Circa 1972 or so, shortly after Martin Gardner published John Horton Conway’s Game of Life in his math column in Scientific American, I coded a version of it that worked on a torus this way. I was using a machine with a 60-bit word, so it had a 60x60 grid. Later, I coded it on a PDP-10 which has a 36-bit word, and I used 6 words per row, so it had a 216x216 grid.
If you aren’t wearing your BCD when you get to the edge of the Universe, you fall off.
*Christopher Columbus was a seaman second class,
When I told him that the Indies could be found
By sailing to the West instead of sailing to the East,
I advised him that I thought the world was round.
So then he went to ask good queen Isabella
To pawn her jewels for all they’re worth.
Next day he set sail, and as everyone knows,
He fell off the edge of the Earth.*
– Allan Sherman, Good Advice
you can’t go past the edge of the observable universe because space would be expanding faster than light
obviously if plotdevicium can something something something faster than light then you could could get there and it would look pretty much the same as from here
if the universe curves back on itself, you’d experience probably the thing a person on the surface of a sphere would experience when they get back to their start when they traverse an object whose centre is in the dimension above
From our POV on earth, yes.
But if you were already at the ‘edge’ of the observable universe as specified in the OP (defined as observable from earth), you sure could. The space right next to you wouldn’t be expanding away from you any faster than the space right next to you does here. It’s unnoticeably small.
To expand (no pun intended) on what I said above: there are two horizons that may or may not be present in a cosmological model:
The particle horizon: this is the surface of how far* a photon can have traveled (in theory) from the big bang until it arrives at an observer on Earth in the present cosmological time. It is the theoretical limit on how far you can see and marks the boundary of the observable Universe.
The event horizon: this the surface how far* a photon, starting now can travel before it reaches the infinite future/big crunch. It is effectively the limit of which galaxies we could reach in the future if we set-off now.
As well as the two horizons, there is another surface which often confused with a horizon:
The Hubble surface: this is the surface where the recession velocity is equal to ‘c’ (the speed of light). For obvious reasons this often confused with the particle or event horizons, however recession velocity has pretty much no direct physical meaning, so the importance of this surface should not be overstated.
Some cosmological models have all 3 of these surfaces, some only have 1 or 2 (e.g. de Sitter space doesn’t have a particle horizon as it doesn’t have a big bang) and the surfaces in a model needn’t exist at all times in a cosmological model (e.g. in a Universe that expands and then contracts the Hubble surface will stop existing the moment the Universe stops expanding). In some cosmological models some these surface coincide (e.g. in de Sitter space the Hubble surface and event horizon coincide).
It is also not fixed which surfaces are bigger, for example in the LCDM standard cosmological model, at early times:
event horizon>particle horizon>Hubble sphere
Whereas at current times:
particle horizon>event horizon>Hubble sphere.
*When I say ‘far’ I mean in terms of ‘co-moving distance’, i.e. the distance mapped onto the present day Universe. The ‘proper distance’, i.e. how far something actually travels, of a photon travelling to the infinite future is of course infinite.
Space is expanding, and expanding faster the farther from earth you see. So, assuming you travel at speeds far higher than the speed of light, you would be actually “chasing” the horizon of the universe that is expanding away from you.
If your speed is high enough, then, ignoring all other relativistic effects, you should have a grand view of the Big Bang itself, as photons released during that explosion start reaching your eyes. (They have been travelling towards us all the time at the speed of light, but space expanding faster than the speed of light meant they could never reach us. But your travelling faster than the metric expansion of space overcomes that and enables the photons reach you.)
Starting as a dim red wall of radiation, building up to infinite brightness at all wavelengths, you’d head right into the grandest cosmic spectacle imaginable.
OK, you’ve seen the Big Bang. Your body is fried but your spirit still lives. What next? Since nothing can travel faster than light, there can be nothing travelling “ahead” of the wall of light. So in effect the universe ends. You’ll find heaven or hell at that point, depending on your karma.
You don’t need to move fast to see the Big Bang. We see it right now. It would, however, become more impressive at high speed, as the portion ahead of you blueshifts into something more energetic than mere microwaves.
