Jerry Wickey

Janus seems very sure of his take on this. But to clarify. Is Janus saying? A) The space between two space ships is closing and it doesn't matter who is moving, both toward each other or one stationary and the other moving, in both cases each observe time dilation in the other, but that when they pass each other, both will have experienced the passage of the same amount of time. B) A space traveler leaves earth, a significant source of gravity, moving at near light speed. Upon his return to earth he will have experienced the passage of less time than those having remained on earth. Earth will have aged more than the traveler. C) A space traveler leaves a space station far from any significant source of gravity, moving at near light speed relative to the motion of the space station. Upon his return to the space station he will have experienced the passage of less time than those having remained on the space station. The space station will have aged more than the traveler. Janus, Are you claiming all three of these statements are true? Or are you claiming that A and B are true and that C is false?

That is very helpful. Thank you. Your diagrams is very helpful, but it is fails to explain the paradox. I understand the vertical axis to be time and the horizontal to be distance through space. Light always moves on this graph at 45degrees, because of course, it is moving as fast through space as it is through time. Your graphs presume a sudden acceleration to a then constant velocity. This impossibility posses no difficulty or error in our examination of the circumstances. Everything is limited to the speed of light and so if we move very fast through space and remained moving at the same speed through time, the sum of our vectors through space and time would exceed the speed of light. Therefore, if we move very fast through space the sum of over velocity vectors sqroot (space_distance ^2 + time_passed ^2) / time must always be c. This is the Lorentz. You are exactly correct in the observation that neither rockets perceive the movement of the other for some time, but the diagram has two errors. First the rate at which the ticks occur changes after the rockets begin to move (see my marks on your graph) and in the second graph the rocket on the right is not stationary but is moving away from the other. This makes your graph appear to explain the paradox, but does not. If the rocket on the right remains stationary in space, it is still moving through time. While the rocket on the left is moving through space and time. Because it can not exceed the speed of light, its movement through time must slow to accommodate its rapid movement through space. Because of this, the rocket on the left perceives light ticks emanating from the rocket on the right at a more rapid rate. He perceives time having quickened for the rocket on the right. He understands, his own time as slowed. When they meet, whether they come to a stop or not doesn't matter. More time will have passed for the rocket on the right as for the rocket on the left. eight ticks for the rocket on the right while the rocket on the left will have passed nine clicks. They both have moved through the same amount of time, but because the rocket on the left has also moved through considerable space, his movement through time must be slowed otherwise the sqroot of the sum of the squares of his distance and time would exceed the speed of light. This I understand. Relativity is why the clocks on GPS satellite run slower. Actually general relativity has more to do with that than special, but the point is if an astronaut ever visits one of those satellites it's clock will not have caught up to his as you claim "each reading ~15" The only reason the same number of clicks appear is because the distance you put between them is adjusted, but neither for the passage of time nor for their respective movement through time. They seem to be adjusted just to make them match up. Here is a graph showing equal distances between clicks. i.e the speed of light for all. As one rocket moves through space it can not move through time as quickly, because of course the rockets aggregate speed would exceed light. The paradox of the relativity of motion is still unexplained. It does't matter for the rocket on the left this he is moving. From his perspective it is just as true to say the rocket on the right is moving instead and his clock should be slowed showing the passage of less time, when they pass each other. This is equally true for the other. I would really like to understand this from someone who truly understands relativity.

michel is right. Accelerations doesn't change anything. As each accelerates closer and closer to the speed of light, time is slowing for them, mass in increasing and distance is shortened in the direction of their travel, but for them all their rules, scales and clocks still read exactly as they expect. They measure their mass the same and their fuel consumption the same. This in spite of the fact that an observer at rest observes the mass of their fuel reserves increasing. But more importantly, both observe the other rocket which is speeding toward them experience the effect of time dilation. Both observe the other passing through time more slowly. This effect does not go away when they slow down to greet each other as Janus poses. Each observes the other passing through time more slowly throughout their whole journey until they come together. At which time each says of the other, you are younger than I. How does relativity resolve the paradox?

