EPTQuestion about twin paradox - Page 2
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nihlon
Sweden5581 Posts
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mcc
Czech Republic4646 Posts
On July 22 2011 01:07 skunk_works wrote: how does traveling at the speed of light keep you from getting old? I assume you meant close to the speed of light as object with stationary mass traveling at the speed of light is iffy concept. With that assumption in mind : it does not. Just from a point of view of someone on Earth you will be aging slower. | ||
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Nawyria
Netherlands140 Posts
On July 22 2011 02:07 nihlon wrote: Are you people just assuming the rate of aging or is this a part of the theory? The rate of aging is part of the theory. Intertial observers travelling at different velocities have different notions of time. This is what's at the core of the Twin Paradox, the travelling twin experiences less time passing by a factor of 1 / sqrt( 1 - v²/c²) where v is his speed and c is the speed of light. This factor is also called the gamma-factor (often denoted by γ) and pops up a lot in the various formulae of the Theory of Special Relativity. | ||
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Capook
United States122 Posts
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XxDefexX
Denmark19 Posts
On July 22 2011 01:02 Nawyria wrote: The Lorentz transformation in flat space-time is a continuous transformation, so the signal will not be discrete; however, the signal will be distorted due to the relativistic doppler-effect. Name the twin that stays on earth twin A and the travelling one twin B; assume further that they communicate by way of a continuous stream of light that varies mildly in wavelength around 550 nanometres (yellow). 1B) As twin B moves away from the earth at high speed, the relativistic doppler-effect redshifts the light signal, the signals he receives are in the red or infrared. He will also receive the signals at a lower pace due to the fact the light signals have to catch up to him, and thus the intensity will be much lower and the transmitted message plays very slowly. 2B) Just after twin B reverses his direction of travel (which we will assume he does instantly), all the signals he has been travelling ahead of will catch up to him in a very short amount of time. Since twin B is now travelling towards earth, the signals will be blueshifted and the signals he receives are in the blue, ultraviolet or beyond. He will now receive the signals at a much much higher pace, so the intensity will be much higher and the transmitted message plays extremely fast. 3B) After this short burst has passed and twin B is travelling back towards the earth, we are in the inverse of situation 1B. The light signals are blueshifted (as in 2B), the intensity is higher (though not as high in 2B) and the message players faster (though not as fast as in 2B). 1A) After twin A says his farewell to twin B, he will receive messages at a very slow pace, with the same redshift, intensity and message speed as in 1B. 2A) As twin B nears earth, all the messages that he has sent since turning around will reach earth in a very short fashion, much like what happens in 2B, only the intensity will be even higher. Edit: Assuming the distances are vast enough for twin A to die as twin B is travelling, it depends on the speed of twin B whether he receives words of twin A's death as he is travelling or soon after he turns around. The faster twin B travels, the less messages he will receive before turning around, thus increasing the chance he will hear of it after he turns around. According to 2A (I guess A means, we watch it from A's perspective?), the messages sent after the turning point will arrive "in a very short fashion". The thing interesting me here is: If they were to do so, looking at the situation from A's perspective, the messages would have to travel faster than the speed of light. I mean, assuming B travelling as close to the speed of light as possible, it would take almost as long for B to return to Earth as it takes for the messages - since they of course can't travel faster than c. Therefore, the speed of the messages, B has sent after turning around, will not be that higher than the speed of B, and they will not reach Earth as fast as you claim? You could say, that looking from A's perspective (as I do in order to claim this), the time dillation kicks in and makes the "time of the messages" go at a slower pace. But according to B travelling nearly as fast, B's time would go almost as slow and therefore the messages shouldn't arrive "in a very short fashion"? Even if we turn the perspective, the distance to Earth (seen from the perspective of the messages) would be relatively short, due to the high speed, but so would the distance to Earth for our twin B. So unless I misunderstood something, which I probably did :D, the messages B sends after turning around, shouldn't arrive in a very short fashion, since you obviously can't just add the speed of B and the speed of light and get the speed of the messages  . | ||
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mcc
Czech Republic4646 Posts
On July 22 2011 02:07 nihlon wrote: Are you people just assuming the rate of aging or is this a part of the theory? I am not exactly familiar with the math, but the rate should depend on the velocities in question, or at least acceleration (as the acceleration and deceleration is in actuality what makes the paradox work as someone already noted). | ||
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JinDesu
United States3990 Posts
On July 22 2011 02:13 mcc wrote: I am not exactly familiar with the math, but the rate should depend on the velocities in question, or at least acceleration (as the acceleration and deceleration is in actuality what makes the paradox work as someone already noted). It's dependent on the velocity/ | ||
