World Sections

[tetra]

I just had an Idea and want to write it down before I forget.

I was reading an article on dimensions, and circles/spheres and the such, which made me think of conic sections for some reason. I dont know why, but that got me to thinking about world lines (not wure this is it, it is that thing that looks like a conic section in Stephen Hawking's book....

Well anyways, since you can take a plane and intersect it with the conic section so that the plane is perfectly level, you get a circle.

So...

If you take a plane and intersect it with the World Line/Cone thingy, you would get a specefic point in time..

If you know what the hell I'm talking about, please respond.

 

[Chagur]

tetra ...

Like a 4d 'plane' intersecting a 4d 'sausage' resulting in a 3d sphere (the Universe) a la 'Flatland'?

Hmmm ... time for lunch.

Take care

 

[Boris2]

Light cones

If you take a plane and intersect it with the World Line/Cone thingy, you would get a specefic point in time..

The "y" axis is time and the "x" axis is space. The sides of a light cone are at an angle of 45^o. This angle represents light, or information, propagating through space at c (the speed of light). If you cut it with a plane parallel to the x axis you have a particular point in time.

An explanation

http://musr.physics.ubc.ca/~jess/p200/str/str22.html

 

[Crisp]

Small detail...

Hi Boris2,

... just a small detail, but important if you want to continue reasoning in this fashion: the angle between the lightcone and the x-axis is not necessarily 45 degrees. It depends on the timescale (y axis) used. If you express something time on the y-axis in seconds or in days, you will find a different angle.

The angle should be such that the derivative of the lightpath is exactly c, i.e. if you take 300.000 meters on the x-axis (length) and 1 second on the time access, then the line connecting the origin and the point (300.000 , 1) is one side of the lightcone.

Bye!

Crisp

 

[Boris2]

Thank you Mr Crisp, clarification and correction are always welcome. I know little bits of a few topics and struggle with what fits where.