Tag Archives: simultaneity
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)!
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6 Comments | tags: line of simultaneity, simultaneity, simultaneous events, space-time, space-time event, Special Relativity, time-space diagram, trains | posted in Physics
For the last three weeks I’ve been laying a firm groundwork for the more interesting part of the series. Perhaps there was too much time and detail: I seem to have lost much of my audience (not that the lecture hall was packed in the first place).
I’ve long believed in the importance of basic knowledge — it’s stood me in good stead through life. But I know not everyone shares my appetite for details. For what it’s worth, the rest is the fun part, where all that groundwork goes into action.
This week, trains; next week, spaceships!
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4 Comments | tags: relativistic speed, simultaneity, simultaneous events, space-time, Special Relativity, time-space diagram, trains | posted in Physics
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!
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5 Comments | tags: 1D, 2D, 3D, Albert Einstein, Emmy Noether, frame of reference, Galilean invariance, light, light clock, light cone, light speed, line of simultaneity, simultaneity, simultaneous events, space-time, Special Relativity, surface of simultaneity, time-space | posted in Physics
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…
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Leave a comment | tags: simultaneity, simultaneous events, space-time, space-time event, Special Relativity, time-space diagram | posted in Physics
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!
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1 Comment | tags: frame of reference, line of simultaneity, simultaneity, simultaneous events, space-time, space-time event, Special Relativity, surface of simultaneity, time-space, time-space diagram | posted in Physics
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.
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3 Comments | tags: Galilean invariance, line of simultaneity, simultaneity, simultaneous events, space-time, space-time event, Special Relativity, surface of simultaneity, time-space diagram | posted in Physics
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