Schneibster

I have a few concepts that help me when I deal with dimensionality. The first concept I find really helpful when talking about dimensionality is, never mistake an axis of rotation for a "dimension." In one dimension, rotation is impossible. "Axis of rotation" is meaningless, like 1/0. In two dimensions, rotation is possible in only one plane: x-y. Note however that the "axis of rotation" points in a direction that does not exist, and is again meaningless. In three dimensions, rotation is possible in three planes: x-y, x-z, and y-z. Now, it's common to imagine the "fourth dimension" as allowing one to rotate out of sight. And it's common to imagine it does so about a "fourth axis." And it is completely wrong. Actually, adding a fourth dimension adds not one but three planes of rotation: x-t, y-t, and z-t. And again, these three extra degrees of freedom have "axes of rotation" that point in directions that do not exist. "Axis of rotation" is fuzzy thinking when it's used in talking about dimensionality. Use "plane of rotation" instead and remember that only in this way is the definition of rotation meaningful in the system containing the rotating component. Second, the shapes of the past and future are the two branches of a hyperboloid of revolution; and this is far more accurate since the math that describes rotations in real 4d spacetime is hyperbolic trig. You can actually substitute degrees of rotation in hyperbolic geometry for meters per second in 3d space + time formulations and get the same answers. You can represent the Lorentz transform as rotations in 4d spacetime, as the sinh and cosh of the angle. You can find references to this in the literature and on the Internet by searching on "rapidity," which is what relativists call that type of rotation. Baez has a page on it. When you realize that such a rotation results in a second observer means seeing time and space directly convert into one another, you will stop making this unphysical mistake of thinking time is "different." The result of this is that one realizes that the relations of the 3 space dimensions to one another are circular and involve circular trig; but the relation of time to the space dimensions is hyperbolic. That's why the Lorentz Transform works; and that's why you can also do it completely in hyperbolic trig as rotations. When relativists speak of rotations in spacetime being equal to velocity, it's not a model, and it's not a tool. It's an actual statement of physical reality. I hope these ideas help you.

As a fun fact, the Schwartzchild radius of the Earth is, IIRC, around the size of a pea.

I would agree with that assessment. How do you feel about the assertion that lambda drove the inflation? And have you heard of "Eternal Inflation?" Or the "cosmic landscape" or "string theory landscape?"

And if we need the equations, we got you! I'd never thought about exotic matter being useful for making antigravity, but of course it is if you can use it to make a wormhole.

Hmmm, I guess I usually think of gravity as just gravity, since the opposite of a gravity field is another gravity field. What your talking about sounds more like the cosmological term: Gμν + Λgμν = (8πG/c4)Tμν that's the Λ. And I'm used to thinking of photons and antiphotons as degenerate; for most purposes it's just as easy to say there are no antiphotons. Same with gravitons. But you're of course technically correct.

Good. I'll be able to help some there, at least conceptually. One of the nice things about nonisotropies in the CMBR is that after they show you the numbers you can look at the whole-sky spectrum (or a piece of it) and see the ripples at that scale. How about inflation?

We know some things about dark matter, and there are others we don't know. We think we've detected it (I do not agree with the recent declaration that we cannot have) but I don't know if it might signal a difference between inertial and gravitational mass. This is probably the weakest underpinning of the Einstein equation: the equivalence principle. If you want an emotional judgement from me I "believe," snicker, that there will be order and that it will require the anthropic principle; I do not believe that all possible cosmoses can support our form of "life." I believe that our form of "life" will probably not make it out of our local region before the surrounding universe goes over the horizon. Over a long period our several large spirals and hundreds of subgalaxies will evolve and eventually the stars will burn up all the hydrogen; I have not seen late figures on that but IIRC it's on the order of 1012 years. The universe is so far 1.365 x 1010 years. It looks like it will "be like this" for a hundred times as long as it has been. If you want to worry about what will happen after the universe is a hundred times as old as it is so far, that is, as if all the universe so far were the first year of an infant's life, and it has all its life ahead of it a hundred years, that is we are the spirit of a single neuron of the barely year-old infant, all humans together, what do you want to worry about? This is perspective about the real length of time. It's like a 1-year-old child being worried about how he'll die after a thousand years.

I totally dig your automatic post consolidation feature. If there's somewhere to vote about that tell me. Very cool. Are there rules or nettiquette or whatnot about using it? Is there a FAQ? Thanks for your kindness to the n00.

