Science: Biggest News?

[ASH]

Re: Science: Biggest News?

How does superluminal expansion isolate the universes?

As I understand it (which is somewhat tenuously), there was a progression of thinking as theories of inflationary cosmology developed. I gather that early versions of the theory thought of a single universe that was finite, but unbounded (in the same sense as Jam's apple analogy). If you were a two-dimensional being confined to move on the surface of a sphere, you could travel forever and never reach an edge (making your sphere-universe unbounded), yet the area of the surface of the sphere would be of limited extent (making it finite). As per the above discussion of metric expansion, the scaling of this sphere's surface could change over time, so that distances across the surface of the sphere would get bigger without having to imagine the sphere itself being embedded in some higher-dimensional space, and expanding into that space. (This is where analogies to inflating balloons and such fail, because they imply expansion through some existing higher-dimensional coordinate system rather than rescaling.) Now, obviously, if you are a two-dimensional being confined to the surface of a sphere, you might walk forever without ever encountering "the edge of the universe", but it would be possible in principle to circumnavigate the sphere by walking in one direction until wrapping around to your starting point. However, if the sphere is expanding faster than light -- and you cannot travel faster than light -- then you cannot walk fast enough in one direction to ever wrap around. That's one way superluminal expansion can isolate you from "the edge of the universe", except in the case of a universe that doesn't have an edge so much as curve back on itself.

Anyway, in the early version of the theory, the universe was assumed to start out with an extremely small scale in an extremely high-energy state called "false vacuum". Said vacuum is termed "false" because some field within it (termed the "inflaton" field) is in a state with extremely high energy, which is a dynamically unstable condition. As the inflaton field evolves toward its ground state ("true" vacuum), the universe experiences cosmic inflation. It was realized that this process was something analogous to a phase change, and that the inflaton field might evolve differently in different regions, resulting in a lot of different neighboring universes. (In the phase change analogy, the high-energy false vacuum state is like a super-saturated solution, and the different universes are like little crystallites which nucleate out of that solution independently; different orientations of the crystallites are like potential differences in the laws of physics which might differ from universe to universe depending upon the path taken in the inflaton field's decay -- chiefly having to do with the relative strengths of the forces of nature.) Interestingly, as each region inflated faster than light, its boundary with neighboring regions would effectively recede from any observer within that region faster than the speed of light, isolating them within what is effectively a distinct universe. So to the extent that I understand the current theory, this is the sense in which superluminal expansion of our universe isolates it from any others which might have inflated out of the original false vacuum state.

Quantum mechanics has mostly convinced me that it may just be the case that the universe is beyond my capacity to understand even a simplified explanation. At least until we get those quantum computers implanted into our brains...

I found that quantum mechanics is easier to accept intuitively if it's presented in terms of linear algebra. It's still unfamiliar, but it seems a whole lot less ad hoc, and a whole lot more cohesive and sensible, when formulated in terms of state vectors in a complex linear vector space. Unfortunately, linear algebra is reasonably hard (at least I found it so), and single variable calculus is comparatively easier, so most people encounter quantum mechanics as presented in terms of Schrodinger's equation and some rules like Heisenberg's uncertainty principle which can seem rather arbitrary. I don't know if attacking quantum mechanics from the direction of linear algebra will clarify things, but for me at least, it helped a lot.

[DSpencer]

Re: Science: Biggest News?

As I understand it (which is somewhat tenuously), there was a progression of thinking as theories of inflationary cosmology developed. I gather that early versions of the theory thought of a single universe that was finite, but unbounded (in the same sense as Jam's apple analogy). If you were a two-dimensional being confined to move on the surface of a sphere, you could travel forever and never reach an edge (making your sphere-universe unbounded), yet the area of the surface of the sphere would be of limited extent (making it finite). As per the above discussion of metric expansion, the scaling of this sphere's surface could change over time, so that distances across the surface of the sphere would get bigger without having to imagine the sphere itself being embedded in some higher-dimensional space, and expanding into that space. (This is where analogies to inflating balloons and such fail, because they imply expansion through some existing higher-dimensional coordinate system rather than rescaling.) Now, obviously, if you are a two-dimensional being confined to the surface of a sphere, you might walk forever without ever encountering "the edge of the universe", but it would be possible in principle to circumnavigate the sphere by walking in one direction until wrapping around to your starting point. However, if the sphere is expanding faster than light -- and you cannot travel faster than light -- then you cannot walk fast enough in one direction to ever wrap around. That's one way superluminal expansion can isolate you from "the edge of the universe", except in the case of a universe that doesn't have an edge so much as curve back on itself.

