The Fast and the Furious in Spacetime


The theory of relativity is counterintuitive. It defies our every day experiences with wild notions such as time dilation and length contraction.

It’s difficult to grasp the speed of light as a hard limit on how fast something can move. Why can’t I go faster? If I’m cruising down the freeway, a little more gas allows me to go as fast as I want. Eventually, my car reaches its engineering limit, but, hey, jump in a Tesla Roadster and I can go faster again. Why isn’t the same thing possible when it comes to spaceships?

Punch it, Chewy.”

Movie: Star Wars

Science fiction loves to toy with the concept of FTL—Faster Than Light travel, with stories such as Star Trek and Star Wars suggesting it’s simply a technical challenge to be solved, like breaking the sound barrier in an aircraft, but the theory of relativity reveals something astonishing about the nature of our universe, a fundamental aspect that defines reality—space and time aren’t two separate concepts, but rather one thing—spacetime. Reality is governed by (at least) four dimensions, not three. Up & down, left & right, forwards & backwards, past & future.

Why can’t we go faster than the speed of light? Dr. Sundance Bilson-Thompson of the University of Adelaide explains on Quora that the answer is quite simple. We can’t go faster than the speed of light because we’re already traveling AT the exact speed of light as we pass through four-dimensional spacetime. Regardless of what we do, we can never travel any faster or slower than the speed of light.

Wait? What???

Yes, we can’t go any faster or slower than the speed of light when viewed from the perspective of all four dimensions.

Perhaps an analogy in three dimensions will help.

Let’s have a race.

Stay with me, and we’ll use The Fast and the Furious to explain relativity.

Mr. T. is going to race Dominic to settle once and for all whether The A-Team or The Fast and the Furious have the best drivers.

The rules are simple. Neither driver is allowed to speed. Both will drive at exactly 100mph, so this will be all about skill.

On your marks. Get set. Go.

As neither driver trusts the other, they’ve fitted their cars with police radar guns, allowing them to monitor each others speed. In addition to the speed cameras, they have web cams inside each others vehicles watching the speedometer. With two ways of verifying their speed, there’s no way either of them can cheat.

As the race unfolds Dominic pulls ahead.

Mr. T. accuses him of cheating, but Dominic swears he’s only ever been traveling at 100mph.

Mr. T. calls Dominic a liar because he too has only ever been traveling at 100mph. Even though he climbed a mountain, he kept his van on exactly 100mph. Mr. T. is convinced the only way Dominic could get ahead of him is if he was going faster. Is he right?

Mr. T. takes a shortcut over the mountains

When Mr. T. looks at the web cam inside Dominic’s car he sees the speedometer reading exactly 100mph, the same speed he’s doing, but if he points his radar gun at Dominic he gets a speed of 110mph. Confused, he asks Dominic what he can see looking back at the A-Team van.

Dominic looks at the web camera showing Mr. T’s speed and sees that he’s also traveling at 100mph, but with his radar gun, he measures Mr. T’s speed as only 90mph.

What’s happening? How can both measurements be correct when they’re clearly different?

The answer is… both vehicles have maintained a speed of 100mph throughout the entire race. Neither slowed down, but as Mr. T. travelled up hill (without losing ANY speed) he traded forward motion for vertical motion. He began moving in another dimension—up. He’s traveling 100mph, but on an angle relative to Dominic. From Mr. T’s perspective, he’s still moving at 100mph, but when he measures Dominic’s speed down on the open plain, it’s clear Dominic is moving faster relative to him even though Dominic too is only going at 100mph.

High school trigonometry is much more fun with Mr. T.

Some high school trigonometry explains what has happened. Both vehicles left from the same point (O) and they’ve both travelled the EXACT same distance in a straight line (O-A for Mr. T and O-D for Dominic), but when viewed in only one dimension, Mr. T has fallen back to point B. It’s as though he’s only traveled the distance O-B, making it look like he’s fallen behind (or Dominic has pulled ahead). In reality, they’ve both travelled EXACTLY the same distance, but for Mr. T. one dimension has been traded for another. By going up hill, Mr. T. has effectively reduced his horizontal motion.

