The block universe concept, pros and cons.

[ajb]

I never really liked the notion of the universe expanding, it leads to so many misconceptions. Think 4-d and think about space-time cuts into space and time. The ideas of expanding and what it expands into just go away.

 

Relativity 1.01 think 4 dimensionally!

 

The analogy I like is the cone. Lets cut out the conical singularity. Then globally the cone looks like a circle times an interval (part of the line). Orientate it so that the smaller circle is facing down. Now do some space-time cuts, that is cut up the cone into a series of circles. You see that they are all of different sizes.

 

Now for the analogy. Imagine that the cone represents space - the circles and time - the interval. Then we see as we go up the interval the circles get bigger and bigger, yet the 2-d surface of the cone is not expanding into anything!

 

(Of course as an analogy there are problems, but it shows thinking space+time is the way to go)

[Martin]

In your picture space is 1 dimensional. A circle. And instead of an expanding circle you say picture a cone. A cone is a static picture of an expanding circle. You can slice a cone into a series of larger and larger circles.

 

...

The analogy I like is the cone. Lets cut out the conical singularity. Then globally the cone looks like a circle times an interval (part of the line). Orientate it so that the smaller circle is facing down. Now do some space-time cuts, that is cut up the cone into a series of circles. You see that they are all of different sizes.

...

 

Some people make the same analogy but with 2D space. Their spacetime is a solid ball. They imagine it as made of spherical layers, like an onion.

Each layer is space at some particular time.

 

Each analogy has some enlightening or convenient feature. Each is useful and all, as you suggest, have problems. No perfect analogy.

 

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Basically what you have presented, AJB, is a toy version of the block universe concept.

 

It could be interesting to discuss the pros and cons of that 4D way of picturing the universe---its degree of realism or not.

 

George Ellis, a worldclass cosmologist and relativist has written about the block universe recently. A couple of papers in the past two years. You may know of him: he co-authored The Large Scale Structure of Space Time with Stephen Hawking back around 1960.

 

Part of George Ellis' message in these papers is that a simple thought experiment involving two weights and a radioactive isotope can show that the block universe concept must be wrong. It cannot correspond to reality because it does not include quantum uncertainty.

 

In the standard block universe picture space time including past and future are part of a single 4D crystal-like entity. Particles have their world-lines snaking through the block.

You can slice the block into time-slices according to some observer's time, or anyway some chosen time.

 

I have to go. Back later

Edited January 12, 2010 by Martin

[Mr Skeptic]

The way I understand those analogies, it shows space expanding into "later".

[Martin]

Heh heh. Nice way to put it.

 

Later space is bigger.

So it expanded into "later" (rather than into some imagined surrounding space).

[michel123456]

Our observation is not a cone expanding. The expanding cone (with a point in the past and a base in the future) is a Theory. What we are observing are spheres expanding from a point (the observer) and spreading into the past (the universe). If you put that into a diagram, it is a cone with its point at the observer and its base in the past, a light cone. It is exactly contrary to the expanding cone. How we go from the one to the other is a Theory. At this moment we are speaking, all datas confirm the expanding cone. But still, it is a Theory.

IMHO before speaking about the expanding universe, we have to analyze more deeply what we are actually observing. I have a strong feeling we have not completely analyzed the light cone, and we are jumping into conclusions.

 

As for the block universe, IMVH it is a stupid concept, but that means nothing, because so many times stupid things do happen in reality.

Why stupid?

_because energy would be infinite: that is a stupid reason, I know.

_because future would already exist: that is a philosophical question about free will, not a scientific reason.

_because i have no strong physical argument to discard it, that's why I call it stupid. Otherwise I would call it wrong.

[ajb]

I am not sure how much choice you really have in not thinking 4 dimensionally when you formulate anything in terms of general relativity. For a class of space-times (the globally hyperbolic, aka causal) you can make cuts into space and time. This allows you to think about 3-surfaces "evolving in time". This is very useful and essential in standard approaches to semi-classical gravity. It allows wave equations to be formulated on the space-time.

 

However, not all space-times are globally hyperbolic. So, I think to some extent we have to think 4-d.

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... is a Theory.

 

Well, I like to discuss things in the context of a specified theory.

 

At the moment general relativity seems to be the backbone of cosmology and gravity. It makes sense to interpret what can be measured in terms of general relativity.

 

This however, does require us to carefully distinguish between a mathematical model and nature herself. But this should not really cause problems.

 

Now in response to Ellis. I doubt anyone thinks that general relativity is the final word on the structure of space-time. For sure, it does not contain quantum gravity. However, I am not sure how "real" any physics theory is. They may agree with nature to some horrible degree of accuracy, but is it nature? My ethos is the only real things are that what can be measured. Theoretical physics then "maps" these measurements to the mathematical world of model building and vice versa.

Edited January 12, 2010 by ajb
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[Martin]

Now in response to Ellis. I doubt anyone thinks that general relativity is the final word on the structure of space-time.

 

Exactly.

 

Ellis is recognized as a top Relativist and Cosmologist and the papers I refer to are aimed at a specific modification of the GR block universe idea to make it more compatible with QM. You cannot "respond" to Ellis without studying his specific proposal.

Anyone interested can look up G Ellis on arxiv.

 

 

As for the block universe, IMVH it is a stupid concept,...

Why stupid?

_because energy would be infinite...

 

Not so. The volume of space does not have to be infinite in block universe.

The quantity of matter/energy does not have to be infinite.

 

One version of block universe can be visualized as a solid ball, layered like an onion---into time-layers.

 

(heh heh some jerk could point out that the slicing into time layers is typically to some extent observer-dependent or arbitrary---that's right---but we are used to time-slicing in cosmology )

 

Logically there is no essential difference but call it a ball universe, if you want.

