# Fabric of the Cosmos by Brian Greene - drneutron tutoring LizzieD

## Keskustelu75 Books Challenge for 2012

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### 1drneutron

LizzieD and I thought Fabric of the Cosmos would be a nice follow-on to The Elegant Universe. We'll be doing this similarly to the previous one - questions and discussion on each chapter as we go.

Chapter 1 is an outline of the book, but some interesting questions have come up. From LizzieD:

Yep, the chapter is an outline of the rest of the book to set the global context. Each of the themes touched upon in the book will be expanded in the rest of the chapters.

So this gets to what physicists do for a living. Mostly, we study how things move and interact. To do this, we want to find equations that describe an object's place in space as different times (technically we say "as a function of time"). If the equation accurately describes reality, we can predict what the object will do in the future. As an example, we can write down the equations that describe how a billiard ball travels on a table when hit by a pool cue. Now, it turns out that the equation (or the game of pool) works the same today as it did yesterday. This is called symmetry in time. Another symmetry in the equations is the direction time moves. In real life, this means that we can take a movie of a billiard ball moving, and if we show that movie backward to someone, they can't tell whether it's showing backward or forward. This means we can "play the equations backward" and the math still works just fine.

Now the interesting thing is we can tell in real life which way is the correct flow of time. For instance if you show someone that movie of a billiard ball traveling, including the cue hitting the ball, people can tell immediately which way time is moving. So there's a disconnect between the math (which works quite well!) and what we can perceive. This is, in a nutshell, the "arrow of time" problem.

Well, as we'll find out, the texture of space is quite important when we consider what happens in quantum theory with energy in what's supposed to be a vacuum. I don't want to spoil it, though. We'll get there!

Shape matter too, though. It's the shape of space that is what we think of as gravity. Again, we'll get to it!

So here we run into a definition. Statistically, if something can't happen, we define the probability that it will happen as zero. If it's certain to happen, we define the probability as 1, or 100%. Anything bigger than 100% means the probability hasn't been properly normalized. As an example of an intermediate probability value, consider a coin toss with a fair coin. The probability that you'll get heads as a result of the toss is 0.5 or 50%. This means if you flip a bunch of times, you should expect to get heads 50% of the time. If you have a two-headed coin, you should expect to get heads every time, or 100% of the time.

Now, when we smash together quantum particles like electrons, we see that they can interact in a bunch of ways. The different reactions that can occur are described by probabilities, and we want to use physics theories (like string theory) to predict the probabilities for these different reactions. If the theory matches our experiments, we think that that theory has some basis in reality. If it doesn't, we throw it away and try something else! In some theories, the probabilities we get from the math are infinite. This is a clear message that something is wrong with the theory!

So the idea in superstring theory is that fundamental particles aren't zero-dimensional dots. Instead, they are little tiny strings that vibrate. Each string can vibrate in only one mode at a time, and each mode represents what we call a particular kind of particle. The vibration is subject to change, but only when two or more strings interact (ie, collide).

The equations used to calculate how these strings move and interact only work in a particular number of dimensions. The number of dimensions depends on the particular theory. In what's called superstring theory, there must be 9 space and 1 time dimension for the theory to work. For the old style string theory, it's 26 space dimensions. For M-theory, a more general theory that includes superstring theory, reality must have 10 space and 1 time dimension for the theory to be right. Now, the kicker is that we have no evidence that these extra dimensions really exist. So again, there's a problem! We'll get into this more as we go.

Chapter 1 is an outline of the book, but some interesting questions have come up. From LizzieD:

*Here I am having read the first chapter. I'm thinking that it's an overview of the whole book and that I'm not supposed to understand everything that I read. That would be a good thing. Here are the things that bother me.....*Yep, the chapter is an outline of the rest of the book to set the global context. Each of the themes touched upon in the book will be expanded in the rest of the chapters.

*p.13 "The laws of physics show no such asymmetry..." ? What would one example of a law be that would violate my living experience by treating time backward like time forward?*So this gets to what physicists do for a living. Mostly, we study how things move and interact. To do this, we want to find equations that describe an object's place in space as different times (technically we say "as a function of time"). If the equation accurately describes reality, we can predict what the object will do in the future. As an example, we can write down the equations that describe how a billiard ball travels on a table when hit by a pool cue. Now, it turns out that the equation (or the game of pool) works the same today as it did yesterday. This is called symmetry in time. Another symmetry in the equations is the direction time moves. In real life, this means that we can take a movie of a billiard ball moving, and if we show that movie backward to someone, they can't tell whether it's showing backward or forward. This means we can "play the equations backward" and the math still works just fine.

Now the interesting thing is we can tell in real life which way is the correct flow of time. For instance if you show someone that movie of a billiard ball traveling, including the cue hitting the ball, people can tell immediately which way time is moving. So there's a disconnect between the math (which works quite well!) and what we can perceive. This is, in a nutshell, the "arrow of time" problem.

