# Why isn't the speed of light infinite?

Stephen Reucroft and John Swain, professors of physics at Northeastern University in Boston, Mass, provided the following explanation:

The common experience of turning on a light switch certainly shows that light travels very quickly. But careful experiments reveal that it travels at a finite speed. This speed, which we call "c," is measured to be 300,000,000 meters per second.

The speed of light is strange in that it has the same value independent of the relative velocity between the source and the observer. This fact is an experimental one that can only make sense if relative motion changes the relationship between space and time intervals to keep the distance covered by light per unit time the same for all observers.

The fact that space and time must get mixed up to keep the speed of light constant implies that, in some sense, space and time must be the same, despite our habit of measuring space in meters and time in seconds. But if time and space are similar to the extent that they can be converted one into the other, then one needs some quantity to convert the units--namely, something measured in meters per second that can be used to multiply seconds of time to get meters of space. That something, the universal conversion factor, is the speed of light. The reason that it is limited is simply the fact that a finite amount of space is equivalent to a finite amount of time.

Another explanation of light's finite nature can be obtained from thinking about what we mean by light itself. Light, by definition, is an electromagnetic wave, a propagating disturbance in space and time that carries information about the acceleration of charges.

Were there an infinite value for the speed of light, light itself would not exist at all. Mathematically, the wave equation that describes light as an electromagnetic wave would lose its time-dependence.

In physical terms, an electromagnetic wave arises due to the finite time it takes for news of the change of location of an accelerated charge to arrive at a distant point. Think of an electric charge as being like a hedgehog with flexible rubber spikes going out to infinity in all directions. These spikes represent the electric field lines, the lines along which a test charge would move.

If the charge is jerked, the segments of the spikes close to the charge will move, but those farther out will still point in their original directions. The result is that each spike will get a kink that moves out to infinity. This kink relays the news that the charge has moved to the distant parts of the spikes and corresponds to an electromagnetic wave. If the wave moves infinitely fast, it is as if it were not there at all; the spikes are infinitely stiff and the news gets out to everywhere without any seeming kinks. In other words, there would be no electromagnetic wave, and thus no light.

The previous two arguments are two slightly different ways to say that if you think light is a wave, then it has to be something that propagates and takes time to go from one point to another. In other words, it has to travel at a finite speed. Infinite speed of propagation is an instantaneous magical change in things everywhere all at once, and not a wave at all!

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1. 1. subhendu 09:34 AM 6/16/10

Which experiment shows that the speed of light is finite? I can see that the Fizeau's experiment is not correct. Is there any modern experiment that shows that the speed of light is finite? Please let me know. My email address is subhendu.das@excite.com

2. 2. dagelf 07:51 PM 3/23/12

As I understand, due to time dilation, when approaching the speed of light, time slows to zero while conversely everything outside the frame of reference speeds up - in accordance to the distance "traveled". This implies that to light itself, while "traveling" through a vacuum, it is in fact teleporting, and slowed only by matter - which in effect means that it's speed is in fact infinite - or zero - from within it's frame of reference.

3. 3. dagelf in reply to subhendu 07:53 PM 3/23/12

The article only addresses one frame of reference: the inertial one. Which is fairly shortsighted in my opinion.

4. 4. dagelf in reply to dagelf 07:55 PM 3/23/12

Reminds in a way of the days of Copernicus. Instead of thinking that the Earth is the center of the universe, we now assume that the inertial frame of reference is the only one that matters.

5. 5. harveylazurmiller 07:48 PM 1/17/13

I'm trying to understand how space and time are equivalent. I know that time can be considered a dimension if one is, say, to locate a moving object in time when it's place coordinates are identified (excluding particles) and I realize that space and time change based on the relative speed to a reference frame but I'd like to see a clear explanation that connects space and time in such a way that it clearly shows that they are the same.

6. 6. davidt0504 04:04 PM 2/20/13

The way I see it, if the speed of light were infinite, then we would always be in the dark because the light would always be past us. Imagine if every photon is a racecar. Since those photon's need to propagate through space as a wave then the crests and troughs of the wave would always be past us and never propagating around us.

7. 7. duselmann 12:38 AM 7/5/13

harveylazurmiller (and any other curious readers),

If you start with an x-y plot and use the x-axis to represent your straight line movement in any physical direction then we can use the y-axis to represent your movement through time. Now, if you are standing still, you are only moving through time as fast as you can in the y-axis. This would be a vertical line. If you then begin to move in the x-direction you will take away from the y-axis because of the universal speed limit - the speed of light. Since you had to remove some speed from your time axis (the y-axis), you travel through time more slowly. The link that time and space are intertwined is clear in that we used the same 'units' on the graph paper. Realize, there is a lot of physics (equations and experimental proof) that are used to justify this linkage and that this type of plot demonstrates the proof. It is not a proof in and of itself.

Time and space are definitely interlinked. If we did not take this fact into account the GPS system that we have come to rely on would not work. The satellites providing this service are both moving fast around the earth and are in a lesser strength gravitational location at their distance from the earth. Something like 20,000 km away.

High speed and gravity slows down your clock. And when I say clock, I mean your clock, electronic circuits, your brain synapses, your heart beat, your metabolism, your rocket engine, everything. This makes the time dilation imperceivable to you as you travel. They tested these concepts with synchronized clocks and took one for a lengthy jet flight. When done it was off a bit.

On last thing, we do not perceive this on a daily basis because the speed of light is so incredibly fast (186,000 miles per second) that we just do not see the effects at our human speeds. Furthermore, our perceptions originate from evolutionary need. There has been no need to understand this to gather food and shelter. It is all new to us.

8. 8. duselmann 12:46 AM 7/5/13

There have been many proofs of the speed of light. One early proof was a curious time discrepancy with Jupiter's moons. They calculated a good estimate for the speed of light from the difference when the earth was different distances from Jupiter.

Anther proof is that when the moon landing astronauts communicated with Houston, there was about a 1.5 second delay (little less). We now use mirrors left behind to bounce lasers light off them to determine the distance to the moon. (It is moving away a bit each day because of the energy lost by the tides. That energy has to come from somewhere.)

And there are others.

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