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mcc
Czech Republic4646 Posts
So the acceleration is there just to make it asymetrical situation(non-inertial frame) and the actual values have no bearing on the resulting age difference ? | ||
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JinDesu
United States3990 Posts
It would have bearing, since to achieve velocity, you have to have some form of acceleration for a duration of time. | ||
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Nawyria
Netherlands140 Posts
On July 22 2011 02:12 XxDefexX wrote: According to 2A (I guess A means, we watch it from A's perspective?), the messages sent after the turning point will arrive "in a very short fashion". The thing interesting me here is: If they were to do so, looking at the situation from A's perspective, the messages would have to travel faster than the speed of light. I mean, assuming B travelling as close to the speed of light as possible, it would take almost as long for B to return to Earth as it takes for the messages - since they of course can't travel faster than c. Therefore, the speed of the messages, B has sent after turning around, will not be that higher than the speed of B, and they will not reach Earth as fast as you claim? You could say, that looking from A's perspective (as I do in order to claim this), the time dillation kicks in and makes the "time of the messages" go at a slower pace. But according to B travelling nearly as fast, B's time would go almost as slow and therefore the messages shouldn't arrive "in a very short fashion"? Even if we turn the perspective, the distance to Earth (seen from the perspective of the messages) would be relatively short, due to the high speed, but so would the distance to Earth for our twin B. So unless I misunderstood something, which I probably did :D, the messages B sends after turning around, shouldn't arrive in a very short fashion, since you obviously can't just add the speed of B and the speed of light and get the speed of the messages .I'm not really sure what your question is, but I'll try to help anyhow. They say a pictures says a thousand words, so I hope these are worth at least two thousand. The idea here is that the observers are emitting messages at fixed intervals according to their own perception of time. Twin A's messages You can see clearly that most of A's messages arrive after B has turned around. Thinking about it, I may have been wrong in my initial post in that 2B doesn't happen when twin B turns around instantaneously, but is in fact due to him having to decelerate. + Show Spoiler [picture] + ![[image loading]](http://i.imgur.com/FVqPk.jpg) Twin B's messages You can see that A receives all of B's messages after he has turned around in the short amount of time before B's arrival. The messages do not actually travel faster than light, but the fact that they arrive quickly after one another is because each messages is sent from a position that is closer to earth than the previous. + Show Spoiler [picture] + ![[image loading]](http://i.imgur.com/Bm0YN.jpg) I'd be glad to answer any more questions you might have. | ||
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Nawyria
Netherlands140 Posts
On July 22 2011 02:36 JinDesu wrote: The acceleration would increase (or decrease) the rate of aging, or rather, increase or decrease the time dilation. It would have bearing, since to achieve velocity, you have to have some form of acceleration for a duration of time. The process of deceleration/acceleration itself isn't actually what causes the twin paradox to occur. The Lorentz-transformation has a directional bias and as long as the velocity of the travelling twin flips direction, the twin's time and space axes will shift to accommodate the lack of aging. | ||
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kellymilkies
Singapore1393 Posts
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XxDefexX
Denmark19 Posts
. The problem was, that I understood your post as if Twin B's messages sent after the turning point would arrive way faster than B (which is not what was meant - clearly seen by the picture.Good luck with your studies . And btw, I'm drinking coke atm., but filled the glass too much. Why didn't it run over the top and out on my desktop? (sorry for off-topic :D) | ||
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Blazinghand
United States25557 Posts
On July 22 2011 02:42 kellymilkies wrote: Where can I find more about this subject? http://en.wikipedia.org/wiki/Twin_paradox or the chinese translation these both have pretty good information on it. You might want to read up on spacetime diagrams as well, because they are also cool. | ||
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Nawyria
Netherlands140 Posts
On July 22 2011 02:42 kellymilkies wrote: Where can I find more about this subject? The wikipedia page for the Twin paradox is pretty good. Another few links that I can recommend: Through Einstein's Eyes The C-Ship: Aberration of light Cool videos: Relativistic Aberration Intensity Effects Relativistic Tram Relativistic Rollercoaster must watch | ||
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Maenander
Germany4926 Posts
On July 22 2011 02:40 Nawyria wrote: The process of deceleration/acceleration itself isn't actually what causes the twin paradox to occur. The Lorentz-transformation has a directional bias and as long as the velocity of the travelling twin flips direction, the twin's time and space axes will shift to accommodate the lack of aging. I see your point, but without deceleration/acceleration one couldn't actually decide which twin flipped direction, i.e. who is in the inertial frame. | ||
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wherebugsgo
Japan10647 Posts
