How fast would a spaceship have to travel in order to experience Einstein Relativity effects of exactly order 2? That is, the time slowed exactly by 1/2, the mass increased by exactly doubling? The solution, expressed as a percent of the speed of light, would come from this equation: .5 = sqr(1-v^2) and solve for v. lessee (mumble mumble) that means the velocity would be .866 or roughly 87 per cent of the speed of light. Hmmm. Kind of reminds me of the recent riddle I saw posted on this forum. What a coincidence. Well, that makes for an interesting question. Physicists are fond of saying Einstein's relativity theory has always proven right when tested, but what does this mean? How can it be? Consider that Einstein's theory is reciprocal. In our earlier riddle, the planets stayed still while the space ship moved. But we could, instead, suppose the space ship was actually still (it would seem to be still to those inside coasting along) and the planets moving in relation to the ship. That would mean, in particular, that the planets would appear to no longer be spheres but squashed ovals! That the time on the planets would appear to have slowed, so that, as they send out annual new year's celebrations, it takes them two years to get each one out! Is it possible that under these conditions, the same events would occur? That is, would the spaceship from the first riddle STILL be expected to receive 21 annual new year celebrations on the way to planet Beta? This is a serious test of Einstein's theory. Because if considering the relative point of view of the spaceship causes us to predict different events from the relative point of view of the planets, then we have definately uncovered a contradiction within Einstein's theory! What do you think? (a) Einstein's theory is safe. The same 21 annual new year celebrations would be expected to be received, because . . . . (insert reasoning/calculating here) (b) There's no way to reconcile these views! Einstein was wrong!

I am a difficult person so... (c) The two frames of reference are not equivalent. Only the people in the spaceship would experience acceleration effects so viewing the situation as if the spaceship remained still and the planet moved away is a different frame of reference. But, even once you consider relativistic effects, I don't think that there would be any difference from the first riddle as far as the number of messages received. Time would be running at half speed on the ship so the timing of the messages from the perspective of the people on the ship would be different. I also think that even though the spaceship is moving, that to the occupants there might be a change in the apparent size of the "stationary" objects they observed outside the ship, but I am not sure. So you might still get your distorted planets. I need to learn more relativity.

Well, I'm not thinking of the time spent accelerating, just the time coasting. You are correct in that the number of messages received must stay the same! Otherwise there's something wrong! The trick is to figure out how that happens from the reference standard of the spaceship as being still while the solar system Beta approaches. Relativity intersects with theology once in a while. For example, in the controversy over whether or not it is the earth that rotates or the sun that moves, people will sometimes cite Einstein's theory of relativity as allowing one to view the sun as literally going around the earth. In discussing Variable Speed of Light theories that allow for distant galaxies to be seen in time frames for a young universe, Einstein's theory becomes involved. So a little understanding is actually relevant.

OK now the very first thing to keep in mind about relativity is - things are absolutely reciprocal. As our spaceship hurtles towards planet Beta, we could consider it to be stationary and, instead, planet Beta is hurtling towards the spaceship. Therefore, all the Einsteinian affects of motion are, to the inhabitants of the spaceship, seen to affect the planet. The planet is seen to have its time slowed by 1/2. distances for the moving planet are reduced by 1/2. In what follows, we consider how things appear to our spaceship in the same hour it leaves planet Alpha on the way to planet Beta. A whole hour will mean the ship hasn't even had time to leave the Alpha solar system. Ponder the affect on the total distance. In our thought experiment we placed the planets at 10 light years apart. But the Einsteinian space contraction means that from the space ship the distance to travel is reduced by one half! It is only five light years away! So as we sit there in the ship, waiting for the planet to come to us, it only has five light years to travel instead of 10, and therefore, on our clocks, we see the actual time passing as half the time. Of course, the planetary systems think of themselves as 10 light years apart, and they percieve the reason the ship counts the time as only half the time is because the time on board the ship has slowed down. Note how neatly the alternate points of view account for the same event; that is, the crew of the ship recording only 5.77 years travel time. The planetary viewpoint, that the spaceship time is retarded; the spaceship viewpoint, that the spatial distance is contracted. Now, the space ship considers the planet's time to be slowed by one/half, so that the spaceship counts the planet as generating a new annual new year's celebration every two years. However, the planet is also rushing towards the spaceship at 86.6% of the speed of light. From the point of view of the spaceship, then, let us ask, how far apart are the oncoming waves of annual new years celebrations? When Beta generates one such celebration, it waits two years before generating another. However, during that same time, the planet draws closer to the ship by .866 + .866 = 1.732 light years. The radio signals themselves, of course, made it all the way to 2 light years closer, and as the planet begins generating the next year's signal, the distance between annual new years signals is 2 - 1.732 or .268 of a light year. How many annual new years events, then, hang in space between the space ship and planet beta? 5 divided by .268 = 18.7! Obviously, 18, with .7 accumulated time for the next one to come. Note the striking difference between this estimate from the point of view of the space ship and the point of view of the planet. The planet bound residents think that there are only 10 annual celebration signals hanging in space, the spaceship thinks there are 18. Who is right? This is one of those things that are not truly determined. Bear in mind that nobody is actually observing these annual new year celebrations, neither the ship nor planet alpha. They are simply estimating the positions of the signals based on the known facts of how often the celebrations occur, and their relative motions. This has bearing on some theological viewpoints! There are those who assert that, 6000 or so years ago, God created all the universe, complete with light on its way towards us from distant galaxies. But we now see that, in fact, there is no true meaning to ascribe to light that is "on the way"! It is not really defined! It is ambiguously described, depending on the state of motion of the receiver. People who hold to this theory are under obligation to redefine what they are saying to account for this complication. I'm not convinced it is possible to do that. Planet Beta, traveling at 86.6% of the speed of light towards the ship, will arrive at the ship in 5.77 years. Planet Beta will experience this as half that time due to time retardation effects of motion, or 2.89 years. Add to this time the .7 we mentioned above, and we have 3.59 years left for planet Beta to experience from the time of its 18th transmission to the time it reaches the spaceship. 18 + 3 is 21, and so our prediction is that the spaceship will recieve all 21 annual new year celebrations from planet Beta before the planet arrives at the spaceship. Hmmm. 2.89 years. This means that the spaceship estimates that the time as reckoned on planet Beta is actually 2.89 years prior to this "very moment". Contrast this with the planet bound view, which views the time on planet Beta as being 10 years prior to the present moment. Relativity theory teaches us that the concept of "same time as" will, therefore, vary tremendously with alternate states of motion across space! There is no true physical definition of "simultaneous" that can be agreed upon by all observers regardless of their state of motion! It is perfectly true, however, that one can make observations on the distant galaxies and even the microwave background radiation and determine whether or not one is moving in relation to them. But in relativity theory, it remains an open question to say which is moving and which is still! There are some "Genesis Rescue" theories that assert light everywhere changed its speed simultaneously. And yet, as we see, the concept of simultaneousness across the universe is essentially meaningless! What is preserved in Einstein theory, and what is lost? Absolute space and Absolute time - must go. They are seen to vary. What remains solid and invariant in Einstein's space-time theory are events and the relations between events. But viewed in this way, the whole universe is not really a structure in time and space, but perhaps more of a grand theoretical concept, or even - an idea. A thought in the mind of God!