A-wal Posted October 14, 2012 Posted October 14, 2012 If an object is stationary in space and it sees another object coming towards it at half the speed of light then you could just as easily say that it's moving towards the other object at half the speed of light and the other object is stationary. There is no distinction between which one is moving. The only statement you can make is that they moving towards each other at half the speed of light. All the laws of physics remain the same in any inertial frame, meaning all frames are equal and no frame can be said to be unique in any way. Having said that, you could use the cosmic background radiation as a frame of reference for all others, but you could do that with any frame of reference. If you're in a car and you throw a ball into the air then it doesn't go flying backwards because the laws in all non accelerating frames are the same, including the speed of light. You can't measure your speed relative to light because you'll always get the same answer of 186,000 miles per second. So if two objects are heading away from Earth at different relative velocities and you shine a flash light then the light beam will pass both of them at the same speed, meaning all three observers measure time and space differently to keep the speed of light the same for all of them. Velocity is just a measurement of distance over time. There's one spacial dimension involved because you can always draw a straight line between any two objects, and time. Both shorten from the perspective of an accelerating observer to keep the speed of light constant. This is called length contraction and time dilation. If a ship were flying away from Earth and a signal was sent from Earth to the ship and from the ship to Earth then would both signals take the same amount of time to reach their destination? Yes, but both Earth and the ship would say no. Both observe outgoing signals taking longer than incoming signals because outgoing signals have to catch up to the receding destination. Outgoing signals have to travel further and take longer than incoming ones do to make the same journey, because outgoing signals are measured to when they arrive while incoming signals are measured from when they're released. Signals sent by the other observer would be travelling a shorter distance and wouldn't take as long to reach the destination as a signals sent from themselves to the other observer because outgoing signals are travelling to where an object is going to be and incoming signals are travelling to where an object is and the difference is length contraction and time dilation. Objects are always travelling through space-time at the speed of light from all frames of reference. In your own frame your stationary and moving through time at the speed of light. Objects also see other objects with a different relative velocity moving at the speed of light because they're moving through time slower (time dilation) from each others perspective and their total velocity through space-time will always equal the speed of light. Imagine two ships moving at different velocities, both with a light beam moving up and down between the ceiling and the roof. It takes one second for the light to travel up or down from mirror to the other. Each would see the light on the other ship move in a zigzag as its relative velocity is added to the lights vertical motion. Light doesn't speed up to make up the difference, so it takes longer than one second for the light to get from one mirror to the other on the others ship from both perspectives. A second for either is a shorter amount of time than a second for the other, so each sees the other moving in slow motion because the light on the other ship has further to go. Now one is stationary relative to a tunnel which the other ship travels though. The ships front end comes out one second after its back end enters, but space is length contracted in the direction that it's travelling in, making anything in the other frame including the tunnel length extended by comparison. Its front end emerges before the back end enters from the perspective of the ship at rest relative to the tunnel. From this frame, the ship is longer than the tunnel. If you (A) flew away at half the speed of light while your twin (E) stayed on Earth then you would change your frames of reference relative to each other. You're always stationery from your own perspective and light is always moving at the same velocity ©. Everything else is relative. From both perspectives the other will be travelling at 0.5c but each sees themselves as stationary. A travels one light-year in two years, but a light-year has changed from As perspective relative to Es because they've moved into a different frame where the speed of light is the same relative to both of them despite their different relative velocities. It moved further from As perspective in the time it took for the light to get one light-year from Earth from Es perspective and the same is true from As perspective of E. So the distance that the other ship covers wont seem like far enough from each perspective over any given unit of time, and if the distance that the other is covering decreases then the space and time separating them must decrease by an equal amount split evenly between the two (there's one time and one spatial dimension as we're moving in straight lines to keep things simple). The measurement of the others space-time has lessened because the other ships time will appear to be in slow motion (time dilation) and there will appear to be less space (length contraction) along the one spatial dimension (straight line) that they are moving from the perspective of both frames and lengthens each ships perception of anything in the others frame, which keeps the speed of light constant from the perspective of both frames. This removes the discrepancy of the speed of light from the persecutive of different relative velocities because it isn't travelling as far in space or in time, and therefore as fast as in other frames as it would if it wasn't for length contraction and time dilation, and bringing it right back to c relative to every frame of reference. Everything up until now has been symmetric, so each twin sees