Ancient Domains Of Mystery, forum overview / General / Any Physicists out there?
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Caladriel Registered user ReGiStErEd UsEr Last page view: 4696 days, 6 hours, 56 minutes and 17 seconds ago. |
Okay, I need a hand finding where I have made a mistake in this model. From my understanding of relativity and this model design, I see a paradox in the theory of relativity, but there is probably in flaw in either my understanding or my design (or both) I apologize that this thought problem will be much more than 20 lines. [Edited 1 time, last edit on 5/26/2008 at 12:28 (GMT -5) by Caladriel] |
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Caladriel Registered user ReGiStErEd UsEr Last page view: 4696 days, 6 hours, 56 minutes and 17 seconds ago. |
Theory of Relativity: As I understand relativity, from any perspective, time is moving slower for any object that is moving relative to that perspective. ie. if a rocket is flying past earth, there are two perspectives. The earth feels that the rocket is moving (relative to earth) so from the earth's perspective, time is moving slower on the rocket. The rocket thinks that the earth is moving (relative to the rocket) so from the rocket's perspective, time is moving slower on the earth. [Edited 1 time, last edit on 5/26/2008 at 11:57 (GMT -5) by Caladriel] |
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Caladriel Registered user ReGiStErEd UsEr Last page view: 4696 days, 6 hours, 56 minutes and 17 seconds ago. |
Synchronizing timers: Okay, I have 2 conveyor belts. one at earth and another at Pluto (Or, at least at their orbits) These conveyor belts have tick marks for each minute. Now then, I take a rod with two spools of thread, one at each end. I attach the threads to earth belt (keeping the threads perpendicular to both the rod and to earth's belt) I then walk to pluto's belt, always keeping the threads at right angles to the rod (note: I have to walk diagonally from earth to Pluto if I want to keep the threads perpendicular to the rod) The position on pluto's belt where I attach the threads is physically directly opposite the position on earth's belt where the threads are attached. I call the position of the threads T-zero. These two belts can now function as timers, and I believe that they are perfectly synchronized. ie. If I walk past the 50th tick below T-zero on earth's clock, I know that the 50th tick is directly opposite me on Pluto's belt. If I then walk in a straight line to Pluto's belt and cross Pluto's 1050th tick, I know that the 1050th tick on earth's belt is directly behind me. Thus, when I reach Pluto, I know that 1000 ticks have passed in the earth/Pluto timeframe. [Edited 1 time, last edit on 5/29/2008 at 20:59 (GMT -5) by Caladriel] |
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Caladriel Registered user ReGiStErEd UsEr Last page view: 4696 days, 6 hours, 56 minutes and 17 seconds ago. |
Recording times: Okay, I build a rocket with a timer that displays the count on the hull. The rocket flies at a constant speed towards the earth and Pluto belts. As it passes, or punches through, the earth belt, the rocket occupants make note of the time on the rocket timer and the tick mark passed on the earth belt. Meanwhile the Earth makes the same notes. As the rocket passes Pluto, the same notes are taken (only this time, everybody records the Pluto Belt's tick mark) All the tick marks on Pluto's belt are opposite the corresponding tick marks on Earth's belt. Therefore, I now know how many of earth's tick marks have crossed the path of the rocket since the rocket passed earth. ie. I know how much time has passed in the earth/pluto time frame. [Edited 1 time, last edit on 5/26/2008 at 12:31 (GMT -5) by Caladriel] |
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Caladriel Registered user ReGiStErEd UsEr Last page view: 4696 days, 6 hours, 56 minutes and 17 seconds ago. |
Paradox: According to the above definition of relativity, from the rocket's perspective, less ticks should have passed in the Earth/Pluto timeframe. From the Earth/Pluto perspective, less tickmarks should have passed in the Rocket's time frame (on the Rocket's timer) Those are two mutually exclusive results. Isn't that a paradox? Okay. I'm done. |
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Caladriel Registered user ReGiStErEd UsEr Last page view: 4696 days, 6 hours, 56 minutes and 17 seconds ago. |
Solutions: The only solution I can think of is that, from the rocket's perspective, the threads were never perpendicular to the rod and earth belt, but I do not know how this could happen. |
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Darren Grey Registered user Last page view: 4238 days, 12 hours, 34 minutes and 37 seconds ago. |
