Seeing Space-time

Minkowski chose some interesting terms to describe the area inside the light cones:

  • The world
  • The universe
  • Reality

People wondered if he was using the terms ironically.  He said he wasn’t, and I believe him.

There are a couple of important philosophical implications.

The first has to do with the way we look at objects inside of this universe.  Although these objects look three-dimensional, we have to think of them as four-dimensional objects, where time is the fourth dimension.

What would you look like, in Minkowski space?

First think of what you would look like if you  could see yourself at every stage of life, past-present-future, all at once.

Vector silhouette of man.

This picture is is a composite.  It shows several slices of life, each taken at a particular moment.   You have to integrate these things in your mind, so that you wind up looking sort of like a sausage, one that’s real little at one end and kind of medium-sized and wrinkly on the other.

You aren’t just sitting still your whole life, so you have to account for movement too.  In Minkowski space-time, an object is described as something called a “world line.”  Something moving at constant velocity makes a straight line at an angle to the axis of time.  One that’s accelerating would make a curve.  Something going around and around, like the earth orbiting the sun, would make a spiral.  The path this object takes through space and time is the thing itself.

From Stanford University

This world-line concept is powerful on a philosophical basis.  It’s helpful to think of humans as objects that exist across the dimension of time.  When my daughter was a teenager, and was going through her door-slamming phase, it was helpful to think of her as an adorable four-year-old, as a cute baby, and as the lovely young lady she turned out to be, and remember that the surly teenager was all of those things.

I met an old woman in a nursing home once who supposedly had Alzheimer’s disease.  As it turns out, she wasn’t as demented as everyone thought.  I think she was just pissed.  Once I got her out of her shell, she talked her head off, and it was obvious she knew what was going on.

The story she chose to tell me about herself was the story of her being an Army nurse in World War II.  She told me how odd it seemed that everyone was wearing brown underwear, until she engrealized that hanging white laundry out to dry was like saying “drop your bombs here” to the German pilots.  She told stories about riding her bicycle into London, where she would go out dancing with the British boys while the blitz was going on.  The point being, she was not always a wrinkled-up, frail 90-year-old.  She still sees herself as a beautiful, young nurse doing important work, and living life right down to the bone.

And moreover, she  sees the role that she played in the march of time.  That the things she did, no matter how small the influence, had some sort of effect on how the world turned out, and how it would turn out in the future.

This is the key insight my patients need, if they are to face their death with dignity and courage, without the benefit of faith.  It is the only way to look at our existence on this earth as something meaningful.

But, there’s bad news in there as well.  And it has to do with the notion of relativity of time.

This is a trickier concept that the notion of relativity of velocity.  I think it’s helpful to think on astronomical terms, because the concept makes more intuitive sense that way.

The simplest way to understand the relativity of time is to think about the relativity of simultaneity.  Events that seem simultaneous to one observer might not seem simultaneous to another.

Let’s say I’m an astronomer working at the Palomar observatory, and lo and behold, while imgreslooking  through my telescope I notice that two stars go supernova at precisely the same time.  I get all excited and call my buddy over at Lowell to tell him the news.

“You’re an idiot,” he says.  “You have no idea if those two stars went supernova at the same time.”   Suppose the first star is 10 light-years away, and the other is 20 light-years away.  The second  star would have to blow 10 years before the first for the light to reach my eyes at the same time.

But what if they are both 20 light-years away?  That makes it simultaneous, doesn’t it?

No.  If my buddy at Lowell happened to be in  a spaceship outside the solar system, say 10 light-years from one and 20 light-years from the other, then the supernovas wouldn’t be anywhere near simultaneous.

So were they simultaneous, or not?  There is no defined answer to that question.  It all just depends on how you look at it.

Now, simultaneity is a key feature of time.  If time is a real thing, then two events are either simultaneous or they aren’t.  If they aren’t, then you can say which one occurred first and which one occurred second.  If you look at the supernova example, different observers may say star A blew first, star B blew first, or that they blew at the same time.  Time is relative; and one way of looking at things that are relative is that they don’t actually exist, not in any objective sense.

There are some crazy implications.  If you have two identical clocks sitting on your dresser, they will show the same time forever.  Take one clock, put it in a rocket and send it into orbit, hope it  survives re-entry, retrieve it and put it back on the dresser.  Believe it or not, the clocks will now show different times.  The one that went on the trip will be behind.

Or, you could launch yourself into space, travel at near light speed to the nearest star and back.  When you come back to earth ten or twelve years later, you’ll find that you haven’t aged as much as your friends and family did, while you were gone.  Depending on the gravitational fields you encounter, you might find that your friends and family have aged considerably; they might even be dead and gone by the time you get back, whereas in your world, you haven’t even reached middle age yet.     Christopher Nolan’s movie


“Interstellar” plays with these concepts of space and time, as he also ponders the question of what it means to be human.  (Well worth watching; I think I’ve seen it 15 times and I get something more out of it with each viewing.)  

Here’s the part you might not want to hear.