On July 22 2011 02:12 XxDefexX wrote: According to 2A (I guess A means, we watch it from A's perspective?), the messages sent after the turning point will arrive "in a very short fashion". The thing interesting me here is: If they were to do so, looking at the situation from A's perspective, the messages would have to travel faster than the speed of light. I mean, assuming B travelling as close to the speed of light as possible, it would take almost as long for B to return to Earth as it takes for the messages - since they of course can't travel faster than c. Therefore, the speed of the messages, B has sent after turning around, will not be that higher than the speed of B, and they will not reach Earth as fast as you claim? You could say, that looking from A's perspective (as I do in order to claim this), the time dillation kicks in and makes the "time of the messages" go at a slower pace. But according to B travelling nearly as fast, B's time would go almost as slow and therefore the messages shouldn't arrive "in a very short fashion"? Even if we turn the perspective, the distance to Earth (seen from the perspective of the messages) would be relatively short, due to the high speed, but so would the distance to Earth for our twin B. So unless I misunderstood something, which I probably did :D, the messages B sends after turning around, shouldn't arrive in a very short fashion, since you obviously can't just add the speed of B and the speed of light and get the speed of the messages .I think you did misunderstand it. The reason the messages arrive faster/slower is not because the speed is added. It's because the point of propagation of the waves keeps changing. Look at it this way: when the spaceship is traveling away from Earth, with every passing unit of time the spaceship sends a signal, but from a position that is constantly changing and constantly getting further away from Earth. Let's take a few example wave pulses to demonstrate this, and say that the total distance to the alien planet is 10 light years. When the spaceship initially leaves, let's say 10 seconds after departure it sends a message, Earth will receive it a little bit less than 10 seconds later, while the spaceship has traveled roughly double the distance of where it was to begin with. If the spaceship sends a message from 5 light years away, it'll take 5 light years for the Earth to receive it. Regardless, on the way there it'll take longer for the messages to reach Earth while the spaceship travels away. Each message will therefore be received further and further apart. On the way back, let's start at 10 light years away. The spaceship sends a pulse while coming back, and it'll take 10 years to hit Earth. Call this message 1. Message 2 is sent at 9 light years away (a tiny bit more than a year later) and it takes 9 light years to get to Earth, etc etc. If you notice, at the end of the journey the receiver on Earth will receive almost every message from the ship that was made on the journey back within a very short span of time, almost immediately before the ship arrives. | ||
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hytonight
303 Posts
On July 22 2011 01:15 AmericanUmlaut wrote: Serves him right if he's talking on his cell phone instead of paying attention... what if it was a drunk driver that crashed into his house? | ||
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XxDefexX
Denmark19 Posts
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Nawyria
Netherlands140 Posts
On July 22 2011 02:49 Maenander wrote: I see your point, but without deceleration/acceleration one couldn't actually decide which twin flipped direction, i.e. who is in the inertial frame. You are entirely correct, sir. On July 22 2011 02:47 XxDefexX wrote: Thanks a lot, they did say at least two thousand words . The problem was, that I understood your post as if Twin B's messages sent after the turning point would arrive way faster than B (which is not what was meant - clearly seen by the picture.Good luck with your studies . And btw, I'm drinking coke atm., but filled the glass too much. Why didn't it run over the top and out on my desktop? (sorry for off-topic :D)This is because of surface tension. There are basically three forces at work here. 1) Water likes to be near water. Water molecules form so-called hydrogen bonds among each other, which makes it energetically favourable for water molecules to be clustered. 2) A body of water "pays energy" for its boundary. Basically, the larger the boundary between a body of water and the outside, the less energetically favourable the situation is. Therefore water will try to minimize its surface area. 3) There is gravity that attempts to pull the water molecules down and spill it over your glass. The lower the water molecules are, the more energetically favourable. What happens to your glass of coke is exactly what happens to a drop of water on your desk. The drop of water attempts to make its state as energetically favourable as it can. Clearly, going by gravity alone, the most energetically favourable state is for it to be as flat as possible, since then the water molecules are as close to the ground as they can be without spilling over your desk. However, the flatter the drop becomes, the larger its surface area will be (this costs energy) and the less clustered the drop becomes (this too costs energy). Therefore, the water droplet will become slightly flattened, but still retain a drop-like shape; this is simply the most favourable state considering the above three factors. In your case, if the water were to spill over the side of the glass, its surface area would increase dramatically and the gravitational energy is not sufficient to compensate for it. However if you were to pour a little more coke into the glass, you would surpass a critical point beyond which it is more favourable for the liquid to spill over and incur the penalty of a larger surface area, and your glass will spill. | ||
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