Do all geodesics begin and end at the big bang?

[gregatphysics]

TL;DR Summary

So I was standing outside one night, and it occurred to be that I was looking back toward the Big Bang. I then realized that every direction I looked toward at, I was looking toward the Big Bang.
So: DO all geodesics begin and end at the Big Bang?

If all geodesics begin and end at the Big Bang, then every point is (always (at)) the Center of the Universe.

So. It was late night, the limpid sky a near cloudless darkness, somewhat lightened by the waxing moon. I being somewhat stoned and looking at the stars and constellations as I sometimes do, and it came to seem to me, in my imagination, that In the spaces between the stars, I was observing (in my imagination, The CMB is too cold to actually light up an electron.) the CMB. And that behind the veil of the CMB was, in my extended imaginary and hopefully straight lined vision, the Big Bang.

And then I thought, wait a minute. I'm looking in a random direction. I could be looking in any direction, and the vector of my imagination, would point to the Big Bang.
Then I thought, Whoa! What kind of space is this,? where all the points at "infinity," in every direction are- the same point?

And then, of course, if my interpretations of my observations were correct, it was trivial to conclude that every point is always at the center of the universe.

 

[phinds]

1) The universe has no center.

2) A geodesic is just the space-time equivalent of a straight line. There is a geodesic from the moon to Earth, for example and if you hold an apple out in your hand and let it go, it follows a geodesic towards the gravitational center of the Earth.

I recommend the link in my signature for some basic cosmology

 

[PeterDonis]

I could be looking in any direction, and the vector of my imagination, would point to the Big Bang.

That depends on how you interpret the term "direction".

The light rays actually reaching your eye are following null worldlines through spacetime; that means that they are telling you how things were in the past in the direction they are coming from. In that sense, yes, you are looking at the Big Bang, because the Big Bang is in the past if you go back far enough, no matter which direction your light rays are coming from.

However, if you are thinking of the "direction" you are looking as pointing to a place you could, in principle, get in a spaceship and travel to, then no, the Big Bang is not in that direction, or in any direction. You can't travel to the Big Bang; it is not a place. It's a moment of time, far in the past.

if my interpretations of my observations were correct, it was trivial to conclude that every point is always at the center of the universe.

No, it isn't. "Every point is always at the center of the universe" is a logical inconsistency. The correct conclusion is that the universe has no center.

 

[Orodruin]

All past-pointing null and time-like geodesics end up at the Big Bang (at least as far as the cosmological standard model is concerned). There is no guarantee that space-like geodesics will do so or not.

As has been said already, light follows null geodesics.

 

[Ibix]

The problem is that anywhere you look you are looking into the past because of the finite speed of light. So you always see the CMB (wherever your view isn't blocked) because it was everywhere in the past. But that doesn't mean it's still there - it was everywhere 14bn years ago, but it isn't anywhere now. You can always see the CMB but you can never get closer to its surface. It will always appear further away from you today than it did yesterday because all you are seeing is light emitted a long time ago, not anything that's there now. Any part of the light that doesn't hit anything will just carry on flying forever, it won't return to the beginning of time, which is what it would have to do for its path to end on the Big Bang as well as start there.

 

[PeterDonis]

that doesn't mean it's still there - it was everywhere 14bn years ago, but it isn't anywhere now

More precisely, the "surface of last scattering" that emitted the CMB was everywhere 14bn years ago, but it isn't anywhere now. The CMB itself is "still there" now, because we're seeing it.

 

[jbriggs444]

DO all geodesics begin and end at the Big Bang?

Others have spoken about geodesics that extend into the past. Under the current model of the universe, those geodesics typically extend infinitely into the future without encountering a singularity. They can also terminate finitely in a black hole.