The Twins Paradox - Alan Gasparutti (top ten books of all time txt) 📗
- Author: Alan Gasparutti
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should land.”
“As far as I'm concerned, I don't think we should go to Earth,” Professor Schmidt commented.
“Why not?” the others each asked.
“Is there something else about Earth that we should know about?” added the Commander.
“I just don't think it's worth it,” replied Professor Schmidt. “We discussed this last time, if you all remember. Life on the 'Pilgrim is a lot longer than a lifetime on Earth.”
“But I thought we found the answer to that,” said Commander Ondichi. “I'm sure you all remember that theory, the Twin's Paradox, which explained the differences.”
“Not fully,” replied Professor Schmidt. “Even after allowing for this paradox, life on the 'Pilgrim is over 10 times greater.”
“But it's all relative,” said Professor Wagstaff. “Besides, I think I've worked out the remaining factor.”
“And what might that be?” asked Professor Schmidt.
“I believe that we're all travelling forward in time,” replied Professor Wagstaff.
“And how did you come to that conclusion?” asked Professor Schmidt. “When we were discussing this recently you seemed to suggest the closer to light speed we got to the more likely time stood still.”
“I know, I know, but think of things the other way around,” said Professor Wagstaff, before explaining what he and Professor Schmidt had debated. “The closer we get to light speed the less we age. From the opposite side of the coin, so to speak, if someone had travelled a 10 light year round trip at light speed, they would arrive back at the same place 10 years later but at the same age. So this could be interpreted as though the person had travelled forward 10 years in time.”
“It all sound good, but what proof do you have?” asked Commander Ondichi.
“Well, I did a little calculation,” Professor Wagstaff told him. “It goes like this: take what may be considered a good Earth age, 90. Allowing for diseases and a faster rate of ageing on Earth, multiply this by 1.25, to get what we may have considered a good life expectancy on the 'Pilgrim, 102.5 years and a bit.”
“I've already tried this out,” emphasised Professor Schmidt. “Can you get to the point.”
“I'll be coming to that in a moment,” replied Professor Wagstaff. “As we may spend up to three times this in hibernation, multiply this by 4, to get 410. Now, you recall Professor, we checked the average speed of the 'Pilgrim?”
“Yes, it was something like 600 million miles per hour, about 88% the speed of light,” said Professor Schmidt, as Commander Ondichi and Major Retono looked at eachother, a little bewildered.
“89.61% actually, but let's just take 89% for now,” said Professor Wagstaff. “Multiply 410 by an additional 89% and you have 775. Multiply this by 12 thousand, the number of generations of people that have inhabited the 'Pilgrim, and you have 9.3 million, which multiplied by a factor of 7 gives you something over 65 million years.”
“Shouldn't that factor of 7 be part of the 89% as they each relate to the speed at which a ship is travelling?” asked Professor Schmidt.
“Not really,” replied Professor Wagstaff. “The time dilation factor is 7, wheras the 'future' factor, for want of a better term, is 89% the speed of light. Or to put it another way, light speed divided by actual speed, multiplied by distance equals the number of years in the future someone has travelled.”
“Actually, I’ve looked at the generation figures again to take other factors into account, and it appears to be nearer fourteen thousand,” said Professor Schmidt. “I’ve since calculated a different solution.”
“Oh,” said Professor Wagstaff. “What might that be?”
“If someone is travelling at 90% the speed of light that will suggest that they will only age by 10% of the rate of someone on Earth.” inferred Professor Schmidt. “By that assumption, for someone to age 120 years, in Earth terms they will be 1200. Are you still with me so far?”
“Yes, yes, yes, Professor,” said Commander Ondichi. “Please carry on.”
“Well, when you consider that we would spend 75% of our lives in hibernation, this would suggest that we age 120 years in 4800 Earth years,” added Professor Schmidt. “Divide 65 million by this figure, and you arrive at just over thirteen-and-a-half thousand.”
“I thought you said it was almost fourteen thousand?” queried Professor Wagstaff.
“Taking into account the probability that the earlier crafts were not as fast as the Interstellar Pilgrim, and occasions when the crafts reduced speeds when approaching planets, should allow for the relatively small difference,” replied Professor Schmidt.