Physicist to the rescue, yo! First of all, let me please try and simplify your description. There are syncronised clocks on Earth and Pluto, right? Rocket leaves at time A and arrives and time B. Whilst it does this it also has a clock on board. Now, what happens when it arrives at Pluto? It sees the clock on Pluto state time B, the same time as the rest observer. However its own clock will show a different time - a lower time in fact. From the rocket's perspective say 10 seconds have passed, whilst the clock on Pluto will say 15 seconds have passed. This is standard time dilation. No paradox - they simply experience time differently. Your idea of "tickmarks" doesn't work because the rocket would see those tickmarks happen every 0.8 or so seconds, not every second. There is also some length contraction stuff that would mean the threads wouldn't be perpendicular, but that doesn't matter for this. You just have to consider it in terms of two separate clocks, and abandon any idea of an independant time that looks to same to both observers. Waldenbrook, the dwarven shopkeeper, mumbles: "I'd offer 9 gold pieces for yer dwarven child corpse." |
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Caladriel Registered user ReGiStErEd UsEr Last page view: 4696 days, 6 hours, 56 minutes and 17 seconds ago. |
So my understanding of the Theory of relativity is wrong? You said that the rocket would see less time pass on its clock than on the earth/pluto clock. I thought that from the Rockets perspective, time would move slower on earth/pluto, since the rocket thinks that the earth and pluto are moving. Shouldn't the rocket, therefore, see less time on the earth/pluto clocks? Yeah, there is the length dilation, but that is via depth (forward/back) not breadth (left/right) so I do not quite grasp how that would make the threads non perpendicular. |
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Darren Grey Registered user Last page view: 4238 days, 12 hours, 34 minutes and 37 seconds ago. |
Very nice. I see the grand mystic has been oddly renamed... Under ninjas: "Two-handed wielding is generally not recommended" I assume you meant two weapon combat? Also maybe worth noting that monks can get away with close range missiling quite easily with high DV or employ hack 'n' back tactics very well with fast movement. Andy: The trident isn't needed against Andy if going for OCG for whatever reason, so a pure bare-handed monk can still go for that special ending (sceptre should be dropped straight away). Also worth noting that some other enemies are bad to melee - ACW, Keriax and Chaos Archmage in particular (along with all stat-draining creatures). It's good to use disabling tactics on them before approaching them in melee. Also GMs and earth elementals should be added to the list of high PV monsters. Monks may also have trouble with DarkForge. Rift: Level requirement is 18. However it's not advised to go in there till reasonably buff. It could maybe be worth noting that monks make excellent candidates for a huge range of challenge games - probably the most used class of all across the whole range of challenges. Anyway like the guide a lot - will have to use it to do a pure bare-handed monk some time. Waldenbrook, the dwarven shopkeeper, mumbles: "I'd offer 9 gold pieces for yer dwarven child corpse." |
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Nezur lurking Unregistered user |
^So that is the post that "disappeared". :) |
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Darren Grey Registered user Last page view: 4238 days, 12 hours, 34 minutes and 37 seconds ago. |
...God damn it! I posted it in the wrong bloody thread... Waldenbrook, the dwarven shopkeeper, mumbles: "I'd offer 9 gold pieces for yer dwarven child corpse." |
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Maelstrom Registered user The Knight of the Black Rose Last page view: 3116 days, 8 hours, 3 minutes and 49 seconds ago. |
Caladriel, from what I understand, it's not that it "seems", but time bends from gravity, hence the relativity of time perception. Think of time as a stream, that bends from gravity - even though the "time distance" is the same on earth and on the rocket, on earth the stream bends, so more "water/time" passes to cover the same distance. The more gravity, the slower time moves - hence the theory that the flow of time is 1/infinity in black holes. A pessimist sees a dark tunnel. An optimist sees a light at the end of that tunnel. A realist sees a train. And the train driver sees three idiots on the tracks. |
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Caladriel Registered user ReGiStErEd UsEr Last page view: 4696 days, 6 hours, 56 minutes and 17 seconds ago. |
"seems" was a poor choice of words, on my part. Am I incorrect that the time dilation is from each relative perspective? eg: Take two rockets racing towards each other. From each rocket's perspective, time is moving more slowly in the other rocket. At least, I think that that is what the theory of relativity states. Is my understanding of the theory incorrect? [Edited 1 time, last edit on 5/29/2008 at 12:31 (GMT -5) by Caladriel] |
