David L. Martin

in praise of science and technology

Faster than Light

In a previous post, I discussed relativity, one of the 3 great scientific revolutions of the 20th century.  Most people have had some exposure to the concept, through science fiction films at the very least.  And many people realize that special relativity holds that no human being can ever travel faster than light – or even travel AS FAST as light.

vega

This is true as far as it goes, and the predictions of relativity have been confirmed over and over.  But it is also quite misleading, and here is an example.  The star Vega, in the constellation Lyra, is one of the brightest stars in our sky.  The reason it is so bright is that it is a very near neighbor, cosmically speaking.  It is “only” about 140 trillion miles from us – this may seem like a lot, but the center of our galaxy is more than 170 QUADRILLION miles from us.  However, light travels very slowly on the cosmic scale.  It takes a particle of light (called a photon) about 25 years to travel from our solar system to Vega, or vice versa.

From these facts we might be tempted to conclude that it would be impossible for a human being to travel to Vega in less than 25 years, and to make the round trip in less than 50 years.  So it may come as a surprise that there is nothing, absolutely nothing in special relativity that says you couldn’t, in principle, make the trip to Vega in 2 years, or 2 days, or 2 minutes for that matter – AS FAR AS YOUR OWN AGING PROCESS IS CONCERNED.  Of course, there’s a catch.  So let’s look at the problem in more detail.

gforce

We’ll ignore the (absolutely enormous) technical problems associated with very high speed travel.  We’re just concerned here with the physics of special relativity.  What does it say about “faster than light” travel?  I build myself a spaceship and climb aboard.  I head off toward Vega.  I accelerate constantly at a very modest 1 g.  This will create a very comfortable artificial gravity – I can walk around the ship much as I would on earth.

Within 350 days, the ship is traveling at about 663 million miles/hour, about 99% of the speed of light.  Its acceleration has been constant, with no limit in sight.  “I’m gonna do it,” I think.  “I’m gonna pass the speed of light.”  And sure enough, within a few days, I seem to.  About 354 days into my flight, I seem to pass the speed of light as if it never existed, and I keep accelerating.  By my own estimation, I MUST have passed it, because I’m still accelerating at a constant 1 g.  It’s a simple calculation.  1 g = 21.93 miles/hour per second.  Accelerating at this rate for a year gives us a speed of about 692 million miles/hour.  The speed of light is about 670 million miles/hour.  And I just keep accelerating.

interstellarspacecraft

When my ship’s chronometer reaches about 3.22 years, I find that I am already halfway to Vega.  Of course I don’t want to simply fly past Vega, so I turn the ship around and start decelerating, again at 1 g.  Eventually the ship comes to a stop at Vega.  Instead of being 25 years older, I am only 6.45 years older!  I did it!  I proved Einstein wrong!  Or did I?

After a brief exploration of the Vega system, I head back to earth.  I do the same thing I did before – accelerating at 1 g until the halfway point, then decelerating at 1 g the rest of the way.  I arrive on earth.  Sure enough, again, I am only 6.45 years older.  The whole trip, which should have taken at least 50 years, has only taken about 12.9 years.  But then I notice something else.  The people on earth are not 12.9 years older.  They are 54 years older.  From their point of view, I didn’t travel 50 light-years in 12.9 years.  It took me 54 years.  From their point of view, I have not exceeded the speed of light – or even reached it.

andromedagalaxy

It turns out that, using a scheme like this, you could reach the Andromeda galaxy in what for you would be a mere 28 years.  This is an apparent speed of more than 70,000 TIMES the speed of light.  The catch of course is that by the time you make it back to earth, at least 4 million years will have passed.  Relativity doesn’t stop you from traversing great distances in short periods of time – from your own point of view.  In fact, nothing in special relativity dictates that an object can’t go galaxy-hopping in a few seconds – again, from its own point of view.

