Sunday, March 08, 2009


Dave sent me a link to this cartoon about the loneliness of being a photon. After wiping the tears from my eyes, I was consumed with rage. Why? The science is wrong!

In the cartoon, 10,000 years pass for the photon, who lives each and every second of it. But this simply won't wash. It's the 21st century now. If you're going to create a cartoon with a photon as the protagonist, you have to have a basic grasp of relativistic time dilation. It's special relativity too, rather than general relativity so really there's no excuse. I will demonstrate using the formula for time dilation between events for a moving observer compared to an inertial observer:

t' = t*√(1-v2/c2)

t' is the time interval for the observer in the moving frame
t is the time interval for the observer in the inertial frame
v is the velocity of the moving frame (in terms of c)
c is the speed of light

As we can see... hello? Is anyone still here? Do you want to come down to the front now all the people scared by equations have left[1]? There. Now I don't have to shout and you can see better.

As I was saying, if you start plugging in values you'll see that if you're travelling at 80% of the speed of light, c=1.0, v=0.8, so t' = 0.6t. Or in other words, if you're travelling at 80% of the speed of light (0.8c), you only experience 60% of the time that observers at rest[2] will record. The faster you go, the greater the difference, and the smaller the time appears to be. At 90% of the speed of light (0.9c), t' =0.33t or time moves at one third that of the outside universe. At 0.99c, t'=0.14t or one seventh to those observing the traveller from a rest frame.

But what happens when v=c? Plug in the numbers and v2/c2=1. So (1-v2/c2)=1-1=0. Square root that and we get t'=0t, which tells us that no time passes while you travel at the speed of light.

In practice, any particle with mass, will have had it's mass increased to infinity (requiring infinite energy) to get to that speed. But photons are massless, and, (almost) by definition travel at the speed of light. So no time passes for them between when they are emitted and when they are absorbed[3].

Or in other words, I'm afraid the cartoon of Sam the photon is fatally flawed for me.

On a lighter note, I wrote this in 2003:
The adventure of Jim and Stan riding a photon in three scenes

Scene 1
Outside Stan's Physics theme park Photon ride - "Ride a quantum mechanical particle at the speed of light! Guaranteed to reach a destination before the universe closes"
Jim "This should be good"

Scene 2
Just about to take the Photon Ride
Jim "Yeee..."

Scene 3
Just after taking the Photon ride
Jim "Can I have another go Stan - I didn't really have time to appreciate it. Oh go. Please. Side effects? Well, for a moment I thought I'd put on some weight..."

[1] Fairly simple derivations of this equation are available on the internet. Ask in comments, or simply google time dilation equation.
[2] In general we'd be thinking of observers at the start or end of the journey, but any in a common rest frame will do.
[3] In a closed universe, all photons will eventually be absorbed. In other universes, they might not. But don't feel sorry for the photons that miss everything ever; they exist in an eternal now, without duration. They'll keep travelling on, following their path to timelike infinity, as fresh and young as the moment they were emitted.

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