New Study Shows Universe Still Expanding On Schedule
The Bad Astronomer writes "A century ago, astronomers (including Edwin Hubble) discovered the Universe was expanding. Using the same methods — but this time with observations from an orbiting infrared space telescope — a new study confirms this expansion, and nails the rate with higher precision than done before. If you're curious, the expansion rate found was 74.3 +/- 2.1 kilometers per second per megaparsec — almost precisely in line with previous measurements."
Hilbert Space
Yesterday's Weirdness is Tomorrow's Reason Why
Nothingness. There is no space & time outside the physical universe. If that doesn't bake your noodle, I don't know what will.
The nice thing about Religion^H^H^^H^H^ science is that it advances one funeral at a time. (With apologies to Max Planck :)
Due to expansion, the speed of objects accelerating away from us is proportional to the distance from us. So according to this, an object at 1 megaparsec from us will be receding at 74.3 km/s, while an object at twice the distance will be moving twice as fast.
We hope your rules and wisdom choke you / Now we are one in everlasting peace
No, a *parsec* is 3.26 light years. A Megaparsec is 3.26 MILLION light years.
General Relativity: Space-time tells matter where to go; Matter tells space-time what shape to be.
Unless you have a generic curiosity, don't try to hard to read that, as it is not related to the universe's expansion. The grandparent was just being random or joking. A Hilbert space is just what you get when you treat the set of all continuous functions as a vector space. It has several different possible basis sets of functions you can add up to make any other function, e.g. sine waves via Fourier analysis. Instead of having unit vectors like x, y, and z, you would have unit vectors like sin(x), sin(2x), sin(3x), etc. (which makes it infinite dimensional). The concept is really important to physics, especially quantum mechanics and any where else things like Fourier analysis would be done with some mathematical rigor. But it is not what the universe is expanding into.
The typical analogy used for what the universe is expanding into is like a balloon being inflated, with that being a 2D universe on the surface of the balloon. You could ask about the third dimension it is expanding into, but that is not really relevant (at the moment at least). The only thing that really matters is the curvature of local space (how non-flat any given spot on the balloon is). Short of discovering some new theories unlike what we've seen before or something like brane theory, the equivalent of the 3D dimension in the balloon analogy would be unreachable and meaningless, as it would not be able to affect things in anyway beyond the curvature of the surface.
Space itself can expand FTL, but anything inside that space is limited to c. This also means that at any given point in the universe, there is a boundary where you can never reach beyond, because the space itself is expanding away FTL, so you can never catch up to observe anything beyond that boundary...
"There is no space & time outside the physical universe.
Are you sure? How do you know?"
He doesn't need to know: that's a per-definition fact.
A different question would be if the physical universe is composed of four dimensions or there are more.
Space itself can expand such that the objects (events?) within it are moving apart at faster than c. Any two objects separating faster than c can't measure that -- they cannot pass any signal between them. Any light (or other signal) which leaves one will be redshifted away to nothing before it gets to the other. They are outside each other's observable universe. I'm pretty sure this has to handled using General Relativity, I don't think Special Relativity has any concept of expanding or contracting space-time. Space-time described by Special Relativity is flat and static.