the same affects on the other, and in exactly the same way. The twin paradox (not actually a paradox at all) is that the one leaving Earth will be younger than their twin when they return. To start with we'll give both twins a rolling start and finish. The twins pass Earth moving in opposite directions at just over half the speed of light relative to an observer on Earth who sees them moving away from each other at over the speed of light, which is fine as long as no one sees themselves moving above light speed relative to anyone else. Each twin sees themselves moving at just over half light speed relative to Earth (Earth sees them moving at that speed so the same must be true in reverse) and each twin sees the other moving at below light speed because of length contraction and time dilation. But this isn't a real affect because each sees the other one moving in slow motion and length extended (because the space is contracted), which stops anyone from moving faster than light relative to anyone else. When they turn round they have to accelerate in the opposite direction (there's no such thing as deceleration in relativity because it's just acceleration in the opposite of some arbitrary direction). If one is at rest and the other accelerates and comes back then it becomes a real affect and one twin is literally younger than the other one. A uses one unit of energy to travel up to half the speed of light relative to E. A is now static in its new frame of course. A then uses another unit of energy to again reach half the speed of light relative to an object in its new frame. From Es frame that second unit of energy didn't accelerate A as much as the first one did, but from As perspective it did because of length contraction and time dilation. So if the same energy is needed to move over a relatively smaller amount of space-time then the mass of A has increased from Es frame, and Es has from As frame as well. So the others energy requirement to accelerate increases from both perspectives as their velocity relative to each other increases, so your mass increases the faster you move relative to something else from their perspective. Energy becomes mass as you accelerate relative to the speed of light from the perspective of other frames of reference. That's how matter and energy are interchangeable, E = mc^2. What separates them is the fact that A has accelerated and E hasn't. If E were to accelerate into As new frame then they'd be the same age again. Length contraction and time dilation would lessen as their speeds become relatively closer to each other. When their relative velocities match they'll be in the same frame again and the only apparent time lag will be caused by how long it takes for light to cover the distance separating them (light hours/days/years). You can effectively travel as fast as you like, there's no such thing as absolute velocity and there's no speed limit because you will be in a new frame every time you stop using energy to accelerate and the speed of light and your energy requirement for acceleration relative to c is always the same in every possible inertial (non-accelerating) frame. If you accelerated to half the speed of light from your starting frame then you'd be in a new frame when you stop accelerating and you'd now be static from your own perspective and the energy requirement to accelerate to half speed of light would be the same as it was in your starting frame. If accelerated again up to half the speed of light relative to an object in your new frame then you wouldn't be travelling at the speed of light from your starting frame because you are length contracted and time dilated from the perspective of your starting frame and so you're moving slower through time and space. Time and space aren't fixed. As you accelerate towards something, it gets closer to you beyond what you would expect from the increased velocity. You can move infinitely fast, but as far as the rest of the universe is concerned you can't. So if you were to accelerate away from Earth and then return, you would be younger than your twin who stayed home because you were travelling slower through time and space from Earths perspective. Gravitys strength is directly proportional to mass and inversely proportional to the square of the distance to the mass. That just means that its strength is divided by four if the distance is doubled and multiplied by four if the distance is halved. In zero dimensions (point/singularity) it's infinite. In one spatial dimension (straight line) its strength would remain constant over any distance. In two dimensions (flat plane) it would be directly proportional to the distance. In three dimensions it's an inverse square. It's proportional to the volume it fills. We feel our own weight on Earth but it's not gravity that we feel, it's the electro-magnetic force between the atoms that are resisting gravity and pushing us upwards by the same amount that gravity is pulling us down. Neutron stars are heavy enough to collapse past this resistance and are held up by the resistance of the neutrons. Black holes are so heavy for their size that nothing can hold them up and they collapse completely. We feel the difference in the amount of force being applied to our points of contact with the ground and the rest of our bodies, which is why it's more comfortable when this difference is spread over a larger area when we lay down. The difference in the strength of a gravitational field is also all that can be felt rather than the strength of the field itself, because it's relative. The relative difference in the strength of gravity is called tidal force. On Earth that difference is very small and can't be felt but in a strong enough gravitational field it's enough to rip solid objects apart. Relativity explains how electricity and magnetism are actually the same force (electro-magnetism). A magnetic field can turn into an electric field if you accelerate relative to it because length contradiction moves the electrons closer together giving the field a negative charge, so the magnetism from the previous frame is felt here as electricity.
ajb Posted October 14, 2012 Posted October 14, 2012 If an object is stationary in space..... Define stationary.
