Well meaningfull is probably a questionable word to use when discussing quantum effects;)
But I think this gives an indication as to why I called the Planck’s distance the smallest meaningful measure of distance –
pdf page.
Cheers, Bippy
Yeah, but Bippy, that sort of assumes that string theory is actually correct and that this inversion happens. I would find it a lot easier to swallow if they could actually make, you know, testable numerical predictions and that sort of thing.
At present, Achernar is entirely correct, as usual; the Planck scales are the scales at which quantum mechanical effects become important in describing gravity and the shape of space-time. How exactly that importance manifests itself is still very much an open question. Heck, we still can’t rule out that some relatively simple naive quantization of gravity is possible and that string theory is completely unnecessary.
Which has taken us rather far afield, now that I look back at it.
Thanks for the info g8rguy, I had thought that it was down to more commonly accepted parts of quantum physics. I have read too many articles (not from the best sources) which seemed to state that distances bellow Planck’s distance were unmeasurable (saying things like the energy necessary to measure a distance, when consentrated within such a small distance scale leads to singularitys at that scale) I’m glad to hear this is not confirmed.
Does this mean that distance may actually exist as a continuum, or is it believed to exist only as a number of quanta? What is the current general view on this?
Sorry but I’ve been away from Physics research for almost 10 years, and am interested in whether any physical measurement can be considered a true continuum (where measurements can theoretically be taken at ever increasing accuracy, never reaching a maximum possible accuracy).
If this requires too much space for this thread, start another, or tell me to start another.
Thanks, Bippy
Time is a dimension and it is currently measured in seconds, minutes, hours, days, weeks, months and years.
The past is exactly 1/30 of a second behind the present. It takes that long for the brain to process information all around it so ant information that had already been assimilated and processed becomes the past. Time is measured in relation to outside changes. There is no time if nothing changes.
One speculation that has appeared throughout this thread, although not conclusive by any means, is that time might be related to c in terms of distance. This would tie into how we see the past today. by looking great distances (telescopes and the like) we are looking back into time because of the time required for light to reach us.
I don’t know how this relates but though I’d throw it in as it does deal with space, time and c.
Well, Bippy, this goes rather outside my area of expertize, but I think the generally accepted view is that no one really knows what happens at really small length scales.
I think it’s safe to say that most of us think that space must be quantized in some way, just like everything else. How exactly that quantization occurs, though, is up in the air. String theory is probably the most popular approach, to be sure. But it’s hardly the only one. I still hold out hope for a quantization of the metric in some way.
I think maybe you have too much confidence in me, g8rguy. I don’t know anything about string theory. The link says you can’t measure below the Planck length. Is that true for the Planck time? It’s certainly not true for the Planck mass, right?
Hell if I know. I’m not a string theorist, I’m just an atomic physicist who would be doing cosmology if he thought he could get a job that way. I can’t see how anything about the inability to measure lengths smaller than the Planck length wouldn’t also apply to the Planck time. Obviously, the Planck mass is a whole separate issue.
But of course, that presumes that the versions of string theory which have this feature (which may be all of them, for all I know) are correct, which is a claim I’d be hesitant to make at present. All I’d say for certain is that something funny happens near the Planck length and Planck time.
About using distance units to measure time: While it’s true that there’s no fundamental reason to measure temporal separations in the same units as spatial separations, there’s also no fundamental reason to measure height in the same units as width. It’s just that if you did use different units (in either of those cases), you’d have to have all sorts of funky conversion factors whenever you rotated something. You don’t want to have to change the units on your meterstick whenever you rotate something in space, and you likewise don’t want to have to change units when you rotate in spacetime. Yes, it’s quite possible to rotate in spacetime: All you need to do is change your velocity.
About the Planck units: The Planck time and Planck distance are the smallest time and distance which we can meaningfully describe, with our current theories. There is currently no strong reason to believe that they’re actually the smallest units possible. And even if there is a hard lower bound, it might not necessarily be exactly at the Planck length. It might just as easily be, say, 137 times the Planck length, or the Planck length over pi, or any of a myriad of other possibilities. The Planck scale is just a rough, back-of-the-envelope estimate of where things start getting weird, and it wouldn’t be surprising if it’s off by an order of magnitude or two. And the Planck scales aren’t even all lower limits, either: The Planck mass, for instance, is about a microgram, which is insanely small compared to “normal” gravitational systems, but insanely large by the standards of particle physics.
