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Chapter 38: Problem 49

A billion years from now our Sun will increase its heat, destroying life on Earth. Still later the sun will expand as a red giant, swallowing the Earth and annihilating any remaining life on all planets in the solar system. In anticipation of these catastrophes, an advanced Earth civilization a million years from now develops a transporter mechanism that reduces living beings to data and sends the data by radio to planets orbiting younger stars. The living beings on Earth are destroyed by this process but are reconstituted and restored to life on the distant planets. Your descendent Rasmia Kirmani leaves Earth as data at a time we will take to be zero and is quickly reconstituted after arrival of her data set on the planet Zircon, 100 ly distant from Earth. Assume that Earth and Zircon are relatively at rest. (a) How much does Rasmia age during her outward trip to Zircon? (b) How much older is Earth and its civilization when Rasmia is resurrected on Zircon? (c) Rasmia has a productive and happy life on Zircon and dies as a pioneer hero after 150 years living on that planet. How soon after her departure from Earth can Rasmia's obituary be received on Earth? (d) Over the millennia between our time and then, specialists whom we now call geneticists discover that there is no such thing as a superperson (man or woman), but rather that a minimum variety of genetic types must be maintained and continually recombined (by whatever method is then current) in order to sustain a healthy population. To this end, several dozen healthy individuals are deconstructed on Earth and transported to Zircon, where each individual is quickly reproduced in thousands of copies (using the same data set over and over) in order to populate the planet rapidly. It takes 5 full generations from birth to death, each generation an average of 200 years, to determine whether or not the new population has been successfully established. How soon after transmission of the dozens of original data sets from Earth can Earth's people learn whether or not this project has been successful?

Short Answer

Expert verified
a) 0 yearsb) 100 yearsc) 350 yearsd) 1200 years

Step by step solution

01

Identify given information

The distance from Earth to Zircon is 100 light-years (ly). Rasmia leaves Earth as data at time t = 0.
02

Calculate Rasmia's age during her trip (a)

Since the data transmission travels at the speed of light, it takes 100 years to reach Zircon. This happens instantly from Rasmia's perspective since she is data during the trip and does not age. Therefore, the answer is 0 years.
03

Determine Earth's increased age when Rasmia is resurrected (b)

While the data travels to Zircon in 100 years, Earth itself will have aged by the same amount of time due to being relatively at rest. Thus, Earth is 100 years older when Rasmia is resurrected.
04

Calculate the time for Rasmia's obituary to be received on Earth (c)

Rasmia lives for 150 years on Zircon. Messages sent from Zircon travel back to Earth at the same light speed, taking another 100 years. Earth ages an additional 100 years for her transmission to arrive. Therefore, her obituary is received on Earth 100 (trip) + 150 (life) + 100 (return message time) = 350 years after her departure.
05

Time needed to determine project success (d)

It takes 5 generations to evaluate the new population, with each generation lasting 200 years. Thus, 5 * 200 = 1000 years for evaluation. The original journey to Zircon takes 100 years, and results return after another 100 years: 100 + 1000 + 100 = 1200 years.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

space-time relativity
Space-time relativity, a concept introduced by Einstein, fundamentally changed how we perceive time and space. In our scenario, Rasmia's journey as data from Earth to Zircon happens at the speed of light. During her transit, she doesn't age because, in the realm of light-speed travel, time effectively stops for anything moving at that speed. This phenomenon is directly linked to the concept of 'time dilation,' which is a critical aspect of relativity. It means that while Earth experiences a passage of 100 years due to the transmission, Rasmia experiences no time. This shows the relativity of time - it's not an absolute measure but changes depending on the observer's motion relative to the speed of light.
data transmission
Data transmission plays an essential role in interstellar travel in our scenario. Here, an advanced civilization has created a way to convert a living being into data that can travel as radio waves. This data travels at the speed of light (approximately 299,792 kilometers per second) and can cover enormous distances quickly. In this case, it allows Rasmia to be 'sent' from Earth to Zircon in 100 years. Once the data reaches Zircon, it's reconstituted to restore Rasmia to life. The same process works for sending messages, such as her obituary, back to Earth. Understanding data transmission helps us envision how real-time communication and travel might evolve with further advancements in technology.
genetic diversity
Genetic diversity is crucial for a healthy population. In our setup, specialists ensure that a variety of genetic types are maintained and recombined. This means that when transporting dozens of healthy individuals to Zircon, these individuals serve as genetic templates. They are quickly reproduced into thousands of copies to establish a diverse initial population. Over five generations, each lasting 200 years, this new population is monitored to ensure genetic health. The result? A process taking 1200 years to determine a successful establishment, including transmission time back to Earth. Genetic diversity ensures resilience against diseases and environmental changes, maintaining a robust community.
speed of light
The speed of light, approximately 299,792 kilometers per second, is central in our example. Nothing with mass can travel faster than light, according to Einstein's theories. Here, Rasmia's data travels at this maximum cosmic speed, taking 100 years to reach Zircon. This speed also applies to data sent back, meaning messages, like her obituary after 150 years on Zircon, take another 100 years to travel back. The unidirectional and return travel times combined influence how we perceive and manage interstellar communication and travel, reminding us of the physical constraints set forth by the universe.

