Chapter S3

The shortest path between the two points

1. Gravity arises from distortions of spacetime. It is not a mysterious force that acts at a distance. The presence of mass causes the distortions and the resulting distortions determine how other objects move through spacetime. 2. Time runs slowly in gravitational fields. The stronger the gravity, the more slowly time runs. 3. Black holes can exist in spacetime, and falling into a black hole means leaving the observable universe. 4. The universe has no boundaries and no center, yet it might still have a finite volume 5. Large masses that undergo rapid changes in motion or structure emit gravitational waves that travel at the speed of light.

Equivalence principle is the fundamental starting point for general relativity, which states that the effects of gravity are exactly equivalent to the effects of acceleration. The effects of gravity are exactly equivalent to the effects of acceleration. For example, you cannot tell the different between being in a closed room on Earth and being in a closed room accelerating through space at 1g.

Dimension (mathematical) describes the number independent directions in which movement is possible. Hyperspace is any space with more than three dimensions. A point has 0 dimensions. Sweeping a point back and forth along one direction generates a 1-dementional line . Sweeping a line back and forth generates a 2-dimensional plane . Sweeping a plane up and down generates a 3-dimensional space . Sweeping space back and forth in some "other" direction generates a four-dimensional space.

These different "pictures" are the differing perceptions of time and space of observers in different reference frames. Thus, different observers will get different results when they measure time, length, or mass, even though they are all actually looking at the same spacetime reality.

Spacetime diagram is a graph that plots a spatial dimension on one axis and time on another axis. Worldline is a line that represents an object on a p=spacetime diagram. Event is any particular point along a worldline; all observers will agree on the reality of an event but may disagree about its time and location.

This overall shape must be one of the three general types of geometry. This fact explains how it is possible for the universe to have no center and no edges.

If you are floating freely, then your worldline is following the straightest possible path through spacetime. If you feel weight, then you are not on the straightest possible path.

Gravity is one of the four fundamental forces; it is the force that dominates on large scales. The fact that Earth goes around the Sun tells us that spacetime itself is curved near the Sun. in other words, what we perceive as gravity arises from the curvature of spacetime.

In flat regions of spacetime, freely moving objects move in straight lines. The mass of the Sun causes spacetime to curve, so freely moving objects (such as planets and comets) follow the straightest possible paths allowed by the curvature of spacetime. Circles that were evenly spaced in flat spacetime become more widely spaced near the central mass. A mass like the Sun causes spacetime to curve, and the curvature of spacetime determines the paths of freely moving masses like the planets.

If the Universe began in an explosion and is expanding, is it or is it not required to have a center? No. Once the Universe began to expand, it became like an expanding surface. Space itself was expanding. Once objects began to appear in the Universe, we had some "markers", if you will, against which to establish coordinate locations. Try as we might, however, we have never been able to use these galaxies to establish a spatial preference in the Universe. There is no center, and all of space seems to be expanding away from all of the rest of space. No matter where you are.

If we shrank the Sun enough, we could eventually curve spacetime so much that it would become a bottomless pit - a hole in the observable universe, which is called the black hole . The boundary that marks the "point of no return" is called the event horizon.

Time runs slower in places where gravity is stronger. Earth is following the straightest path possible through spacetime, but this path happens to go around and around the Sun. we use it to represent spacetime. The issue is it is 2D and we have to ignore any effects of friction bc there is no friction in space.

Gravitational time dilation is the slowing of time that occurs in a gravitational field, as predicted by Einstein's general theory of relativity. a . In an accelerating spaceship (but not in one at constant velocity), time must run faster at the front end and more slowly at the back end. b . By the equivalence principle, time must also run more slowly at lower altitudes in a gravitational field.

Einstein proved that time runs more slowly and space is more curved on the part of Mercury's orbit that is nearer the sun. Gravitational lensing is the magnification or distortion (into arcs, rings, or multiple images) of an image caused by light bending through a gravitational field, as predicted by Einstein's general theory of relativity.

Gravitational waves are waves, predicted by Einstein's general theory of relativity, that travel at the speed of light and transmit distortions of space through the universe. Although they have not yet been observed directly, we have strong indirect evidence that they exist.

Wormholes is the name given to hypothetical tunnels through hyperspace that might connect two distant places in our universe. The curved sheet represents our universe, in which a trip form Earth to Vega covers a distance of 25 light-years. This trip could be much shorter if a wormhole existed that created a shortcut through hyperspace.