Chances are, you probably haven't.

Still, it is intriguing to think that we can potentially, given infinite time, observe a star/emitting body at the very end of the universe. This is all thanks to the non-zero Poynting vector in the equation for electromagnetic (EM) radiation.

I decided to write this blog post after my EM theory prof said "We can see stars because Poynting vector is non zero." I won't include any complicated theory or equations because 1) It's final exam season and I shouldn't even be writing this blog post and 2) you only need to know the basic concept.

**What is a Poynting vector?**

I assume you know what electric and magnetic fields are. (Electric fields are present when dealing with charged particles (like electrons), and magnetic fields when dealing with MOVING charged particles) Combine these fields, and you get an 'electromagnetic (EM) field'. These fields have a sense of direction about them, and depending on what you do with the field, you can get energy out of them. Poynting vector represents the

__directional rate of energy transfer of an EM field__.

**What is EM radiation?**

Charges that are accelerating have EM fields that can transport energy "irreversibly out to infinity", and this is what we call "radiation." Given a charged particle that is accelerating in space, you can calculate the total power passing through its surface by integrating the Poynting vector. Clearly, this is non-zero if the Poynting vector is non-zero. But then, the EM 'news' travels at the speed of light, which means the energy left our charged particle at an earlier time. Have I lost you yet?

Think of it as pulling one end of a long slinky quickly. The other end of the slinky starts moving only after a certain amount of time. Now imagine that the slinky is 'energy', and you're moving it at the speed of light. (This might be an unfair analogy, since slinky expands while there is no sense of physical 'expansion' for energy)

Nonetheless, you measure the time at which the energy left the source (t0), and then measure another time point (t') when the energy crosses you at some other point in space, a distance 'r' away from the source. This means t' = t0 + r/c, where c is the speed of light. The power that is 'radiated' is essentially the amount of energy detected as r --> infinity. Obviously, since speed of light is constant, the further you move away from the source, the longer radiated energy will take to reach you -- but no matter how far away you are, it WILL reach you (even when there is a giant star between you and the source, thanks to gravitational lensing).

And this is precisely why we see stars!

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