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Dr. Christopher S. Baird

Why is time frozen from light's perspective?

Category: Physics      Published: November 3, 2014

Time is not frozen from light's perspective, because light does not have a perspective. There is no valid reference frame in which light is at rest. This statement is not a minor issue that can be approximated away or overcome by a different choice of words. This statement is fundamental to Einstein's theory of Special Relativity, which has been experimentally validated thousands of times over the last hundred years. The whole framework of Special Relativity is based on two fundamental postulates:

1. The laws of physics are the same in all inertial reference frames
2. The speed of light in vacuum is the same in all inertial reference frames.

If there were a valid reference frame in which light was at rest, then that would violate Postulate 2 because the speed of light would be different in various reference frames (i.e. the speed of light would be c in some frames and zero in its rest frame). And if Postulate 2 is discarded, then the entire theory of Special Relativity is discarded, because Special Relativity is derived from these two postulates. Asking the question, "If we just pretend that light has a reference frame, then what would happen?" will only lead to nonsense answers. Once you pretend that, you have thrown out all of Special Relativity, and you are just left with nonsense and science fiction. In all reference frames that actually exist, light travels through space and time in a normal way just like any other object.

plot of length contraction versus speed
According to Special Relativity, as a frame goes faster, it shortens more in the direction of motion, relative to the stationary observer. In the limit that it travels at exactly the speed of light, it contracts down to zero length. In other words, there is no valid reference frame at exactly the speed of light. Public Domain Image, source: Christopher S. Baird.

To make more sense of this, let's review quickly what Special Relativity establishes. Special Relativity tells us that a moving frame of reference has its spatial dimension shortened in the direction of motion relative to the stationary observer, and has its time dimension slowed down relative to the stationary observer. These effects are known respectively as "length contraction" and "time dilation". Here on earth, we don't notice these effects in everyday life because we are going far too slowly. Length contraction and time dilation only become significant when you are traveling close to the speed of light. The speed of light is very fast (300,000 km/s or 670,000,000 mph), far faster than any speed that a typical human experiences relative to the stationary observer. Note that the key phrase is "relative to the stationary observer". Relative to itself, a reference frame is at rest and experiences neither length contraction nor time dilation.  An astronaut on a speeding spaceship does not see his own rulers shortened nor his own clocks running slow. Rather, it is the man on the ground who sees the rulers on the spaceship shortened and the spaceship's clocks running slow. Also note that there's nothing wrong with the clocks and rules. Space itself is shortened and time itself is slowed down for a moving reference frame, relative to the stationary observer. These interesting effects, which have been verified experimentally many times, are all derived from the two basic postulates mentioned above.

The mathematics of Special Relativity tells us that as a reference frame moves at ever higher speeds, its space contracts ever smaller and its time becomes ever slower, relative to the stationary observer. In the limit that its speed approaches the speed of light in vacuum, its space shortens completely down to zero width and its time slows down to a dead stop. Some people interpret this mathematical limit to mean that light, which obviously moves at the speed of light, experiences no time because time is frozen. But this interpretation is wrong. This limiting behavior simply tells us that there is no valid reference frame at the speed of light. A reference frame that has exactly zero spatial width and exactly zero time elapsing is simply a reference frame that does not exist. If an entity is zero in every way we try to describe it, how can we possibly say that the entity exists in any meaningful way? We can't. Space and time simply don't exist at and beyond the speed of light in vacuum. Therefore, taking the limit towards c simply reaffirms the two postulates.

Since there is no valid reference frame at the speed of light in vacuum, there is also no way for an object with mass to ever go exactly the speed of light. If it did, then the object with mass, which certainly exists, would be jumping into a reference frame that does not exist, which makes no sense. In reality, an object with mass can go ever faster and get ever closer to the speed of light c, but never exactly reach it. The fastest speed achieved on earth by humans is 99.9999991% of c for a group of protons in the LHC particle accelerator relative to another group of protons. Getting this handful of subatomic particles so close to the speed of light requires more energy from the electric power grid than is consumed by a city. Special Relativity also tells us that the closer an object gets to the speed c, the more energy it takes to get the object one increment faster. As the object gets closer and closer to the speed of light, the amount of energy it needs in order to go faster spikes up rapidly. It takes an infinite amount of energy to accelerate an object with mass to exactly the speed of light in vacuum.

Topics: frozen time, length contraction, light, photon, relativity, spacetime, spacetime, special relativity, time, time dilation