Monday, February 6, 2012

The Zero Universe

The world is like a great theater where we watch history unfold. This colossal story features a cast of billions, who not only witness the arc of its epic plot, but also actively take part in its creation. Look around you; it’s raucous and noisy inside this theater we call “the world.” But, if it were possible for us to step outside the theater and take a look, there would be nothing.

Inside, the theater is a mind-boggling swirl of information, actions, and reactions; from the outside, as seen by a cosmic Google Earth beyond space and time, it’s completely empty. I am not just making a cute metaphor here — this is a real feature of our universe, with profound implications.

It seems that in the final analysis, when all things are considered, the universe adds up to exactly zero. For one example (there are others at the bottom), consider the relationship between space and time. Bear with me as I review an idea from high-school geometry. If we have a triangle that includes a 90° angle, we can use the Pythagorean theorem to determine the length of the diagonal from the length of the right-angle sides:

a2 + b2 = c2

where a and b are the lengths of the right-angle sides, and c is the length of the diagonal. A nifty geometrical diagram proves why this is true. If you make a square box along each of the three sides, then each box has an area of the length of that side, squared. The area of the smaller squares adds up to the area of the largest square: If a = 3 and b = 4, then c = 5.


The Pythagorean theorem works in three dimensions, too. If you see a blimp in the sky, you can calculate the exact straight-line distance to the blimp by knowing its altitude above the ground (the value z), as well as how far east-west (x) and north-south (y) you'd have to go to get right under the blimp:

x2 + y2 + z2 = d2

where d is the distance to the blimp. I don't have a 3D diagram, but you can prove it for yourself with a little effort.

Now it gets interesting. This trick extends to four dimensions. Time is typically cited as the fourth dimension. Does the decidedly non-geometric idea of time work into the Pythagorean theorem? Incredibly, it does — but first, you have to convert the time measurement into a distance-like measurement. Then, the total distance you’re calculating is the spacetime distance in the bizarre four-dimensional world where east-west, north-south, up-down, and earlier-later mean the same thing, only in eight different directions. Represented by the letter s, spacetime distance (also known as a Minkowski interval) is determined by an amazing formula. Let’s break it down:

x2 + y2 + z2 – (ct)2 = s2

As before, x is the distance (for example) to the east, y is north, and z is up, but we’ve added a fourth term for time (t), which gets multiplied by a constant, c. Notice the minus sign before the term for time. When it comes to distance through spacetime, elapsed time counteracts spatial distance, and vice versa: If we travel a distance through space, and do it in a very short interval of time,* the distance traversed is effectively reduced. This is why a space traveler could reach stars across the galaxy within their lifetime if they got close enough to the speed of light. Time goes in the opposite “direction” of space!

That constant, represented by c? It’s the same c that represents the speed of light in equations such as E = mc2. What better number to convert units of time (seconds) into a distance-like measurement — after all, we know that for light, there are 186,000 miles per second. See what Einstein did there? The speed of light is more than just a speed; it’s a universal conversion factor that turns time into a distance-like measurement. By treating time as a negative and multiplying it by c, we can exchange time and space in our formulas as readily as nature exchanges them. That’s what special relativity is all about.

This extra meaning of the speed of light has interesting consequences. If you could look out the window of a rocket going at the speed of light, you wouldn’t “c” a thing — the entire universe would vanish to a point through Lorentz contraction. In order for space and time to enter into what we call “reality,” they must be measured by an observer, something not traveling at the speed c. In the real world, that’s anything with mass. For any observer with mass (make your own couch-potato joke), zero spacetime distance separates into the components familiar to us: a measurable amount of space and a measurable amount of time.

It’s as if the presence of mass causes “zero” to pull apart into the familiar ideas of spatial distance and temporal duration, like taffy. But since the universe is by definition everything there is, you have to be inside the universe to witness this incredible stretching apart of zero, to experience space and time as different things. If you were taking in the all-seeing “God’s-eye view” from a timeless, spaceless, massless perspective outside, you would see the same thing the speed-of-light traveler sees — nothing. To witness the action, you have to be inside the theater, in your seat.

