For Igor

Mike inspired me to waste even more time at work today, so I did some research about our favorite discussion topic from this weekend.

 

Space-time

 

Space-time can be thought of as a 4 dimensional grid mapping the history of a particular object/event in the universe: 3 spatial dimensions (x,y,z) and 1 temporal dimension. A beam of light from an exploding star not only travels through a classic 3 dimensions of space, but is additionally marked off in time as it progresses. The history of Earth's orbit around the sun involves the use of 2 out of 3 spatial dimensions (X, Y) and the temporal dimension. While Earth periodically maps an ellipse around the sun in the XY plane, it traces a helix in space time along an orthogonal (perpendicular to the plane) time axis.

 

In classical mechanics, the concept of space-time was not needed, as time was generally held to be constant and independent of all observers; however, modern theory has predicted that velocities which approach the speed of light cause time for travelers to dilate (slow down), and so space-time was needed to model fast objects and give them a location with meaning relative to inertial (non moving or slow moving) objects.

 

Time Dilation

 

Einstein's theory of Special Relativity predicted two important yet counterintuitive results:

 

1) The laws of physics are the same for all bodies in the universe.

2) The speed of light in a vacuum is the same for all observers, regardless of their motion or the motion of the source of light.

 

For example, imagine two ships and a separate light source, together at a starting point. Ship A takes off and maintains a constant velocity of half the speed of light, while ship B maintains a constant velocity of a fourth the speed of light. As both ships travel far away from the starting point, the light source is turned on. In classical mechanics we would expect the observer in ship A to say the light traveled twice as fast as he is, and ship B to say four times as fast; however, special relativity predicts that the light will travel equally as fast past both ships, regardless of their speed. (imagine driving down the highway and seeing someone pass you if this example is unclear)

 

Because the speed of light is constant no matter the velocity you travel, it must be time that changes relative to the observer.

 

Let T be the time measured by a stationary observer (seconds), and T' be the time measured by an observer in motion (seconds), v be velocity (km/s), and c be the speed of light (km/s). Special relativity predicts that the two times, T and T', are related by:

 

T' = T / sqrt (1 - (v/c)^2)

 

So imagine an observer standing on the side of a highway with two points marked off on the road, A and B. As a car drives by, the stationary observer will record the time it takes the car to move between the points, and the person driving the car will do the same. If the car moves 100 miles/hour (.045 km/s), the time dilation is small:

 

T' = T / sqrt (1 - (.045/300,000)^2)

T' = T / sqrt (.9999999999999775)

T' = T / .9999999999999874999999999999993672

 

Since youre dividing by a number so close to 1, in effect the two observers have the same time recorded for this event. However say you travel at half the speed of light and try the same experiment. Then,

 

T' = T / sqrt (1 - (150,000/300,000)^2)

T' = T / sqrt (1 - .25)

T' = T / .866

 

So if the stationary observer (T) says it takes X seconds for the event to occur, the moving observer will say it took.866X seconds to happen (that is, a fraction of time smaller than X). So depending on how you view it, either time is moving slower for the moving person (relative to the stationary person), or faster for the stationary person (relative to the moving person).

 

Of course time dilation at the speed of light causes the equation to break down, as you end up dividing T by 0. In theory though, if you moved the speed of light, youd say a stationary clock ticked infinitey fast (relative to your moving clock) or that a moving clock stopped ticking (relative to a stationary clock).

 

THERE IGOR!

Edited April 22, 2008 by Ryee

hmmmm

 

*points gun to head*

I need to re-read the time-dilation, but I just might not mathematically inclined enough to understand it. I'll have to re-read this when I get to work and probably waste your time discussing this next time we meet up.

 

The thing about space-time, is the way you describe it, its a mapping tool. I can deal with that, even though I might not fully understand it, it's a mathematical problem and it has to do with the way time interacts with space at certain speeds. The thing that puzzled me always is when people talk about space time "taring" or it's a "rubber sheet" gravity supposedly has this great impact on space-time...which in my mind makes space time a "thing" not just a conceptual "grid".

 

I'm not well versed in physics, so I'll have to re-read what you wrote again and probably ask you to explain it to me using hand sings, puppets and maybe a crayon drawing or two.

New nerd information, God I love this shiz.

Sorry I didn't get to see you this weekend Ryee, swollen disk in my back made it tough to do stuff=(

I LIKE PUPPETS. i have crayons too! let's color

everything i need to know about the relation of time and space i learned from time cop.

tl;dr

 

if i could only count the number of times i've heard "but how can space BEND???" from igor.....

can space touch its toes?

I think I have you all beat on that Klaudia=P oh the hours! oh the pain!

At least chad isn't reading this too man XD

But if we take this box Trev....