Tag Archives: Galilean invariance

April 3, 2015

SR #13: Coordinate Systems

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!

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

March 30, 2015

SR #10: Simultaneous Events

By Wyrd Smythe

sr10-0 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.

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

March 20, 2015

SR #4: Two Rules

By Wyrd Smythe

Equinox It’s Friday, and I’m sure you’re thinking about the weekend, so today will be just a review and some more details about the speed of light.

And speaking of light, today is the Vernal Equinox. For the next six months (for those of us in the northern hemisphere), our days will be longer than our nights. No doubt the combination of spring, the Equinox, and the weekend, have you wondering what you’re doing at your computer reading about Special Relativity.

I’ll try to be very brief…

8 Comments | tags: Albert Einstein, equinox, Galilean invariance, Galileo Galilei, light, light speed, light year, moon, Special Relativity, spring equinox, Sun, vernal equinox | posted in Physics

March 19, 2015

SR #3: Relative Velocity

By Wyrd Smythe

Throwing like a girl!

I’ve introduced the idea of an inertial frame of reference. This is when we, and objects in our frame, are either standing still or moving with constant (straight-line) motion. In this situation, we can’t tell if we’re really moving or standing still relative to some other frame of reference. In fact, the question is meaningless.

I’ve also introduced the idea that objects moving within our frame — moving (or standing still) along with us, but also moving from our perspective — move differently from the perspective of other frames. Specifically, the speed appears different.

Now I’ll dig deeper into that and introduce a crucial exception.

11 Comments | tags: Albert Einstein, Emmy Noether, Galilean invariance, Galileo Galilei, Mo'ne Davis, motion, scalars, Special Relativity, speed, vectors, velocity | posted in Physics