The Edges of The Universe

<chirp, chirp> “Moire here.”

“Um, Uncle Sy?”

“Hi, Teena! I didn’t know you knew my phone number. It’s past your bedtime. How are you? Is everything OK?”

“I’m fine. Mommie dialed you for me. I had a question she said you could answer better than her and that would be my bedtime story.”

“Your Mommie’s a very smart person in several ways. What’s your question?”

“Where’s the edge of the Universe?”

“Whoa! Where’d that question come from?”

“Well, I was lying on my bed and I thought, the edge of me is my skin and the edge of my room is the walls and the edge of our block is the street but I don’t know what any of the bigger edges are so I asked Mommie and she said to ask you. She’s writing something.”

“Of course she is. One answer is you’re smack on an edge, but some people think that’s a wrong answer so let’s talk about all the edges, OK?”

“On an edge??!? I’m in the middle of my bed.”

“Hey, I heard you sit up. Lie back down, this is supposed to be a bedtime story so we’re supposed to be calm, OK? All right, now. Once upon a time —”

“Really?”

“Yes, really. Now hush and let me start. Once upon a time, people thought that the sky was a solid bowl or maybe a curtain that came down all the way to meet the Earth just over the horizon, and that was the edge of the Universe. But then people started traveling and they realized that the horizon moved when they did.”

“Like rainbows.”

“Exactly like rainbows. Eventually they’d traveled everywhere they could walk. As they went they made maps. According to the maps, the world they knew about was surrounded by ocean so the edge of the Universe was the ocean.”

“Except for Moana’s people that crossed the ocean.”

“Right, but even they only went from island to island. Their version of a map was as flat as the paper maps the European and Chinese explorers used.”

“But the world is really round like my world ball.”

“Yes, it is. It took humans a long time to accept that, because it meant their world couldn’t be all there is. A round world would have to float in space. Think about this — what’s the edge of our world?”

“Umm … the air?”

“Very good, sweetie. Way up, 60 miles high, the air gets so thin that we call that height the Edge of Space.”

“That’s the inside edge of space. Where’s the outside edge of space?”

“It’s moved outward as our astronomers have gotten better at looking far away. For a long time they thought that the outermost stars in our Milky Way galaxy marked the edge of the Universe. Then an astronomer named Edwin Hubble—”

“Oh, like the Hubble Space Telescope that made the pretty pictures in my ‘Stronomy book!”

“Mm-hm, the Hubble was named for him because he did such important work. Anyway, he showed that what people thought were stardust clouds inside the Milky Way were actually other galaxies like ours but far, far away. With the Hubble and other telescopes we’ve pushed out our known Universe to … I don’t even know the name of such a big number.”

“So that’s the edge?”

“We don’t think so, but we don’t know. Maybe space and galaxies go on forever, maybe galaxies peter out but space goes on, maybe something weird. But there’s a special ‘direction’ that we think does have an edge, maybe two.”

<yawn> “What’s that?”

“Time. One edge was the Big Bang, fourteen billion years ago. We’re pretty sure of that one. The scientists and philosophers argue about whether there’s another edge.”

“Wouldn’t jus’ be f’rever?”

“Mr Einstein thought it would. In fact, he thought that the future is as solidly real as the past is and we’re just watching from the windows of a train rolling along the time tracks.”

“Don’ like that, wanna do diffren’ things.”

“Me, too, sweetie. I prefer the idea that the future doesn’t exist yet; we’re on the front edge of time, building as we go. Dream about that, OK?”

“Okayyyyyy

~~ Rich Olcott

Light’s hourglass

Terry Pratchett’s anthropomorphic character Death (who always speaks in UPPER CASE with a voice that sounds like tombstones falling) has a thing about hourglasses.  So do physicists, but theirs don’t have sand in them.  And they don’t so much represent Eternity as describe it.  Maybe.

The prior post was all about spacetime events (an event is the combination of a specific (x,y,z) spatial location with a specific time t) and how the Minkowski diagram divides the Universe into mutually exclusive pieces:

  • “look but don’t touch” — the past, all the spacetime events which could have caused something to happen where/when we are
  • “touch but don’t look” — the future, the events where/when we can cause something to happen
  • “no look, no touch” — the spacelike part that’s so far away that light can’t reach us and we can’t reach it without breaching Einstein’s speed-of-light constraint
  • “here and now” — the tiny point in spacetime with address (ct,x,y,z)=(0,0,0,0)

Light_s hourglassLast week’s Minkowski diagram was two-dimensional.  It showed time running along the vertical axis and Pythagorean distance d=√(x²+y²+z²) along the horizontal one.  That was OK in the days before computer graphics, but it  loaded many different events onto the same point on the chart.  For instance, (0,1,0,0), (0,-1,0,0), (0,0,1,0) and (0,0,0,1) (and more) are all at d=1.

This chart is one dimension closer to what the physicists really think about.  Here we have x and y along distinct axes.  The z axis is perpendicular to all three, and if you can visualize that you’re better at it than I am.  The xy plane (and the xyz cube if you’re good at it) is perpendicular to t.

That orange line was in last week’s diagram and it means the same thing in this one.  It contains events that can use light-speed somehow to communicate with the here-and-now event.  But now we see that the line into the future is just part of a cone (or a hypercone if you’re good at it).

If we ignite a flash of light at time t=0, at any positive time t that lightwave will have expanded to a circle (or bubble) with radius d=c·t. The circles form the “future” cone.

Another cone extends into the past.  It’s made up of all the events from which a flash of light at time at some negative t would reach the here-and-now event.

The diagram raises four hotly debated questions:

  • Is the pastward cone actually pear-shaped?  It’s supposed to go back to The Very Beginning.  That’s The Big Bang when the Universe was infinitesimally small.  Back then d for even the furthest event from (ct,0,0,0) should have been much smaller than the nanometers-to-lightyears range of sizes we’re familiar with today.  But spacetime was smaller, too, so maybe everything just expanded in sync once we got past Cosmic Inflation.  We may never know the answer.
  • What’s outside the cones?  You think what you see around you is right now?  Sorry.  If the screen you’re reading this on is a typical 30 inches or so distant, the light you’re seeing left the screen 2½ nanoseconds ago.  Things might have changed since then.  We can see no further into the Universe than 14 billion lightyears, and even that only tells us what happened 14 billion years ago.  Are there even now other Earth-ish civilizations just 15 billion lightyears away from us?  We may never know the answer.
  • How big is “here-and-now”?  We think of it as a size=zero mathematical point, but there are technical grounds to think that the smallest possible distance is the Planck length, 1.62×10-35 meters.  Do incidents that might affect us occur at a smaller scale than that?  Is time quantized?  We may never know the answers.
  • Do the contents of the futureward cone “already” exist in some sense, or do we truly have free will?  Einstein thought we live in a block universe, with events in future time as fixed as those in past time.  Other thinkers hold that neither past not future are real.  I like the growing block alternative, in which the past is real and fixed but the future exists as maybes.  We may never know the answer.

~~ Rich Olcott