This Slate posting recounts Justin Trudeau’s off-the-cuff description of quantum computing during a press conference. Not just a handsome face, and not just a prime minister! (of Canada) His words:
“Normal computers work, either there’s power going through a wire or not, it’s one or a zero. They’re binary systems. What quantum systems allow for is much more complex information to be encoded into a single bit. A regular computer bit is either a one or zero, on or off; a quantum state could be much more complex than that because as we know things can be both particles and waves at the same time and the uncertainty around quantum states allows us to encode more information into a much smaller computer. That’s what’s exciting about quantum computing…”
Following links from the splendid piece on Trudeau, I was very much struck by this article by Dennis Overbye. From it:
“So where is the center of the universe? Right here. Yes, you are the center of the universe.
“When Albert Einstein married space and time in his theory of relativity back in 1905, he taught us that our eyes are time machines. Nothing can go faster than the speed of light, the cosmic speed limit, and so all information comes to us, to the present, from the past.
“And so Einstein’s relativity teaches us that the center of the universe is everywhere and nowhere. It is the present, surrounded by concentric shells of the past. History racing at you at 186,282 miles per second, the speed of light, the speed of all information. Your eyes are the cockpit of a time machine, filmy wet orbs looking in the only direction any of us can ever look: backward.”
A good article by Overbye about a widely misunderstood matter.
Also often misunderstood is the difference between the Universe and the observable Universe. The former being all of space-time, and the latter being the sphere centered on us from within which light from distant stars has had time to get here. This sphere is expanding at one lightyear per year. Furthermore, those distant objects have been moving away from us since the light we see today left there, so the radius of the observable sphere now is about twice the distance to the most distant objects in our view.
Finally as you can imagine, there must be some objects, say galaxies, so far from us that the space between us is expanding faster than c. Well, in general relativity the concept of velocity is not so simple over global distances, and the universal speed limit, which arises to prevent time paradoxes, is a local concept. Light from those very distant objects heads our way at c, measured where it is. For a while the light heading our way appears to be swept away from us, but eventually it will reach a region that is not being swept away greater than c, and it will begin shortening its distance to us.
When you say “observable” do you mean literally via light in the range our eyes can perceive? Or do you mean all electromagnetic radiation? What about the “speed” of gravity? Am I feeling gravitational attraction at this very moment from a galaxy I will never see and in fact could never see? Inquiring minds…
> [Wayne wrote] When you say “observable” do you mean literally via light in the range our eyes can perceive?
No. Electromagnetic (EM) radiation of all emitted frequencies is coming to us from all directions. Of course no EM radiation was emitted by anything before t = 0. And the early universe was opaque until about t = 500,000 years. The EM radiation that was rattling around then now travels unabsorbed for the most part, and it has been stretched by the expansion to form the 3 K black body radiation.
The earliest stars and galaxies formed a few hundred million years after t = 0. Consider a bright new galaxy that formed around t = 800,000,000. That was 13 billion years ago. If EM radiation from that galaxy is reaching us today it must have left there about 13 billion years ago. Due to the universe’s expansion, all of it is red shifted some amount, so uv might be visible, visible might be in the ir, ir shifted from short to longer wavelength, and so on.
Physicists are not too careful expressing themselves, and you have to attend to context. Usually they will say light when they mean visible EM radiation, only, but light is much shorter than electromagnetic radiation, so they will sometimes use light to refer to ir and uv as well, or even all EM radiation.
> Or do you mean all electromagnetic radiation? What about the “speed” of gravity?
The speed of gravity is c. To prevent paradoxes of time travel and causality, there is a universal speed limit. Forces carried by massless particles travel at that speed, this includes photons and gravitons.
> Am I feeling gravitational attraction at this very moment from a galaxy I will never see and in fact could never see?
No. Such galaxies likely exist, but the news and effects of their existence has not had time to get here during the 13.8 billion years since t =0. The same for their EM radiation, “light”.
This is the idea of the observable universe, a sphere centered on us. Light from things less than 13.8 billion light years from us may have gotten to us, but things that were 15 billion light years away from us 13.8 billion years ago is still on its way.
Our observable universe expands in radius by 1 light year each year.
Consider some distant galaxy. We might be within its observable universe, but its observable universe, we guess, includes things outside our observable universe, and ours has things outside its.