*p.14 The questions that arise - as "why space has the overall shape" that it has - remind me that in HS physics I always asked the wrong/non-applicable questions. I would be wondering about the texture of space, for example.......................*Well, as we'll find out, the texture of space is quite important when we consider what happens in quantum theory with energy in what's supposed to be a vacuum. I don't want to spoil it, though. We'll get there!

Shape matter too, though. It's the shape of space that is what we think of as gravity. Again, we'll get to it!

*p.16 Speak to me about infinite probability. What if infinite probability is the way reality operates?*So here we run into a definition. Statistically, if something can't happen, we define the probability that it will happen as zero. If it's certain to happen, we define the probability as 1, or 100%. Anything bigger than 100% means the probability hasn't been properly normalized. As an example of an intermediate probability value, consider a coin toss with a fair coin. The probability that you'll get heads as a result of the toss is 0.5 or 50%. This means if you flip a bunch of times, you should expect to get heads 50% of the time. If you have a two-headed coin, you should expect to get heads every time, or 100% of the time.

Now, when we smash together quantum particles like electrons, we see that they can interact in a bunch of ways. The different reactions that can occur are described by probabilities, and we want to use physics theories (like string theory) to predict the probabilities for these different reactions. If the theory matches our experiments, we think that that theory has some basis in reality. If it doesn't, we throw it away and try something else! In some theories, the probabilities we get from the math are infinite. This is a clear message that something is wrong with the theory!

*p.18 Superstring Theory.... Does each discrete filament vibrate in only one way or is the vibration subject to change? And why does it demand 9 or 10 dimensions? And what are they?*So the idea in superstring theory is that fundamental particles aren't zero-dimensional dots. Instead, they are little tiny strings that vibrate. Each string can vibrate in only one mode at a time, and each mode represents what we call a particular kind of particle. The vibration is subject to change, but only when two or more strings interact (ie, collide).

The equations used to calculate how these strings move and interact only work in a particular number of dimensions. The number of dimensions depends on the particular theory. In what's called superstring theory, there must be 9 space and 1 time dimension for the theory to work. For the old style string theory, it's 26 space dimensions. For M-theory, a more general theory that includes superstring theory, reality must have 10 space and 1 time dimension for the theory to be right. Now, the kicker is that we have no evidence that these extra dimensions really exist. So again, there's a problem! We'll get into this more as we go.

### 2LizzieD

Jim, I'm flabbergasted! I actually understand all of this, or at least I think I do. Thank you! Thank you!! Tomorrow - chapter 2!!!!

### 3LizzieD

Back at last, and my head is spinning - a lot like the bucket!!

Chapter 2

I really do think I understand the concepts of accelerated motion and constant velocity and Newton's theory. That's amazing in itself. Here's some of what I don't get.

Figure 2.1 - What are those gray arcs over the middle two pictures of the bucket? (I realize that not getting that may invalidate my whole understanding of the theory!)

p. 27 -

(Now I'm on p. 34.) "in an otherwise empty universe there is

p. 37 I'm not getting

Chapter 2

I really do think I understand the concepts of accelerated motion and constant velocity and Newton's theory. That's amazing in itself. Here's some of what I don't get.

Figure 2.1 - What are those gray arcs over the middle two pictures of the bucket? (I realize that not getting that may invalidate my whole understanding of the theory!)

p. 27 -

*Absolute Space*- My mind jumped immediately to the shape of the universe......It is shaped by its container, which is something other than absolute space???? Never mind. I'll wait until we get there. I will say that I have less a problem with AS being a physical entity than I do with the interpretation of Mach that space is language for the relationships that exist between objects.(Now I'm on p. 34.) "in an otherwise empty universe there is

*no distinction*between spinning and not spinning" I don't get it. I understand not being able to see anything to suggest motion, but when I close my eyes and spin, I still get dizzy. I'm assuming that even in the empty universe I'd still have sensations. Mach says not, and I don't understand. Are we talking the nullity of vacuum? I don't think so.p. 37 I'm not getting

*"You feel acceleration only when you accelerate relative to the average distribution of other material inhabiting the cosmos." That sort of makes sense except that it builds on the idea in the question before.....*### 4LizzieD

Jim, I'm reading in chapter 3, but if I can formulate a question, I'll save it for the end. I have to say that I'm feeling a lot the way I feel when I read a post-modern novel: I know I'm missing a lot, but I'm picking up what I can, going with the flow, and trusting the author to give me something I can take away in the end.

### 5drneutron

I snuck chapter 2 in a lunchtime, but didn't have a free minute until now to get back to you. Hope this helps!

Great! Things will get a little weird when we talk about relativity, but the concepts of acceleration and constant velocity will still be the same.

