Light’s hourglass

The Colour of MagicMarnix Van Den Broeke ©RHI/Bill Kaye

Marnix Van Den Broeke as Death
in BBC’s The Colour of Magic
Image ©RHI/Bill Kaye

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

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