Space and time cancel out to exactly zero for the universe as a whole. But that’s just one example of the zero-sum nature of the physical world. A few others:
• The mass–energy of everything in the universe is exactly balanced by the universe’s gravitational energy. The latter is expressed as a negative number, just as time is in the spacetime formula. A while back Alex Filippenko, who’s a familiar smiling face to science-TV geeks, co-wrote an essay about how this means the universe may have come from “nothing at all.” Like the pulling apart of space and time, mass–energy and gravitational energy were also pulled apart in the Big Bang.
• For similar reasons, the net charge of the universe is generally believed to be zero, with the number of positively charged particles equaling the number of negative. (This is unproven.)
• Certain pairs of phenomena, like electricity and magnetism or mass and the curvature of space, are linked such that they seem to keep each other in check. The great physicist John Wheeler was fascinated by these “automatic” connections, pointing out how they are constrained together by zero sums, the way the ends of a see-saw are always the same total distance from horizontal. “That this principle should pervade physics, as it does,” he asked in 1986, “is that the only way that nature has to signal to us a construction without a plan, a blueprint for physics that is the very epitome of austerity?”

On the one hand, it’s surprising that quantities totaling zero show up again and again in nature. But on the other it makes sense, if the universe is a closed system incorporating everything there is. As a teen I remember being into the Taoist idea of Yin and Yang — I thought that in the final analysis, the universe as a whole couldn’t be anything but perfectly balanced. On a level deeper than I imagined, I may have been right.


* Slow speeds (which mean long elapsed times) cause the time part of the formula to overwhelm the space part, resulting in large spacetime distances. Spacetime distances only get small when you approach the speed of light, for example, covering 186,000 miles in 1.1 seconds — then the (negative) time part almost cancels the space part.

8 comments:

  1. A reader hipped me to this entertaining video from richarddawkins.net, in which physicist Lawrence Krauss explains how to get a universe out of nothing:
    http://www.youtube.com/watch?v=7ImvlS8PLIo

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  2. Austin P. TorneyMay 6, 2012 at 6:22 PM

    The Deduction of the Theory of Everything

    1. There is existence; we are in it. While we are only privy to what is formed within our brains, we know there is a reality ‘out there’ because our senses take it in. This point is made since some say that reality is a projection; however the projector would still have a real existence.

    2. The base, root existence could have no prior existence making it up, leaving only nonexistence to constitute it somehow. Either existence or nonexistence is the basis of all.

    3. The basis of all, then, is either a thing or no-thing, each necessarily eternal and everywhere.

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  3. Austin P. TorneyMay 6, 2012 at 6:23 PM

    4. The basis of all must be eternal, of forever duration, for it would not be the basis of all if another basis was before it.

    5. The basis of all must be infinite, of everywhere’s extent, for it would not be the basis of all if another basis was outside it.

    6. A lack of everything (nothing) did not happen, for there is existence.

    7. We cannot say that nothing begets nothing, for we do not know what the lack of anything could or couldn’t do. We can say, though, that it has no ‘what’ (contents), no where (place), no laws, no math, no known constraints, not anything to it, etc.

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  4. Austin P. TorneyMay 6, 2012 at 6:24 PM

    8. Either (A) the basis of all is a base existent, which is necessarily a thing, or (B) the basis of all is nonexistence, a no-thing.

    9. The basis of all must be the simplest state, because it wouldn’t be the basis if it could be decomposed further. We do also see that composites are formed of simpler and simpler things, down unto the minuscule.

    10. There can be no cause for the basis of all, since, again, then it is not the basis of all, so, it is necessarily causeless. We do see cause and effect above and beyond it, though. For the causeless, we have to find something other than cause and effect, such as an equation, perhaps.