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Hendar23 Registered user Last page view: 5656 days, 2 hours, 38 minutes and 12 seconds ago. |
OK, heres one: A hare and a tortoise have a race, but the tortoise gets a meter head start. Assuming the both start simultaneously, the hare cannot catch up with the tortoise. Why? Well, even if the hare moves at light speed, it must take some finite amount of time to catch up to the tortoises starting point. If the tortoise is moving at all, no matter how slowly, in that small unit of time it will cover some distance - no matter how microscopically small - before the hare gets to the tortoises starting position. Then they are back to square one. The hare has narrowed the lead of the tortoise, but the same situation will repeat itself, the distance between the hare and the tortoise getting ever smaller but never reducing to zero. So how the hell do fast objects overtake slower objects?????? "Men are born for games. Nothing else. Every child knows that play is nobler than work" - Cormac McCarthy, Blood Meridian [Edited 1 time, last edit on 5/29/2008 at 17:08 (GMT -5) by Hendar23] |
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Maelstrom Registered user The Knight of the Black Rose Last page view: 3116 days, 8 hours, 3 minutes and 49 seconds ago. |
There's so much wrong with your "here's one", that it's not even worth explaining. It's in the same league as sticking your cat into a microwave to dry it... A pessimist sees a dark tunnel. An optimist sees a light at the end of that tunnel. A realist sees a train. And the train driver sees three idiots on the tracks. |
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Caladriel Registered user ReGiStErEd UsEr Last page view: 4696 days, 6 hours, 56 minutes and 17 seconds ago. |
Hendar: Classic! I love it. (although I heard about it as Achilles and a tortoise) Your problem is that at the start of each 'step' in the race, the hare will have to reach the starting point of the tortoise from that step (the hare actually has to pass that point, but, in order to pass that point, the hare first has to reach that point) Each time, when the hare reaches the tortoise' starting point for that step, the tortoise will have moved a little forward, thus creating a new starting point for the next step that the hare will have to reach. By the time the hare reaches that new starting point, the tortoise will have again moved a little bit forward. etc. Each time, that "little bit forward" will be smaller, but it will always be there. I think I have an intuitive grasp of a solution, but I do not know if I can verbalize it. The paradox exists because you are viewing the race as an infinite series of finite steps. It is actually a continuum. A continuous wave rather than a set of discrete plateaus. The distance that the Hare has to travel reduces to 0, at which point the hare overtakes the tortoise. ie. if you continually chop a tree branch in half, you will never reach the trunk, you will simply wind up with smaller and smaller discrete chunks of wood as you get closer and closer to the trunk. However, if you sand the branch instead of chopping it, you will reach the trunk and wind up with a pile of sawdust. [Edited 1 time, last edit on 5/29/2008 at 20:58 (GMT -5) by Caladriel] |
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Darren Grey Registered user Last page view: 4238 days, 12 hours, 34 minutes and 37 seconds ago. |
The problem was invented by the ancient greeks, and they never solved it. The problem lies in the concept of infinity, and the human mind's difficulty in grasping it. The Greeks didn't realise that adding up an infinite series of numbers could lead to a real number - they thought that an infinite sum must be infinite itself. This is not true. If you add up the sum of 1/(2^n) (ie 1/2 + 1/4 + 1/8 +...) for an infinite value of n you will get 1. In pure maths this is generally expressed as the infinite series converging on a real number. More commonly you could simply look at it as a form of integration - the area under a curve is the sum of infinite small slices. In the example presented imagine that the distance between the hare and the tortoise is halved each time, and you will have the same mathematical series as above. There is no paradox - just a lack of understanding of adding infinite numbers. Waldenbrook, the dwarven shopkeeper, mumbles: "I'd offer 9 gold pieces for yer dwarven child corpse." |
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Caladriel Registered user ReGiStErEd UsEr Last page view: 4696 days, 6 hours, 56 minutes and 17 seconds ago. |
I have some other favorites. I have moved this to Paradoxes So was I wrong about relativity? (I think I am wrong about synchronicity) [Edited 1 time, last edit on 5/29/2008 at 21:55 (GMT -5) by Caladriel] |
