Maggie: In our last conversation we talked about Stephen Hawking’s career and personal life. Can you tell me about his science now?

John: Yes. But why don’t we begin with a few background ideas that we will need to know in order to understand his theories?

Maggie: Okay. Where shall we begin?

**Changes in Scientific Theories**

John: The first thing we need to understand is that science and scientific ideas change, a lot!

Maggie: I thought scientific ideas, like math, never changed. Once the ideas are proven, they are proven for eternity.

John: That is what most people think because that is what we are taught in high school. But it is not true.

Maggie: Weird. So how do scientific ideas change?

John: Good question. Generally speaking, there are two types of changes that happen in science.

The first type of change occurs because scientific ideas are cumulative. They build on one another. Think about it like this. A scientist comes up with an idea, such as gravity. Another scientist then takes that idea and refines it, making it more succinct. A third scientist comes along and builds on the previously refined idea, applying the idea in a new manner. And then a fourth scientist builds on that, and so on.

Maggie: I get it. Ideas build on each other. I think Hawking had that same idea also, when he said that he stood on the shoulders of giants.

John: Right. I am so glad you remember that.

Maggie: Well, you’ve quoted Hawking so much it’s hard to forget. What is the second type of change?

John: The second type is called a paradigm shift. It occurs when a scientific theory takes a large and radical shift so that a previous model or way of thinking about a subject changes or is proven wrong.

Maggie: I am going to need an example, I think.

John: And I think I have a good example. It is even in astronomy, part of our general topic.

Ptolemy was an astronomer born in A.D. 100. He came up with a model of the solar system that put the earth at its center, with all the planets circling around the earth. This is called a geocentric universe. He worked out the math so that the model was geometrically correct, calculating the future positions of the planets. The model was internally consistent and was used by scientists for close to 1,500 years. In other words, it was believed to be the true and correct model for all those years.

Then in 1543, the same year that he died (which is weirdly interesting to me), Nicolaus Copernicus published his book *On the Revolutions of the Celestial Spheres*. This book shook the scientific world in Europe, causing what is now known as the Copernican Revolution in astronomy. In this book, Copernicus proved that the solar system is in fact heliocentric, not geocentric. Heliocentric means that the sun is at the center, not the earth, and the planets rotate around the sun. This is what we believe to be correct today.

The Copernican Revolution is an example of a paradigm shift. Astronomy took a radical shift when the Ptolemaic system, which had been relied on by European scientists for 1,500 years, was proven to be incorrect, and western scientists began to rely upon Copernicus’ model.

Does this make sense to you?

Maggie: It makes perfect sense. So let me see if I can summarize our discussion so far. There are two ways in which science changes. The first is when an idea is refined or applied in a new way. This happens often because science is cumulative. The second is when science takes a radical shift because a scientific idea is proven wrong or is superseded by a new idea, and this is called a paradigm shift. Is that right?

John: I am always impressed with how well you can summarize our discussions. That is a real talent.

Maggie: As always, embarrassing! So what is next?

John: In order to understand Hawking’s theories, we also need to understand a little bit about Isaac Newton and Albert Einsten. Let’s start with Newton.

Maggie: We are not going to do a bunch of math are we? I don’t really want to do that.

John: No, I think we can have this discussion without delving into mathematical formulas. But that would be pretty cool, wouldn’t it?

Maggie: It would be, but I don’t think I have the skills to do it right now. Or the patience. But do you think we can fully understand Newton and Einstein without the math?

John: We don’t need to fully understand Newton and Einstein, and we don’t need to be precise. We just need enough information and insights for our specific purpose: to understand Hawking. Does that make sense?

Maggie: I think so. We don’t need to fully and precisely understand a subject to put the information that we do know to good use.

John: I like that. Now on to Newton.

**Isaac Newton**

Maggie: Oh, yeahhhh! Let’s go!

John: Sarcasm?

Maggie: A little bit. But you have to admit, it’s kind of funny.

John: Not really.

Maggie: Sorry. Let’s move on.

John: The first thing we need to understand here is that gravity is the most important subject to a cosmologist.

Maggie: How come? I would think space would be more important.

John: Gravity is the thing that keeps the sun and the planets in orbit around each other. Think of it like this: without gravity, the planets and sun would shoot off into space by themselves. Gravity keeps the entire solar system together, forming it into one workable structure.

Maggie: What do you mean by a workable structure?