“Excuse me, gentlemen, but we should discuss this theory some other time,” said Commander Ondichi, before turning to Professor Schmidt. “I accept your views and why you may not be keen to visit Earth, but I’d like to forget your views for the time being. Now, where were we?”
“I think we were about to agree that the United States was not the best place on Earth to start a reconnaissance mission,” Major Retono informed him.
“Yes, I like the idea of going to an island on Earth to start with,” said the Commander. “What was the name of that island you mentioned, Professor Wagstaff?”
“I don't think Lanzarote would be the ideal place to start,” Professor Schmidt quickly jumped in saying.
“Why ever not?” asked Professor Wagstaff.
“English is not the spoken language there, for one reason,” replied Professor Schmidt. “It would also appear to be a volcanic island, as are the other islands nearby. Besides, there are other, more appropriate islands to commence a reconnaissance mission.”
“Where might these be?” Commander Ondichi queried.
“Australia, for one,” suggested Professor Schmidt, before pointing it out on the map on screen. “They speak the same language, too.”
“It's a pretty big island,” commented Major Retono.
“It also appears rather barren,” said Professor Wagstaff. “It's not very populous for it's size, and most people live in cities on or near the coast. I fear that if you landed in the middle of Australia, it would take you sometime to find habitation.”
“How about the other three islands nearby?” asked Commander Ondichi.
“The bottom island, Tasmania, is part of Australia,” explained Professor Wagstaff. “I’d need to find out a little more about the place first. As for the other two islands to the east, it might be considered a good place to start, if you wanted to talk to sheep.”
Major Retono then looked north on the map and referred to Japan.
“That's probably too overcrowded,” said Professor Schmidt. “It is one of the busiest places on Earth, and technologically, probably the most productive. Unfortunately, they speak their own language, which we haven't recorded. It is also volcanic.”
Commander Ondichi then referred to Hawaii and it's surrounding group of islands, but being in the middle of a massive ocean, didn't seem ideal. He then pointed east on the map, first referring to Iceland, and then towards two large islands surrounded by many smaller ones.
“The smaller of the two main islands is relatively sparse,” said Professor Schmidt. “This, I believe, is called Ireland.”
“How about the largest island?” asked Major Retono.
“This is Britain,” said Professor Schmidt. “It’s very populous. They do speak our language, though. In fact, that's where English is believed to come from. It is busy, productive and influential.”
“Sounds good to me,” said Major Retono. “What do you think, Professor Wagstaff?”
“Well, it wouldn't be my first choice, but I suppose it has it's benefits,” he replied. “Can we zoom-in on Britain?”
The four of them looked carefully around the island, and also at Ireland. Whereas Ireland seemed empty, Britain seemed crowded. They did, however, notice several areas of empty land.
“Zoom-in further please, Professor Schmidt,” the Commander requested.
“What are those roundish things down there?” Major Retono then asked.
“I believe these are mountains, or more likely in this case, hills,” Professor Schmidt told the others.
“How about these curvy lines?” asked Commander Ondichi.
“That's probably a railway track,” explained Professor Wagstaff. “They're designed for trains to run along, carrying people from one city to another.”
“What about this white stuff nearby?” asked Major Retono. “It's not ice, is it?”
“Zoom in on this a little more, please,” the Commander ordered.
“I think that's calcium carbonate, otherwise known around this area as limestone,” said Professor Schmidt.
“l think I'm right in saying that calcium carbonate dissolves in water,” Professor Schmidt commented.
“What are you eluding to, Professor?” asked the Commander.
“Well, I've noticed plenty of rainfall when I monitored this area, so I would think there should be several caves in this region,” Professor Schmidt explained. “I think that would be the ideal place to base any mission.”
“Hhmmm, good point,” muttered Major Retono. “How close to the ground can we zoom-in on this screen?”
“As close as you want to, I believe,” said Professor Schmidt.
Professor Schmidt then concentrated on that particular region. As the images on-screen got closer and closer to ground-level, they each began to notice some holes in the ground.
“These holes,” queried Major Retono. ”Do you think they may be big enough for a small craft to land?”
“Most of them appear to be too small, but there a couple which may be suitable,” advised Professor Wagstaff. “We don't know how deep they are, though.”
