This is why mathematics makes my head hurt...

Vernon on 2/10/2007 at 15:24

good guess, but the correct answer is :idea: cyberspace! :sly:

*Zaccheus* on 2/10/2007 at 16:27

:cheeky:

Koki on 2/10/2007 at 18:36

Quote Posted by belboz

Actually due to there size, the air resembles water and they are actually swimming through it, not flying.

Sorry but Dynamic Stall sounds cooler, I'm going with that.

Spike14 on 11/10/2007 at 22:05

Infinity isn't mathematically quantifiable, due to the eccentricities mentioned in the second post.

Ergo, your pain lies not with mathematics, but much rather with the concept of "infinity" which is something that the human mind finds to be much less than "intuitive".

Marecki on 12/10/2007 at 01:37

Quote Posted by RocketMan

Relativity does NOT prohibit faster than light expansion of space itself. It prohibits sub-luminal matter from surpassing the light barrier, from super-luminal matter dropping below it and from luminal (massless)particles to travel at any other speed.

Quote:

It is in fact almost guaranteed that the universe is wayyyyy bigger than you have suggested because the outer regions of the universe expand faster than any regions closer to the center.

I've got my doubts about the validity of that statement, given the current knowledge postulates an excess of energy and matter ("dark matter" and "dark energy") within the visible universe rather than the opposite. Then again, I might be wrong; would you mind citing a reference?

RocketMan on 12/10/2007 at 02:46

Quote Posted by Marecki

While it is true that general relativity merely forbids massive objects to reach the speed of light in vacuum and therefore allows for faster-than-light travel, that final statement about fixed speed of massless particles is not correct - both photons and gluons can, depending on the medium they are in, travel at a variety of speeds, including zero (see e.g. (http://news.bbc.co.uk/1/hi/sci/tech/1124540.stm)).

I've got my doubts about the validity of that statement, given the current knowledge postulates an excess of energy and matter ("dark matter" and "dark energy") within the visible universe rather than the opposite. Then again, I might be wrong; would you mind citing a reference?

With regards to that first link, I won't challenge its validity. It sounds valid enough. I will however speculate that this is an example of how one's perspective can distort one's understanding of the problem. I don't think the light is actually stopping. I believe it mearly seems to stop and that there must be some sort of interference going on or the light is interacting with the matter somehow directly or indirectly so as to produce a wave with 0 velocity. If that were the case then the light's energy must be stored in the medium in some way. Maybe a standing wave? I dunno. I really doubt light (the photons themselves) can stop because that would violate a shitload of conservation laws and the light wouldn't be light anymore. A light's energy content is a function of plank's constant and its frequency so if you stop light, you necessarily rob it of is energy, thus my suspicion that the medium somehow holds this energy (and in the mean time, the light ceases to exist but is held in the medium). Of course i have no clue but i don't think light can just stop.

With the second problem, I don't see how dark matter has much to do with the size of the universe. It has to do with the speed of inflation and whether or not the universe stops expanding and perhaps contracts at some point. The energy density of the universe has to exceed a certain threshold for there to be enough gravity to bind matter to itself and stop the eternal expansion of space. Since the universe seems to be expanding without any sign of slowing down, it seems there is not enough mass in the universe. This is why dark matter is suggested as a means of accounting for the missing mass. Its not made up or anything but since we can't see it directly, we can't effectively measure the expansion rate of the universe.

(http://en.wikipedia.org/wiki/Big_Crunch)

Marecki on 13/10/2007 at 00:57

Regarding your comments about light, you are in fact correct: at micro scale, photons travel at c regardless of where they are - even if only for the simple reason that even the most dense matter consists mostly of vacuum. Why the lower speed in the macro world then, some may ask? Simple! Given photons travel at c but light in non-vacuum does not, the only logical explanation is that photons don't exist all the time* :P Seriously: approximately speaking, what happens is that original photons use up their energy exciting the medium which in turn emits secondary photons returning to the ground state, those in turn excite the medium a bit further along the path and so on; the light's path appearing to remain unchanged (statistically speaking, direction of emission of secondary photons is, if you don't count special cases, uniformly random) is the result of interference.
Even so, at the macro level it is entirely possible for massless objects to travel slower than c. Hell, a moment after I'd posted my previous reply I remembered it is in fact for massive objects to travel faster than light too! Look up "Cherenkov radiation", for instance - that's when the massive object is electrically charged (as a side note, I hope you'll find a page with pictures on the subject - I've seen Cherenkov light in real life and it's beautiful).

In other words, you would have saved yourself from me being picky had you added "in vacuum" in your original statement :cheeky:

As for the mass excess, speed of expansion and so on - all I'm saying is that just because something is possible doesn't mean it actually happens under normal circumstances, especially if there are alternatives which require less effort. Perhaps some matter does travel faster than light - but maybe it just sits around in forms we cannot detects instead? The universe is lazy... Take subatomic particles, for instance: we've got at least six flavours of quarks but only two of them are stable (or what passes for stable for quarks), a similar thing for leptons, finally even though those two quark flavours could combine in quite a number of ways there is only one stable combination. As a result, out of hundreds of possible forms of matter nature only features four: two stable (the proton and the electron), one only-stable-in-bound-states (the neutron) and one stable-but-with-split-personality (the neutrino).

* whoever got that right has got a good mind to study physics :)

*Zaccheus* on 13/10/2007 at 10:05

Quote Posted by RocketMan

With the second problem, I don't see how dark matter has much to do with the size of the universe. It has to do with the speed of inflation and whether or not the universe stops expanding and perhaps contracts at some point. The energy density of the universe has to exceed a certain threshold for there to be enough gravity to bind matter to itself and stop the eternal expansion of space. Since the universe seems to be expanding without any sign of slowing down, it seems there is not enough mass in the universe. This is why dark matter is suggested as a means of accounting for the missing mass. Its not made up or anything but since we can't see it directly, we can't effectively measure the expansion rate of the universe.

(http://en.wikipedia.org/wiki/Big_Crunch)

I don't understand why, if there were enough matter to stop it expanding indefinitely, the universe would be expanding at all.

Jeshibu on 13/10/2007 at 14:01

Marecki, Cherenkov radiation is the result of something moving faster than the speed of light in that medium (which is influenced by being absorbed and emitted all the time, like you said).

Quote Posted by *Zaccheus*

I don't understand why, if there were enough matter to stop it expanding indefinitely, the universe would be expanding at all.

The big bang.

*Zaccheus* on 13/10/2007 at 18:33

The big bang is not thought to have been an 'explosion'.

As I understand it, scientists think that the universe has been expanding because new 'space' is coming into existence everywhere all the time, even now.

So my question is, why would gravity be able to stop that in the future when it cannot stop it now.