This is what happens when it comes to relativity. Motion in one dimension is traded for another, only instead of the trade occurring between spacial dimensions like horizontal or vertical, relativity involves trading with time.

Instead of racing along at 100mph we are all racing along at one second per second. Sounds strange to think of time itself as a speed, but it’s just another dimension in which we can move—and we are in motion within time.

So long as everyone’s “racing” along in the same direction (which in this context means sitting still next to you as time races along), there’s nothing to see. We’re tied for first place. But should one of us start moving off in any other physical direction, all of a sudden we’re trading our speed through time for our speed in a physical dimension.

Fly away from me in a spaceship and you’ll swear time moves at exactly the same pace for you as it did when you were sitting next to me, just like Mr. T. seeing his speedometer reading 100mph. But when I measure your motion, just like Dominic, I’ll see you moving slower—not physically, but in time—I’ll see time slow down for you.

In the same way as Mr. T. watches Dominic race ahead along the open plain, you’ll look back at me and see time appear to speed up. Sounds crazy, but it’s been experimentally tested and holds true. The faster you fly away from me, the more pronounce the effect becomes, giving rise to the concept that if you left Earth in a spaceship traveling close to the speed of light you could return one year later to find that twenty years had passed on Earth.

The key point is that both of us—you in your super fast rocket and me waiting here on Earth for twenty years—have ALWAYS travelled through four dimensional spacetime at EXACTLY the same overall speed. Like Dominic and Mr. T. we simply traded speed in one dimension for another. The net result, though, is always the same—always equal. A whole bunch of time and a little space equals a whole bunch of space and a little time.

Spacetime is elastic, stretching and squeezing so that the net result is you’re always moving at the speed of light in all four dimensions, regardless of what you’re doing in any one dimension. Speed up in this dimension, relative to me, and I’ll see you slow down in the dimension of time to equal things out.

Now it becomes obvious why you could never travel faster than light. Once you get that fast, there’s no time left to trade. You’ve hit the speed limit and maxed out.

But why is the speed of light a hard limit?

If we rephrase the question in the light of Einstein’s most famous equation: E=mc2, the answer becomes obvious.

Can light go faster than light? No. The notion itself is obviously absurd. But we think of matter as different, special, even though it’s not—the equivalence between matter and energy (ala E=mc2) means it too could never go faster than light.

Speed is distance traveled over time taken. Miles per hour. Kilometers per second. If you trade all of your motion through time for motion through space (ie, travel at the speed of light) then there’s no time in which to record your speed. You have the miles but no per hour.

Light travels at the speed of reality (which for convenience we call the speed of light) because it has no mass. Looking at Einstein’s equation, it’s all E and no M.

Remember, regardless of what speed you’re doing relative to someone else, light is ALWAYS traveling away from you at 299,792,458 meters per second. You, Dominic and Mr. T. will always agree on that speed regardless of where you are and how fast you’re going. 299,792,458 meters per second is you traveling through four-dimensional spacetime at one second per second. Others may see time slow down or speed up for you, but you’ll never see that yourself. For you, it’s absolutely constant.

Spacetime is the wonderfully weird way in which the universe unfolds. It may seem counterintuitive, but it is actually astonishingly consistent and describes the way the cosmos works with astounding precision.

Strange, but true.

 

 

 

 

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3 thoughts on “The Fast and the Furious in Spacetime

    • Hah… yeah I was trying to work the “pity the fool” into the analogy, but sometimes it’s a square peg in a round hole

      Interesting concept, though, huh? Takes some mental gymnastics to understand 🙂

  1. That’s assuming that the direction travelled is linear rather than curved by mass.

    It seems to me that the path of a photon on the outer side of the curve must be travelled along travel faster than the path on the inner side of the curve, if looked at linearly by the observer.

    Oh, and perhaps loss in space time along the inner side due to this could help explain the Golden Ratio?

    Also, if space time is ALWAYS curved, rather than linear, then the rate that the minimum curve spirals in on itself might be used to measure the maximum lifespan of any given universe.

    That may be the set point for gravity in wave form, potentially causing all universes to have the same laws of physics.

    Just spitballing here!

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