For those who have studied more in depth about quantum theory, general relativity, is The Universe in a Nutshell a watered down version? Or does it explain the theories with minimal math equations, as I've heard. I'm halfway through the second chapter, and I'm wondering what people with a better comprehension of the math and theory, think of this book.

Even with people who are just read the book for fun, what do you think of the book? Agree with Hawking, disagree? Are you confused?

Also, in this book (beginning of the second chapter) he explains something called a past light cone. Much of the rest of the chapter relies on knowing what a past light cone is, but I don't understand is there only one of these, representing the entire universe? That was my first though, but then later in the chapter he explains black holes, with light cones, and that was what confused me. When looking further outward in space, does each observer have their own "light cone"?

What other books do you recommend that are similiar to subject of this one?

Originally posted by grazzhoppa
For those who have studied more in depth about quantum theory, general relativity, is The Universe in a Nutshell a watered down version?
Yep, like all of Hawking's writing, it's watered-down pop-sci.
Or does it explain the theories with minimal math equations, as I've heard.
This is a common misconception -- you really can't understand the theory without understanding the math.
I'm halfway through the second chapter, and I'm wondering what people with a better comprehension of the math and theory, think of this book.
It'll make you think -- but it won't really teach you anything.
Much of the rest of the chapter relies on knowing what a past light cone is, but I don't understand
As a preparation for learning about light cones, let's take a simple situation: think about sending a signal to someone far away with a big flashlight -- say you flash it on and off to encode some message. Let's say we define time t=0 to be the time at which you start flipping the switch.

Light propagates at (guess what) the speed of light, c. This means that the information of your flashing, your message, spreads out from you in a big sphere, which grows larger with time. The radius of the sphere is just ct, where c is the speed of light and t is the time since you started flashing your message.

Now imagine your friend, some distance away -- let's just say a light-year away. You'd like for your friend to get your message, and you know that since light travels one light-year every year, you know it'll take your friend a year to get your message.

Now imagine that big sphere, which is now a light-year in radius. There are three kinds of points: points inside the sphere, points outside the sphere, and points on the surface of the sphere.

The points inside the sphere are points with which your flashlight is causally connected. Your flashing has had time to reach those interior points, and so could affect people there. Your message could be the cause for some effect there.

The points outside the sphere are not causally connected to you (yet) because the information of your flashing hasn't gotten there yet. Nothing you've done with your flashlight has anything to do with the people outside the sphere (yet).

Now, to extend this idea to the idea of the light-cone, we have to think in terms of both space and time simultaneously; the flashlight system I described above only concerns space.

We will assign a special name to a particular point in space-time: an event. An event is just a mathematical entity that represents a location and a time together -- for example, an appointment at 100 Elm Street at 4:00 pm is an event. An event is represented by a four-vector, like (x, y, z, t) -- a group of four numbers. The first three are the location in space; the fourth is the time.

Let's think about two pairs of events. The first pair will be your office at 5 pm, and your dinner table at 7 pm. These two events are causally connected; you can drive from your office at 5 pm and be at your dinner table at 7 pm. What happens at the office at 5 pm can affect what happens at the dinner table 7 pm -- you could tell your family a story about what happened at the office. How about another pair? How about the Andromeda Galaxy (2.4 million light-years away) at 5 pm, and your dinner table at 7 pm? These two events are not causally connected. There is no way that any signal can leave the Andromeda galaxy at 5 pm and arrive at your dinner table at 7 pm. The fastest that a signal can travel is c, the speed of light. At that speed, a signal would take 2.4 million years -- quite a bit longer than two hours. Nothing you do at your dinner table at 7 pm can be affected by something that happened in the Andromeda Galaxy at 5 pm.

This is the idea of the light-cone: at any point in space time -- say, your dinner table at 7 pm -- there are two associated regions of space-time. The first region is the past light-cone, which includes all of the events in the past that are causally connected to you. For example, your office at 5 pm is an event that is causally connected in your past, and thus is included in your past light-cone. The Andromeda galaxy at 5 pm is not causally connected to you, and is said to exist outside your past light-cone.

The second region is the future light-cone, which includes all of the events in the future which are causally connected to you in the same fashion. Your dinner table at 7 pm and your bed at 11 pm, for example, are causally connected -- the bed at 11 pm is said to be inside the future light-cone.

