A photon left galaxy G, 12 by ago and is reaching Earth now

[Serifos]

... where was our current place in spacetime, call it A, when that photon started its journey 12 by ago?

Did A even exist 12 by ago?

 

[rootone]

This isn't easy to understand, are you talking about light years?
If that is so, a light year is the distance light travels in one year.
If photons are emitted by a star which is 12 ly away from the solar system we see them 12 years later.
If you meant 12 billions of light years, the same is still true, we see then 12 billion years later.

 

[fresh_42]

... where was our current place in spacetime, call it A, when that photon started its journey 12 by ago?

Did A even exist 12 by ago?

Assuming you mean by by billion years, then the answer is simply yes. Where else should have the photon come into existence?

 

[kimbyd]

... where was our current place in spacetime, call it A, when that photon started its journey 12 by ago?

Did A even exist 12 by ago?

I assume "by" is an abbreviation for "billion years"?

There's some inconsistency in the question you're asking there. You say "where was our current place...when [it was] 12 [billion years] ago". This doesn't make sense: our current place is our location at the current time.

That said, this is a really difficult thing to turn into a meaningful question that has a precise answer, and it's difficult to communicate that answer in a clear way. The problem is that in General Relativity, absolute notions of space, time, and simultaneity get thrown out the window. What we can say is that the Milky Way galaxy existed 12 billion years ago (it's about 13.6 billion years old). Before that, the matter that made up the Milky Way was a cloud of gas. Presumably the photon itself was emitted from some star in some galaxy far, far away. That galaxy still exists, though it may have merged with one or more other galaxies in the ensuing time. That star will still exist in some form, though much of its matter may have been scattered through its host galaxy.

 

[Serifos]

If you meant 12 billions of light years, the same is still true, we see then 12 billion years later.

Did that "we" exist 12 by ago?

 

[Serifos]

Assuming you mean by by billion years, then the answer is simply yes. Where else should have the photon come into existence?

So, the current place Earth occupies, existed 12 Billion Years ago? How about 13, or 14 BY ago? apparently, the universe did not exist more than 13.8 BY ago!

 

[rootone]

Did that "we" exist 12 by ago?

No. there were no people and no Earth simultaneous with when the photons were emitted.
Those photons still were emitted though. and arrived at Earth later.
If the Earth never formed, the photons could still eventually arrive somewhere.else where they could be seen.
Then also they may not.

 

[kimbyd]

So, the current place Earth occupies, existed 12 Billion Years ago? How about 13, or 14 BY ago? apparently, the universe did not exist more than 13.8 BY ago!

1. Labeling a specific location in space doesn't mean that location has physical existence in any meaningful sense. The abstract concept of "this location" varies depending upon your assumptions. In particular, it varies depending upon your reference frame. Imagine, for example, two cars going opposite directions on a highway and passing by one another. What is the "real" past location of that point where they pass? Is it the location of an observer standing beside the highway? Of one of the drivers? There's no absolute way to say whose perspective is the "right" one.

The typical way we try to resolve this ambiguity in cosmology is by picking an observer for whom the universe looks simplest: an observer who is stationary with respect to the cosmic microwave background. But this is an arbitrary choice. Any valid slower-than-light trajectory can be used to define the past position of a point in space (these are known as timelike curves).

2. We can't extrapolate back before the singularity in the big bang model. The math breaks down at that point, so even if we make a choice about which observer to use to define the past location, we just can't go back before the start of our observable universe. There are some ideas about what may or may not happen before this, but no solid evidence.

 

[Serifos]

...

The typical way we try to resolve this ambiguity in cosmology is by picking an observer for whom the universe looks simplest: an observer who is stationary with respect to the cosmic microwave background. But this is an arbitrary choice. Any valid slower-than-light trajectory can be used to define the past position of a point in space (these are known as timelike curves).

...

Thank you very much for your comments. I'm trying to understand them and hopefully I'll get there :-)

For an alternate phrasing of my original question, and to clarify it for a couple more posters that had questions, here's an analogy that hopefully can be a bit clearer about what I'm trying to ask:

In our current everyday and common time scale, if start from some point A in space and travel at human-scale velocity V towards some direction in space (disregard planets, stars or other objects), after some human-scale time T I will arrive at some point B. That point B was there already when I started my travel from point A. Correct?

In cosmological time scale, is that also true for that photon that left a galaxy 12 Billion Years away, traveled at the speed of light, and hit a telescope right now on Earth at a 3D point, let's say B? Did that point B exist when the photon left the galaxy? Earth did not exist 12 BY ago, for sure, but did that point B exist when that photon left the galaxy?