“Surely the deeper they are the better,” said Major Retono.
“Not if you want to get out of the hole,” replied Professor Schmidt.
“Surely they must have regional maps on Earth,” said the Commander. “Can you see if you can trace some on the World Wide Web?”
Sure enough, Professor Schmidt traced Ordnance Survey maps, and after a short search, managed to find the appropriate map they were looking for. Though the images on screen gave a more detailed view of the area in question, they found it useful to locate the names of places and potholes they were looking at.
From here it was decided that this indeed was the best place to land a small reconnaissance craft. A couple of the potholes were large enough for the mission, and one in particular had a narrow passage leading out from it.
“Where do you think we should go from here?” asked Commander Ondichi.
Major Retono pointed to one which seemed to be suitable. He then brought this up on screen, before looking into it.
“Seems okay to me,” he said. “There are a couple of caves leading out lower down the pothole. Can any of you see any problems with landing the craft in it?”
“No, no, there shouldn't be any problem landing the craft in there,” Professor Wagstaff said smugly. “If we can direct a comet to smash into ZR4, sorry, Mars, from millions of miles away, this shouldn't be a problem.”
“Well I'm glad you're so confident about that, as you'll be coming on the mission with me,” Major Retono told him.
“Oh,” mumbled Professor Wagstaff.
“How many people can we get into the craft?” Major Retono asked. “Hasn't it been modified since the last time we used it?”
“Yes, I believe it has,” said Professor Schmidt. “However, I don't think you'll get a dozen people into the craft after the council have been informed of the short length of life on Earth.”
“That's as maybe, but regardless of your thoughts, Professor, there are some people on the 'Pilgrim who would like to visit Earth,” said Commander Ondichi before turning to Major Retono. “Are there any particular people you want to take along with you?”
“From what I've seen of Earth and it's inhabitants, we'll need someone who's technical and someone mechanical,” Major Retono stated. “Oh, and we'll probably need the replicator.”
“I think the large replicator would be too big for the craft,” suggested Professor Schmidt.
“Do you think the small replicator will be able to replicate those vehicles they have on Earth?” Major Retono queried.
“That should be fine for vehicles,” said Professor Wagstaff. “I'm
“As far as I'm concerned, I don't think we should go to Earth,” Professor Schmidt commented.
“Why not?” the others each asked.
“Is there something else about Earth that we should know about?” added the Commander.
“I just don't think it's worth it,” replied Professor Schmidt. “We discussed this last time, if you all remember. Life on the 'Pilgrim is a lot longer than a lifetime on Earth.”
“But I thought we found the answer to that,” said Commander Ondichi. “I'm sure you all remember that theory, the Twin's Paradox, which explained the differences.”
“Not fully,” replied Professor Schmidt. “Even after allowing for this paradox, life on the 'Pilgrim is over 10 times greater.”
“But it's all relative,” said Professor Wagstaff. “Besides, I think I've worked out the remaining factor.”
“And what might that be?” asked Professor Schmidt.
“I believe that we're all travelling forward in time,” replied Professor Wagstaff.
“And how did you come to that conclusion?” asked Professor Schmidt. “When we were discussing this recently you seemed to suggest the closer to light speed we got to the more likely time stood still.”
“I know, I know, but think of things the other way around,” said Professor Wagstaff, before explaining what he and Professor Schmidt had debated. “The closer we get to light speed the less we age. From the opposite side of the coin, so to speak, if someone had travelled a 10 light year round trip at light speed, they would arrive back at the same place 10 years later but at the same age. So this could be interpreted as though the person had travelled forward 10 years in time.”
“It all sound good, but what proof do you have?” asked Commander Ondichi.
“Well, I did a little calculation,” Professor Wagstaff told him. “It goes like this: take what may be considered a good Earth age, 90. Allowing for diseases and a faster rate of ageing on Earth, multiply this by 1.25, to get what we may have considered a good life expectancy on the 'Pilgrim, 102.5 years and a bit.”
“I've already tried this out,” emphasised Professor Schmidt. “Can you get to the point.”
“I'll be coming to that in a moment,” replied Professor Wagstaff. “As we may spend up to three times this in hibernation, multiply this by 4, to get 410. Now, you recall Professor, we checked the average speed of the 'Pilgrim?”