A-wal Posted October 14, 2012 Author Posted October 14, 2012 Inertial, I think I did that in the rest of the paragraph. (: I wouldn't normally word it like like but I was trying to make it accessible to complete beginners and I thought I'd start gently. The idea was to show that stationary isn't what most people think it is. If it wasn't right at the beginning I'd have said non-accelerating (inertial).
John Cuthber Posted October 14, 2012 Posted October 14, 2012 "I wonder if I can get this pinned?" probably not. "You can effectively travel as fast as you like" How would you go about travelling to the moon in under a second? 1
ajb Posted October 14, 2012 Posted October 14, 2012 Inertial, I think I did that in the rest of the paragraph. (: I wouldn't normally word it like like but I was trying to make it accessible to complete beginners and I thought I'd start gently. The idea was to show that stationary isn't what most people think it is. If it wasn't right at the beginning I'd have said non-accelerating (inertial). Right, there is no universal notion of stationary. Which is why it seem very strange to open your post in the way you have.
A-wal Posted October 14, 2012 Author Posted October 14, 2012 "I wonder if I can get this pinned?" probably not. "You can effectively travel as fast as you like" How would you go about travelling to the moon in under a second? Easy, just accelerate. It would take over a second from the perspective of anyone staying on Earth, but the accelerator could do it in under a second from their own perspective because length contraction would mean they don't have so far to go and time dilation would mean they have longer to do it.
md65536 Posted October 14, 2012 Posted October 14, 2012 (edited) Easy, just accelerate. It would take over a second from the perspective of anyone staying on Earth, but the accelerator could do it in under a second from their own perspective because length contraction would mean they don't have so far to go and time dilation would mean they have longer to do it. I think you have to introduce the topic differently, so that people who don't know anything about SR don't mistakenly think there's no speed limit, and those who know a thing or two about SR but don't understand it don't mistakenly think that that's what you're trying to say. -- Edit: Which should be expected since you do mistakenly say "and there's no speed limit"... In this case, the length contraction argument is good but I don't think throwing in time dilation helps. Considering only length contraction, you use the moon's contracted ruler and the traveler's clock, and you can reach the moon in arbitrarily small local time. You break no speed limit; you don't get a valid measure of speed using your clock and someone else's ruler anyway. Considering also time dilation, the mixing of reference frames becomes a problem. If you say "you have longer to do it" you're implying using the moon's clock. If you do this it's not complete unless you include relative simultaneity as well as length contraction and time dilation. And you would have to do this, because you say "just accelerate"... so there will be a change in relative simultaneity. And as with the twin paradox, it's inescapable that the moon (in this case like the "stay at home twin") will age relative to you in a change to relative simultaneity, negating your "you have longer to do it" advantage. -- These problems are not there if you just stick to using your local clock, which doesn't experience time dilation or change in simultaneity relative to you. You can get places in arbitrarily small local times, but anywhere you get to will effectively age at an advanced rate. If you say you get there "fast", it implies might be confused with velocity, which is relative to your destination. It would be better to phrase it so that it's clear you're using only a local clock, because relative to any other clock you're not moving arbitrarily fast at all. Edited October 14, 2012 by md65536
imatfaal Posted October 15, 2012 Posted October 15, 2012 ... If a ship were flying away from Earth and a signal was sent from Earth to the ship and from the ship to Earth then would both signals take the same amount of time to reach their destination? Yes, but both Earth and the ship would say no. Both observe outgoing signals taking longer than incoming signals because outgoing signals have to catch up to the receding destination. Outgoing signals have to travel further and take longer than incoming ones do to make the same journey, because outgoing signals are measured to when they arrive while incoming signals are measured from when they're released. Signals sent by the other observer would be travelling a shorter distance and wouldn't take as long to reach the destination as a signals sent from themselves to the other observer because outgoing signals are travelling to where an object is going to be and incoming signals are travelling to where an object is and the difference is length contraction and time dilation. Objects are always travelling through space-time at the speed of light from all frames of reference. In your own frame your stationary and moving through time at the speed of light. Objects also see other objects with a different relative velocity moving at the speed of light because they're moving through time slower (time dilation) from each others perspective and their total velocity through space-time will always equal the speed of light. ... How do you measure when a signal arrives at a distance location? The only way is to send a signal back
