger pulls the trigger at the instant the bullet is fired. But in the other perspective, we have the bullet being fired when the killer’s finger is in his pocket. Now the distance to this observer is probably outside the dimensions of our universe and far, far into the future from now. But that observation point does exist in theory. In theory, viewing any two events at the appropriate “timeslice” of the spacetime loaf will yield contradictions in cause and effect. Naturally, these are on such a large scale that for all practical purposes we can ignore them.
So once again, we can relate this back to what I’ve said about the logical before. Cause and effect is determined by what logically must occur before another thing can happen, NOT by what temporally occurs. Usually the logical and temporal correspond, but when it does not we have evidence that we have to adjust our frame of reference. There will be some frame of reference where that cause will temporally precede its effect, but that might not be our observational frame of reference. Our frame of reference, taken at face value, would cause us to be mistaken.
By the way, I also point out that this is the basis of the Lorentz transformation equations anyway. Those equations in essence seek to show the relationship between various frames of reference. And the point isn’t that cause and effect are destroyed at all—that’s never been what I claimed. Rather it’s the fact that cause and effect are temporally meaningless when there is no objective time; instead, they can only remain logically meaningful.
Logical precedence is not bound by frame of reference; it is the objective quality that causes must precede effects. Temporal “before” are strictly bound to frame of reference; it will always be a subjective quality. On Earth, it usually matches the objective frame of reference because the relative speed between observer and observee remains very small.
Hopefully that helps clear it up a bit.