He's just trying to show the speed of the bucket rotation. In the second one, the bucket is rotating slowly, in the third it's rotating faster.

Well, when we get to general relatively, we'll find out that the universe, and space itself, is shaped by the mass that's in it. :)

This idea was his picture about how things work. It turns out that his ideas weren't quite right, but did lead Einstein to general relativity. Your objection is one of the main ones that physicists raised to argue against Mach's ideas. So you're in good company! :)

What we're discussing is called a "frame of reference". When we describe motion, no matter what kind, we have to specify a point from which that motion is observed. In equations of motion, this means we have to pick a zero point. Newton's theory is written such that the frame of reference is his concept of absolute space. Mach's ideas were that you can only pick a frame of reference if other matter exists in the universe. That's what Greene is trying to express in a nontechnical way.

So far it seems like you're getting the gist of Greene's discussion!

*I really do think I understand the concepts of accelerated motion and constant velocity and Newton's theory. That's amazing in itself. Here's some of what I don't get.*Great! Things will get a little weird when we talk about relativity, but the concepts of acceleration and constant velocity will still be the same.

*Figure 2.1 - What are those gray arcs over the middle two pictures of the bucket? (I realize that not getting that may invalidate my whole understanding of the theory!)*He's just trying to show the speed of the bucket rotation. In the second one, the bucket is rotating slowly, in the third it's rotating faster.

*p. 27 - Absolute Space - My mind jumped immediately to the shape of the universe......It is shaped by its container, which is something other than absolute space???? Never mind. I'll wait until we get there. I will say that I have less a problem with AS being a physical entity than I do with the interpretation of Mach that space is language for the relationships that exist between objects.*Well, when we get to general relatively, we'll find out that the universe, and space itself, is shaped by the mass that's in it. :)

*(Now I'm on p. 34.) "in an otherwise empty universe there is no distinction between spinning and not spinning" I don't get it. I understand not being able to see anything to suggest motion, but when I close my eyes and spin, I still get dizzy. I'm assuming that even in the empty universe I'd still have sensations. Mach says not, and I don't understand. Are we talking the nullity of vacuum? I don't think so.*This idea was his picture about how things work. It turns out that his ideas weren't quite right, but did lead Einstein to general relativity. Your objection is one of the main ones that physicists raised to argue against Mach's ideas. So you're in good company! :)

*p. 37 I'm not getting "You feel acceleration only when you accelerate relative to the average distribution of other material inhabiting the cosmos." That sort of makes sense except that it builds on the idea in the question before.....*What we're discussing is called a "frame of reference". When we describe motion, no matter what kind, we have to specify a point from which that motion is observed. In equations of motion, this means we have to pick a zero point. Newton's theory is written such that the frame of reference is his concept of absolute space. Mach's ideas were that you can only pick a frame of reference if other matter exists in the universe. That's what Greene is trying to express in a nontechnical way.

So far it seems like you're getting the gist of Greene's discussion!

### 6LizzieD

"Mach's ideas were that you can only pick a frame of reference if other matter exists in the universe. That's what Greene is trying to express in a nontechnical way." Thanks, Jim! That is so clear --- I'm going to save chapter 3 until tomorrow.

"The universe and space itself is shaped by the mass that's in it...." Hot DOG!

"The universe and space itself is shaped by the mass that's in it...." Hot DOG!

### 7LizzieD

I'm still struggling with chapter 3, but I hope you realize that you and B. Greene are now my #1 defense against the onset of dementia. Very good of you!!!

So..... I am pretty much O.K. with the arguments about special relativity. I can't tell you how often I've heard this discussed and simply not dealt with it. However -----

pp. 55-56 - The illustration of Itchy and Scratchy on the moving train have thrown me for a loop. If I and S and the flash of light are all moving at the same speed, why is the effect not the same as it would be if they were standing still? I know that the objection is from the pov of the observer on the platform, but why isn't the difference simply in what he observes as opposed to being as valid as that of the man on the train? Or is validity of observation what it's about at all? So he sliced spacetime differently from the other guy?

Then I read on anyway about absolute spacetime, and the anxiety sort of eased off. I'm going to move on to gravity and see what happens there. And, by the way, I always, always read end notes, and these with the mathematical formulas are driving me nuts. Since I'm by no means a mathematician, will I lose a lot if I just skim and move on?

So..... I am pretty much O.K. with the arguments about special relativity. I can't tell you how often I've heard this discussed and simply not dealt with it. However -----

pp. 55-56 - The illustration of Itchy and Scratchy on the moving train have thrown me for a loop. If I and S and the flash of light are all moving at the same speed, why is the effect not the same as it would be if they were standing still? I know that the objection is from the pov of the observer on the platform, but why isn't the difference simply in what he observes as opposed to being as valid as that of the man on the train? Or is validity of observation what it's about at all? So he sliced spacetime differently from the other guy?

