The Twins Paradox, Alan Gasparutti [online e reader txt] 📗

use the terms minutes, hours, days and years,” replied Commander Ondichi. “I'm not fully conversant in the timescales, however.”
“Well let me explain,” said Professor Schmidt. “A second is one very brief moment, sixty seconds make up a minute, and sixty minutes make up one hour. Each Earth day is twenty-four hours. Are you with me so far?”
The Commander and Professor Wagstaff quietly acknowledged Professor Schmidt, before Major Retono asked what the significance of one day was.
“You may have noticed that the Earth rotates,” Professor Schmidt explained. “Twenty-four hours is the length of time it takes the Earth to complete one full rotation, which is one day. Additionally, it then takes the Earth three-hundred-and-sixty-five days, or one year, to orbit Zorontin, or as humans refer to it, the sun.”
“Is this a problem?” Commander Ondichi asked. “Otherwise I'd be grateful if can you elaborate on what you're eluding to?”
“Time isn't a problem in itself,” Professor Schmidt emphasised. “I should state, however, that the life expectancy on Earth is only about eighty years.”
The others all looked a little confused.
“How long are we expected to live on board here?” Major Retono asked.
“I've calculated life expectancy on the Interstellar Pilgrim to be over five thousand years,” explained Professor Schmidt.
“That can't be right, can it?” Professor Wagstaff queried. “Don't forget we spend much of our time in hibernation.”
“True, true,” replied Professor Schmidt. “But even if we spend three-quarters of our life in hibernation, it still means that we live to over one thousand Earth years. Do any of you want to reduce you're lifespan?”
“Perhaps you miscalculated somewhere along the way,” suggested the Commander. “How did you work that out?”
“Well, on Earth they refer to the monsters which our forefathers encountered as dinosaurs,” Professor Schmidt explained. “You may be aware that our forefathers left Earth when an asteroid was due to collide with it. I've read information on some massive network called the World Wide Web, which indicates that this occurred sixty-five million Earth years ago.”
“So how did you make your calculations from there?” asked Major Retono.
“Do any of you know how many generations of people have lived on the Interstellar Pilgrim?” Professor Schmidt asked the others.
“I would say about ten thousand,” said Professor Wagstaff.
“I calculated it to be nearer twelve thousand,” Professor Schmidt replied. “These are only rough calculations, but can you see how I've done this? I accept that we do spend about 75% of our time travelling in hibernation, but this still leaves an average age on the Interstellar Pilgrim of over 1.3 thousand years. Do any of you know if I've missed anything out?”
As Major Retono and Professor Wagstaff tried to think of any additional calculations, Commander Ondichi was in deep thought.
“Hhmm, I wonder,” he muttered.
“Wonder what?” Professor Schmidt asked curiously. “Have I overlooked something?”
“I was looking on the World Wide Web about humans and their views of the cosmos just the other day,” said the commander. “I came across something referred to as the theory of relativity, by some professor known as Eensteen.”
“I think you'll find the name is pronounced as Einstein,” Professor Schmidt informed him.
“How do you know?” Commander Ondichi queried. “Have you come across him before?”
“Yes,” replied Professor Schmidt. “I've heard the name mentioned and read some of his work.”
“Well, this theory of relativity contained a chapter referred to as the Twin's Paradox,” Commander Ondichi added. “If I understood this correctly, it suggests that if one of two twin brothers went on a long space journey, on a rocket travelling at almost the speed of light, when the traveller returned, he would be younger than his twin who stayed put. Search for it on the World Wide Web.”
Professor Schmidt searched under the title 'Twins Paradox', and sure enough, came across a couple of paragraphs confirming what the Commander had said, reading the following out to his colleagues:
The Twin Paradox: Introduction
Example: Story of twins, Homer and Stella. Homer sits at home on Earth., while Stella travels in a spaceship at nearly the speed of light to a star 7 light-years away. On reaching her destination, Stella turns around , thrusters blazing, and returns.
When our heroes meet again, what do they find? Did time slow down for Stella, making her years younger than her home-bound brother? Or can Stella declare that the Earth did the traveling, so Homer is the younger?
Special Relativity (SR) suggests the first answer is correct: Stella ages less than Homer between the departure and the reunion. SR does not declare that all frames of reference are equivalent, only so-called inertial frames. Stella's frame is not inertial while she is accelerating. And this is observationally detectable: Stella had to fire her thrusters midway through her trip; Homer did nothing of the sort. The Ming vase she had borrowed from Homer fell over and cracked. She struggled to maintain her balance, like the crew of Star Trek. In short, she felt the acceleration, while Homer felt nothing.
We've said why Stella can't simply adopt Homer's viewpoint, but we haven't said how things look from her perspective. It seems strange that Homer could age several years just because Stella engages her thrusters. The Time Gap and Distance Dependence Objections put a sharper edge on this uneasy feeling.
What about General Relativity (GR)? Doesn't that say that Stella can still claim to be motionless the whole time, but that a humongous gravitational field just happened to sweep through the universe when she hit her "thrusters on" button? (For that matter, Homer experiences the Earth's gravity; is his frame truly inertial?) Some people claim that the twin paradox can be resolved only by invoking GR. We disagree, but the "GR Explanation" of the twin paradox does shed some light. The GR viewpoint is nearly mandatory for understanding some of the twin paradox variations. Let's lay out a "standard version" of the paradox in detail, and settle on some terminology. We'll get rid of Stella's acceleration at the start and end of the trip. Stella flashes past Homer in her spaceship both times, coasting along. Here's the itinerary according to Homer:

Start Event - Stella flashes past. Clocks are synchronized to 0.
Outbound Leg - Stella coasts along at (say) nearly 99 percent of light-speed. At 99 percent, the time dilation factor is a bit over 7, so let's say the speed is just a shade under 99 percent and the time dilation factor is 7. This part of the trip takes 7 years, according to Homer.

