A Mental Conundrum -- The Big Bang & the Speed of Light

[ckirmser]

OK, knowing enough astrophysics to get myself hurt, I'd like to pose the following poser that whupped me upside the head while watching the Black Hole marathon last night on the Science Channel.

We have;

1) The Big Bang theory,
2) An expanding - at least, for the moment - universe, and
3) The speed of light.

Now then, given #1, that would mean that, at some point in time, everything was at one specific point. So, as #2 progressed, I figure we can probably assume a general trend of all things moving - more or less - in a straight line from that point and each other, at least in the context of using an expanding balloon as an analog (on the surface of that balloon, everything is pretty much moving directly away from everything else, with proper motion in local space that would probably be absorbed by the noise).

Given #3, the maximum speed at which the universe expands is pretty much set in stone.

So, those points led me to the following path along Thinking Street, whereupon I am probably walking smack into various streetlamps of ignorance;

Let's take a look at GRB 090423, a Gamma Ray Burst 13.035 billion ly away. As I understand current theory, the light reaching us from GRB 090423 today, was emitted by that burst 13.035 billion years ago. As the story goes, we'd be seeing what that burst looked like in the past.

But, 13.035 billion years ago, GRB 090423 was not 13.035 billion ly away. It was closer, due to expansion, so that light it emitted 13.035 billion years ago had already reached the Earth.

This thought caused my brain to coalesce into a rather viscous goo which then drained from my sinus passages into a particularly unpleasant slop on my desk.

Do I have that right? Wasn't every object, in the past, CLOSER to the Earth, such that the light we are receiving now was already received back when the emitting object was closer?

What am I overlooking?

 

[Bandersnatch]

The confusion stems mostly from point #3, although point #1 is not correct either.

The expansion of space is not limited by the universal speed limit. The reasons for that are somewhat hard to grasp intuitively. The expansion is a geometric effect, which in a way means that everything stays in the same place, but the distances are all* increasing. One way of seeing that is how despite the faraway galaxies moving at >3c, nothing can overtake light localy.

#1 is wrong in the sense that you can extrapolate backwards in time to get the observable universe to occupy arbitrarily small volume, but given how the universe can very well be infinite it doesn't mean that all of it was concentrated in a point. Not to mention that you can't really talk about point in space when it's that very space that you're trying to visualise as being a point (i.e., a point in where?).

 

[ckirmser]

Well, as the Big Bang is referred to as a singularity, isn't a singularity a point?

Further, I've heard and read of how, at one time, the Universe was the size of an electron. Well, OK, an electron in where?

If a distant galaxy is moving away from us at greater than 3c, then that galaxy is in violation of the speed of light, is it not?

OK, you mention the "observable universe." I can go with that. So, the "observable universe" is contained within the actual universe. But, still, the light reaching us from that distant object supposedly determines how far from us that object is. That's fine, if the object's position is static. But, if it's moving away from us, then it follows that, when the light from it reaches us from such vast distances, it was reflected - or, emitted, depending on the object - when the object was closer. If it was closer, the that light had already hit us. So, the light hitting us seems to be light that started it's journey in the future of the object, not the past.

 

[phinds]

Well, as the Big Bang is referred to as a singularity, isn't a singularity a point?

Absolutely not. It is a shorthand word that means "the place where we know our math model has broken down because it gives results that can't be physically possible".

Further, I've heard and read of how, at one time, the Universe was the size of an electron. Well, OK, an electron in where?

This is TV nonsense that you will not find in physics books. Even the observable universe would not have been that small.

If a distant galaxy is moving away from us at greater than 3c, then that galaxy is in violation of the speed of light, is it not?

absolutely not, and for the reason that ckirmser explained. Google "metric expansion" for a full expanation"

OK, you mention the "observable universe." I can go with that. So, the "observable universe" is contained within the actual universe. But, still, the light reaching us from that distant object supposedly determines how far from us that object is. That's fine, if the object's position is static. But, if it's moving away from us, then it follows that, when the light from it reaches us from such vast distances, it was reflected - or, emitted, depending on the object - when the object was closer. If it was closer, the that light had already hit us. So, the light hitting us seems to be light that started it's journey in the future of the object, not the past.

No, the light started out as you say, close to us than the object is now, but that was still in the object's past. You DO need to be careful here about non-local time comparisons and when objects are moving. They don't always work the way you would expect. Google "relatively of simultaneity" for more.

I recommend the link in my signature.

 

[ckirmser]

I recommend the link in my signature.

It looks like the basic theme of that link is not so much that the balloon idea is invalid, but that it has some issues that lead to misconceptions and confusion. However, it seems that, overall, the concept of the pennies spreading as the "balloon" expands, seems to still hold.

Then, let us take Penny 1 and Penny 2. Then, let us introduce a packet of light leaving P₁ on its way to P₂, represented by an ant. The ant, being the light analog, walks at a certain speed and nothing can go faster than that speed, let's say 1cm/s. Then, for this illustration, let the expansion of space be 0.25cm/s.

Then;

Well, even if what I'm pondering is correct, I was still wrong in my conclusion, if I've done this right.

The ant that left P₁ at T₀, didn't reach P₂ until T₆ - well, actually, a little past T_5.5 - so, the light hitting P₂ traveled FURTHER than what the distance was between P₁ and P₂ at T₀; I guess around the distance they were from each other at T_4.75.

Now, am I totally screwed on this, or is there any merit?

