Simultaneous not simultaneous

According to special relativity, something can happen both before and after something else – depending on the observer’s frame of reference.

Greg Hewgill from Christchurch, New Zealand [CC BY]
Okay, phew, gonna take a deep dive today into Einstein’s special relativity. Buckle up, because it may hurt your brain a bit.

Special relativity (among other things) observes that time moves differently for different people, depending on how fast they’re moving and in what direction. In other words, time is relative. Think of all those sci-fi movies where someone comes back from an interstellar voyage to find that thousands of years have passed on Earth. And also that the Earth has been taken over by apes. You maniacs!

As if it weren’t already weird enough, this phenomenon introduces a rather odd twist: two events that are sufficiently separated in space can occur at the same time, or one before the other, or the reverse… all depending on where they are observed from.

To understand this, we need to talk about light cones. Put simply, nothing can travel faster than the speed of light. That means that nothing can affect anything else at speeds faster than light. Say I wanted to blow up the sun. I have a sun-destroying missile in my backyard, and it travels at the speed of light. My missile would take a little over eight minutes to get to the sun… and it’s impossible to blow up the sun any faster, no matter how impatient I am.

In fact, no matter where I shoot my missile it cannot affect anything beyond the speed of light multiplied by the time it is in flight. So the range of the missile is an ever-expanding circle… or, if we think of time as a dimension, a cone of influence extending out into the future:

Light cone
Okay, so far so good? Stay with me. You may have noticed in the picture above that there’s a light cone in my past as well. Just as I cannot affect anything I cannot reach, nothing can affect me if it can’t reach me travelling at the speed of light. So if the sun blows up (because someone else got their missile there first!) it doesn’t matter to me for a little over eight minutes. At which point, I would probably be slightly alarmed. The crucial point is this: cause and effect cannot travel faster than light.

Let’s get back to simultaneity. And away from sun-destroying missiles, because they’re a bit of a bummer. Einstein presented this thought experiment: a train is hit by lightning. Not once, but twice – once at the front of the train, and once at the rear. I’m sitting on a platform and the lightning strikes as the train is passing me. From my perspective, the two strikes happen at the same time, because the light from the strikes reach me at the same time. For me, they are simultaneous.

However! Consider someone riding in the middle of the train. The train is moving forwards, so the light from the front strike reaches them before the light from the rear strike. From their perspective, the lightning hit the train from the front before the rear. For them, they are not simultaneous.

And if another train is travelling in the opposite direction, and it passes by the first train and the platform, then for them the other lightning strike happens first. It’s not simultaneous either, but the order of the lightning strikes is flipped!

And this is the crux of the matter: it’s not just their perception of simultaneity that’s different, but their reality of simultaneity. Just as time moves differently for different people, so simultaneity is different for different people.

I recognise that this is a bit heavier than my usual blog posts. To supplement my explanation above, the following videos may help:

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