These videos are great fun and I do read over
most of the comments you make. Sometimes the comments give me ideas for future videos,
and that’s why I decided to make this one. Some viewers claimed that photons do not actually
experience time and that’s a complex topic, with some interesting features. Let’s take a look.
(intro music) It's a well-known feature that in Einstein’s
theory of relativity different observers will experience time differently. Specifically,
it is often claimed that an observer moving quickly will experience time more
slowly than one that is stationary. This phenomenon is called time dilation.
Now, there are a lot of subtleties
and misconceptions in such claims. To help dispel those claims, I made
a video on how time dilation is often misrepresented.
And I also made not one, but two videos about the
twin paradox, which deals with a seeming paradox of relativity, which seems to make contradictory
claims. It turns out that this isn’t really a paradox, but I’m not going to get into that
here. I mention these videos because there is a ton of confusion about these topics. If you’re
interested, I strongly recommend watching them, and I put links to them in the description below.
However, what I want to talk about here
is whether a photon experiences time. If it’s true that a moving clock ticks more slowly
than a stationary one and a photon moves at the speed of light, is it possible that the photon
is moving so fast that no time is experienced?
To get a handle on that, we first need to understand two important concepts.
The first is that in special relativity, there is a mathematical term that pops up all of the time.
This term is called gamma. In this video, I don’t want to get into exactly what gamma is, and
how it arises. I made an entire video on that, which I also put in the video description below.
Basically, gamma is what makes all of
the weird bits of relativity happen. It is written as gamma equals one over the square
root of the object’s velocity, divided by the speed of light, all squared.
Like I said, it’s not super important to
understand where gamma comes from. Just know that if there’s a relativistic
equation, that gamma is going to be in there.
So, let’s see how gamma comes into play when
we consider what goes on with a photon. If you’re standing somewhere, perhaps waiting
for the bus, and see a photon go flying by at the speed of light, what happens with gamma?
Well, we can put in for the velocity, the velocity
of the photon, which is the speed of light, which we always write as c. We see that
we get c over c, which is equal to 1. And, with that, we see that gamma reduces
to one over zero, which is undefined.
So, that’s key point number one. The equations of relativity don’t work for objects
traveling at the speed of light. That means that relativity theory also fails for photons.
On the other hand, we can borrow an idea
from calculus, which is called limits. While we can’t use the relativity equations for
objects moving at exactly the speed of light, we can evaluate them for objects moving at ninety
percent the speed of light, ninety nine percent of the speed of light, ninety nine point nine nine
the speed of light, and so on. In principle, we could do the calculation at speeds that are
ninety nine point many, many nines times the speed of light.
By doing this approach, you can see what happens
as you get closer and closer to the speed of light and use that to figure out what happens when you
finally hit the speed of light (if you could, which, of course, you can’t).
So, let’s do that and ask how long a
super-fast object will think it takes to get from Earth to the nearest star. The
nearest star is about four light years away, so a person on Earth will say it
takes four years to get there. How much time will a person traveling at 90%
the speed of light take? Roughly a year and nine months. How about at 99 percent the speed
of light? A little over half a year. 99.9 % the speed of light? About two months.
We can continue this trend. At the staggeringly
fast speed of 99 point nine more nines the speed of light, it will take a bit shy of ten minutes.
From this, we can conclude that in the limit of
going at the speed of light that a photon will experience zero time.
So that’s pretty wild. Taken to an extreme, this
means that a photon can cross the entire universe in zero time.
And it gets weirder. Not only does
relativity predict that times will shrink, but it also predicts distances will too.
Indeed, I made an entire video on this subject, which is called length contraction. And,
as usual, the link is in the description.
A fast-moving object will shrink distances in the direction of motion,
although not side to side. If we made a cylinder that stretched from here to the next star, we’d
see it as four light years long, while the photon would see it as a circle with no thickness.
Again, taken to the extreme, a photon views the
distance traveled as it crosses the universe as having no thickness at all. In a sense, as far
as the photon is concerned, it is everywhere along its path at once.
Now we have to be careful, since the equations
of relativity don’t apply for traveling at the speed of light, but hopefully you see that this
limit trick allows us to get arbitrarily close.
So, I think that we can say that a photon experiences no time as it
passes from place to place as it travels through the cosmos. Furthermore, it experiences all
locations along its path at the same time. Photons are ageless.
This photon thing is pretty wild, but that’s
relativity for you. If you enjoyed getting your mind blown, please like and subscribe and
share on social media. Gotta blow other people’s minds too. It’s the kind of thing we expect
from physics because, as you must know by now, physics is everything.
(outro music)