 

[Bandersnatch]

Let's take a look at GRB 090423, a Gamma Ray Burst 13.035 billion ly away. As I understand current theory, the light reaching us from GRB 090423 today, was emitted by that burst 13.035 billion years ago. As the story goes, we'd be seeing what that burst looked like in the past.

But, 13.035 billion years ago, GRB 090423 was not 13.035 billion ly away. It was closer, due to expansion, so that light it emitted 13.035 billion years ago had already reached the Earth.

This thought caused my brain to coalesce into a rather viscous goo which then drained from my sinus passages into a particularly unpleasant slop on my desk.

Let me address this more directly, as you are absolutely correct both in what your intuition is telling you as well as in appreciating the difficulty imagining a dynamically changing universe poses.

The first intuition when hearing about the current cosmological model is usually, as you said, to imagine a static universe. Here, its age of ~14 billion years leads one to think that it's spatial extent is 14 billion light years.
It's nice and simple, although there tends to be some resistance to grasping the fact that the farther you look, the older an object is. We have to come to terms with age not being a universal constant across the universe.
This is way too often the level of understanding presented by TV science shows.

When nudged to include expansion in the picture, a mind should correctly reach the same conclusion you have. Light reaching us after X years used to be closer than X*c light years. But that's not all. If we were to freeze-stop the expansion now, and try to find out where that objects we see is at this moment, we'd find out it's much farther than X*c.
Taking as an example the oldest thing we can observe, the cosmic microwave background radiation:
-after 13.8 billion years of travel the light reaches Earth
-it was emitted about 42 million light years away from the point corresponding to Earth's current location
-at this moment, it is about 46 billion light years away

The example of an ant walking between two pennies that you used in the post above is almost correct. You'you've made a mistake in assuming that the expansion of the distance between the pennies is a constant value per unit time, while it should be a constant* growth per unit time per unit distance. In other words, you should use a percentage growth per unit time, e.g. 0.1%/s. This results in the pennies' accelerating recession (in a similar way to how money in a savings account grows exponentially).
This is related to Hubble law: $V=Hd$, where the recession velocity increases with distance. And since velocity means that the object is moving farther away, it's recession velocity will keep on increasing rather than being constant.

One of the results of this seemingly minor adjustment is that there exists a distance between the pennies above which their recession velocity will be higher than the ant's walking speed, so for every step it takes towards the far away penny, the same extra space "appears" for the ant to walk. In other words, the ant won't be able to ever reach the other penny if it starts farther than that distance.

In the actual universe, the recession rate expressed in terms of a percentage growth is currently* 1/144th of a percent per million years. That's how much every distance grows over that time interval.
The boundary marking the farthest distance from which light signal emitted NOW can ever reach us is called the Hubble radius, and is the reciprocal of the inverse of the Hubble's constant. It currently* equals about 14.4 billion ly.
It's worthwile noting that it being close to the age of the universe is a coincidence.

*As if this wasn't mind bending enough, there's still the non-constant rate of expansion to take into account.
The Hubble constant is not constant in time, but across space. It had a different value in the past, and will asymptotically approach a different value in the future. This changes a few things that I shan't explain here as I'm sure it's already a royally confusing mess.A side note, have you read any of the links provided at the bottom of phind's "balloon analogy" webpage? I especially recommend the second one (the one by Lineweaver and Davies). It's probably the most clearly laid out and accessible treatment of the whole shebang I've ever seen.
They have also written a more in-depth and technical primer on cosmology (linked in that article), should you ever feel the need to delve deeper into the subject.

 

[ckirmser]

The example of an ant walking between two pennies that you used in the post above is almost correct. You'you've made a mistake in assuming that the expansion of the distance between the pennies is a constant value per unit time, while it should be a constant* growth per unit time per unit distance.

Well, it wasn't so much an assumption as it was a simplification. I didn't want to go into the variable rates as Hubble's Law states. I just wanted a simple illustration to graphically show my understanding. Although, in retrospect, I guess I could have used a logarithmic rate, rather than linear, to model the pennies' movement.

A side note, have you read any of the links provided at the bottom of phind's "balloon analogy" webpage? I especially recommend the second one (the one by Lineweaver and Davies). It's probably the most clearly laid out and accessible treatment of the whole shebang I've ever seen.
They have also written a more in-depth and technical primer on cosmology (linked in that article), should you ever feel the need to delve deeper into the subject.

I'll have to go over those and see if I can make that puddle of goo larger...

 

[phinds]

I'll have to go over those and see if I can make that puddle of goo larger...

Don't feel bad, we all go through this. Things in cosmology (the very large) and Quantum Mechanics (the very small) are WAY outside of human's evolutionary experience and not anything that there was any survival value in knowing (because it was all unknowable for all but the tiniest portion of human evolution) so "common sense" and "intuition" are often not only not helpful in those arenas, they are downright counter-productive. When I was first learning both, I used to run around screaming "THAT CAN'T BE RIGHT !" and tearing my hair out.

 

[Bandersnatch]

If you're the kind of person that likes to think in numbers, I'd recommend exploring the calculator made by one of the forum members (Jorrie). Here's the link:
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html
It calculates all the various distances, redshifts and velocities at various times in the universe's history for a given set of parameters.
We've got a sticky thread in the cosmology section of the forum about the "leaner" version of it(A20). Either exploring that thread or searching for forum memeber's marcus' posts (he does a great job at explaining) should help you understand how to read the output of these calculators. It's less daunting than it seems at first glance.
These are pretty powerful tools and can offer great intuitive insight into the expansion process.