Not so, They can establish simultaneous clocks before beginning their journey toward each other. This is how. Before beginning their journey toward each other, both ships send a light signal to the other. Each bounces it back. This tells both exactly how far apart they are. They do this twice to establish that the distance between them is not changing over time. At this point neither is moving relative to the other and they could also have transmitted the reading from their respective clocks. Since both know and agree how far apart they are before they begin to move, both know what each other's clock read and how far, how long ago it read that. Both know what the other's clock reads simultaneous to their own before they begin the journey toward each other. As their journeys begin, both observe the other experiencing time dilation. How is this paradox resolved?

There may be a more explanatory way to ask this question. This may require a real expert to answer. Rocket ship A and B are traveling toward each other at some relativistically significant portion of the speed of light in intergalactic space. They are unaffected by any significant gravitational forces and they are so far from any other object that essentially, they have only each other for spacial reference. They have no way of knowing who is going faster. They can't even tell if one is standing still and the other is doing all the moving. This is just a simple way of saying all motion is relative. It doesn't really matter which is moving. Each observes the other as the one moving closer each from their own respective frames of reference. With a very powerful telescope each can see the clock placed on the front of the other rocket ship. Rocket ship A observers the clock on rocket ship B moving at a slower rate than his own because B is moving at relativistic speed with reference to A's frame of reference. A observes time dilation of B. In the 1 day travel time it takes B to arrive at A, B's clock will show only one hour has passed. Paradoxically, Rocket ship B simultaneously observers the clock on rocket ship A moving at a slower rate than his own because A is moving at relativistic speed with reference to B's frame of reference. B observes time dilation of A. In the 1 day travel time it takes A to arrive at B, A's clock will show only one hour has passed. As they pass each other, which clock will show more time passed?

I go along with what you say here. Lightning responses are not needed for this game and your point is well taken. Those who do well at these puzzles usually take a long time. I think it is fair to say that someone who can solve these puzzles will sit and think about it for a while and those same people have a huge advantage in real life problem solving for real life everyday problems.

Let's see if I can put it in a different way. General purpose logic can be used to solve this puzzle as well as inform a chess move or a poker hand. However, the rules which constrain players in chess and poker and other arbitrary logic games can not be used to solve this puzzle. This puzzle is not constrained by any arbitrary rules. There are no tricks to solving it. No methods. No shortcuts or strategies. The only thing that works is general purpose logic. So if some gets good at this game, he is good at general purpose logic that can be applied to any subject. This is not true for chess as you accurately point out. But it is true for this puzzle.

Satellites were my first choice for explanation as well. The problem is I know where the sun is and can calculate the exact apparent altitude above the horizon for any given satellite altitude above the surface at which the shadow of the earth falls. In fact when I star gaze with my sexton, I have a calculator and a note pad handy. Two of the lights I saw passed into the earth's shadow remaining visible the whole time and one passed out of the earth's shaddow having been visible while in it. Also one of the lights remained completely stationary with respect to its apparent altitude above the horizon. That is the stars moved behind it at their usual speed 15 arc minutes per minute, but this point of light did not move. That is the one that most puzzles me. Nothing in ballistic orbit can stand still with regard to the horizon unless it is powered or in geosynchronous orbit. And of course, I also know the arc in the sky in which all geosynchronous orbits must lie. This light was no where near that arc. I didn't make a mistake on that. I point satellite dishes at geosynchronous satellites. And despite that an object in geosynchronous orbit is way too far to be visible. So someone has to come up with something other than satellite or propose some new government propulsion system which could keep a craft under powered flight outside the atmosphere. And frankly, it would be harder to sell me on government conspiracies than UFOs. I'm pretty skeptical.

