# Brian Greene's Spacetime Loaf

1. Mar 6, 2013

### ChrisXenon

I'm getting older and dumber, it seems.

In his book "The Fabric of the Cosmos", from page 49, Green points out some basic vector thinking. Given a fixed speed over the ground, as you head more West of North, your speed North decreases, whilst your speed West increases. He suggests that this is analogous to our movement through space-time. As our speed through space increases, our speed through time slows down - i.e. time slows down.

From page 53, Greene develops the model of space-time being a block of slices of 2D space. In this model, the third dimension is time, the two dimensions of the page are space, and the entity as a whole is space-time.

Here's my problem, and it hits before we even get in to the interesting stuff. He says that a photon, moving through space at light-speed, will experience no time. This would be analogous to moving across one of his bread slices without moving in the time dimension. However, in his end note 9, he says that something moving at light speed sweeps out a line at 45 degrees to the crust-to-crust axis of the loaf. So on the one hand, the angle is 90 degrees and on the other it's 45 degrees.

Where have I gone wrong?

2. Mar 6, 2013

### Staff: Mentor

You haven't gone wrong. The analogy is an analogy, it isn't perfect or it wouldn't be an analogy. You have uncovered one of the limitations.

The source of the limitation is geometry. In Euclidean space the geometry is defined by the Pythagorean theorem $ds^2=dx^2+dy^2+dz^2$, but in spacetime it is defined by the Minkowski metric $ds^2=-dt^2+dx^2+dy^2+dz^2$. In Euclidean space the only way to have 0 length is to have 0 on all three axes, but in Minkowski spacetime you can also have 0 length by having equal dx and dt, which corresponds to 45 deg.

Last edited: Mar 6, 2013
3. Mar 6, 2013

### A.T.

Yes, if you put proper-time on the time axis. That is a so called Epstein-diagram.
That refers to a Minkowski-diagram, where coordinate time is on the time axis.

In this applet you can compare the two diagrams:

See this thread on the same topic:

Last edited: Mar 6, 2013
4. Mar 6, 2013

### Naty1

Hey Chris...
that's a great book!! with what i found to be some nice conceptual analogies to get one started with the ideas of relativity. Those confounded time slices were, for me, however, more trouble than they were worth. I must have read that part three or four times on different days and decided to give up..... but the rest of his ideas, like figure 3.7 [paths through spacetime] were ones I still use in thinking about relativity.

Some of his ideas are disliked in these forums....If something bothers you with his explanations I found checking in Wikipedia sometimes provides a different perspective that can be helpful trying to figure out Greene's view....

"Eternity is no time at all for a photon" is a nice quote I found to think about that....

It's also helpful to remember that in many frames, YOU are right now moving at near light-speed...and 'SOMEBODY' thinks you are really,really 'time dilated' for example....But I don't think that, I'm just sitting here 'stationary' typing.....

5. Mar 6, 2013

### Staff: Mentor

Dale Spam's comment is right on target. Nowhere in Brian Greene's development does he mention that he is not looking at the actual universe, but at a 4D Euclidean analog of the real universe. His discussion would be right on target if the actual universe were Euclidean, but it is not. Still, it is sometimes helpful to study Greene's Euclidean analog universe because it exhibits many of the same phenomena as actual spacetime: relativity of simultaneity, length expansion (rather than contraction), time contraction (rather than dilation), a 4-velocity, and many other interesting features of behavior analogous to the real universe. I have found it very helpful in studying accelerated frames of reference, for example.

Chet

6. Mar 6, 2013

### bobc2

Hi ChrisXenon, Greene's illustration is actually quite good and very consistent with special relativity. And remember that the slices at the various angles represent the cross-section views of the universe for the observer in motion at various velocities. So, remember that this means that as the moving guy's time axis rotates clockwise with increasing speeds from the long axis of the loaf (rotation with respect to rest time axis), the spatial axis (X1-axis of the moving observer) is rotating counter clockwise, such that the world line of a photon would always bisect the angle between X4 and X1. Hopefully, the sketch below illustrates this.

Your problem with Greene's description is assuming he meant that the moving observer's time axis would rotate all of the way through 90-degrees to become colinear with the at-rest X-axis. You can see in the sketch below a sequence of diagrams where the moving observer moves faster and faster in the sequence. If the moving guy reaches the speed of light his time axis would have to become colinear with his X axis. I'm afraid I can't give you any ideas about what goes on at that point (others here will explain why that would not happen). So, his time axis needs to rotate just 45-degrees, not 90-degrees.

Notice that by the photon worldline always bisecting the angle between t and x, all observers measure the ratio, dX/d(ct), to equal 1.0, i.e., speed of light is the same for all observers, not matter their speed.

Last edited: Mar 6, 2013
7. Mar 7, 2013

### ChrisXenon

DaleSpam (err, why??), do analogies have to be imperfect? Surely, it's not an analogy's imperfections which label it an analogy - but it's similarities to that which is an analog of.

Nevertheless, knowing that the analogy is imperfect and that I can look there for my failure to understand Greene's analogy is something of a relief. It does seem astonishing that he would say two mutually contradictory things about an angle in the same section of the book and not mention the problem though.