John: Our solar system is held together by gravity. It is the glue, so to speak, that keeps the sun at the center and the planets all in orbit around the sun. It keeps the moon orbiting around the earth, which helps with the tides. It keeps Mars from crashing into the Earth or another planet. And it keeps Pluto circling out there in the cold and dark. In other words, because of gravity our solar system works, and works well.

Maggie: Pluto is not a planet, you know. Neil deGrasse Tyson killed it.

John: Well, him and the astronomer Mike Brown. I am not happy with either of them.

Maggie: We should write a letter to Neil deGrasse Tyson complaining. That would be funny to me. And I am sure he would think it was hilarious.

John: Agreed. Let’s do it. But we got way off topic again.

Maggie: Okay, back to work. Are you saying that without gravity there is no solar system?

John: Exactly right! The planets would fly off by themselves or crash into one another.

Maggie: So life wouldn’t exist on earth without gravity?

John: What an astute observation. Without gravity the solar system wouldn’t exist, and therefore life wouldn’t exist.

Maggie: So cool.

John: I know! And Newton figured out what gravity is.

Maggie: Okay here we go.

John: More sarcasm?

Maggie: Again, just a little. But to make up for it I will help you out and ask the lead-in question. “Say, my friend, what is gravity according to Newton?”

John: I am so glad you asked. Gravity is a force, but not a force that pushes things away. It is a force of attraction, causing objects to be pulled towards one another. It’s like the force of a magnet, drawing things together.

And this is interesting: the bigger the object, the bigger the attraction. Well, that is just generally speaking. The rule actually says that the more mass a planet has the stronger its gravitational pull is on other planets. This is what Newton figured out.

Maggie: That doesn’t seem so hard.

John: It’s not. Newton then went on to determine the amount of gravitational force there is between two objects in space, suggesting that it is related to the distance between the two objects. His theory says that the further two objects are apart, the weaker the gravitational pull between them. The closer they are, the greater the gravitational pull.

Maggie: Okay, that still makes sense to me.

John: See, this isn’t so hard. And it’s really fun.

Newton then came up with a mathematical formula called the Law of Universal Gravitation. We do not need to understand the formula for our purposes, but I am going to include it here just because it is one of the two greatest mathematical formulas ever conceived. The formula is

F (gravitational force) = G (gravitational constant) __M _{1} M_{2}__(masses of two objects)

R

^{2}(distance between masses)

^{ }

This formula is pretty cool because it is still used today by scientists like those at NASA for calculating the gravitational force on space ships in flight. It only stops working well when calculating gravity close to a very large object. For example, it doesn’t work perfectly for calculating the orbit of Mercury, since Mercury is so close to the sun. But for most other things, it is spot on.

Maggie: I have two questions. First, if this is one of two great formulas, what is the other one?

John: Einstein’s formula “E = mc^{2}.”

Maggie: That makes sense. My second question is about Mercury. If Newton’s formula doesn’t work well, then what do scientists use?

John: Really good question. They apply Einstein’s theory, which we will discuss shortly.

The thing to remember about Newton’s theory is that gravity is a force that pulls objects together. So the planets rotate around the sun, and the moon rotates around the earth, due to the pull of gravity.

Does this make sense to you?

Maggie: Yes, I think I understand. Are we on to Einstein now?

**Albert Einstein**

John: Yes, on to Einstein.

Stephen Hawking was known as a relativistic cosmologist. That is a big phrase, but it is really quite easy to understand. He is known as a cosmologist because he studied the universe as a whole, which is what cosmologists do. He is relativistic because he applied the theory of relativity to the universe. And we all know who came up with the theory of relativity.

Maggie: Yes, we do. Einstein.

John: Right, which is why we need to know a little about Einstein’s theory to understand Hawking.

Maggie: Einstein baffles me.

John: He is tough. But I will try to make it fun.

Maggie: And easy!

John: And easy.

Einstein thought long and hard about the law of gravity and Newton’s theory of gravity, and he began to question whether gravity was really a force of some kind that causes planets to rotate around the sun. And then he had this grand idea: what if the planets rotate around the sun not because of this mysterious force, but because space itself is curved.

Maggie: Whoa, whoa, whoa! That does not make any sense to me.

John: Let me see if I can explain this. When we think of space, we think of an empty area, correct?

Maggie: That’s right.

John: And when a spaceship flies from point A to point B, it flies in a straight line through this empty area. Is that correct?

