# Einstein's frozen wave?

Here's the quote from Stephen Hawking's latest book.

At the age of sixteen, when he (Einstein) visualised riding on a beam of light, he realised that from this vantage light would appear as a frozen wave. That image ultimately led to the theory of special relativity.

What does "frozen wave" mean?

• Hi Harry, sorry for butchering your question a bit. But the part about the grammatical correctness of the sentence is quite off-topic. For what it's worth, I don't believe there's a comma missing. I am not a native speaker though. – Nephente Dec 16 '18 at 10:48

Suppose we consider a plane wave:

$$y(t,x) = A\sin(\omega t - kx + \phi) \tag{1}$$

The velocity of the wave is:

$$v = \frac{\omega}{k}$$

If you are moving at the same velocity as the wave your position is given by:

$$x = vt = \frac{\omega}{k} t$$

The value of the wave at your position is given by substituting your position into the value for $$x$$ in equation (1), and if we do this we get:

$$y(t,x) = A\sin(\omega t - k \frac{\omega}{k} t + \phi) = A\sin(\phi)$$

So to you the wave just has the constant value $$A\sin(\phi)$$ and doesn't change with time. This is what Hawking means by the wave being frozen.