Recently I had a debate with someone who was downright evangelical about the Block Universe (BU) being, absolutely, positively, the way things are. Because Special Relativity. In particular because of what SR says about simultaneity between inertial frames.
Up to that point I’d never given the BU a great deal of thought other than to file it under «Probably Not the Case» (for reasons I’ll get to). But during my morning walks I’ve turned it over in my mind, and after due consideration,… I still think it’s probably not the case.
I get why people feel SR seems to imply a BU, but I don’t see the necessity of that implication. In fact, it almost seems contrary to a basic tenant of SR, that “now” is strictly a local concept.
Last time I focused on how it was possible for Al to see — even enclose in a tunnel — a train that appears shorter to him due to its motion. It turns out that the train Al sees is a stack of time slices of the train at different moments. As we’ve seen, lots of things look different in a moving frame.
Today I want to say a little about Em’s point of view, run some numbers, and take you through a little math (just one equation, I promise). Then, because it’s Friday (when I try to write about light), I’ll introduce you to light cones.
They’re not actually necessary, but they’re kinda cool.
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!
The last two train examples (Lightning Strikes and Treaty Train) focused on how simultaneity is relative to motion. Our final train example focuses on how length is relative to motion. The faster something goes relative to you, the more it appears foreshortened along its direction of travel.
This example involves a train that, if it stopped halfway through, is too long for a tunnel — it would stick out both ends. But motion contracts length, so if the train goes fast enough, it becomes short enough to fit entirely inside the tunnel.
And it’s not an illusion; the train really does fit inside!
The main topic this week was how simultaneity is relative to your frame of reference. How there are (virtual) lines of simultaneity where all points on some line — at all distances from you — share the same moment in time. For any instant you pick, that instant — that snapshot — includes all points in your space.
A line of simultaneity freezes the relative positions of objects at a given moment — which enables distance measurements. Simple example: When their watches both read 12 noon, Al and Em were 30 miles apart. A more mathematical example uses x, y, & z (& t), but it amounts to the same thing: a coordinate system.
The gotcha is that simultaneity and coordinate systems are relative when motion is involved!
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.