Last time’s Too Long Train illustration demonstrates that length is relative. Observers moving at different rates measure the length of an object differently. The faster something moves in your frame of reference, the more its length contracts along the direction of motion.
In previous weeks we saw that motion, speed, and simultaneity, are relative; now we see that length is also relative. Next week I’ll talk about the relativity of time. Today I want to dig a little deeper into the length contraction part of Special Relativity.
It’ll be a factor when we get to the spaceships!
Last time we explored the Simultaneous Lightning Strikes illustration of Special Relativity. In that scenario, on-the-ground observer Al sees simultaneous lightning strikes to a passing (very) high-speed train. On-the-train observer Em agrees both bolts hit the train (one front; one rear), but sees one happening first followed by the other.
The next scenario reverses the situation. This time traveler Em sees simultaneous events on the train and bystander Al sees them happening one after the other.
Today we explore: Peace Treaty (on a Train)!
We started by exploring the idea that motion is relative. Now we see that the idea of simultaneity is relative! Events that Al sees as simultaneous in his frame of reference do not appear simultaneous to Em — she sees them happening one after another!
A frame of reference has lines of simultaneity that allow us to assign time coordinates to events in the reference frame. If Al and Em have different lines of simultaneity, then their coordinate systems differ— they assign different coordinates to an event!
Let’s explore that in a bit more detail…
Last time our friend Al used lasers and timers to create a regular grid-like map of the space and time near him. The map allowed him to assign space-time coordinates to events in his frame of reference (even if it takes time for him to see light from those events).
An important concept is the idea of simultaneity — of events in different locations happening at the same moment according to some observer (who has to wait for the event’s light to reach their eye).
So far the events weren’t moving relative to us. What if we — or the events, same thing — are moving (and moving fast)? It turns out, this changes the picture!
In the last two weeks I’ve covered relative motion as the ancients understood it (Galilean Relativity), touched on how light doesn’t follow those rules, and introduced time-space diagrams that we can use to visualize motion. I also introduced the topic of space-time events, which are simply locations in space at a given time.
In particular, I showed how our friend Al can use a laser to determine both the location and the time (relative to himself) of an event. This allows him to map his nearby space and time using a system of regular (that is, grid-like) space-time coordinates.
Today we continue with that idea.
Last time I introduced you to the idea of a space-time event. In physics, an “event” has the same meaning as when Hollywood blares out about a “major motion picture event” — that is to say, nothing at all special — just something that happens at a specified location and time.
If you attend a social event, it has a location and a time. When we talk about space-time events, all we mean is a specific location and a specific time (hence the name, space-time event).
Today we’ll explore some interesting aspects of such events.
The last two posts introduced and explored the concept of time-space diagrams. This time I’ll complete that exploration by using them to consider motion from two points of view. This will be an exercise in application of our diagrams.
I’m going to connect that application with something I stressed last week: that motion has a symmetrical component. It’s perfectly valid to think of the world moving past the train as it is to think of the train moving through the world.
It happens that here our dueling points of view are resolved by something else I discussed last week. See if you spot it before I mention it.