“Yes, it was something like 600 million miles per hour, about 88% the speed of light,” said Professor Schmidt, as Commander Ondichi and Major Retono looked at eachother, a little bewildered.
“89.61% actually, but let's just take 89% for now,” said Professor Wagstaff. “Multiply 410 by an additional 89% and you have 775. Multiply this by 12 thousand, the number of generations of people that have inhabited the 'Pilgrim, and you have 9.3 million, which multiplied by a factor of 7 gives you something over 65 million years.”
“Shouldn't that factor of 7 be part of the 89% as they each relate to the speed at which a ship is travelling?” asked Professor Schmidt.
“Not really,” replied Professor Wagstaff. “The time dilation factor is 7, wheras the 'future' factor, for want of a better term, is 89% the speed of light. Or to put it another way, light speed divided by actual speed, multiplied by distance equals the number of years in the future someone has travelled.”
“Actually, I’ve looked at the generation figures again to take other factors into account, and it appears to be nearer fourteen thousand,” said Professor Schmidt. “I’ve since calculated a different solution.”
“Oh,” said Professor Wagstaff. “What might that be?”
“If someone is travelling at 90% the speed of light that will suggest that they will only age by 10% of the rate of someone on Earth.” inferred Professor Schmidt. “By that assumption, for someone to age 120 years, in Earth terms they will be 1200. Are you still with me so far?”
“Yes, yes, yes, Professor,” said Commander Ondichi. “Please carry on.”
“Well, when you consider that we would spend 75% of our lives in hibernation, this would suggest that we age 120 years in 4800 Earth years,” added Professor Schmidt. “Divide 65 million by this figure, and you arrive at just over thirteen-and-a-half thousand.”
“I thought you said it was almost fourteen thousand?” queried Professor Wagstaff.
“Taking into account the probability that the earlier crafts were not as fast as the Interstellar Pilgrim, and occasions when the crafts reduced speeds when approaching planets, should allow for the relatively small difference,” replied Professor Schmidt.
“Excuse me, gentlemen, but we should discuss this theory some other time,” said Commander Ondichi, before turning to Professor Schmidt. “I accept your views and why you may not be keen to visit Earth, but I’d like to forget your views for the time being. Now, where were we?”
“I think we were about to agree that the United States was not the best place on Earth to start a reconnaissance mission,” Major Retono informed him.
“Yes, I like the idea of going to an island on Earth to start with,” said the Commander. “What was the name of that island you mentioned, Professor Wagstaff?”
“I don't think Lanzarote would be the ideal place to start,” Professor Schmidt quickly jumped in saying.
“Why ever not?” asked Professor Wagstaff.
“English is not the spoken language there, for one reason,” replied Professor Schmidt. “It would also appear to be a volcanic island, as are the other islands nearby. Besides, there are other, more appropriate islands to commence a reconnaissance mission.”
“Where might these be?” Commander Ondichi queried.
“Australia, for one,” suggested Professor Schmidt, before pointing it out on the map on screen. “They speak the same language, too.”
“It's a pretty big island,” commented Major Retono.
“It also appears rather barren,” said Professor Wagstaff. “It's not very populous for it's size, and most people live in cities on or near the coast. I fear that if you landed in the middle of Australia, it would take you sometime to find habitation.”
“How about the other three islands nearby?” asked Commander Ondichi.
“The bottom island, Tasmania, is part of Australia,” explained Professor Wagstaff. “I’d need to find out a little more about the place first. As for the other two islands to the east, it might be considered a good place to start, if you wanted to talk to sheep.”
Major Retono then looked north on the map and referred to Japan.
“That's probably too overcrowded,” said Professor Schmidt. “It is one of the busiest places on Earth, and technologically, probably the most productive. Unfortunately, they speak their own language, which we haven't recorded. It is also volcanic.”
Commander Ondichi then referred to Hawaii and it's surrounding group of islands, but being in the middle of a massive ocean, didn't seem ideal. He then pointed east on the map, first referring to Iceland, and then towards two large islands surrounded by many smaller ones.
“The smaller of the two main islands is relatively sparse,” said Professor Schmidt. “This, I believe, is called Ireland.”