If you want to wave goodbye to your family on earth in the morning, then head off across the galaxy and be home in time for supper – that’s what is prohibited by relativity.  In fact, you can’t even leave our solar system and be home in time for supper.  The speed of light is very, very slow on cosmic scales.  It takes days for light to traverse our solar system.  Years to reach the nearest star.  Millions of years to reach the nearest galaxy.

specialrelativity

One of the most confusing things about relativity is this:  All motion is supposed to be relative.  Therefore, if I am traveling away from earth, earth is also traveling away from me.  If am traveling toward earth, earth is traveling toward me.  No one is “at rest.”  Special relativity says that time on earth is passing more slowly than my time, from my point of view.  But it also says that my time is passing more slowly than earth’s time, from earth’s point of view.  So why do I end up only 12.9 years older, while everyone on earth is 54 years older, when I come back from my Vega trip?  Isn’t everything symmetrical?

The answer is, things are only symmetrical if no one changes their inertial reference frame – in plain English, if no one changes their velocity.  As soon as either object accelerates or decelerates, it changes its inertial reference frame.  Symmetry is broken.  Clearly, if I leave the earth, there’s no way for me to get back to it without SOMEONE changing their velocity.  Either I have to do it, or the earth has to do it, or both.  In my scenario, I’m the one who does it.  That’s why I end up being younger.

speedversusvelocity

“What if you just make a loop around the Vega system, without changing your speed, and head back to earth?” you might ask.  But speed and velocity are 2 different things.  A change in direction is a change in velocity, with or without a change in speed.  It is therefore a change in inertial reference frame and will break the symmetry.

The classic illustration of these issues is what is called the twin paradox.  One of a set of twins stays on earth.  The other heads off into space at high speed.  Eventually the space-faring twin heads back to earth.  Rejoined, they find that the space-faring twin is now younger.  This paradox confuses many.  On the one hand, special relativity demands symmetry.  No one is actually at rest.  But the resolution lies in the fact that when someone (in this case the space-faring twin) changes velocity, he changes his inertial reference frame.  Symmetry is broken.

dopplereffect

On my trip to Vega and back, what do I see?  Well, since it takes me 6.45 years (my time) to get there, it stands to reason that I will have no impression of motion at all, once I get far from the earth.  It will take me days to get out of the solar system.  And for some time, everything outside will look quite normal, other than the fact that the sun is receding into the distance behind me.  But as I accelerate, I will begin to notice that Vega, ahead of me, seems to be changing in color.  From earth, Vega is a blue-white star.  In my ship, it is becoming more purplish.  Meanwhile, the sun behind me seems to be getting more reddish.  As I go faster and faster, Vega gets more purplish.  The other stars ahead of me are getting more bluish, while the sun and other stars behind me seem to be disappearing.  Most the sky is now populated with what appear to be reddish stars.  On top of all of this, the familiar constellations are slowly distorting as the days and weeks go by.  The stars all seem to be migrating slowly toward Vega, directly ahead of me.  Stars that were somewhat behind me now seem to be somewhat in front of me.

As I continue to accelerate, Vega finally seems to wink out altogether.  Directly ahead of me there is only blackness.  Outside of this black area is a ring of purplish stars, and outside of that bluish stars.  There is beginning to be a kind of rainbow effect in the stars.  Meanwhile, behind me is blackness.  Most of the stars I can see are crowding toward my forward view.  Much of the sky now contains reddish stars.  More days and weeks pass.  Now there is a large area of blackness ahead of me, and an even larger area of blackness behind.  Between the two is a kind of rainbow ring of stars surrounding the blackness ahead.  The sky seems very distorted now – all of the stars that are still visible are crowding toward my forward view.  Stars that were once well behind me now seem to be ahead of me.

bowman

As I approach my midpoint, the sky looks very strange indeed.  Most of the sky is completely black.  Ahead of me is also a circle of blackness.  Outside of this is a rainbow ring of stars, firmly in my forward view.  There is no sense of motion, only this strange-looking sky.  The earth and its sun are quite invisible, as is Vega.