A-wal Posted October 15, 2012 Author Posted October 15, 2012 (edited) I think you have to introduce the topic differently, so that people who don't know anything about SR don't mistakenly think there's no speed limit, and those who know a thing or two about SR but don't understand it don't mistakenly think that that's what you're trying to say. -- Edit: Which should be expected since you do mistakenly say "and there's no speed limit"... I think I clarified that afterwards when I said in the same paragraph; "You can move infinitely fast, but as far as the rest of the universe is concerned you can't". In this case, the length contraction argument is good but I don't think throwing in time dilation helps. Considering only length contraction, you use the moon's contracted ruler and the traveler's clock, and you can reach the moon in arbitrarily small local time. You break no speed limit; you don't get a valid measure of speed using your clock and someone else's ruler anyway. Considering also time dilation, the mixing of reference frames becomes a problem. If you say "you have longer to do it" you're implying using the moon's clock. If you do this it's not complete unless you include relative simultaneity as well as length contraction and time dilation. And you would have to do this, because you say "just accelerate"... so there will be a change in relative simultaneity. And as with the twin paradox, it's inescapable that the moon (in this case like the "stay at home twin") will age relative to you in a change to relative simultaneity, negating your "you have longer to do it" advantage. -- These problems are not there if you just stick to using your local clock, which doesn't experience time dilation or change in simultaneity relative to you. They're the exact same thing! The time dilation argument is identical to the length contraction argument, just in a different, but equivalent dimension. From Earths frame they can't get there in under a second but from the accelerators frame they can. I'm using proper time and space from both frames to show the difference. You can get places in arbitrarily small local times, but anywhere you get to will effectively age at an advanced rate. If you say you get there "fast", it implies might be confused with velocity, which is relative to your destination. It would be better to phrase it so that it's clear you're using only a local clock, because relative to any other clock you're not moving arbitrarily fast at all. It's true that I could have worded it more precisely but I'm trying to keep things as simple as possible in this thread. I think I was always clear about which frame I was using, I think. How do you measure when a signal arrives at a distance location? The only way is to send a signal back That only applies to the observers perspectives, it's a true statement from the readers perspective god-like perspective. Edited October 15, 2012 by A-wal
md65536 Posted October 16, 2012 Posted October 16, 2012 (edited) I think I clarified that afterwards when I said in the same paragraph; "You can move infinitely fast, but as far as the rest of the universe is concerned you can't". But ideally you'll want to interact with the rest of the universe, no??? If not, then what are you moving infinitely fast relative to? If you're moving a great distance, a great amount of time will pass. Sure, in your frame you can minimize both, but if you only care about your frame then you're not really moving at all. The time elsewhere in the universe is kind of important. This is what a lot of people describe as "time travel to the future", which is just you ageing little and everything around you ageing a lot. But the problem with a time-travel description is that you have to understand the meaning behind it before you can make sense of it without a lot of confusion. It's similar to the problem you face, which is that if you try to explain these things too simply, without explaining the prerequisite understanding, I'd think it more likely that people be mislead and confused than educated by it. I cringe to think of people arguing something like "you can exceed the speed of light, just by exploiting length contraction!" I think it's better to just understand the basics, which include "nothing can accelerate to faster than c", and then understand why and what it means (and your explanations probably fit there), and then only once one understands the basics would one get into how they can be exploited. If you understand the basics, then you understand the meaning of exploiting SR, and the caveats and the details. Edited October 16, 2012 by md65536 2
imatfaal Posted October 16, 2012 Posted October 16, 2012 How do you measure when a signal arrives at a distance location? The only way is to send a signal back ... That only applies to the observers perspectives, it's a true statement from the readers perspective god-like perspective. But science is observations. The idea of a god-like perspective seems to bring in ideas of absolute space and time, of simultaneity, and much of what SR taught us were incorrect assumptions 1