“How about the largest island?” asked Major Retono.
“This is Britain,” said Professor Schmidt. “It’s very populous. They do speak our language, though. In fact, that's where English is believed to come from. It is busy, productive and influential.”
“Sounds good to me,” said Major Retono. “What do you think, Professor Wagstaff?”
“Well, it wouldn't be my first choice, but I suppose it has it's benefits,” he replied. “Can we zoom-in on Britain?”
The four of them looked carefully around the island, and also at Ireland. Whereas Ireland seemed empty, Britain seemed crowded. They did, however, notice several areas of empty land.
“Zoom-in further please, Professor Schmidt,” the Commander requested.
“What are those roundish things down there?” Major Retono then asked.
“I believe these are mountains, or more likely in this case, hills,” Professor Schmidt told the others.
“How about these curvy lines?” asked Commander Ondichi.
“That's probably a railway track,” explained Professor Wagstaff. “They're designed for trains to run along, carrying people from one city to another.”
“What about this white stuff nearby?” asked Major Retono. “It's not ice, is it?”
“Zoom in on this a little more, please,” the Commander ordered.
“I think that's calcium carbonate, otherwise known around this area as limestone,” said Professor Schmidt.
“l think I'm right in saying that calcium carbonate dissolves in water,” Professor Schmidt commented.
“What are you eluding to, Professor?” asked the Commander.
“Well, I've noticed plenty of rainfall when I monitored this area, so I would think there should be several caves in this region,” Professor Schmidt explained. “I think that would be the ideal place to base any mission.”
“Hhmmm, good point,” muttered Major Retono. “How close to the ground can we zoom-in on this screen?”
“As close as you want to, I believe,” said Professor Schmidt.
Professor Schmidt then concentrated on that particular region. As the images on-screen got closer and closer to ground-level, they each began to notice some holes in the ground.
“These holes,” queried Major Retono. ”Do you think they may be big enough for a small craft to land?”
“Most of them appear to be too small, but there a couple which may be suitable,” advised Professor Wagstaff. “We don't know how deep they are, though.”
“Surely the deeper they are the better,” said Major Retono.
“Not if you want to get out of the hole,” replied Professor Schmidt.
“Surely they must have regional maps on Earth,” said the Commander. “Can you see if you can trace some on the World Wide Web?”
Sure enough, Professor Schmidt traced Ordnance Survey maps, and after a short search, managed to find the appropriate map they were looking for. Though the images on screen gave a more detailed view of the area in question, they found it useful to locate the names of places and potholes they were looking at.
From here it was decided that this indeed was the best place to land a small reconnaissance craft. A couple of the potholes were large enough for the mission, and one in particular had a narrow passage leading out from it.
“Where do you think we should go from here?” asked Commander Ondichi.
Major Retono pointed to one which seemed to be suitable. He then brought this up on screen, before looking into it.
“Seems okay to me,” he said. “There are a couple of caves leading out lower down the pothole. Can any of you see any problems with landing the craft in it?”
“No, no, there shouldn't be any problem landing the craft in there,” Professor Wagstaff said smugly. “If we can direct a comet to smash into ZR4, sorry, Mars, from millions of miles away, this shouldn't be a problem.”
“Well I'm glad you're so confident about that, as you'll be coming on the mission with me,” Major Retono told him.
“Oh,” mumbled Professor Wagstaff.
“How many people can we get into the craft?” Major Retono asked. “Hasn't it been modified since the last time we used it?”
“Yes, I believe it has,” said Professor Schmidt. “However, I don't think you'll get a dozen people into the craft after the council have been informed of the short length of life on Earth.”
“That's as maybe, but regardless of your thoughts, Professor, there are some people on the 'Pilgrim who would like to visit Earth,” said Commander Ondichi before turning to Major Retono. “Are there any particular people you want to take along with you?”
“From what I've seen of Earth and it's inhabitants, we'll need someone who's technical and someone mechanical,” Major Retono stated. “Oh, and we'll probably need the replicator.”
“I think the large replicator would be too big for the craft,” suggested Professor Schmidt.
“Do you think the small replicator will be able to replicate those vehicles they have on Earth?” Major Retono queried.
“That should be fine for vehicles,” said Professor Wagstaff. “I'm
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