What is the age of a photon?
Revisiting Special Theory of Relativity from Brian Greene's perspective
It takes a touch of genius — and a lot of courage — to move in the opposite direction
- Albert Einstein
Greetings, fellow Bohron
I am currently reading The Elegant Universe by Brian Greene. In the second chapter, he discusses Einstein’s Special Theory of Relativity. I know we have previously discussed this theory through a series of articles. Then why waste another week on it? The reason, my friend, is that Greene's insight lures us into the world of very fast and makes us realize that sometimes there is more than one way to solve a problem.
Let’s just focus on the titular question first. As you’ll find out by the time you finish reading this article, the attempt to answer it impetuously would make us realize all is not as it seems. So let’s delve right into it.
An Obvious-Looking Answer
How do we calculate the age of something? Well, we simply measure the time interval between its birth and the present moment. Let’s consider a very simple example.
Consider a photon that is produced at an instant inside the core of the Sun. Disregarding the enormous amount of time it takes a photon to reach the Sun’s surface, we calculate the age of the photon only after it leaves the surface. Since it takes only 8 minutes and 20 seconds for the photon to reach us, this is precisely the age reported by an Earth-bound observer.
But the notion of age has little relevance unless talked about from the perspective of the very thing whose age we are interested in finding out. This is equivalent to asking a photon, “What is your age?” and letting the photon answer it from its own frame of reference.
So before we tackle this question again, I want you to revisit the notion of Time Dilation the way Greene does in his book. Unlike the example of moving spacecraft carrying a light clock we discussed to explain Time Dilation the last time, we would conduct a simple activity and see how it led Einstein to proclaim the revolutionary idea underlying the essentials of special relativity. The answer to the above question would reveal itself naturally from the ensuing discussion.
Distributing motion among various dimensions
Consider a 10 km straight track that runs in the north-south direction. Imagine that I race a car at a constant speed of 100 kmph on this track. From simple mathematics, you deduce that it should take me 6 minutes to complete this journey; this is precisely what you find when you time my run. Let’s denote this time by T₁.
Now I race the same distance again with the same speed but at a slight angle from my previous north-south direction. Since the path traversed is longer when travelling at an angle, it will take me more time (T₂) to cover the track. If I keep increasing my angle in the subsequent runs, the corresponding time durations T₃, T₄ and so on would increase as well.
T₁ < T₂ < T₃ < T₄ … and so on.
Why so?
When travelling at an angle, part of my 100 kmph speed is spent going east-west. This means that I have a somewhat lesser speed left to cover the track in the north-south direction. So it takes me more time to finish the test run.
In other words:
The car—in the subsequent test runs—shares this speed between the two independent spatial dimensions (north-south and east-west) and hence appears to be going slower than 100 kmph in the north-south direction.
Einstein’s genius insight
From the above experiment, we infer that motion can be shared among different spatial dimensions. What does the simple result of the above investigation have to do with a revolutionary idea of relativity?
We know that special relativity treats time as another dimension of the universe. Einstein realized that an object’s motion could be shared not only among spatial dimensions but the time dimension as well.
According to Einstein, all objects in the universe are always travelling through spacetime at one fixed speed—that of light. This might seem ridiculous to you but pay attention: here we are talking about an object’s speed through spacetime, not space. The speed through spacetime is the combined speed through all four dimensions.
Time Dilation
The realization that an object’s velocity can be shared among the spatial and temporal dimensions leads directly to Einstein’s proposition that time can dilate. For this, we consider two cases discussing an object’s state of motion through space, one of which would lead us to our final and correct answer.
Case 1: Object at rest w.r.t. us
Such an object experiences no motion through space. So all of the motion is used to travel through the time dimension. (This is analogous to the first run of the car in which all of the motion is used to travel through one dimension: north-south.) So the object moves with the speed of light through the time dimension. Hence it ages at exactly the same rate or speed as us.
Case 2: Object in motion w.r.t. us
Such an object experiences motion through space which can only happen when some of the previous motion through time is diverted. (This is analogous to the subsequent runs of the car in which the motion is distributed among multiple dimensions.) This sharing of motion implies that the object will travel more slowly through time than in Case 1. In other words, a clock tied to an object will tick more slowly if it moves through space. This is Time Dilation!
The Universal Speed Limit
What is the maximum speed an object can attain to travel through space?
The maximum speed through space occurs if the entire motion through time is transferred to motion through space. This is the fastest speed through space that the object can possibly achieve, and it is the speed of light.
The Answer, Finally Revealed
We know that a photon travels with the speed of light through space. This means that it doesn’t move through time at all because there is no speed left for such a motion. In other words, there is no passage of time at light speed. All the photons in the universe—that were produced during the big bang or the ones produced 8 minutes 20 seconds earlier from Sun—are of the same age and this age is zero.
Fun Fact: This also means that if we could travel at the speed of light, we would achieve the state of immortality.
So it’s better to treat those 8-minutes-20-seconds as merely the time photon took to reach us. As far as the question of a photon’s age is concerned, we now know that photons don’t age at all.
Sources:
Ch 2 - Space, Time and the Eye of the Beholder, The Elegant Universe, Brian Greene
Turns out, being damn quick and never aging are the same super powers.
Very concise and very well explained. But I still can't wrap my head around the fact that a photon really lived 8+minutes for us but for it's own self it's age is zero. Really strange!