Still another way to put it: if I leave now from where I am, and travel at the speed of light for 12 billion years towards some empty spot in the sky (assuming I won't hit any planet, star, etc), is the destination I will arrive to, there already? I think it is, but I may be wrong.

 

[kimbyd]

Thank you very much for your comments. I'm trying to understand them and hopefully I'll get there :-)

For an alternate phrasing of my original question, and to clarify it for a couple more posters that had questions, here's an analogy that hopefully can be a bit clearer about what I'm trying to ask:

In our current everyday and common time scale, if start from some point A in space and travel at human-scale velocity V towards some direction in space (disregard planets, stars or other objects), after some human-scale time T I will arrive at some point B. That point B was there already when I started my travel from point A. Correct?

Well, regions don't just begin to or cease to exist. I'll try to explain how General Relativity describes the universe, and hopefully that will help you to see how this works (I have a hard time just directly answering your question because, well, General Relativity is weird and doesn't necessarily describe the universe the way you'd think).

In strict terms, General Relativity describes the universe as a single, four-dimensional structure, with three dimensions of space and one of time. A useful thing to do to understand this structure, then, is to come up with a way of dividing the universe up into equal-time slices. It turns out that there are many ways of doing this. One way you can do it with our universe is that observers within a given equal-time slice will observe the same time when the average CMB temperature they observe is the same. There are other possible slices (in pedantic terms, an equal-time slice can be made from any space-like surface, and the whole set of equal-time slices is a bunch of space-like surfaces that fill the space and don't overlap). But this is the simplest one when you're trying to describe the expanding universe.

Observers within this structure experience time moving forward, which they see as moving from one equal-time slice to the next. All of the slices are there, but we only experience them one at a time. There's no concept of the individual slices themselves changing because there is no "super-time" which let's it change. It's just a static structure, and time is experienced by moving forward through these equal-time slices.

Then there's the ambiguity of the point "B". Any point in space would be described, with the above system, as a point that moves from one equal-time slice to the next, without ever going backward or traveling faster than light (in pedantic terms, this would be a space-like curve). There are lots and lots of possible curves that go through point B and time T. So, let's imagine you pick one. Every point along that curve is described by General Relativity in a continuous line, with the observer that follows the curve seeing the points on the curve pass one by one (e.g. by watching a clock tick). The whole curve "exists" in a sense, but with different parts of it at different times.

 

[PeterDonis]

where was our current place in spacetime, call it A, when that photon started its journey 12 by ago?

Our current place in spacetime is a single event, here and now; it makes no sense to ask where it was at some other event.

I think you mean our current place in space. That depends on how you choose your coordinates; but I assume your intent is to use standard FRW coordinates. Then our "current place in space" is marked by the worldline of whichever comoving observer (observer who always sees the universe as homogeneous and isotropic) intersects the worldline of the Earth here and now. That worldline extends however far back in time the universe itself extends.

Even with the above corrections, however, asking "where" our place in space was is kind of redundant; a "place in space" is a "where" already.

Did A even exist 12 by ago?

The spacetime event A marks us on Earth here and now. It makes no sense to ask whether it existed anywhere else in spacetime. See above.

If by A you mean the place in space where the Earth is now, see above.

if I leave now from where I am, and travel at the speed of light for 12 billion years towards some empty spot in the sky (assuming I won't hit any planet, star, etc), is the destination I will arrive to, there already?

There are comoving worldlines everywhere, each of which marks a "place in space" as described above. Every one of those worldlines can be extended back as far as the universe extends. So any "place in space" that exists now, or after you've traveled for 12 billion years, has existed as long as the universe has existed.

 

[timmdeeg]

• @Serifos The spacetime diagram shown here in Figure 1 might be of help. Our worldline corresponds to the vertical dotted line at 0. It shows among other issues the increasing proper distances between us and receding galaxies whereby it is only meaningful to talk about cosmological distances at a distinct time (horizontal in the diagram). E.g. a distance between the "place" where a photon was emitted and a "place" where it is absorbed later makes no sense because in this case it isn't defined in general relativity.

 

[Serifos]

...

I think you mean our current place in space.

Yes. Thank your for your comments.

 

[Serifos]

• @Serifos The spacetime diagram shown here in Figure 1 might be of help. [...]

Thank you for that reference. It will take me a while, but I'll try to understand it.