Turnaround - Stella fires her thrusters for, say, 1 day, until she is coasting back towards Earth at nearly 99 percent light-speed. Some variations on the paradox call for an instantaneous Turnaround; we'll call that the Turnaround Event.

Inbound Leg - Stella coasts back for 7 years at 99 percent light-speed.

Return Event - Stella flashes past Homer in the other direction, and they compare clocks, or any other sign of elapsed time.

According to Homer, 14 years and a day have elapsed between the Start and Return Events; Stella's clock however reads just a shade over 2 years.

They each read the screen a few times to try to fully understand the information.
“So let's get this into perspective,” said Major Retono. “When travelling at light speed time becomes diluted.”
“Dilated,” Professor Schmidt corrected him. “Light speed would appear to give a time dilation factor of seven.”
“So presumably, time dilation decreases the slower the speed of travel,” suggested Professor Wagstaff. “On that basis, the speed at which we are currently travelling at, or indeed, at which ZR3, sorry, the Earth is travelling at become relatively stable.”
“I'd like to take a closer look at this theory,” commented Professor Schmidt. “At first glance it doesn't seem to fully account for time difference. There seem to be quite a lot of calculations, so I think this needs to be checked out.”
“I can think of other factors which haven't yet been taken into account which reduce the average lifespan on Earth,” added Major Retono.
“Such as?” asked Professor Wagstaff.
“Several spring to mind,” replied the Major. “Pollution, disease, crime, violence and warfare seem very common on Earth. I'm sure there are other factors too.”
“I take your point, Major, but I'm still not fully satisfied with the theory,” said Professor Schmidt. “I'll check this over and let you all know at our next meeting. Perhaps we may know a bit more about this by then.”
“How is your Earth Monitoring project coming along?” Commander Ondichi asked Professor Schmidt.
“Rather slowly, I'm afraid,” replied the Professor. “There are a very large number of people on Earth, speaking many different languages. Each time I've recorded and saved a new language someone in my team has discovered a new one. On top of that there are as many regional variations, referred to as dialects.”
“How many languages have you traced so far?” Major Retono asked.
“Over one hundred, and still counting,” said Professor Schmidt. “However, there are about six or seven major languages spoken, by about half of the Earth's population. These include our own language, which is referred to as English.”
“Concentrate on the major languages only,” the Commander ordered. “You can forget the dialects for now.”
“Presumably you've identified which lands these languages cover?” Major Retono queried, to which Professor Schmidt acknowledged. “What about the Mapping process - how is that coming along?”
“I haven't yet started that, I'm afraid,” said Professor Schmidt. “I've discussed this with Professor Wagstaff, who has kindly agreed to help.”
“Yes, we're going to assess how best my team can help and how to go about it,” Professor Wagstaff confirmed. “This shouldn't affect my current project too much, though I will keep a check on the ZR4, er sorry, Mars comet.”
“The comet sent to Mars is due to collide with the planet sometime soon, I believe,” queried Commander Ondichi.
“That is correct,” replied Professor Wagstaff. “However, I don't expect there will be much to examine to start with, as either the impact will leave a thick smoggy atmosphere with little visibility, or else the gasses from the impacting comet will wander back into the cosmos, depending on the strength of the Martian gravity.”
Just then, a call came through to the Commander from Major Kong, upon which the four of them agreed to abandon the current discussion, and meet again when the Martian comet had impacted.

As the comet impact on Mars drew nearer, Professor Schmidt’s team had almost completed recording the main Earth languages. The professor himself, meanwhile, was looking into the Theory of Relativity and precisely how the Twin's Paradox is calculated. As this wasn't yet fully understood, it was agreed that everyone on the Interstellar Pilgrim would be made aware only that there was an abnormal difference between life expectancy on Earth and on the Interstellar Pilgrim. This deflated most of the interest in eventually settling on Earth. Instead, the main focus was now on Mars, and the forthcoming event.

Then, one evening, as the sun went behind Earth’s horizon, the light from Mars increased in a flash. The comet had exploded on the Martian surface. One of Professor Wagstaff's team leaders, Sanchez, went into his office.
“Professor, Professor, the comet has smashed into Mars,” he told him.
“Splendid!” Professor Wagstaff replied. “Did you get to see much of the impact?”
“Our telescope was focused directly at the point of impact,” Sanchez informed Professor Wagstaff. “We had been monitoring the comet closely for some time now.”
“At what angle to did the comet approach Mars?” the Professor asked.
“About 45 degrees, more or less,” replied Sanchez. “The remnants of the comet were spread over a wider area than we first anticipated.”
“Splendid!”