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I have heard that the speed of light is absolute. But, what about if you are (theoretically) traveling at the speed of light, will light be going the speed of light faster than that? Why is the speed of light absolute, how does it work out?
Question Date: 2008-01-26
Answer 1:

Even if you're traveling at 99.9999999% of the speed of light, you will still find that light travels exactly at C, relative to you. The reason you don't measure light traveling at 2*C is that your measuring tools are measuring something different than when you're standing still.

We measure speed as distance divided by time, like miles per hour, or meters per second. The astonishing thing about the universe (as discovered by Einstein) is that both "distance" and "time" are variable. If I was holding a 1 meter long stick and traveling past you at 1/2 of the speed of light, my "meter" stick would appear to be just 0.75 meters long to you. The same thing happens to time: 1 second to me will be longer than 1 second to you. So the "speed" of light is constant because both "meters" and "seconds" change.

If you could actually travel exactly *at* the speed of light, then there's no way to measure anything at all, because time has totally stopped for you. No time would pass at all. You are frozen and will not change forever, or at least not until you slow down. If you could magically travel along with a photon of light from the moment it was generated until the moment it was absorbed, the universe would simply seem to instantly change for you. It would seem like it was instantly replaced. You would not notice--or even be able to measure--anything along the way, even if the photon traveled for millions of "years" as they would be measured by a stationary observer.

The old joke asks: What happens if you're driving at the speed of light and you turn your headlights on? The answer is: You can't, because if you're traveling *at* the speed of light, you won't move, breathe, or think, much less reach for a switch. You and your car will simply fly across the universe in a state of suspended animation. Of course, if you're traveling at any speed less than C, then it's not that special. Your headlights will still emit light that travels exactly at C--both for you and for the rest of the universe.

As for your last question, I don't actually know why the speed of light is a constant in the universe. I'm not sure anybody does. It's one of those questions waiting for a bright young student to come up with a new idea, and test whether that idea matches experimental observations.

Answer 2:

One way to get a better insight on this problem would be to play around with one very useful formula relating to the relativity of speed:

u = (u'+v)/(1+u' v)

This equation lets you find u, the velocity of an object relative to a frame of reference S (for example 'stationary' Earth), given u', the velocity of the same object, relative to another frame of reference S' (for example a flying airplane), and v, the velocity with whichS' moves relative to S (in this example the velocity of the airplane relative to Earth). To keep the math simple, this equation assumes that motion is only in one dimension and that all velocities are given as a fraction of the speed of light so that if say, an object moves at half the speed of light, then its velocity would be numerically equal to 0.5. This means that if you are using m/s, ft/s mph or (why not?) knots, you need to first translate that as a fraction of the speed of light.

Example: Say an airplane is flying at 575mph relative to Earth (typical airliner). If you divide this speed by that of light (around 671 000 000 mph!) then v would be equal to 0.000 000 857 (or 8.57-7 if you are familiar with computer notation for very large or very small numbers). Now imagine someone at the back of the airplane throws a pillow toward the front with a speed of say, 15mph (that's relative to the airplane). Then u' would equal 0.000 000 022 4 (you do the math, as they say, bearing in mind that my results are rounded to three figures). If you use our magic formula above (you will need a scientific calculator given such small numbers) you'll get u = 0.000 000 879 which translates, after multiplying by the speed of light, to a pillow moving at 590 mph relative to Earth. But wait, isn't this simply the sum of 575 mph and 15 mph? It is in indeed; that's what you would expect and what Galileo already knew almost 400 years ago! This is what is known as Galilean relativity; the idea that motion is relative to the frame of reference you use to measure velocities or speeds.

Now, the difference between the relativity theory of Galileo and that of Einstein (where our magic equation belongs) is only apparent when you are moving REALLY fast. So... let's run another...

Example: Say you are in a spaceship and you launch a shuttle at one-half the speed of light relative to you (you are reference frame S and the shuttle is reference frame S') so that v = 0.5. Now the shuttle launches a probe in the same direction of travel, at one-half the speed of light relative to the shuttle. If you asked Galileo, he would tell you that the probe will travel with the speed of light relative to you ( 0.5 + 0.5 = 1 ), however, if you use the formula above, Einstein will tell you that the probe will travel at 'only' 0.8 times the speed of light relative to the spaceship (again, try to get that number on your own).

You ask in what sense is the speed of light absolute, so let's do some algebra with our equation. Imagine you are traveling with speedv relative to Earth, say. If you light a flashlight in front of you, the beam of light will travel with a speed u' equal to 1 (of course) so if we now substitute 1 for u' we get:

u = (1+v)/(1+v)

but this simplifies to u = 1 !!! This means that relative to Earth, that beam of light you emitted will travel also with the speed of light. It is in this sense that the speed of light is absolute, (and yet we call it "Relativity Theory", right? ). Please note that the previous simplification is valid for ANY value of v, no matter how fast, including v = 1 (you traveling with the speed of light). In this last case however, other parts of the theory brake down when you try to calculate things in a reference frame that moves with the speed of light relative to some valid reference frame. On the other hand, from a physical point of view, it would take an infinite amount of energy for you to acquire the speed of light so it would be actually impossible and thus, well, not really a problem, right? Still, you may imagine traveling at 99% the speed of light (possible, though expensive (very!!!)). In such case, v = 0.99 and a beam of light emitted by your flashlight would still travel with the speed of light relative to both, you and Earth. That runs against common sense, yet that's real; no science-fiction here.

In the end, it comes down to the relativity of time. That same time you need to measure speed, for instance.

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