I may have to lever myself up of my forelimbs and waddle into Mincowski's world. Or I may accept my own ignorance and return to the thorny topic of earning a living...

A.T. Greene made no mention of this "proper time" malarkey. I want a refund... The applets are very ... colourful...

Naty1, well, on page 56 I find he did the dirty on me. He done lied! So I hate him, but I'll try to man up and press on.
I do find his talk of Itchy, Scratchy et al an annoying distraction. I ahve a 3K brain to work with here, and he's filled 1K of it with cartoon characters. Those other frames you mention...you may think you're sitting there stationary, typing, but - pah - ask your wrist, buddy. You was rattlin' round like some mad man with dyspensia.

Chestermiller, I've always understood that these analogies drop dimensions in order to illustarte points, but i've never heard before that they also use THE WRONG GEOMETRY. This is new to me. I may look into this further if I can find an appropriate vvector.

bobc2. You say Greene's analogy is quite good, but for me, if it contradicts itself on its own terms, without apologising, then it's always going to be, well, rude and annoying. As for your diagrams. No, sorry - too many lines... I always thought I was smart. Thanks you so much for ermoving that amusing little notion.

Hehe. But seriously, I appreciate your efforts folks. I'm thinking next stop - cross stitch...

8. Mar 7, 2013

### A.T.

If he talks about fixed speed in space time where only direction changes, and relates the movement along the time dimension to individual aging, then he must be thinking in terms of a space-propertime diagram. The rate of advance in space-propertime is the same for all objects and the Euclidean distance corresponds to coordinate time. Here is another applet using this diagram:

9. Mar 7, 2013

### Staff: Mentor

It is hard to tell with Greene, but I think he is just talking about a spacetime diagram, not a space proper time diagram. The "fixed speed" in spacetime is the unit norm of the tangent vector, the four-velocity.

10. Mar 7, 2013

### Staff: Mentor

When we make an analogy we are saying that this new unfamiliar thing X has some of the same features of this different familiar thing Y. If X has some features that Y does not have (or vice versa), then the analogy is imperfect. If it does not, then X is Y, and it isn't an analogy, they are the same thing. Therefore, all analogies are imperfect.

Out of all of the pop-sci authors, Brian Greene causes more confusion and questions here than all of the others put together. This analogy, in particular, is a common problem, so you are not alone in this.

11. Mar 7, 2013

### Naty1

What did you find on page 56??? can you quote a few lines of the offense??

My book is numbered differently than yours...

Even Leonard Susskind in his Youtube videos resorts to 'Alice and Bob' observers.....
didn't help me grasp much of anything any better.

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12. Mar 7, 2013

### bobc2

You seem like a pretty smart guy. Greene is definitely using the 4-dimensional Minkowski space-time model. If you really have a burning desire to understand his loaf of bread, google "space-time diagram" and "block universe."

13. Mar 7, 2013

### Staff: Mentor

That model underlies what he is saying, yes, but he also mixes in concepts from his space-proper time model. Mathematically, the two models are equivalent, but conceptually Greene's way of putting things seems to lead to a lot of misinterpretation.

I don't know why Greene insists on putting things the way he does, of course, but I wonder if it's because he doesn't actually expect his audience to do any interpretation at all; he just expects the audience to nod their heads and say "wow, neat!" and look no further. So when people actually try to reason things out further from what he's saying, naturally they have problems; he wasn't intending for anyone to reason things out further from what he's saying.

Ok, I'll stop ranting now.

14. Mar 7, 2013

### nitsuj

Ah so a physics bible of sorts,

perhaps his book would be better placed in Religion or Art & Poetry; as opposed to the physics section.

15. Mar 7, 2013

### Naty1

Complaining about a few of Greene's descriptions seems to me like ranting about the 'balloon analogy' in cosmology....even if some people draw incorrect conclusions, seems to me a much larger group is intrigued and undertakes additional study....

16. Mar 7, 2013

### Staff: Mentor

I think the problem with Greene's descriptions is the relative size of the two groups--many more people seem to draw incorrect conclusions.

17. Mar 7, 2013

### Alain2.7183

The simultaneous time slices used by Brian Greene are the same as the lines of simultaneity that Taylor and Wheeler use in their Example 49 (pages 94 and 95) of their "Spacetime Physics" book.

18. Mar 7, 2013

### Staff: Mentor

Sure. But that doesn't change the fact that Greene's explanation is the one that causes problems. I don't know if it is primarily due to his wording or his popularity or what, but Greene's explanations bring decidedly more confused people here than anyone else.

19. Mar 7, 2013

### WannabeNewton

You can only sacrifice so much mathematics for "intuition" in an exposition of a complicated physical theory before it starts confusing the hell out of people. It's like trying to use diagrams and "real - world" physical examples to explain the relationship between C* - algebras and physical systems in QM.

20. Mar 7, 2013

### bobc2

Good point, Alain2.7183. Brian Greene tries to get across one of the most profound aspects of special relativity, cutting the loaf at different angles to illustrate the notion of different cross-section views of a 4-dimensional universe--a discussion very tough to take on with those non-math and non-science folks with curiosity about special relativity. I thought it was a jolly good effort.