A hypercube is the geometrical concept of an n-dimensional cube. A typical cube exists in three spacial dimensions, where as a square exists only in two. The four dimensional hypercube is called a tesseract, or a 4-cube. It looks a bit like this:
If you want to try draw a tesseract:
- Draw a point, this is the zeroth dimension
- Draw another point and connect the two points with a line, you have a one-dimensional line
- Add three more lines to create the classical square
- Draw the remaining five faces to create a cube, this is now three dimensional
- Now, the fourth dimension. Start by drawing another cube. Connect the respective corners of the cube together.
- Well done, you dimensional physicist, you.
The pretty rainbow above picture is an enneract, or a 9-cube, that exists in nine spacial dimensions.
Time dilation is pretty much the basis for Einstein’s theory of special relativity. To explain what it is, it’s important to know what a frame of reference is.
A common analogy used is to imagine someone is on a train bouncing a basketball. When the train is moving, whoever is bouncing the ball will simply see the ball moving up and down. However, to someone who is not on the train, the ball will appear to move a bit like this:
This is an example of two different frames of reference, the one on the train and one off the train both observe different things. Now imagine that train is going really fast, like half of the speed of light, and replace the basketball with a device to measure time.
Since electromagnetic radiation (light) travels at the same speed in a vacuum, the ‘timer’ should measure light in some way. The timer, shown below, has an emitter that emits a photon or beam of light, and a receiver, that detects the light. For simplicity, I’m going to assume that L0 is very large compared to d0 so that the light travels directly up and down. The time taken for this process, which we call ∆t is equal to the distance the light travels, divided by the speed of light (c).
∆t0 = 2L0/c (equation 1)
So while the train is not moving, both observers can agree on what ∆t equals. When the train reaches a constant velocity, half the speed of light, the observer who didn’t get on the train will see train-person’s ‘timer’ do this:
Now the light has to travel much further to reach the receiver (rather than just straight up and down), and therefore the stationary observer sees the person on the having a slower time interval. Focusing on the frame on reference that the stationary observer is in, the time interval ∆t is the same as equation 1, but from the stationary observer’s point of view, the time interval will be different.
If you want to read the math part:
SCIENCE NEEDS YOUR HELP!
Help! The Los Angeles Science Fair is being cancelled just three weeks before the event due to insufficient funding.
Over 4,000 students have been working diligently since July to compete in this science fair. They are not able to compete in any other counties and will not be able to compete regionally or nationally this year or next if the LA Science Fair is cancelled. One of my best friends is one of these students. He’s been working towards his culminating project since he was 13 and building microbial fuel cells; he’s now a high school senior and may graduate having never been able to compete with his final project.
We need help right now to make this year’s competition happen. Every dollar helps; you can donate here: http://www.lascifair.org/donorspartners/donate-now/
We’re one of the most competitive science fairs in the country; in cancelling this science fair, we’re cutting hundreds of incredible young scientists clean out of the race.
This is about kids loving science. Please don’t let them down. Please please please donate. We’re currently $70,000 short for this year and, if things don’t look up, there will be no 2013 or 2014 science fair.
Still alive. Life reached new low. Probably going to avoid tumblr forever. Thank you all. Keep science-ing it up.
I started inventing things, and I couldn’t stop, like beavers, which I know about. People think they cut down trees so they can build dams, but in reality it’s because their teeth never stop growing, and if they didn’t constantly file them down by cutting through all of those trees, their teeth would start to grow into their own faces, which would kill them. That’s how my brain was.
- Oskar Schell, Extremely Loud & Incredibly Close by Jonathan Safran Foer