i came across the assertion that weirdness abounds below planck’s length (1.616x10[sup]-33[/sup] m). one half of planck’s length is indistinguishable from twice planck’s length.
–aggida-aggida-aggida–
what? the hell? can someone explain this to me? does this hold true for planck’s length of time, as well? was this an unexpected paradox, or was this part and parcel since planck formulated his law?
and more to the point, does this mean that i may, in point of fact, be 1.293x10[sup]-66[/sup] m tall?
Long answer is, “we don’t know, but we have a few hints.”
By fooling around with fundamental constants, you too can come up with the Planck length and the Planck time. They are considered sort of the borders where we don’t know what goes on. In some formulations of theory, when we try to combine gravity and quantum mechanics we end up with absolute absurdities at about the Planck length/time. Other ways of thinking about the problem afford us utter complexity that no one has been able to work out yet. This is the current state of superstring theory at this time. It’s one of the more popular fields for people to go into. The reward is, if you come up with the right theory, you will be the next Newton/Einstein. The downfall is many people since Einstein have been working on the problem and we don’t seem to be none the more closer.
Right now, our clues about what happens at the Planck length aren’t very many. It’s so small, you see, that we really have a hard time probing it experimentally. That and the fact that the Heisenberg Uncertainty Principle enjoys messing with us when we really try to figure out where we are to really fine precision. Without seeing the text you’re reading, I’m guessing that that may be what the “1/2 the length and twice the length are indistinguishable” may be about: The indeterminacy of position and momentum is a necessary consequence of quantum mechanical considerations. The same problem holds true for Planck time-scales as well. It is impossible to know with arbitrary accuracy the time taken for an event and the amount of energy. Current thought is that the higher we go in energies, the closer we will be to understanding all this weirdness. This is just as good an approach as any I’ve heard and has some good theoretical rationale behind it as well. To some extent, for some time now, physics has been taking something of a wait-and-see approach to paradigmatic development. There is clearly something going on we don’t yet have our finger on, but nobody has been able to describe exactly what that something is.
As for your last question: you, jb, are not a quantum object. I think. Unless electrons suddenly gained consciousness when we weren’t looking. In any case, as far as we can tell the world that we work and live in is generally not indeterminate like the quantum world. You are somewhere and you are not somewhere else. You are the height you are and not 66 orders of magnitude smaller.
I think what he’s referring to are the various (5 or 6) string theories which turn out to be dual forms of M theory (for example, see here). Two of these theories (IIRC) are dual under r <-> R[sub]Planck[/sub] / r , a duality mapping large distances to sub-Planck distances and vice versa.
Unfortunately for the original poster, I don’t really know anything about this, so I can’t give a coherent answer. But I think that’s the question, anyway. (You might be able to find something interesting with a Google search including terms like “M theory” “1/r” “duality”.)
Are you talking about the spin of a particle? Some particles dont ‘look the same’ unless you spin them 2 times. Those particles are said to have a 1/2 spin…I have no clue why but im guessing it has to do with some really complicated (and ‘shady’) math…
Omphaloskeptic, you are dead on with the R–1/r duality. on the nose. why, pray tell, aren’t you contributing to this thread?
anyway, i’m not reading a text, per se. just surfing. i came across this duality when googling (yahooing, actually, but yahoo uses google, soo… yeah) on Brian Greene.
off-topic brain wandering follows:
the big bang seed is considered to be at planck size, right? i can imagine a homogenous, almost non-universe, in which a weird planck-sized heterogeneity popped up for a brief instant, and then shrank away to nothing quickly (keep in mind, limits- getting closer to nothing, but never reaching it). with R–1/r, this shrinking away would be equivalent to a hyper-expansion.
it’s like the big bang and the big crunch are even more intimately connected that i ever thought. i don’t remember the details at the moment, but in A Brief History of Time, Hawking talks of a post-Big Crunch collapsing universe as being equivalent to a pre expanding one. because all but one arrows of time reverse, maybe. again, don’t have the book and am shaky in my memory.
No, the “Big Bang seed” needn’t be any size at all. A Planck length is just game playing with constants. Most of the string theory stuff you read about is simply speculation, and this is no exception. A lot of this stuff has taken on the “what if…?” brand of running with the ball which will be useful if and when someone comes up with the right model. Until then, it’s probably best to not get too overly-concerned with any one idea.
BlahMan – no need to talk disparagingly about ‘shady’ math in quantum spin measurements. It’s well observed and a very real quantity (though TOTALLY unrelated to this topic). Also, half spin does not mean you spin a particle two times! It is simply an artifact of the way the angular momentum eigenstates work out in relation to Planck’s constant.
What??? My CRS disease must be really really bad, I coulda sworn thats what the Hawk King said…opening A Brief History of Time…
Page 66&67:
These particles have a property called spin. One way of thinking of spin is to imagine the particles as little tops spinning about an axis. blah blah blah What the spin of a particle really tells us is what the particle looks like from different directions. Spin 0…looks the same from every direction. Spin 1…Only if one turns it 360 degrees does it look the same. blah blah blah …there are particles that do not look the same if you turn them through one revolution: you have to turn them through 2 complete revolutions! Such particles are said to have a spin of 1/2.
Is this way off from the way it really is? Should I post this as a new thread in General Questions?
Also I said ‘shady’ math because I assume there is no way to actually ‘look’ at a particle…
-Blah
Blah, Hawking is simplifying things for you. The math is quite okay; there are a bajillion implications of spin and all of them work out the way the math predicts. One property of spin 1/2 objects is that a 360 degree rotation on the spinor (the thing that describes the spin) gives you the same thing back, only with a minus sign; in order to rotate a spin 1/2 spinor and get the same sign back, you need 2 full rotations. That is not to say that they actually look different if you spin them around once.
Again, g8rguy with the one-two knockdown! Problem is Hawking is talking about spin to people who have a different idea of what “spin” is in their heads than physicists do. While there are similarities, thinking about particles as spinning tops is pretty misleading. For one, particles actually have angular momentum other than spin. It’s pretty hard to explain that concept classically.
I’m afraid I don’t understand what you’re talking about here. There are definitely ways to ‘look’ at the particle. Measurements of spins are done all the time in the lab with no “shadinesss” and no smoke-and-mirrors.