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Darren Grey Registered user Last page view: 4238 days, 12 hours, 34 minutes and 37 seconds ago. |
Getting back to the original problem, both observers think the other person's clock is moving slower - that's all fine in relativity. However one thing that is not relative is acceleration. If the rocket wants to stop at Pluto and compare times then it must decelerate, which is when relativity stops working and the whole clocks thing gets kinda reset, with the rocket being the one that ends up experiencing less time. (Same applies to the twins paradox - it's the twin that travels away and comes back that is younger, because he underwent the acceleration/deceleration to return.) The maths of the acceleration stuff are outside of my understanding I must say. One thing to consider with the ropes that if you put dots on them they'll look like they're moving horizontally in Earth/Pluto, but diagonally from the rocket. In relativity there is a stronger effect - the lengths of the ropes will actually appear contracted, and the dots will come in a curve (for low velocities it would just appear as a straight diagonal). Erm, can't draw this here, but if the dots are coming from the right imagine the curve being flatter on the top and left side as it comes in. The diagonal movement keeps getting steeper - almost head-on (I suppose for a photon everything would be head-on). A dot that looks like it was going to sail past the front of the rocket ends up falling steeply towards it. So instead of the line passing it at dot 2 it would pass at dot 3. Now whilst this is happening the lines go past less than once per second according to the rocket - time outside seems to be slow. When it decelerates the opposite happens, we get a curve that is flat on the right and bottom. A dot that looks like it would go past the back of you ends up hitting you. This is just a normal feature of acceleration - I don't exactly know what the added relativistic effects would be. Now instead of the line crossing at dot 8 it would be dot 7. In a way it would look like your time counter is suddenly speeding down extremely - all those lines are suddenly flooding in from the side. The seconds "catch up" in a way, and the rocket's clock would end up showing 10 seconds whilst the outside world has had 15 seconds pass. Though originally the rocket thought the Earth/Pluto clock was taking less seconds it ended up seeing a lot more ropes pass by whilst it was slowing down. If the rocket never decelerate it would still observe the Earth/Pluto clock as slow, and vice-versa. Note that the ropes don't necessarily appear diagonal or curved in this set-up - just their motion. How the ropes themselves would look is quite beyond my imagination... Waldenbrook, the dwarven shopkeeper, mumbles: "I'd offer 9 gold pieces for yer dwarven child corpse." |
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Caladriel Registered user ReGiStErEd UsEr Last page view: 4696 days, 6 hours, 56 minutes and 17 seconds ago. |
I'll have to read the ropes/dots bit again. I do not yet grasp it. However, I already accounted for acceleration/deceleration. The rocket is traveling at a constant speed from earth to Pluto. Acceration occurs and is finished before it reaches earth and deceleration occurs after passing pluto (and after all time measurements are taken) |
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Darren Grey Registered user Last page view: 4238 days, 12 hours, 34 minutes and 37 seconds ago. |
Well if you're looking at it like that then the clocks will seem inconsistent - both will see the other as slow. There is no inconsistency in the universe though because to actually compare clocks properly the rocket would have to slow down. Waldenbrook, the dwarven shopkeeper, mumbles: "I'd offer 9 gold pieces for yer dwarven child corpse." |
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Caladriel Registered user ReGiStErEd UsEr Last page view: 4696 days, 6 hours, 56 minutes and 17 seconds ago. |
. . . But we are only comparing the amount of time that passed while the rocket was moving. I think that the rocket would actually show less time passing, and that, somehow, the conveyor belts are out of synch from the rocket's perspective. |
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 littlebrather Registered user Last page view: 4802 days, 13 hours, 1 minute and 38 seconds ago. |
The mainpostulate of special theory of relativati is that nothing can be simultaneous in different sistems - OK man on Pluto think that rocket flight beside him at 10 am, !but! man in rocket think that was happend in 9 am etc. They are both right, and there is no paradox - we COULD NOT look at Pluto's clocks simultaneously from rocket and from Pluto. this is something that fight with our ordinary wisdom but it's right. A lot of experiments were made - without rockets and Pluto but also very complicated =) until it sleep |