Then I read on anyway about absolute spacetime, and the anxiety sort of eased off. I'm going to move on to gravity and see what happens there. And, by the way, I always, always read end notes, and these with the mathematical formulas are driving me nuts. Since I'm by no means a mathematician, will I lose a lot if I just skim and move on?

### 8drneutron

First, you won't lose much if you skip the notes, or at least the math. If you decide you're interested in the math, we can try to work through it.

As to the train example, the whole point is that the observation is strongly dependent on point of view. And the thing that makes this true is that light has the same speed no matter what frame you're in. That's what makes things seem different for the two observers. And yep, it's different slicing.

As to the train example, the whole point is that the observation is strongly dependent on point of view. And the thing that makes this true is that light has the same speed no matter what frame you're in. That's what makes things seem different for the two observers. And yep, it's different slicing.

### 9LizzieD

Whew. I misread (and remisread and remisread) then. I'll jump in again tomorrow with thanks. I'll definitely give the math a miss.

### 10LizzieD

Here I am back again with chapter 3 read and reread and maybe misread and misread again. I can't say that I understand any of this in the same way that I understand the use of the subjunctive in Latin, for instance, but I do have occasional flashes of clarity. This is progress!!!

So --- if I said what I got from chapter 3, which is tightly and consecutively argued, it would have to be that acceleration is the exact equivalent of gravity, and that the only valid vantage point for time and motion is something in freefall, not fighting the pull of gravity..... Gravity warps time more drastically than it warps space........ So, just to try to apply this ---- for an astronaut accelerating out of earth's gravity, time slows down because he is accelerating, but the higher he rises above the earth, the more time speeds up so that the two cancel each other, and for that part of his flight, his time is what it would be standing still on the earth surface? Or not?

I don't know where else to go with this, so I'm tackling chapter 4 - and by the way, I read your conversation with Mary about chapter 3 of *Elegant Universe* and wonder what the tornado illustration was.

Thanks Jim!!!

So --- if I said what I got from chapter 3, which is tightly and consecutively argued, it would have to be that acceleration is the exact equivalent of gravity, and that the only valid vantage point for time and motion is something in freefall, not fighting the pull of gravity..... Gravity warps time more drastically than it warps space........ So, just to try to apply this ---- for an astronaut accelerating out of earth's gravity, time slows down because he is accelerating, but the higher he rises above the earth, the more time speeds up so that the two cancel each other, and for that part of his flight, his time is what it would be standing still on the earth surface? Or not?

I don't know where else to go with this, so I'm tackling chapter 4 - and by the way, I read your conversation with Mary about chapter 3 of *Elegant Universe* and wonder what the tornado illustration was.

Thanks Jim!!!

### 11drneutron

Accelerated motion and gravity are indeed equivalent. So you got that pretty well! Something in free fall is traveling along what's called a geodesic - the shortest distance between two points. In flat space, this is a straight line, but in curved space, geodesics have different shapes. Geodesics form that vantage point you're reading about.

Time dilation, the technical term for time slowing down, depends on relative velocity. So, the faster you go relative to some observer at rest, the bigger the discrepancy in the passing of time between the two people. So suppose an astronaut takes a trip to Alpha Centauri while his twin stays on Earth. To get out of the Earth's gravity, he accelerates, gaining velocity relative to his twin. So the twin sees time passing more slowly for the astronaut than for himself. So the faster he goes, the younger the astronaut is relative to his twin! This is called the Twin Paradox, though it's not a true paradox. The math is all worked out, and the equations are at a high school algebra level. If you like, I can probably come up with a write-up for you.

Time dilation, the technical term for time slowing down, depends on relative velocity. So, the faster you go relative to some observer at rest, the bigger the discrepancy in the passing of time between the two people. So suppose an astronaut takes a trip to Alpha Centauri while his twin stays on Earth. To get out of the Earth's gravity, he accelerates, gaining velocity relative to his twin. So the twin sees time passing more slowly for the astronaut than for himself. So the faster he goes, the younger the astronaut is relative to his twin! This is called the Twin Paradox, though it's not a true paradox. The math is all worked out, and the equations are at a high school algebra level. If you like, I can probably come up with a write-up for you.

### 12LizzieD

Jim, I would like that if it's not a great deal of trouble. It might give me a better feel for the whole math thing anyway.

### 13drneutron

This is an introduction that claims to be at a 6th grade level, so the math is done in a relatively clear way. http://conduit9sr.tripod.com/

Wikipedia has a pretty good page, but written more tersely.

http://en.wikipedia.org/wiki/Introduction_to_special_relativity

Wikipedia has a pretty good page, but written more tersely.

http://en.wikipedia.org/wiki/Introduction_to_special_relativity