The number that I gave (1.4x10[sup]26[/sup] meters) was based on a calculation. It is very likely meaningless, but this is how I arrived at the number.
300,000,000 meters/sec
X 3600 (seconds in an hour)
X 24 (hours in a day)
X 365 (days in a year)
X 15,000,000,000 (years since Big Bang)
I ran your numbers a couple times, rsa, and I consistently get 1.4x10[sup]25[/sup] meters. Methinks you popped in an extra 0 someplace. 
[sub]Like I haven’t done that 10[sup]6[/sup] times, myself.[/sub]
Quite likely Q.E.D. But what’s an order of magnitude among friends.
Indeed. Say, can I borrow $10 from you? 
slipster, I think you have a few problems with your description of how Tipler Cylinders work. I have started a new thread entitled “A few questions about the Tipler Cylinder theory” to discuss 'em, if you’re interested.
Not to say that this is wrong, but the black hole FAQ at http://antwrp.gsfc.nasa.gov/htmltest/gifcity/bh_pub_faq.html says something else that seems hard to reconcile with what Ring said:
“…inside the event horizon, t is actually a spatial direction, and the future corresponds instead to decreasing r.”
and elsewhere, more poetically,
“But as soon as I fall through, I’m doomed. No bungee will help me, since bungees can’t keep Sunday from turning into Monday.”
All of which implies to me that time is in fact literally another spatial dimension, at some kind of angle (right angle?) to the three we customarily do measure in meters, and subject to the pythagorean theorem et cet like all the rest.
Or is this plain wrong?
Or am I missing something here, where another cite could help?
You’ve almost got the Pythagorean theorem bit right, but not quite. In 3D, it tells us
(ds)[sup]2[/sup] = (dx)[sup]2[/sup] + (dy)[sup]2[/sup] + (dz)[sup]2[/sup]
which is to say that the total length is the square root of the sums of the squares of the lengths in the 3 directions. Time doesn’t come in that way. Instead, in 3D with time, we have
(ds)[sup]2[/sup] = -(c dt)[sup]2[/sup] + (dx)[sup]2[/sup] + (dy)[sup]2[/sup] + (dz)[sup]2[/sup]
It’s that minus which makes all the difference.
Regarding black holes, what happens is that inside the event horizon, there’s not a minus but a plus in front of the time part (hence time becomes spacelike). But that’s okay, because there’s a minus in front of the radial part (so that radius becomes timelike). It’s not so much a question of rotating time into space, it’s just, if you like, that time and space do messed up things inside event horizons.
So in 3+1 spacetime if (dx)[sup]2[/sup] + (dy)[sup]2[/sup] + (dz)[sup]2[/sup] < (c dt)[sup]2[/sup] then ds becomes imaginary?!?
Not to put too fine a point on it, but basically yeah.
You could have points separated by positive (ds)[sup]2[/sup], which basically tell you that in 3+1 spacetime something can get there from here. You could have points separated by (ds)[sup]2[/sup] = 0, which tells you that stuff with mass can’t get there from here, but anything travelling at the speed of light could. And you could have points separated by negative (ds)[sup]2[/sup], which tells that you nothing that we know of can get there from here.
For some reason, though, most physicists don’t like imaginary numbers showing up in the answer, so we just say “Done!” when we find (ds)[sup]2[/sup], and don’t bother to take the square root.
OK, But your equation seems to imply that if two points are not separated in space at all then we get (ds)[sup]2[/sup] < 0. Isn’t the minus sign in the wrong place? It actually made sense to me when I made the spatial quantities negative. Then you get a standard light-cone type interpretation (helps to visualize a two dimensional universe with the z-axis as time). You now see that for points with large spatial separation and small time separation you are in the imaginary region outside the light cone and thus in your unreachable zone. With large time difference and small spatial difference you are within the light-cone and the solution is a real. Am I missing something?
Here’s a link that seems to bear this out.