Dr. Jekyll

Thanks for the reply Martin! Since I'm a bit drunk again, let us divide: (13.7e9/sqrt(0.003))/1e9 = 250 billion light years. How is [math]\Omega_k[/math] or [math]\Omega_{tot}[/math] estimated? I don't remeber the details, and weeding through the Nasa articles to refresh is a bit tedious. [math]\Omega_{tot}=\Omega_m+\Omega_r+\Omega_k+\Omega_{\Lambda}[/math] correct? I mean, does WMAP data give a [math]\Omega_{tot}[/math] (loosely speaking), and then we can derive [math]\Omega_k[/math]. Or, is [math]\Omega_m[/math], [math]\Omega_k[/math], etc. measured and they sum up to give a value of [math]\Omega_{tot}[/math]? I have assumed the latter.

Everytime I get into this subject I get confused. All these [math]\Omega_j[/math] and [math]\Lambda_k[/math]. Hmm...now, where was I? Oh here, let us take the latest WMAP-data. Maybe I got some decimals wrong (disregard that), but let us assume a density parameter as [math] \Omega_{tot}=1.003 \pm 0.010[/math] I'm a bit drunk atm, , but [math]\Omega_{tot}[/math] is a sum of different ratios (density ratios), also including a possible cosmological constant - [math]\Lambda_{something}[/math]? Now, assume, hypotetically, that [math]\Omega_{tot}=1.0000000...[/math]. As I get it, that only implies that the universe will expand on and on. However, the universe CAN still be closed. Which parameters measured, determine if the universe is spatially closed or open? Back in the mid 90s, when I studied physics, it was thought that it all depends on gravity vs. mass. But, now we all know that shit is wrong due to dark energy. So, can someone (Martin?) elaborate on this subject?

When it comes to microinjection of cells, I've seen quite varying magnifications used, around 50X-300X. I figure it depends a lot on the type/size of the cell, and where in the cell the injection shall be, but still it feels like rather small magnifications. Can anyone elaborate some?

Just a mind twisting remark. Mathematically, universe could be finite in volume but spatially infinite. (Disregarding established models)

At present I would say that we do not have enough data or/and lacking some theoretics to determine the case. But, if I would place a bet I would go for a finite universe; that I "believe." (If we discard scenarios/assumptions as, e.g., other, additional universes that could sum up to "infinitely many finite universes.")

Have there been any new discoveries/data regarding this? Got the impression from the latest WMAP articles, and statements from cosmologists regarding WMAP, that they seem "more confident" that universe is flat/infinite.

I read the SciAm article, I have seen it before but didn't pay much attention to the Hubbe distance-part . It is 100% clear that light from galaxies beyond the Hubble distance can reach us, if the Hubble constant decreases. But, I thought that the Hubble constant increases with time, since the expansion of the universe is accelerating. I mean, that for a distance [math]d[/math] we have [math]v(t)=H(t)d[/math] and the expansion of the universe is accelerating giving [math]v'(t)>0 \Rightarrow v'(t)=H'(t)d>0 \Rightarrow H'(t)>0[/math]. I guess I misunderstood something? Physics wasn't my major, math was!

Indeed! Hahaha . However, everyone who has tried to prove something has at one time or another ended up with 0=0, 1=1 or such. To defend the poster, I think it is a very important equation since it tells us we have ****ed up!

Trick question: What if [math]T=a[/math]? Quite surprised none even mentioned that (it was my first thought), maybe I overlooked some defs..

I take a 2 by 3 case as example and you can work out the general m by n case easily. Let [math]a= \left[\begin{array}{c} a_1 \\ a_2\\ \end{array} \right] [/math] and [math]b= \left[\begin{array}{c} b_1 \\ b_2\\ b_3\\ \end{array} \right] [/math] Then [math]ab^T=\left[\begin{array}{ccc} a_1b_1 & a_1b_2 & a_1b_3\\ a_2b_1 & a_2b_2 & a_2b_3\\ \end{array} \right] [/math] Each column vector is on the form [math]b_i \left[\begin{array}{c} a_1 \\ a_2\\ \end{array} \right] \ \ i=1,2,3.[/math] Then all column vectors are linear dependent, i.e., column rank is 1. If we discard the knowledge that row and column rank are equal, the same applies to the row rank, as each row vector is on the form [math]a_i \left[\begin{array}{ccc} b_1 & b_2 & b_3\\ \end{array} \right] \ \ i=1,2.[/math] All rows are linear dependent and row rank is 1.

I only got a BA in physics and it was around 13yrs ago since I studied physics, at that point the accelerated expansion of universe wasn't even known. I know that the expansion of space does not contradict the typical "information being send faster than light," in relativity. I just thought that it is possible to set up the typical thought experiment "traveling train on a rail that emits light" and also include expansion of space. I figure that the expansion of space does not play any role, and we still get the same SR formulas. But I havn't sat down and calculated on it. Yes, I mixed up Hubble radius with cosmic horizon. I meant Hubble radius. If we get signals from galaxies outside the Hubble radius, then if we traveled at the speed of light (hypothetically) we could go there? The converse is true, since those galaxies sends information to us at the speed of light. Maybe I misunderstood your post where you say one could only reach z=1.7 galaxies when traveling at the speed of light, I got the impression that those galaxies are at the Hubble radius. I imagined that the Hubble radius would be kinda like the event horizon. When a galaxy exits the Hubble radius, we would only observe photons emitted at that boundary. Forever and ever, similar to what you as an outside observer would see when an object hits the event horizon. I will check out the SciAm article, I figure it clears things up!

First I thought it was monomial, but that is without any coefficient. It seems as a monomial [math]x^n[/math] with a coefficient is called "term." http://mathworld.wolfram.com/Monomial.html http://mathworld.wolfram.com/Term.html

Yes, I find this interesting. The galaxis (well "any space") at the cosmic horizon travels away from us at the speed of light, and the galaxies beyond at an even greater speed. How does relativity theory handle these velocities, that arise due to the expansion of space? If we can observe galaxies beyond the cosmic horizon, we must be observing them as they were just before they exited the horizon, or? Is the cosmic horizon something like the event horizon for a black hole? Do all these questions have an answer? If not, why?

Hello Pete! Can't one just re-measure the particles? I mean, then you should get the same result as the previous. If the results are the same, the particles are no longer entangled, or they never were entangled.

Oki, thanks! I have no intuition regarding the size of such small quantities, e.g., 0.05ml. Didn't even bother to make a simple calculation of it, since I figured it would be kinda like dipping a needle in a cup of water . But, it is much larger than I thought: [math](0.05\times 10^{-3})^{1/3}\approx 3.7\textrm{mm}^3[/math].