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The Mathematics of Relativity for the Rest of Us |  | Author: Dr. Louis Jagerman M.D.
Publisher: Trafford Publishing
List Price: $33.50
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Seller: sllauhk
Rating:  14 reviews
Sales Rank: 189370
Media: Paperback
Pages: 454
Number Of Items: 1
Shipping Weight (lbs): 0.4
Dimensions (in): 10.7 x 8 x 1
ISBN: 155212567X
Dewey Decimal Number: 530
EAN: 9781552125670
ASIN: 155212567X
Publication Date: February 23, 2001
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Product Description
The Mathematics of Relativity for the Rest of Us provides a detailed explanation of relativity, particularly its mathematics, designed for the non-professional audience. The subject is developed from basic principles and observations in physics and mathematics, starting with algebra and geometry as taught in thorough high school courses. On the premise that this background suffices to build an appreciation and understanding of the subject, the crucial concepts are spelled out, and the key derivations are disclosed step-by-step. The relativity of time, space, and mass is covered first, giving some attention to the history of the two main divisions of relativity, the special and the general. Once special relativity and its mathematics are established, general relativity is covered, beginning with its relationship to Newton's laws and advancing through its revolutionary concepts as well as its mathematics. This process is carried all the way to the level of tensor equations. The Mathematics of Relativity for the Rest of Us treats topics such as: The constant speed of light, the invariant laws of physics, the basis and meaning of the equation E = mc2, the nature of curved four-dimensional space-time, the importance of non-Euclidean geometry, the gravitational bending of light, experimental confirmation of relativity, the philosophical and intellectual appeal of relativity, the nature of black holes, and the cosmologic significance of relativity -- both as concepts and as mathematical issues. As a result the sufficiently attentive reader is set at ease with the reputedly incomprehensible but essential details about relativity. Even subjects such as "tensor calculus" and the "covariant partially differential field equations of general relativity" will be clear. For instance such a reader will know just what a "tensor" is, why the equations are "covariant," why they are "partially differential," why they are "field" equations, why relativity can be "general," and most importantly just what is meant by "relativity." Furthermore, if a reader is shown the fundamental equation of general relativity, Rik - 1/2gikR = -XTik he or she will understand what every term of this equation means, why each is included, what obstacles Einstein and his colleagues overcame to derive each term, what impact this equation has on modern science, and why this equation revolutionized our understanding of our universe. The Mathematics of Relativity for the Rest of Us also devotes a chapter to the relationship between relativity and quantum mechanics. It reveals the limitations of relativity and the direction of future work in this branch of science. The chapter concludes with the role of string theory in reconciling relativity and quantum mechanics.
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Showing reviews 1-5 of 14
 Page 5 (a long explanation...) July 27, 2009
F. Munoz (Miami, Florida United States)
After reading the previously mentioned page 5 which you can preview also. It seems to me that the author couldn't explain the real phenomenon or that I didn't understand a word (possible but that also says something about the book.
It is interesting to see that the conclusions at the end of the page are right but the previous digression is totally wrong!
The problem: 2 astronauts move at constant speed (inertial frame fr) with respect a third one-not mentioned in the text but referred as the empty space (ether revisited?)- keeping a constant distance (according to the moving astronauts only!). The fact is that all 3 see the same speed of light and equal to c, no matter how each one moves with respect to the others.
In the text is suggested that if the two astronauts change theirs speed referred to the third one, their clocks (the moving ones) would get out of synchrony one from the other. That assertion is wrong!! that would suppose that one could detect an absolute speed just looking at your clock and seeing the time difference between two observers in the same inertial frame which according to the relativity theory is impossible. First of all there is no such a thing as an absolute speed, speed is always referred to an observer. Second when they instantaneously change their speed, the distance between them -according to the observer- is reduced (Lorentz transform). Third the time is delayed -again according to the observer that didn't change his speed- by Lorentz transform. So finally all converge to show that they still are in synchrony.
The best way to see it is with a minkowski diagram (see wikipedia for more information ).
The crucial point here is that for the astronauts in movement the distance between them has not changed, neither has the speed of light. So the time the light takes to travel between both astronauts doesn't change either (according to them). Hence there is no such a delay for the astronauts in their inertial frame.
what about the astronaut not moving (according to his own frame of reference)?
Well, in that case is necessary to do some math.
For those of you who want a math explanation, here it is:
Let's see that the distance and time were contracted to certain values x and t for the 2 moving astronauts (referred to the frame of the lonely astronaut-"not moving"). So if according to the text, time were not synchronised for the moving astronauts, then there would be a difference in the speed of light measure among the 2 inertial frames.( Remember they had a delay according to the text)
To prove that there is no delay in the arriving of the light of the second astronaut It suffices to show that the new time between the 2 astronauts is equal to the new distance divided by c, because that is the way to synchronize clocks. So (new time) = (new distance)/c or what is the same (new distance)/(new time) = c.