A-wal Posted October 16, 2012 Author Posted October 16, 2012 But ideally you'll want to interact with the rest of the universe, no??? If not, then what are you moving infinitely fast relative to? If you're moving a great distance, a great amount of time will pass. Sure, in your frame you can minimize both, but if you only care about your frame then you're not really moving at all. The time elsewhere in the universe is kind of important. This is what a lot of people describe as "time travel to the future", which is just you ageing little and everything around you ageing a lot. But the problem with a time-travel description is that you have to understand the meaning behind it before you can make sense of it without a lot of confusion. It's similar to the problem you face, which is that if you try to explain these things too simply, without explaining the prerequisite understanding, I'd think it more likely that people be mislead and confused than educated by it. I cringe to think of people arguing something like "you can exceed the speed of light, just by exploiting length contraction!" I was trying to balance being concise and keeping it simple. Maybe I came down a bit too far on the simple side. I hope it was clear and doesn't lead to misunderstandings. I think it's better to just understand the basics, which include "nothing can accelerate to faster than c", and then understand why and what it means (and your explanations probably fit there), and then only once one understands the basics would one get into how they can be exploited. If you understand the basics, then you understand the meaning of exploiting SR, and the caveats and the details. I was trying to to make the point that there really is no speed limit in a sense. You can go anywhere in as shorter an amount of time as you like if you have enough energy, it's just that objects can't reach the speed of light relative any other objects, so space and time make up the difference by being relative rather than fixed. Maybe I should have worded it like that. But science is observations. The idea of a god-like perspective seems to bring in ideas of absolute space and time, of simultaneity, and much of what SR taught us were incorrect assumptions That wasn't my intent. It is true that time dilation and length contraction are caused by the fact that energy has to travel different distances from the perspective of two observers in motion relative to each other, and the difference is length contraction and time dilation. I think that's the simplest way of looking at it.
md65536 Posted October 16, 2012 Posted October 16, 2012 I was trying to balance being concise and keeping it simple. Maybe I came down a bit too far on the simple side. I hope it was clear and doesn't lead to misunderstandings. It is certainly an interesting way to put things, and an interesting way to explain the details of SR and maybe even show how or why they're consistent. Personally I would prefer that any conclusion made from a simple explanation would be equivalent to a conclusion made from the most difficult explanation of SR, in terms of wording. That way the simple understanding can't contradict a complete understanding. For example a complete understanding uses a precise definition of "speed", and a simple explanation shouldn't use the word with a different meaning just for the sake of simplicity. (To call it limitless speed in SR you're probably mixing reference frames, using one for time and another for distance.)
A-wal Posted October 16, 2012 Author Posted October 16, 2012 I never mix reference frames! It's limitless proper speed, as long as you keep on accelerating. (;
md65536 Posted October 16, 2012 Posted October 16, 2012 I never mix reference frames! It's limitless proper speed, as long as you keep on accelerating. (; Oh, I see. I might not have been confused if you'd used the word proper-velocity all along, even though it is not the simplest word. I don't think that it's a good trade-off to make things simpler at the expense of added ambiguity. 1
Peregrin Tuk Posted October 19, 2012 Posted October 19, 2012 it's easier to explain using a ds^2 = -dt^2+ dx^2 +dy^2 +dz^2 ....or different coordenates in the lagrangian
mireazma Posted November 29, 2012 Posted November 29, 2012 I came here thru Google, cause I was looking for explanations on time dilation. Physics has always intrigued me but my knowledge and understanding is somewhere close to 1, on a 1-10 scale and was even 0.2 like 2 weeks ago (before digging up youtube for vids). The satisfaction and joy in (roughly) understanding relativity and answering questions in different "what if" thought experiments started with the creation of a space game. This is to let you know what my level is. I'm glad I got here and I thank A-wal for this initiative -- it slaps you in the face with clear, concise and substantial explanations, it looks like a synthesis of how to look at things from relativistic perspective. If I were to say it's exactly what I was looking for well, I'd be lying: it's more! With a little systematization, revision in expressing and with an aid of pictures, this deserves to be the reference article on relativity, to which all new comers and amateurs to be referred to. Now the ontopic: Altho I've read it like 2 times I still have a couple of misfit things in my mind and I'd like to set them right. 