I guess the part that confuses me is that even if the being is two-dimensional, the sphere is still 3 dimensional. Your explanation makes sense to me if we are trapped in a single universe that expands faster than we can reach the new parts. However, if I imagine multiple universes of this nature I can't help but picture one sphere growing into another and having overlapping universes.

[sunskyfan]

Re: Science: Biggest News?

When considering either Special Relativity or General Relativity it is good to keep in mind that the key concept is the speed of information transfer from one point in space to another. The speed of light in a vacuum in flat space happens to correspond with this limit. "Expanding space" at a rate faster than this speed does not create any problems since information is not being transfered.

[ASH]

Re: Science: Biggest News?

I guess the part that confuses me is that even if the being is two-dimensional, the sphere is still 3 dimensional. Your explanation makes sense to me if we are trapped in a single universe that expands faster than we can reach the new parts. However, if I imagine multiple universes of this nature I can't help but picture one sphere growing into another and having overlapping universes.

With the caveat (again) that this isn't something I understand well: The picture I have in my head is from an article written by Alan Guth and Paul Steinhardt and published in The New Physics. Only a portion of the article is publicly available on Google Books (the link I posted), but if you scroll down a bit, there are a series of illustrations on pages 47-51 which address the issue... as it was understood back in 1989. (More recently, in 2007, Alan Guth wrote that "Since the proposal of the inflationary model some 25 years ago, inflation has been remarkably successful in explaining many important qualitative and quantitative properties of the universe." My understanding is that the early version of the theory from 1989 is still pretty close to current.)

Anyway, the drawings depict a bunch of neighboring universes, forming like bubbles in a multiverse. Inside each bubble, a particular set of physical laws obtain. Different universes have potentially different physical laws, and yes -- neighboring universes can touch at boundaries called "domain walls" in analogy to domain boundaries in ferromagnetic materials. At the time, some theorists thought we should be able to find "defects" in our universe created by the point of contact with a neighboring universe with different physical laws -- defects termed "cosmic strings". However, inflation explains why we don't see such defects -- superluminal inflation moves the boundaries between universes beyond the "horizon" we can interact with. The key point, I think, for inflation (and stretching of space in general) is that the "growth" is basically internal. If I understand it correctly, the metric expansion of space doesn't advance one universe's boundary toward its neighbors; it just rescales distances within its boundaries.

Here's a little digression on the spacetime metric. I only understand how to do calculations for "flat" spacetime, but I gather that the concept is general. The way I was taught to think of relativity is that events are fundamental, but their relationship to each other in space and time depends upon one's perspective. In other words, there is an underlying concrete reality defined by events -- they are points on a map. You can hang your map on the wall, and for convenience, you can talk about the vertical and horizontal separation of points on the map; in physics, we talk about the separation of events in space and time. If you tilt your map on the wall, then the vertical and horizontal separation between points will change; likewise, if you move (or accelerate), the separation of events in space and time will change. But there is something fundamental about the relationship of two points on a map which doesn't change no matter how you hold it: the distance between the two points is the same, even if how that's divided into vertical and horizontal displacement depends upon your orientation of the map. In special relativity, the "distance" is called the spacetime interval, and it does not change between inertial reference frames. The metric is basically the rule for calculating the differential distance in the appropriate geometry. For the map we have Euclidean geometry, so the "metric" is just the Pythagorean theorem: ds² = dx²+dy², where "s" is the straight-line distance on the map. For the "flat" spacetime of special relativity, the Minkowski metric is ds² = -c²dt²+dx²+dy²+dz². This is basically just the Pythagorean theorem with the time coordinate scaled by a factor of i*c (i being the square root of -1, and c being the speed of light). In some respects, it's helpful to think of the speed of light as just a unit conversion factor from time to space. After all, if you measured your vertical displacement on the map in centimeters and your horizontal displacement in inches, you'd need to include a unit conversion factor to make the Pythagorean theorem work -- it only works for a consistent set of units. So anyway, in general relativity, the metric is a lot more mathematically complicated, but it's the same idea. The key point is that when we're talking about space expanding because its metric is changing, what we're saying is that something like the Pythagorean theorem for finding the distance between two points is changing with time. That's different from the universe expanding into some outside space. It's more like yesterday two stakes in the ground were separated by 10 meters and today they're separated by 11 meters, but nothing has moved.

[ASH]

Re: Science: Biggest News?

When considering either Special Relativity or General Relativity it is good to keep in mind that the key concept is the speed of information transfer from one point in space to another. The speed of light in a vacuum in flat space happens to correspond with this limit. "Expanding space" at a rate faster than this speed does not create any problems since information is not being transfered.

That is a good point, clearly stated.