As I decelerate, all of this reverses.  The sky slowly returns to its former appearance.  Vega eventually reappears, purplish as first, then bluish.  The constellations return to their familiar shapes.  The sun eventually appears, very red at first, but eventually regaining its familiar yellowish color – of course it is now 25 light-years away, merely a bright star among many.

aberrationoflight

What happened to produce these bizarre effects?  The Doppler shift for one.  Light from objects ahead is blue-shifted at high speed.  Light from objects behind is red-shifted.  In both cases, the light is eventually shifted out of our visual range.  Thus the blackness in forward and rear view.  There is also the aberration of light.  It’s kind of like when you drive through the rain at high speed.  Even if there is no wind, the rain will appear to traveling horizontally toward your windshield.  The faster you go, the more intense the effect.  It’s the same with the light from the stars.  It will appear to come from ahead, even if it’s from the stars to either side of you.  At a great enough speed, all of the starlight, and therefore the images of the stars themselves, will seem to come from the forward view.  The constellations will be highly distorted.  Most of the sky will appear black, because most of the sky shows only the stars that are well behind you – and the light from those stars has been red-shifted out of your visual range.

Some idea of these effects can be gained from watching this video:

https://www.youtube.com/watch?v=0uunSMipnxA

It shows how the aberration of light crowds what is visible to the naked eye toward the forward view, as well as the effects of blue- and red-shifts.  Of course, there would still be plenty of photons coming from within the black circle directly ahead – they just aren’t visible to the naked eye.  In fact, at high speed the high-energy radiation from directly ahead would be a serious danger to anyone on the ship.

highspeed

If you had a camera sensitive to high-energy photons, it would clearly record Vega, still directly ahead of you.  At your midway point it would seem like you’re closing on Vega at well beyond speed of light.  Which you would be – from your own point of view.  From the point of view of earth, the highest speed you would reach on your trip would be about 99.7% of the speed of light.

As incredible as it may seem, the white lines on the floor in the video above would be completely straight for an observer at rest.  The observer is passing over these lines like a car over a series of cross streets.  At high speed the distortion is so great that the cross streets would appear to bend toward his destination, and he would actually see around the corners of buildings on either side.  Of course, we don’t see these kinds of effects on our trip to Vega, because all of the stars are very far from us.  But we do see the distortion of the constellations and the crowding of the stars into our forward view due to the aberration of light.

The technical problems of such “faster than light” travel are quite daunting.  The danger of high-energy radiation that I mentioned is just one of them.  But there’s nothing in physics that says it can’t be done.  Whether it ever WILL be is an entirely different question.  It seems likely that by the time we (or our descendants) master such technologies, the travelers (whether they are human or not) that will make such journeys will have lifespans measured in centuries rather than years.  The “time problem” will therefore solve itself.  And there is an even more exotic possibility.

beaming

In the many versions of Star Trek, people “beam” from one place to another.  Presumably, while the person’s pattern is in transit, there is no active consciousness.  The individual winks out of existence at the starting point, and is materialized at the destination – with no consciousness of the passage of time in between.  So this would amount to an instantaneous journey, REGARDLESS OF THE DISTANCE TRAVELED, for the person “beaming.”  A trip to another galaxy would be as instantaneous as a trip across town.  Of course, it would require a sophisticated “reader” that would record the person’s every atom, from head to foot, and an even more sophisticated replicator at the other end, to reconstruct them.  And if the beam involved was a light beam (visible or invisible), this still doesn’t get around the speed of light limit.  You still couldn’t “beam” across the galaxy in the morning and be back to earth in time for supper.

Some scientists have raised objections about whether this is actually possible, even in principle.  Perhaps there are aspects of the functioning of the human body, and particularly human consciousness, that simply can’t be “copied” in this way.  Perhaps the function of the brain incorporates some genuine quantum randomness – if so, you would inevitably lose some of who you are in the so-called “copying.”  We really don’t know.  And of course the technical obstacles involved in “reading” an entire human being and reconstructing them elsewhere are extremely daunting.  But it remains a possibility in principle.

wormhole

If it is possible, then conscious beings, human or not, could, in principle, hop around the galaxy essentially instantaneously, once all of the technology was in place – although it would take tens of thousands of earth years to put the technology in place in only 1 quadrant of the galaxy.  To travel to the center of the galaxy and back would take about 60,000 years of earth time.  There’s no way around it, if Einstein was right.  Are there other, even more exotic possibilities?  Shortcuts through other dimensions of space and/or time?  Wormholes connecting very distant places to one another?  Some sort of space/time-warping drive that “cheats” special relativity?  Who knows?

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