1. The twin paradox This is what I understand: The more you move thru space, the less you move thru time. So a twin A who travels more, ages less than his twin E, remained on Earth (even if A flies away and then reverses direction, getting back to Earth). I tried to get it by reading A-wal's post multiple times but I think I'm biased by a vid on YouTube to not see it right. This is what I don't understand: motion is relative to one another, so from perspective A, E is also moving away and then closing. How come A is younger? And for the same reciprocal reason, A should see all things around him, not lengthened but shortened and slow. Yet another logical consequence: the time dilation, length contraction or both would not be isotropic, which brings me to: 2. The ceiling floor light beam We have ship A passing by ship E. A measures time by a photon bouncing between the ceiling and floor. But this time, the photon is shot diagonally, towards the back of the ship, so it appears to the stationary E that the photon is bouncing vertically, up and down. So for A the light path is longer and for E it's shorter, which makes time (activities) on A to appear faster seen from E. Following the idea, the direction of motion of an object (or more precisely, region of it) inside A, relative to traveling direction of A, sets the duration of that motion. As you'd suspect, the slowest motion would be in the direction of traveling. Ignoring length contraction, it would be (1 - vA) * tE, where vA is A velocity fraction of c, tE is the time perception of E. In the opposite direction i.e. motions towards back, we'd have (1 + vA) * tE. Any motion in between would be as faster as it approaches 180o but I don't know if I got it right about time anisotropy. I would very much want to understand how these things work. I have other questions as well (like is there theoretically possible to unify gravity time dilation with motion T.D.) but at least I would get these right first. I may not have elsewhere to get clarifications from and this seemed the perfect place. Thank you in advance.
elfmotat Posted November 30, 2012 Posted November 30, 2012 (edited) A-wal: Trying to explain any physical theory without math is a bad idea. When I was in High School I used to read popsci books that attempted to explain Special and General Relativity, Quantum Mechanics, etc. in a similar fashion to your post. They generally left me more confused than before I had read the books. They also created misconceptions that took me a while to shake when I started learning the theories for real. If you want to learn a theory, you have to learn the math. There's no way around it. 1. The twin paradoxThis is what I understand: The more you move thru space, the less you move thru time. So a twin A who travels more, ages less than his twin E, remained on Earth (even if A flies away and then reverses direction, getting back to Earth). I tried to get it by reading A-wal's post multiple times but I think I'm biased by a vid on YouTube to not see it right. This is what I don't understand: motion is relative to one another, so from perspective A, E is also moving away and then closing. How come A is younger? And for the same reciprocal reason, A should see all things around him, not lengthened but shortened and slow. Yet another logical consequence: the time dilation, length contraction or both would not be isotropic, which brings me to: The situation is perfectly symmetrical (i.e. both twins see each other's clocks running slowly) until one of the twins turns around. One twin must turn around to get back to his sibling, and in doing so he must accelerate. Only one twin actually feels an acceleration, and that's how the symmetry is broken. The twin that turns around will register less overall time on his clock. 2. The ceiling floor light beamWe have ship A passing by ship E. A measures time by a photon bouncing between the ceiling and floor. But this time, the photon is shot diagonally, towards the back of the ship, so it appears to the stationary E that the photon is bouncing vertically, up and down. So for A the light path is longer and for E it's shorter, which makes time (activities) on A to appear faster seen from E. Following the idea, the direction of motion of an object (or more precisely, region of it) inside A, relative to traveling direction of A, sets the duration of that motion. As you'd suspect, the slowest motion would be in the direction of traveling. Ignoring length contraction, it would be (1 - vA) * tE, where vA is A velocity fraction of c, tE is the time perception of E. In the opposite direction i.e. motions towards back, we'd have (1 + vA) * tE. Any motion in between would be as faster as it approaches 180o but I don't know if I got it right about time anisotropy. You might like this little pdf I wrote last year: http://pdfcast.org/p...al-relativity-2 . It's mostly a compilation of different forum posts I had written addressing people's questions about relativity. I tried to take a historical approach and make everything as clear as possible for someone with very little experience with physics. Most of the math is just mid-High-School-level algebra. I think it should clear up your confusion here. Edited November 30, 2012 by elfmotat