Lorentz transform between the 2 astronauts in the moving frame referred to the lonely astronaut.:
Let's @= 1/sqrt(1 - v^2/c^2) then
x' = @*(x +v*t)
t' = @*(t +v*x/c^2)
One should do {x(1)' - x(0)'}/{t(1)'-t(0)'} and prove that is equal to c
But the x(0)'=0 and t(0)'=0 (the origin in both frame coincide) so the problem is reduced to x(1)'/t(1)' or simply:
x'/t'= (x + v*t)/(t+v*x/c^2) but x/t = c (by hypothesis the light speed is equal to c and must be the quotient between distance x on time t)
then x'/t' = t*(x/t+ v)/(t*(1+v/c^2*x/t)) simplifying
x'/t' =t/t*(c+v)/(1+v/c) = 1*(c+v)/[(c+v)/c] then
x'/t' = c
(!)
I give 2 stars as a warning, after the reading I have serious doubts about the book..
I rather would consider a book written by a physic not a Dr. in M.D.
Please correct me if I'm wrong.
Very readable and detailed (yes page 5 is correct) June 20, 2009
rickzz (New Jersey)
1 out of 1 found this review helpful
This 450 page book covers Special Relativity in ~50 pages and the remainder of the book is devoted to General Relativity. Some of the chapters have very little math and their point is to give a verbal description of the key points of SR and GR. However, the bulk of the book is devoted to developing the math of General Relativity in all of its gory details.
It's been said that Special Relativity can be understood, using only High School Math, but that's certainly not true for GR. So this book will be highly useful for those who are trying to tackle the "heights" of GR because there isn't any other book (i.e. non-textbook) that attempts to do that for the general reader. For those, looking only to understand SR, another book like Mermin's "It's About Time" is probably much better.
There's a number of reviews that discuss page 5 and whether or not it's a big blunder on the part of the author. To be honest- I'm not sure myself esp. after the previous review. I think there's some confusion over whether the author is incorrectly saying time dilation can occur in the case of two spaceships which are NOT "moving" wrt each other. (My take is that the author is talking about simultaneity and NOT time dilation.)
He covers time dilation explicity on page 17, and does it correctly I believe. Either way, the book is really devoted to GR, so for those readers interested in that topic, it may not matter much.
The book truly does cover all the math of GR, but I'm not qualified to say if his coverage is correct. However, it's definitely much more user-friendly than a real physics textbook, and the author writes very well.
Update: Page 5 is correct after all. The other 2 reviewers below are confused- check out the relativity book by Lillian Lieber (one of Jagerman's references), which was favorably reviewed by Einstein. It has the same thought experiment with more detail. I'd change my review to 5 stars, but amazon won't let me.
 Mr One Star is wrong! June 19, 2009
matthew Byrd
3 out of 3 found this review helpful
The thought experiment is not wrong,the whole point being made was that the ships A & B although at rest "relative" to each other were not at rest "relative" to the vacuum and hence the invariance in the "propagation" velocity of em radiation caused "relative" errors in time of reception. Remember they were in rectilinear motion, say they were moving at .5c relative to the vacuum, then you cant have the forward moving pulse moving at 1.5c through the vacuum and the responding pulse moving backwards at .5c just to keep the timing right! thats the whole point of this. The speed of light is "invariant" to the inertial frame. please reread and retract. oh yeah by the way the book is GREAT buy it! Regards.
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Guidelines
Informative and intersting March 19, 2009
Dr. Darius Bahiraey
0 out of 1 found this review helpful
Although initially it did not appear to follow an easy step by step guide but as you progress through the pages this becomes more and more apparent. This is perhaps because the nature of the topic is as such that makes it difficult to know where to start with. The book deals with problems in a fascinating and informative way and makes it fun for the reader. It is a type of book that you do not want to put down. This is a wonderful book providing the reader has a secondary school mathematical background. I strongly recommend this book to be taught to the undergraduate students of relativity and cosmology. This is to make them have a better feel for the subject area and appreciate the subject more and recognise the beauty of the topic and not think of it merely a set of lifeless equations.
Fantastic accessibility and explanatory power March 18, 2009
J. Jenkins (Toronto, Canada)
1 out of 1 found this review helpful
I thought I would never find a book that would explain tensors well and Einstein's general relativity in its mathematical description but this book amazingly is able to do it. Previous more mathematical books take a bit too much higher level math for granted. The author, as he himself states, begins with high school math and explains every other piece of calculus, geometry, etc., that he introduces. I am really amazed at how well he is able to explain everything, starting with the metric of space-time, tensors relating to curvatures, moving on to the energy-momentum tensors, then on the solutions of Einstein's equations.
This author really has a skill at explaining complicated math well, obviously predicated on the fact that he understands general relativity and the equation through and through. The fact he spent so much time on this large book and effort to make it clear and concise, astounds me and I am really grateful that he produced it. I can imagine how much time, as a medical doctor, he had to devote to this extracurricular labour of love.
In short, this is such a well written and clear book, anyone who has even high school math can wind up understanding not just the principles of general relativity, which are themselves quite simple, but the equations that are used for solving problems of gravity, I guarantee it.
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