The Cosmic Microwave Background (CMB) is made of the photons released at the time of recombination, about 380,000 years after the Big Bang. We do not see the Big Bang itself. If we could see the Big Bang, we would also have already seen the farthest corners of this universe, as nothing is farther away from us than the photons of the Big Bang.
Light reaching us from the big bang would be the light that has travelled all the way from the particle horizon (in theory that is), i.e. from the very edge of the observable Universe. Where there exists a particle horizon there will be space beyond the particle horizon for which light has not have had time to travel to reach us and in some models there are parts of space which lie permanently outside our event horizon and from which light will never reach us.
There are no photons left from the moment of the Big Bang, because at the moment of the Big Bang the universe was opaque and any photon that was emitted was almost instantly reabsorbed.
The universe ceased to be opaque at the time of recombination that you make reference to. The CMB are the red-shifted photons that were emitted at the time the universe became transparent to EM radiation. That’s as far back as we can see.
Since the Big Bang happened everywhere in the universe simultaneously, it makes no sense to say “nothing is father away from us than the photons of the Big Bang”. If there was some exotic form of radiation that was capable of propagating through the primordial cloud, we could use it to “see” the moment of the Big Bang. But there would still be other things in the universe more distant than the source of that radiation.
We could “see” further back via neutrinos, or further yet via gravitational waves. Even those have limits, though, and at early enough times (far less than a second), the Universe was opaque even to gravitational waves.
According to special relativity, it is not possibly for “something” to move faster than c without conflicting with causality. The “edge of the universe” is not a thing, per se, but an abstract concept, so it can travel faster than a thing. But logically, it makes no sense, the edge of the universe is moving backward in time. Yet, it might make sense if we were to perceive 3-space as flat with a curved 4th dimension: the universe (spacetime) may be temporally circular (with respect to the spatial dimensions – unless, of course, time is multi-dimensional).
I’m not following… how is the “antipode” moving away faster than the speed of light if the predominant theory is that the speed of light is the fastest possible speed?
My understanding is that the speed of light is constant, and that even two beams of light pointing pointing in opposite directions would still move at only the speed of light relative to each other (contorting time to do so?). So not even light while riding on one of the first photons produced at the Big Bang would the other end of the illuminated universe be moving away faster than the speed of light.
Speed of light is a limit for massive particles, because it would take infinite energy to accelerate an object to the speed of light. Even subatomic particles have been clocked very, very close to the speed of light, but not surpassing it, because they have mass, and it takes an infinite amount of energy to push that little mass to c and beyond. This even applies to neutrinos, which are currently the lightest particles discovered to exist.
Non-material “objects” do not have this limitation - the metric expansion of space is one such. Space itself is expanding, and as it expands, it carries away objects embedded in it (such as galaxies) “faster” than c - the galaxy itself is NOT moving faster than c. But the galaxy does appear to recede faster than c - this indicates the metric expansion of space, not a local velocity faster than c.
I was about to write a post about my confusion but in thinking about it I think I may have answered my own question.
(First thoughts)
How can the event horizon be larger than the Hubble sphere. If the universe is expanding such that the space between us and an object is increasing faster than the speed of light how can we hit it with an light pulse.
(Second thoughts)
The space between us and the lightpulse will also be expanding, and this extra boost will allow our light pulse to hit the object beyond the Hubble sphere.
Is that right?
Assuming the space carries the light particles along with it. If every step your light pulse takes does a little Zeno’s Arrow thing in reverse, and puts your destination slightly farther away from you, then you’ll never get there.
Your thinking is pretty much correct, though it depends on the detail of expansion. If the expansion is ‘less than’ exponential then the light (departing now) will reach to the space beyond the current Hubble sphere.
I am using the below paper as the basis for my comments on the LCDM model, the most instructive diagram (IMO) is the third diagram on page 3 in which the relative size of various surfaces are expressed conformally:
No, this is not right: it depends on the details of expansion.
Well, that’s kind of what I meant by “if”.
Because I don’t know. I guess I should have tried to phrase that more as a question .
You find a planet ruled by apes.
It’s Earth.
Hey, it’s impossible to leave the observable Universe if you start from the observable Universe and don’t exceed the speed of light, right?