md65536 Posted November 30, 2012 Posted November 30, 2012 (edited) This is what I don't understand: motion is relative to one another, so from perspective A, E is also moving away and then closing. How come A is younger? There are lots of different ways to analyse the twin paradox (see http://math.ucr.edu/.../twin_vase.html), and many different explanations depending on how you set it up. There's the "lack of symmetry with proper acceleration" explanation already given. If you describe the paradox in terms of Doppler effects or regular signals sent between the twins, you'll find that each twin receives the other's signals at a lower rate on the outbound journey and an accelerated rate on the inbound journey, but that the two halves of the journey appear to take equal times for the traveling twin while the Earthbound twin sees the outbound journey appear to take a much longer time than the inbound journey, thus receiving a smaller number of signals from the traveling twin (ie. a lower count of aging). Another explanation is that the changes in inertial frame correspond to changes in simultaneity. So while you might say that both are "measuring" or predicting the other twin aging slower than one's self, the traveling twin's turnaround corresponds to a change in simultaneity that involves the Earthbound twin essentially changing to a much later, much more aged relative simultaneity. This is why I said in post #7 that you must include relativity of simultaneity and not just length contraction and time dilation, because otherwise it's possible to derive false contradictions. Edited November 30, 2012 by md65536
mireazma Posted November 30, 2012 Posted November 30, 2012 Thank you for the explanations and the study materials. It'll take some time before I assimilate what's written both in the pdf and the article and I pinned these as the next steps in appropriating relativity. I got to read the time dilation (TD) and length contraction (LC) in the pdf and it raised even more questions I'm trying to put the ideas in order and temper the exponentially growing questions and solve them in order. I know it's not fair to ask you for answers without properly studying physics and mathematics but with planned study in mind, please, bare with me and answer as much as your time and mood allows you Generally I'm trying to provide as much and as clear info in order to help you help me. TD and LC are inseparable in that whenever/wherever one is present, the other is its consequence, right? 1. About the twin paradox, besides the TD/LC occurring between 2 different inertial frames I now know of TD (and LC?) resulting from acceleration. They're not the same thing because the latter effect is irreversible. I mean, it would be necessary that the whole system in which an accelerating ship senses "youth" but not the ship, to accelerate, so to reverse the effect. Here I'm trying to determine whether there's a difference in the way of looking at the two situations, rather than attempting to understand the accelerating TD. For the actual understanding I will study. 2. About the light beam clock, altho I read the "Special Relativity 2" pdf, I can't relate to what happens in the example from the post above, if the light is shot diagonally towards the aft of the flying ship. There are now extra risen questions for which I'll study for answers but it's too much for the moment (like whether TD and LC are mutually exclusive, LC from acceleration and others)
A-wal Posted December 8, 2012 Author Posted December 8, 2012 (edited) Sorry, I haven't checked this topic in a while. A-wal: Trying to explain any physical theory without math is a bad idea. When I was in High School I used to read popsci books that attempted to explain Special and General Relativity, Quantum Mechanics, etc. in a similar fashion to your post. They generally left me more confused than before I had read the books. They also created misconceptions that took me a while to shake when I started learning the theories for real. If you want to learn a theory, you have to learn the math. There's no way around it. That would defeat the object. It's much clearer without the equations if it's explained well. 1. About the twin paradox, besides the TD/LC occurring between 2 different inertial frames I now know of TD (and LC?) resulting from acceleration. They're not the same thing because the latter effect is irreversible. I mean, it would be necessary that the whole system in which an accelerating ship senses "youth" but not the ship, to accelerate, so to reverse the effect. Here I'm trying to determine whether there's a difference in the way of looking at the two situations, rather than attempting to understand the accelerating TD. For the actual understanding I will study.Okay, I think youre getting confused with the different affects of velocity and acceleration. When two objects are moving and a constant velocity relative to each other they are inertial and each sees the other as length contracted and time dilated. Neither view is