Space, time, and the speed of light are all related, and they are all related in terms of reality.  If time is relative, guess what.  Reality is relative also.

Go back and look at the Minkowski diagram.  The boundary of reality is represented by the light cone.  That boundary is relative to you.  The guy standing ten feet from you has his own light cone.  He is living in a slightly different reality.  Where your light cones intersect, there is a shared reality.  As for where the light cones don’t intersect — well, there are things in your world that can’t possibly exist in his world.  If it’s your plan to “live in the present,” I expect you’ll be lonely.  (Way I look at that diagram, I wonder if anything actually exists at all in the present moment).


Now, to be clear, you guys have realities that do overlap to a  very great extent.  In order for there to be a significant gap, you would have to be really far apart, and I don’t know that it would be fair,then, to say you are travelling in the same frame of reference.

This concept of “frame of reference” is important.  Another word for “frame of reference” is “a chunk of space.”  To have a shared reality — one where, say, clocks all keep the same time — you and your buddy need to occupy the same chunk of space.   When you look around, space all looks about the same.  It appears to be indivisible.  Not so, says Einstein.  It’s more helpful to think of space as existing in chunks, and one chunk might not be the same as the next. It just depends on where it’s going, and how fast.  And how warped it is.  If you’ve ever been dusted off by some lunatic on a Ducati, you know what I’m talking about.   (Note: Einstein got the last laugh. We’ve been talking about the Theory of Special Relativity, which was based on the work of Minkowski and many others.   Einstein’s Theory of General Relativity showed space actually has to have five dimensions.  Who’s the dope now, eh.)

With regard to the people near you, you can agree on a lot of things.  Among them, you can agree on a conceptualization of time.  As long as you are  in the same frame of reference — meaning, you’re close, and in the space you both occupy, you are both traveling in the


roughly the same direction —  then things that seem simultaneous to you will probably seem simultaneous to her, also.  The converse also applies.   If you’re trying to come up with a theory of cause-and-effect — in other words, how an earlier event is related to a later event — your theories might differ a little, but you should at least be able to agree on what happened first, and what happened second.   Take off in your own direction, and things will be substantially different.

There are more people on this planet than just the two of you.  There are some 7 billion people on earth traveling in the same frame of reference.  We have an extensively overlapped common reality.  And, as far as we are concerned, that’s it.  Modern physicists say space exists, there really is a three-dimensional matrix that has matter and energy stuck to it, things we can see and touch and feel.  But that’s only from the God’s-eye view.  There is no such

So awesome.

thing as objective reality, not from where we’re standing. (Check out the Lilly Tomlin quote in physicist Lisa Randall’s “Warped Passages.”)

Whether “reality by committee” bothers you or not depends on how you view the world.  If you think the shared reality is awful, then there’s hope I suppose.  On the other hand, if you can only see yourself as a three-dimensional object hurtling through space, you have to question whether you exist.   It all depends on your definition of “you.”

Go outside, and look up at the sky.  Remember, you’re only sort of looking out into space.  It would also be correct to say you are looking back in time.  You can see pretty far back, but not all the way.  In that respect, you’re no different than a cave man.

But we aren’t cave-men anymore.  As astronomers developed better and better telescopes, they developed the ability to look further and further into the past.  Or to listen, using radio telescopes.  As we really started reaching into the depths of time with these instruments, we started to encounter an odd signal.  It was a high energy signal, suggesting that we were listening to something really big. But we couldn’t localize it.  It seemed to be coming from everywhere in the sky at once.

Well, not from the sky.  That’s a flat-earth concept..

Hop in your souped-up starship and go for a ride.  Get way out there, in interstellar space. Far enough out so the glare of the sun doesn’t mess up your view of the stars.  Out there where planets won’t block your view.  Jump into your space suit, hook up your tether, and go out for a walk.

Seems peaceful, doesn’t it?   Until you start thinking about it.  You wonder if you are sitting still, or bombing through umpteen dimensions at the speed of light.  Best to quiet your mind and not concern yourself with such things, because it doesn’t matter.  You perceive that you are in the center of your own universe, and out here in your own frame of reference, you are.


Now you see that the signal you detected back there on earth is coming from all around you.  It is coming from everywhere at once.  What is it?

If the past is in every direction around you, then the thing you hear is coming from everywhere in the past at once.  There’s only one thing it could be.

You carry within you an archaic memory of a time when people said they knew that sound.  Rumor has it, it was a word.  The Greeks remember it was a word – Logos – but they couldn’t seem to remember what word it was.  Their spiritual ancestors who settled on the shores of the Black Sea thought they knew what it was.


Hear it?  It’s the sound of the Big Bang.

Couple of questions.

First.  If the past is all around you, then where is the future?

Second.  The Hindus say there is a singularity at the beginning and end of each cycle of creation.  We still sort of buy into that concept.  We believe the universe came flying out of a singularity at the beginning of time, and some of us think the whole thing will end when the last molecule of matter gets sucked into the last giant black hole at the end of time.

As for these singularities we perceive at the beginning and the end of the universe: to whose universe do you refer?


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