Let's use a space-time diagram. Time runs vertically, space runs horizontally. On this diagram I've drawn two points, each representing an event. An event means "something happens at this point in space at this point in time", which is a unique location in space-time. On this diagram, Event 2 happens in the future from Event 1, and in space further to the right than Event 1.

I also put in yellow lines leading from event 1 to represent the speed of light (imagine event 1 is a flash grenade going off). In a space-time diagram we often choose units of space and time so that the speed of light is a 45° angle (for example, 1 light year of distance in 1 year of time), so this pulse of light extends upward as a 45° cone. A.K.A a "light cone". Since nothing can go faster than light, all allowed paths from event 1 must lie inside the light cone.

Finally, I've drawn two possible paths that a person could follow to get from the first event to the second event. Both paths are at speeds slower than light, but one is more direct. Path B in blue moves at constant velocity, while path A starts off moving to the left, then slows down and changes direction to reach Event 2.**Question: Which path is shorter? (Has the shortest distance in space-time?)**The counter-intuitive answer: Path A is shorter!

In Euclidean geometry, a straight line between two points is always the shortest. But space-time obeys a different geometry. Instead of the Pythagorean theorem where distance is defined as sqrt(x^2 + y^2), distances in space-time are sqrt(t^2 - x^2). That minus sign makes all the difference. Instead of the most direct path between events having the shortest distance, it's the

*longest* distance! Any change from a straight line between two events will make the length of that path

*shorter! *And if your change in x equals your change in t (such as moving 1 light year in space in 1 year of time, meaning moving at the speed of light), then the length of the path is zero. (That's right, those two yellow lines have zero length!)

And the final bit of insight: What we perceive and measure as time is not the time axis. Clocks do not measure

**t!** What they measure is the distance they have traveled in space-time,

**t**^{2}** - x**^{2}. That means if you move from Event 1 to Event 2 on the direct path B, you measure the

*longest* time elapsed on your clock! If you instead follow the less direct path A, you will measure a shorter time! Or if you move at the speed of light between two events (you can't actually, but we can consider the limit that your speed approaches c), then your clock will never tick! The entire trip goes by in an instant according to you.

Salvo wrote:Source of the post It seems like more you're inside a curvature of space more you move faster inside time. Actually, you also move faster inside space, so it makes sense...?

It's the other way around! Clocks tick more slowly in a stronger gravitational field (more space-time curvature). Time at sea level on Earth passes more slowly than time on top of a mountain. But you're also not moving in space. If we're using coordinates fixed to the Earth, then as you sit on the surface you are not changing your position. Your change in x is zero. You are moving in time, but again what you measure on your clock is the distance traveled in space-time, and because that space-time is now curved that distance is shorter than it would be in flat space-time. Or put another way, that slower passage of time on a massive object is a direct manifestation of the curving of time by the gravitational field near that mass.

Salvo wrote:Source of the post Well, if you was in complete void inside intergalactic space and no gravity source from any direction you should stay still in time too, right?

Again just the opposite. If you're floating still far from any gravitational sources (flat space-time), then you are not moving in space and only moving in time. Since the time you measure is sqrt(

**t**^{2}** - x**^{2}), and you're only moving in

**t***, *your clock ticks at the fastest possible rate (compared to anything else in the same flat space-time). Any movement you make will change your x and make your clock tick slower.

Put another way, clocks always tick the fastest in a frame of reference where the clock is at rest (i.e. you move with the clock).

Salvo wrote:Source of the post Probably not, instead the illusion is that parts of the universe that contains no visible matter are the ones that expands faster, and they expand faster and faster more is the void that they contain. Probably because they mainly contain dark energy so there is not an opposite force from baryonic matter's curvature of space that opposes the "negative pressure" of dark energy.

The whole universe expands uniformly at large scales. Pick any two points sufficiently separated in space, and the rate at which they recede from each other is proportional to the distance between them.

Locally, matter in the form of galaxies and clusters of galaxies "break off" from the expansion, because they are bound together by gravity. So galaxy clusters and everything within them do not expand at all, while the space around them expands and drives the clusters apart.The expansion itself is a consequence of the Big Bang. If the universe was empty then that expansion rate would stay at the same value forever. Introducing matter and radiation pressure to the universe acts to slow the expansion rate down, while dark energy causes it to speed up.