right or wrong. They're both right from their own frame of reference. When an object accelerates from one frame to the other it moves into a frame of reference where the TD/LC that could be said to be an illusion from its starting frame are now real. Look at the moon example after the main post for how acceleration works. The accelerating object can't reach the moon in less than a second from the perspective of anyone staying on Earth but it can from its own perspective as length contraction and time dilation together mean that it covers a shorter distance than from Earths frame and in a shorter amount of time from Earths frame. The same is true when it accelerates back so the accelerating ship is constantly moving through length contracted and time dilated space from both perspectives and the accelerating twin is younger. 2. About the light beam clock, altho I read the "Special Relativity 2" pdf, I can't relate to what happens in the example from the post above, if the light is shot diagonally towards the aft of the flying ship.If a ship flies past Earth and half the speed of light then a light beam that's moving straight up and down from the perspective of anyone on the ship is following a zigzag path from the perspective of someone on Earth so it has further to travel but can't move faster because its speed stays constant, so the light travels less distance making a narrower angle between the zigzags as length contracts in the direction that it's moving and is moving slowly through time from Earths perspective. The same would also be true of a light clock on Earth from the ships perspective. Edited December 8, 2012 by A-wal
mireazma Posted December 8, 2012 Posted December 8, 2012 (edited) I'm glad someone replied at last and TBH I'm glad it was you, A-wal. Well, I don't mean any discrimination but it's probably cause A-wal is the op. It's just relativity (especially the problems from above) has been drawing half of my mental resources for the past week and it's disturbing the normal college-work-resting cycle Anyway, about the twin paradox no matter how I don't want to allocate time, it's more and more obvious that I have to study more intensively -- I can't see the "picture" and it feels like the answer will come with study and not with contemplating alone.But it's not the case with problem no. 2. I would appreciate very much if I could be told what happens in my example with the 2 ships from my first post. Here it is again, revised: 2. The ceiling floor light beamI'm aware that what follows contradicts the theory of special relativity and it's like a heresy but my intention is to clarify myself by rising questions based solely on deduction from light constant speed -- the very same deduction described in all TD / LC presentations.We have this ship A passing by our stationary ship E. A measures time by a photon bouncing between the ceiling and floor. But this time (as opposed to the classical example), the photon is shot locally diagonally, towards the back of the ship, so it appears to the stationary E that the photon is bouncing vertically, up and down. So for A the light path is longer and for E it's shorter, which makes time (activities) on A to appear faster seen from E. Following the idea, let's consider a motion of an object inside A, other than the so "special" constant-speed light, say a football. The direction along that particular motion is done relative to traveling direction of A, sets the duration of that motion i.e. its speed. (Well, this holds for a translation motion; note that if the motion has a rotational component, every microscopic region of the object experiences different speed).I marked every "variable" of A as observed by E with "E" just for the sake of clarity (never enough). As you'd suspect now, the slowest motion would be in the direction of traveling. Ignoring length contraction for the time being, the distance of the motion of an object would be the same observed distance for both ships, but for accomodating LC we note it dE instead of just d. Per unit of time perceived by E, it would bed = (1 - vE) * tE, where vE is A velocity fraction of c, tE is the time of the motion. So the speed of that motion is d / tE. In the opposite direction i.e. motions towards back, we'd have d = (1 + vE) * tE. So a swifter motion. Any motion in between would be as faster as it approaches 180o so time would flow anisotropically. Again, my intention is to correct my view so what does really happen in the given situation, instead of what I wrote it would? Please, let me know. Edited December 8, 2012 by mireazma
A-wal Posted December 12, 2012 Author Posted December 12, 2012 If the light is moving vertically from Es perspective then the light clock is stationary relative to E. All the dimensions are at right angles to each other. I made the light clock vertical so that its speed in that direction would represent its speed through time.
phyti Posted December 12, 2012 Posted December 12, 2012 I'm still looking for an explanation of how the vertical oscillation in the light clock aquires a horizontal speed component when the clock moves horizontally in order to work for an observer moving with the clock at any speed less than c.
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