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  5. Austin P. TorneyMay 6, 2012 at 6:26 PM

    11. For (A), the base existent thing would have to be unbreakable, as it could have no lower parts, and also unnamable, since it was never made, having been around forever. We don’t see a way that a thing could be already made and defined in its particulars without ever having been made and defined as such. This is not to say that there couldn’t be many, different base existents, this being separation instead of unity. We also don’t see what could have decided the total amount of instances of the base existent(s), nor why they would be workable as they are, rather than inert. This leaves the notion incomplete, and so it cannot become right until its incompleteness goes away. Incomplete notions are always wrong, if only by the virtue of their incompleteness. Having an infinite regress of smaller and smaller things does not help the incompleteness problem, but only adds to it.

    12. For (B), having the basis of all being nonexistence, the base existent(s) would have to have been created from it. not being eternal in themselves, but this is not to say that they are not ever being created, as well as canceling back into nonexistence. A great support for this notion is that there is literally nothing to make anything of, that is, no other thing could contribute to the creation of the thing of the base existent(s), and so it appears inviolate, having no way around it.

    13. We still don’t know what a lack of anything could do, for sure, all in all, even if we propose that it is lawless, and so anything goes, but we do know for sure that existence had to come from it, as there is no other source. Evidently, the notion of a lack of anything, or nonexistence, is not what we thought it was.

    There's more. Look up 'The Deduction of the Theory of Everything' and you will find it

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    Replies
    1. Sounds interesting. The thing about a text-based theory is that the terms need to be precisely defined in order for the argument to have any rigor. For example, the first point ends with the phrase "real existence" -- this can mean various things. Does it mean ontology independent of an individual's subjective experience, or in terms of actual experimental data, or potential experimental data, or in a purely metaphysical (non-empirical) sense? Point 2 mentions "prior existence" -- is that invoking time as a background which necessarily has a real existence, and if so, what is the basis for that hypothesis? And so on.

      Words aren't mathematics. People take phrases such as "if X exists..." for granted, but they cannot be thrown around in a specific logical argument. Without precise definitions, terms can take whatever meaning the reader wants them to take, so the argument cannot be fairly and objectively evaluated.

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  6. "For any observer with mass (make your own couch-potato joke), zero spacetime distance separates into the components familiar to us: a measurable amount of space and a measurable amount of time."

    If you mean s²=0, then this is only true for *MASSLESS* particles. The interval is not generally zero. -s² is the time (squared and multiplied by c²) measured on an observer's clock (called "proper time").


    "Space and time cancel out to exactly zero for the universe as a whole."

    I have no idea what you're talking about here, but it seems like pseudoscientific mumbo-jumbo.


    "The kinetic energy of everything in the universe is exactly balanced by the gravitational potential energy of everything in the universe."

    More nonsense. The "gravitational potential energy" isn't even *DEFINED* in general relativity, so I have no idea how you could possibly be making sweeping statements about it. And, kinetic energy is only defined locally, so talking about "the kinetic energy of everything in the universe" is complete nonsense.



    I believe I know what you're talking about when you mention Wheeler: it's that certain quantities are associated with time and certain quantities are associated with space, which falls directly out of special relativity (and is related to the spacetime interval). For example, electric potential is a "timelike" quantity while magnetic vector potential is a "spacelike" quantity. Power is timelike while force is spacelike. Energy is timelike while momentum is spacelike. Charge density is timelike while current is spacelike, etc.

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    1. (1) I was talking about measurements of massless particles made by massive observers, not measurements of massive particles.
      (2) I was claiming that measurements of space and/or time could not be made from a hypothetical bird's eye view of the universe, as one needs to be inside the universe (and have mass) to do this.
      (3) I was wrong. I should have said mass–energy and (negative) gravitational energy; I will correct the error. I was referring to the zero-energy hypothesis, as in:
      http://www.astrosociety.org/pubs/mercury/31_02/nothing.html

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