Stop thinking UFO, I'm looking for more plausible, or perhaps credible answers. I am a boater and am currently practicing using a sextant. I've been observing the night sky far more often over the last two months. On several occasions I see points of light move across the sky slowly. They do not exhibit parallax, the relationship between the apparent altitude, distance and velocity. (for example, The difference between the moon's apparent altitude in the early evening and early morning is appears greater than from an observer located on the surface of the earth because the observer's location moved.) Remember, I'm practicing the use of my sextant. So I can see even very slow motion. I can see the slow motion of the stars as they move across the sky at 15degrees per hour with the earth's rotation. These lights are not stars nor are they high flying airplanes. I know this because a high flying airplane must be less than about 7 miles above my head as it flies over head. As it flies into the distance it's altitude above the horizon decreases at a slower and slower rate, because of course it is moving away from me at the same time it's apparent motion is moving away from zenith. And also, this is aside from the additional fact that it has no flashing lights. The only thing that I know of that could behave this way is a distant object (far above the atmosphere) where its height when at my zenith is little different than when at a lower angle. If any answer that someone poses does not account this parallax, it must be dismissed. I'm not really looking for answers from someone who doesn't understand the geometry of parallax or understands it only in practical use. I'm just trying to keep down the number of incorrect answers. I have seen this four times over the last three months. They are points of light with no resolvable dimensions, suggesting great distance. However, they move from one degree per minute to fifteen degrees per minute. Just for reference visible satellites must move at four degrees per minute, no faster no slower. Meteors move much faster, if a meteor's trajectory ends near you, it will be visible for less than 10 seconds. Since meteors must travel faster than earth's escape velocity, there is a relationship between the time they are visible and their angle of entry, exhibiting similar parallax as a high flying airplane. Does anyone else see these lights? What are they? I imagine many laymen see them, but don't realize that they are remarkable, passing them off as airplanes or meteors, when sextant measurements show they can be neither. Jerry

You repeat your first argument without adding anything. Do you disagree that games like chess rely upon arbitrary rules which do not translate well into real life and that the above game instead has no arbitrary rules? One must use his wits alone in the same way that one must use his wits in all real life decisions which require logic? Or do you believe that this game also uses arbitrary rules arbitrarily constraining the guesses which the player may or may not make?

You are exactly correct about strategy games. A brilliant logician should play chess better than most, but it is also possible that someone who plays chess better than a brilliant logician could be of only average intelligence. This is because chess is a strategy game. It has arbitrary rules. A knight moves this way and a bishop moves that way. These rules don't translate into real life situations. One learns chess heuristically. However, this game has no strategy, no tricks to learn. No arbitrary rules. It is only natural logic with all the context removed. If one is very very good at playing chess, the same is not necessarily good at general purpose logic, just the arbitrary rules of chess. On the other hand, if one is good at this game, he must be good at general purpose logic, real life logic. If A is true and B is false than what does that make C? true or false? Anyone who can play this game well, knows how to figure that out and do so completely independently from any arbitrary rules or strategies he might have learned.

Imat, your are exactly correct about everything even about the second row. It is refreshing to see people who can think. It is scary how many "smart" and "successful" people can't think even half so well.

Good try. But I don't think you understand point 6 This is what I want. People to give it their best thoughts. It is true that the sequence of your DNA occurs at least once, in you. And you are correct. That does not mean that the chance that any sequence of DNA must be one in seven billion. Also it is not true that the sequence of an organism's DNA is dependent upon the organism's existence. The sequence arises then the organism of which it is genetic might come to fruition or it might not. There is not dependency on seven billion to give rise to your particular sequence of DNA. Your particular DNA sequence comes from a number of permutations greater than the number of atoms in the entire universe. However, in case of the arising of intelligent life, That is dependent upon the existence of the planet first. It is not true to say that the chance that any sequence of DNA occurring is one in the number of living organisms. It is true to say that the chance of civilization arising on any given planet is the number of civilizations over the number of planets. Do you agree? Is the chance that civilization arises on any given planet the number of civilizations divided by the number of planets? And do you agree that the chance that your particular DNA sequence arose in you has nothing to do with the number of people who have DNA?

Well if you are a mod, then I won't argue with you. However, if you claim it is speculation, then which point in particular might be in error? I've numbered them to make that easier. A useful and apropos tautology. If none are incorrect, then all is correct.

There are only 16 fundamental logical operators which describe the fundamental relationship between any two arguments. That is if A is true and B is false then C is false. This is consistent with the logical operator AND, but it is also consistent with the logical operator NOR. The difference between the two lies in their response to the other permutations of A and B. Can you use the logical operator NOR to describe the relationship between the sensors and actuators in this simulation of a swinging ball? Use three NOR gates to connect the sensors to the actuator so that the pin ball is launched upwards at exactly the time needed for the swinging soccer ball to push it out of the way. If you do it right, the pin ball will fall back down and be launched again at the right time every time. link to the simulation