Universe: Stars And Galaxies
Universe: Stars And Galaxies
6th Edition
ISBN: 9781319115098
Author: Roger Freedman, Robert Geller, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 26, Problem 42Q
To determine

Whether the string theory an attempt to formulate a theory of quantum gravity, and the dimensions of space and time that might exist if the theory is correct.

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The mass density of our universe is measured to be about 10-29 kg/m3. If an arbitrary point is chosen as the center, how large is the radius of a spherical surface centered at the point so that the mass enclosed in the surface will become a blackhole observed by someone outside the surface? A. 4.2 trillion light years B. 420 billion light years C. 42 billion light years D. 4.2 billion light years   Is the answer D? Thanks!
1. For centuries, we accpeted Newton's 2nd Law as the standard model for motion. Then Einstien came along and siggested a modification in cases of high velocity. The Lorenz factor:                                         γ(v)=(1/square-root of 1−(v^2/c^2)) a) The constant (c) is the speed of light, which is 3 * 10^8 m/s. What is the lim as v approaches 400 γ(v)? You will have to track many decimal places to see a difference from 1. A bullet travels 400 m/s; this limit indicates that time dilation is extremely small (and basically negigible) at that speed.    b) In the movie Interstellar, time dialation occurs as 1 hour on the water planet corresponds to 7 years on earth. What is the factor γ in this case (what is the ratio of 7 years to 1 hour)?   c) If we rearrange the equation for γ and solve for v, we get:                                    v = c square-root of (γ^2 - 1/γ^2) What velocity v is necesary to get the γ you found in part (b)?   d) What is the lim as v approaches c γ(v) ?…
The time before which we don’t know what happened in the universe (10-43 s) is called the Planck time. The theory needed is a quantum theory of gravity and concerns the three fundamental constants h, G, and c. (a) Use dimensional analysis to determine the exponents m, n, l if the Planck time     tP = hmGncl . (b) Calculate the Planck time using the expression you found in (a).
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