There are two possible interpretations of entanglement, and we don't know which is correct. One interpretation is that entangled particles share hidden state information, which is revealed when either particle is measured. The same measurement on the other particle yields the complementary value (not always either the same or the opposite, but always related the same way for any given entangled pair production method- see Aspect Experiment). Another interpretation is that entangled particles truly have no values, until the first measurement of either particle, but that once the measurement is made that state is superluminally transmitted to the other particle. However, as several folks have pointed out, no information other than that state can be sent, and the state cannot be known until measured, and it is not affected by local conditions; in fact, local conditions cause the state to be lost, by decoherence. The measurement got made but the observer never saw the result, is what decoherence means. Which of the two or three major subsets of interpretations of quantum mechanics you understand the most easily generally depends upon which of these interpretations of the outcomes of Bell's Inequlity experiments, such as Aspect, you most easily accept. As a relativist I tend toward the opinion that data cannot be transferred superluminally and therefore like the first alternative, with hidden varibles. However, it's also necessary to understand that the first alternative rules out simple hidden variable theories. I am tempted to say that I think it's hidden states, not hidden variables. And I think there's a big conversation about TIQM/Wheeler-Feynman Absorber Theory and reverse causality and Everett/Many Worlds and other nontraditional interpretations that we all have to have. Personally I'm most comfortable with Consistent Histories and decoherence; it seems to me that this interpretation works well with the Fluctuation Theorem, which is also extremely important in all of this since it explains entropy and the limits of entropy. What you really want to do, Addictive Science, is go start a conversation in the Speculative section about "ansibles." Those are FTL communication devices. There are some amusing suggestions along this line, but nothing so far anyone has come up with beats relativity. It's not really possible to, you know; the shape of time dictates the speed of light limit. Precisely. I should say that I define "amusing" as "not contrary to known physics but way far away from a testable hypothesis" and "interesting" as "maybe testable in the foreseeable future but not now" and "provocative" as "probably testable soon" and "fascinating" or "captivating" or "worth watching" as "imminently testable or just tested."

There's no anti-gravity because there's no anti-space. The opposite of one gravity field is another gravity field, and since we can't shape gravity fields it's only "anti" at a particular location. For instance, you could exactly cancel Earth's gravity at a point on its surface by poising another (anti-?)Earth exactly above that point. That would exactly cancel the gravity at that point on Earth. That's "anti-gravity." The lesson is that since gravity is curvature of space "anti-gravity" is "anti-curvature" which is curvature. Therefore anti-gravity is gravity. Physicists have a method for proving this mathematically and I'm certain there's someone here who can do it; it's based on the fact that gravity interacts with spacetime, not the other six dimensions. It's why there aren't anti-gravitons.

Interestingly, it wasn't until SN1987a that we had clear evidence that the speed of light is the same in the Magellanic Clouds as it is here on Earth; we were able to see the explosion sequentially lighting up clouds that had previously been emitted by the star, that were light years away from it. The Clouds are far enough away to let us see this effect clearly over years, but close enough that we can measure the sizes of the cloud structures pretty accurately by trigonometry. As a result we can say that the speed of light hasn't changed measurably in the last 187,000 years (which is how long ago SN1987a exploded; remember, we first saw the light in 1987). And a changing speed of light would be an effect of a changing alpha. Also changing ε0 and μ0 can be expected. Stars would burn differently. Chemistry would work differently, because the electron cloulds would interact differently. Likely molecules for us, like CO2 and CH4 and H2O and NH3 would be rare or nonexistent. Benzene likely would not be possible; depending on the exact change, a four-carbon or eight-carbon ring would be more likely than a six-carbon ring. Organic chemistry would be totally different, and petroleum from the ground would be of a different composition. Algae might not be able to live. "Human beings" as we know them could not exist; they'd be chemically impossible. Alpha is a pretty basic constant.

I saw that there is a debate going on about whether some topics are "mainstream" or "speculative," both in a sticky, and in an announcement as well. Just trying to get along; if ΛCDM cosmology is considered "speculative" here I didn't want to offend. Lambda-CDM is currently being called the "Standard Model of Cosmology." I'm quite surprised not to find it a major subject of conversation with all the interesting baryon acoustic oscillation observations, and interesting large cosmic structure and large cosmic void discoveries that have happened over the last year. I guess you don't discuss cosmology here much. Frankly I haven't found anyplace that does yet. Also I'm surprised there isn't any discussion of ΛCDM cosmology on the Cosmo Basics sticky thread. It's kind of like going to an astronomy site and they don't know the phases of the Moon.

My recollection is the same as swansont's, a handful of thousands of atoms. Supercooled and contained either magnetically or by some BEC effect or other. Aren't BECs coherent? I think it was a National Geographic article on BECs I read it in, IIRC. Perhaps 2006 or 2005; certainly pre-mid-2007.

The value of alpha or α is 1/137. A good way (though not mathematically precise) is to think of it as the chance, given everything else is just right, i.e. the angles of the electron and photon are just right, and they'll intersect at a given spacetime location with a known uncertainty, that an electron and a photon will actually interact. If they were little balls they'd interact every time, since they're subatomic quantum particles they only interact 1/137 of the time. But as I say it's a notionally, but not numerically, accurate answer. So don't get too stuck on the analogy.

I notice that no one is discussing ΛCDM cosmology here. Is this considered "speculative," or do most folks here just not know about it?

By the time the BB happened only 10-42 seconds had elapsed, but the universe was a minimum of tens of billions of light years wide; remember that gravity acts at c. The Universe was never gravitationally bound; it might eventually have been had dark energy not surpassed gravity seven billion years ago. But it was inevitable dark energy should do so; it is a property of space, not of energy and matter. It is lambda, the cosmological constant in the Einstein equation. And the more space there is, the more lambda there is. And space is not conserved.