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Most popular questions from this chapter

Sara Settlemyer is an intelligent layperson who carefully reads articles about science in the public press. She has the objections to relativity listed below. Respond to each of Sara's objections clearly, decisively, and politely- without criticizing her! (a) "Observer A says that observer B's clock runs slow, while \(\mathrm{B}\) says that A's clock runs slow. This is a logical contradiction. Therefore relativity should be abandoned." (b) "Observer A says that B's meter sticks are contracted along their direction of relative motion. B says that A's meter sticks are contracted. This is a logical contradiction. Therefore relativity should be abandoned." (c) "Anybody with common sense knows that travel at high speed in the direction of a receding light pulse decreases the speed with which the pulse recedes. Hence a flash of light cannot have the same speed for observers in relative motion. With this disproof of the Principle of Relativity, all of relativity collapses." (d) "Relativity is preoccupied with how we observe things, not with what is really happening. Therefore relativity is not a scientific theory, since science deals with reality." (e) "Relativity offers no way to describe an event without coordinates, and no way to speak about coordinates without referring to one or another particular reference frame. However, physical events have an existence independent of all choice of coordinates and reference frames. Therefore the special relativity you talk about in this chapter cannot be the most fundamental theory of events and the relation between events."

Quite apart from effects due to the Earth's rotational and orbital motion, a laboratory reference frame on the Earth is not an inertial frame, as required by a strict interpretation of special relativity. It is not inertial because a particle released from rest at the Earth's surface does not remain at rest; it falls! Often, however, the events in an experiment for which one needs special relativity happen so quickly that we can ignore effects duc to gravitational accclcration. Considcr, for cxamplc, a proton moving horizontally at speed \(v=0.992 c\) through a 10 -m-wide detector in a laboratory test chamber. (a) How long will the transit through that detector take? (b) How far does the proton fall vertically during this time lapse? (c) What do you conclude about the suitability of the laboratory as an inertial frame in this case?

In the 24 th century the fastest available interstellar rocket moves at \(v=0.75 c .\) Mya Allen is sent in this rocket at full (constant) speed to Sirius, the Dog Star, the brightest star in the heavens as seen from Earth, which is a distance \(8.7\) ly as measured in the Earth frame. Assume Sirius is at rest with respect to Earth. Mya stays near Sirius, slowly orbiting around that Dog Star, for 7 years as recorded on her wristwatch while making observations and recording data, then returns to Earth with the same speed \(v=0.75 \mathrm{c}\). According to Earth-linked observers: (a) When does Mya arrive at Sirius? (b) When does Mya leave Sirius? (c) When does Mya arrive back at Earth? According to Mya's wristwatch: (d) When does she arrive at Sirius? (e) When does she leave Sirius? (f) When does she arrive back on Earth?

You are taking a trip from the solar system to our nearest visible neighbor, Alpha Centauri, approximately 4 light-years distant. At launch you experienced a period of acceleration that increased your speed with respect to Earth from zero to nearly half the speed of light. Now your spaceship is coasting in unpowered flight. Compare and contrast the observations you make now with those you made before the rocket took off from the Earth's surface. Be as specific and detailed as possible. Distinguish between observations made inside the cabin with the windows covered and those made looking out of uncovered windows at the front, side, and back of the cabin.

You wish to make \(a\) round trip from Earth in a spaceship, traveling at constant speed in a straight line for 6 months on your watch and then returning at the same constant speed. You wish, further, to find Earth to be 1000 years older on your return. (a) What is the value of your constant speed with respect to Earth? (b) How much do you age during the trip? (c) Does it matter whether or not you travel in a straight line? For example, could you travel in a huge circle that loops back to Earth?
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