Why is it called a light-cone? Well, because its boundaries represent the distances that are travelled in a given time by light. If you're sitting at your dinner table at 7 pm, a signal could get to you from anywhere inside your past light-cone; the edges of the cone are the events from whence a signal would have had to be sent at exactly the speed of light. Points outside the past-light cone would have had to send a signal faster than light to reach you in time for dinner -- and we believe that is not physically possible.
What other books do you recommend that are similiar to subject of this one?
I do not ever recommend pop-science paperbacks to anyone, because I feel they explain too little, while establishing incorrect "notions" which are hard to shake when the subject is learned more thoroughly. Because the prose in such a book is not precise or rigorous, there are many different ways to interpret it -- and this [may] lead to much confusion.

I can highly recommend any of the Feynman books or lectures, however -- such as "Six Easy Pieces" and "Six Not-So-Easy Pieces." They are very easy to read, but use enough basic math to show the precise nature of the theory. Special relativity, for example, is very well handled by Feynman in "Six Not-So-Easy Pieces."

If, however, you're looking for books on wormholes and time warps and what-not (which seem to be Hawking's specialty of late), I can't recommend anything -- I think they're garbage. You'll gain more from reading another kind of book.

- Warren

In which light-cone I can find information on what is wrong and what is right?

Warren,

I am curious - do you agree or disagree with what
this reviewer has to say about Hawking's book?

http://physicsweb.org/article/news/5/11/3

Even with people who are just read the book for fun, what do you think of the book?

I found it a book for idiots. there was more concern about flashy pics and stupid "humor" than anything else
what a waiste of money!

"This is a common misconception -- you really can't understand the theory without understanding the math."

i kinda knew this but seeing it in black and white totally bummed me out

:(

Posted by chroot
This is a common misconception -- you really can't understand the theory without understanding the math.

This must be false. Einstein had to understand his theory before he could formulate the math. As he did it, so can anyone understand the theory before understanding the math.

Originally posted by zanket
This must be false. Einstein had to understand his theory before he could formulate the math. As he did it, so can anyone understand the theory before understanding the math.
That's a good point, and you may be right -- I'm not entirely sure. Most of the math for special relativity (Lorentz transforms, etc., Maxwell's equations, etc.) was already in place before Einstein even got started though. People know something was wrong with either Newtonian mechanics or Maxwell's equations -- they just didn't know which.

Do you have any suggestions on where I could find more about how Einstein discovered relativity?

- Warren

Originally posted by EvilPoet
I am curious - do you agree or disagree with what
this reviewer has to say about Hawking's book?
The reviewer says it's essentially "an accessible" treatment of Hawking's "nushell" model, which "makes absolutely no predictions that are verifiable."

In effect, the reviewer is saying that this book will make you think, but won't teach you squat about physics. So, yes, on the whole I'd say I agree with this reviewer.

- Warren

chroot

I am pleased that this small book ... should now appear in the native language of the country in which I found the necessary concentration for developing the basic idea of the general theory of relativity which I had already conceived in 1908. In the quiet rooms of the Institute of Theoretical Physics of Prague's German University in Vinicna Street, I discovered that the principle of equivalence implies the deflection of light rays near the Sun by an observable amount ... In Prague I also discovered the shift of spectral lines towards the red ... However, the decisive idea of the analogy between the mathematical formulation of the theory and the Gaussian theory of surfaces came to me only in 1912 after my return to Zurich, without being aware at that time of the work of Riemann, Ricci, and Levi-Civita. This was first brought to my attention by my friend Grossmann

'About the Special and General Theory of Relativity in Plain Terms'
Einsten -1923

Originally posted by (Q)
chroot
So essentially the math and theory advanced hand-in-hand -- and he discovered, for example, the deflection of starlight by solving his own equations. Correct?

- Warren

Warren: Thanks for the reply, much appreciated. :)

spookz: I’m mathematically impaired so I know
what you mean - imo it sucks. :(

evil

now lets just say that a greater appreciation of theory can be had if the math is understood as well

Originally posted by EvilPoet
Warren: Thanks for the reply, much appreciated. :)

spookz: I’m mathematically impaired so I know
what you mean - imo it sucks. :(
Pick up a copy of The Feynman Lectures on Physics, and you'll find yourself rapidly becoming more competent!