Maggie: Yes. Unless gravity pulls it one way or the other.

John: Right, because gravity is a mysterious force.

Maggie: Yes, that is what I think.

John: Well let’s do a thought experiment. Let’s set aside Newton’s law of gravity, notions of empty space, and straight line space flights. Just put those out of your mind for a short time, okay?

Maggie: Okay, done.

John: Now think of space as a something, not a nothing. What if space is like a big block of jello, ten miles high, ten miles wide, and ten miles long. So space is actually a something. Do you have that image in your mind?

Maggie: Yes, I got it.

John: Now put fruit in the jello, like your grandmother used to do.

Maggie: Okay. The fruit is in the jello, just like the planets are suspended in space.

John: Good. You are getting it. Have you ever shaken a jello square before?

Maggie: Yes.

John: What happened?

Maggie: It didn’t stay perfectly square. It moved so that the top was no longer perfectly aligned with the bottom, and the sides were no longer perfectly aligned with each other. It kind of curved.

Hey, wait a minute. I see what you did there.

John. Right. The jello square is no longer perfectly square, but curved and bendy, just like space.

Maggie: So if I were in a space ship traveling in the jello from a piece of orange (point A) to a piece of apple (point B), I would travel following the curve of the jello.

John: That is exactly right. You are so smart.

Let’s try another good analogy. What if we think of space as a trampoline. In Newton’s theory, when we roll a ping-pong ball across the trampoline, it moves in a straight line from a point A to a point B. Correct?

Maggie: Right. Unless gravity pulls the ship one way or the other.

John: Right, and then the ship would have to compensate for the pulling of the gravity. And like we said before, this theory is good enough for most space flight, such as flights to the moon. So no worries there, Newton has got that covered.

But what happens if I place a huge cannonball on the trampoline at its center?

Maggie: The cannonball causes the trampoline to collapse in the center, and move downward. How far down it goes depends on how heavy the cannonball is.

John: Again, correct. So, while the cannonball is on the trampoline, what happens when I roll our same ping-pong ball across the trampoline?

Maggie: It rolls from point A, across the trampoline, down one side of the curve caused by the cannonball, up the other side of the curve, and then onto point B. It moves across the trampoline, but follows the curve.

John: Now imagine that the cannonball is a big object in space with lots of gravity, just like our sun. This big object causes space to curve, just like the trampoline. And space has a greater curve the closer it gets to the object. Here is a picture for you to contemplate.

All this happens because space is a something, not a nothing. What do you think of this idea?

Maggie: It is really different from how I normally think of space, but I kind of get it.

John: You don’t have to understand it perfectly, and most do not. You just need to understand it enough for our purposes here.

Maggie: Was this theory ever proven?

John: Einstein proved his theory mathematically, but more importantly for us, it was also proven by experiment. And I think this experiment will provide a helpful illustration.

During a full eclipse of the sun, an astronomer named Arthur Eddington was able to measure light from a star as it passed close to the sun. He predicted where it would appear to someone on the earth if it followed Einstein’s theory of a curvature in space. And he was correct. As the light passed close to the sun (a large object with lots of gravity) the light followed the curvature of space, and did not travel in a straight line. This proved Einstein’s theory. So cool!

Maggie: That is cool.

**Summary**

John: So let’s summarize our main points. Science changes. That doesn’t seem so controversial, does it?

Maggie: No, not now that you have explained it.

John: Newton’s theory of gravity is that gravity is a force that holds the solar system together.

Maggie: That seems easy to me now.

John: Einstein comes along and decides that the planets curve around the sun because space itself is curved, and gravity causes space to curve. And Einstein proved this both mathematically and by experiment.

Maggie: That makes some sense to me.

John: And, while Newton’s theory works just fine most of the time, we need Einstein’s theory to calculate the rotation of objects close to other large gravitational objects. For example, using Einstein’s theory and math, scientists are able to perfectly calculate the rotation of Mercury, which they were not able to do with Newton’s theory.

Maggie: That is really cool. But tell me, how does this apply to Hawking?

John: As we will see, the theory of curved space is going to help explain two of Hawking’s theories: his theory about the origin of the universe and his theory about black holes and radiation. These will be the subjects of our following two conversations.

Maggie: This is hard stuff to think about, but I enjoyed our chat.

As always, I appreciate your Maggie and Me posts. I’ve started reading them to our son (even though he’s way too young to understand). But thank you. Hope you and the family are enjoying springtime.

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