 

The balloon model is just another (necessarily imperfect) way of looking at the ball universe. As the balloon inflates, it represents successive layers of the ball.

 

So the balloon model is essentially a 3D model.

It gives a way to think of a full 4D model. Think of a 3D hypersphere (in place of the 2D balloon surface) and think of the 3D hypersphere inflating.

 

Watch the movie of photons creeping over the 2D balloon surface, as distances on it grow. Extend that in imagination to photons creeping through an expanding 3D hypersphere.

 

Specific visualization-aid concepts are not inherently stupid. Picking and choosing can be stupid. Rejecting and favoring can be stupid. Since various ones can be useful in various contexts, one should be ready to use whichever aid to the imagination is appropriate. As for the concept itself, obviously what most matters is how you use it.

Edited January 12, 2010 by Martin

[ajb]

You cannot "respond" to Ellis without studying his specific proposal.

 

Yes, ok point taken. "Respond to Ellis" not quite what I meant.

 

What I mean is that I am in no way surprised that someone of Ellis' standing is thinking about such things and how relativity could be better suited to quantum questions.

Edited January 12, 2010 by ajb

[jajrussel]

I am not disagreeing with you ajb, but wouldn't thinking 4D always, imply that what is moving can be thought of as being within a 4D object and that the outside 4D object would also be moving?

Also, aren't most misconceptions because one assumes that one changing shape effects the other dimensionally, 3D?

Edited January 12, 2010 by jajrussel

[ajb]

I am not disagreeing with you ajb, but wouldn't thinking 4D always, imply that what is moving can be thought of as being within a 4D object and that the outside 4D object would also be moving?

 

I am not quite sure what you are asking.

 

Are you asking about paths in a space-time or the 3-surfaces (Cauchy surfaces)?

[jajrussel]

Part of the question is out of context, a misunderstanding on my part. I am still not certain that it wouldn't apply in the thought of a universe expanding. My misunderstanding, began when I assumed the misconceptions you were speaking of.

When one views an expanding universe, one can tend to see any portion of that universe as changing shape because of the expansion. A defined portion of space time does not need to change because the universe is expanding. By questioning my questions, you have given me something else interesting to read about. Sometimes I do speak in ignorance, then have to do a quick catch up on the conversation, or simply listen. I'll listen for a while.

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Okay, I said I would just listen for a while, but then I thought of your cone example. Each section gets larger, and the cone is defined by each section. If you decided to lengthen the cone all you would be doing is adding larger and larger sections until you reached the desired length. The definition of each individual section is unchanged. Only the cone is larger.

The cone representation just changes the shape of the block. The layering is the same. I don't think that any geometric shape can accurately define space/time but the cone shape better represents expansion than does the block.

However, this being said what I have read about a block universe describes it as an unchanging 4 dimensional block universe. No stacking is mentioned. It doesn't allow for a sense of time. The only thing implied is movement, hence the 4th dimension. Suggesting to me a philosophical vision of time

I have yet to figure out where a Cauchy curve fits into an unchanging block universe, unless you were asking if I was suggesting that a Cauchy surface changed the structure of an unchanging block. The answer would be no, though it might suggest a view of philosophic time in an unchanging block universe.

However, you never mentioned the word unchanging, when you said a block universe, so maybe I am still out of the loop, and maybe you can tell me what block universe view, you are talking about?

[ajb]

However, you never mentioned the word unchanging, when you said a block universe, so maybe I am still out of the loop, and maybe you can tell me what block universe view, you are talking about?

 

 

 

In my toy model it was quite clear that the cone is globally [math]S^{2}\times I[/math], with [math]I \subset \mathbb{R}[/math]. I decided that the circle was space and the interval was time. (I have said nothing about a metric, though we do have one induced by the embedding in three dimensional Euclidean space.)

 

 

So, again neglecting the metric and causal structure etc. most space times that are considered "physical" can be decomposed as [math]M = \Sigma \times I[/math], that is globally they look like 3-space and time. In fact it is important for may applications and theorems that we have such a splitting. The thing is that such space-times have a very similar causal structure to Minkowski space-time. This is very important for QFT, for example. (I have thrown away lots of technical stuff here, maybe we should come back to that later.)

 

However, general relativity by itself does not insist on such space-times. Nor does the ethos of general relativity say that we should make such a cut into space and time. The block view is exactly this. You must consider 4-d space time in its entirety. Time is then just laid out in front of you on equal footing as space.

 

"Physicists prefer to think of time as laid out in its entirety - a timescape, analogous to a landscape - with all past and future events located there together ... Completely absent from this description of nature is anything that singles out a privileged special moment as the present or any process that would systematically turn future events into the present, then past, events. In short, the time of the physicist does not pass or flow." --Paul Davies

 

This really is what general relativity suggests.

 

However, we have problems. By no means exhaustive, two spring to mind

 

1)Can we formulate quantum field theories without such a cut? Well, there has been some work based on algebraic quantum field theory in this direction. Also, one can formulate classical field theories without such a cut. This is multisymplectic field theory. The formalism here is very similar to classical mechanics viz symplectic geometry. Lots more to say here, but quantisation is a long way off. (I started to do some work on multisymplectic geometry but did not get any were with it, I got distracted with other generalisations of symplectic geometry that may or may not turn out to be useful.)

 

2)What about free will? Is everything simply predetermined? Philosophically is "now" now? etc...

 

Things like 2) I am not very worried about, 1) and similar are much more interesting.

 

Then there is the question of quantisation of gravity. Will this require a cut or not? How can one include the non-deterministic nature of quantum mechanics into such a rigid 4d space-time?

Edited January 12, 2010 by ajb