- Warren

Originally posted by chroot
Do you have any suggestions on where I could find more about how Einstein discovered relativity?

My best book about this is Albert Einstein: A Biography (http://www.amazon.com/exec/obidos/ASIN/0140237194/qid=1041024053/sr=2-1/ref=sr_2_1/102-4659908-8560954). The reviewer says it depicts the “mental odyssey that culminated in Einstein's remarkable discoveries.” It has the story about how Einstein and his friend Michele Besso spent three years trying to find the equations that both fit Einstein’s intuitive vision and explained the then-anomaly in the perihelion of Mercury.

Mine was a fine point. Certainly someone attempting to understand a theory should attempt as well to understand its math, which concisely expresses what the author thought.

my understanding is that einstein did not connect the dots!
the theory remained separate from the math.

?


:D

grazzhoppa – By far the best book I’ve read on relativity for laymen is Relativity Visualized (http://www.amazon.com/exec/obidos/tg/detail/-/093521805X/qid=1041026313/sr=1-1/ref=sr_1_1/102-4659908-8560954?v=glance&s=books). Hardly any math in it. A reviewer says “Even to the mathematically inclined, it may provide an eye-opening intuitive ‘ah-hah!’ that the equations never elicited.”

Warren: Thanks for the suggestion. The Feynman Lectures on
Physics is kinda pricey for my budget atm so I will have to see
if my local library has it. I really think my MI is hopeless but I
will give it shot. Thanks again. :)

Originally posted by spookz
lets just say that a greater appreciation of theory
can be had if the math is understood as well
Ok - a greater appreciation of theory can be had if the
math is understood as well. There I said it/typed it. :D

evil

now i am blushing/embarrased!

:D

Originally posted by zanket
This must be false. Einstein had to understand his theory before he could formulate the math. As he did it, so can anyone understand the theory before understanding the math. Didn't they invent operators specifically to use with Schrodinger equations?

chroot,

Your explanation of light cones is excellent. However, I dispute:

How about the Andromeda Galaxy (2.4 million light-years away) at 5 pm, and your dinner table at 7 pm? These two events are not causally connected. There is no way that any signal can leave the Andromeda galaxy at 5 pm and arrive at your dinner table at 7 pm.

There is a way. Let the Earth become a black hole between 5 pm and dinner. As the Earth collapses I’d notice the clocks on Andromeda speed up. I’d notice the clocks on Andromeda elapse millions of years before I reached the event horizon. Before dinner I’d see what happened at Andromeda at 5 pm.

Points outside the past-light cone would have had to send a signal faster than light to reach you in time for dinner -- and we believe that is not physically possible.

It is physically possible. As the Earth collapses the light from Andromeda moves faster than c on average from my perspective at my dinner table. The light decelerates from (c * the blueshift factor) at Andromeda to c in my frame. Andromeda’s clocks being faster than mine is concomitant with Andromeda’s speed of light being faster than c from my perspective. The speed of light is proportional to the speed of time.

Light faster than c is supported by Einstein, who says here (http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html) “A curvature of rays of light can only take place when the velocity of propagation of light varies with position.” The site says “This interpretation is perfectly valid but a more modern interpretation is that the speed of light is constant in general relativity.” This is true when you further consider that my measured distance to Andromeda decreases as the Earth collapses, as described here (http://www.sciforums.com/showthread.php?s=&threadid=14369), to maintain c.

In principle your past-light cone may include any past event whose light has not yet reached you. Granted my books disagree with me on this, but their explanations are inconsistent with the math.

Originally posted by zanket
chroot,

Your explanation of light cones is excellent. However, I dispute:
...
In principle your past-light cone may include any past event whose light has not yet reached you. Granted my books disagree with me on this, but their explanations are inconsistent with the math.
Tell it to someone who cares. :rolleyes:

- Warren

Nasor - As your question relates to my point, assuming they did, that would be to better impart the understanding. A formula conveys knowledge, which comes first.

chroot - Baby.

Chroot, Thank You!

I appreciate all the replies, thanks.