/sci/ - Science & Math

>>2147947
forgot pic

Now suppose there's some event, like a pencil making contact with a table. To observer O, the event can be specified by x, y, z, and t, where x, y, and z give the position of the event, and t gives the time of the event (all from O's perspective). Now the question is, what are x', y', z', and t'?

At some later time, the situation looks like this.

The usual way of describing an event is to use Cartesian coordinates (ie specify an event by its x, y, and z position).

For a moment, let's look at things classically. How will an event appear to two observers moving relative to each other?

Suppose that observer O is at rest, and that observer O' is moving at speed v in the x-direction. We'll make some simplifying assumptions: as in the picture, we'll say that the two coordinate systems coincide at time t = 0. (The reason I'm not drawing the lines overlapping is because you wouldn't be able to see the two lines! But presume they're overlapping).

First, let's define a few terms. An event is something which occurs in a specific place and time. Under this definition, World War 1 wasn't an event, because it happened in many distinct places (all over Europe) and over a large span of time (four years if my history is correct). The assassination of Franz Ferdinand was an event, because it happened in one particular location and time (more or less; his death probably took a few seconds, but you get the point).

A coordinate system is a way of describing an event. If a pencil hits the ground next to you, you can describe the location of this event by its position relative to you. Its position relative to me would be very different, yet it is the same event. We just have different ways of describing it.

Alright then, let's recapitulate:
-Einstein showed that the only way for the principle of relativity to be consistent with Electricity n' Magnetism/ Light is for Light to always travel at the same speed <span class="math">c[/spoiler], regardless of how fast observers are moving relative to each other.
-This can only be true if some of our assumptions about space and time are wrong. We require these assumptions to be modified, and that's what we'll do here: show how space and time change between observers.

Okay, so the usual way special relativity is taught is with thought experiments. These are very elegant, very clear...but I'm thinking of trying a different approach, which I believe is more powerful. At the very least, it offers a different way of looking at special relativity (imo, a better way of looking at SR). So, seeing as >>2147835 appears to be the only one hear, I'll let you decide...so you want the usual way, or a diferent way?

>>2147807
So this thread is still alive...nice. I'm in the process of diagramming and stuff, just hold on.