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Depth of Field

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> The oldest of the photons that ended their life in the electronics of the Hubble had traveled from their birth star across the universe for 13.2 billion years. These photons had already completed half of their journey when the earth coalesced.

Somehow this made me think of playing a video game in which you’re trying to steer between a bunch of obstacles and one magically grows right in your path.

If anyone missed it, the last paragraph is of interest in its own right.

I often think about these kinds of numbers when talking with my father-in-law, who's a marine geologist, and who regularly talks about time in millions of years. I wonder if he has a real grasp of the scale of what that means, in the same way that I might understand hours / days / months / years / decades. The only way he can explain it to me is by metaphor, which is what this post does. It's sort-of-effective, but what it mainly does it prove to me how little I comprehend numbers like that. I find even centuries are a little difficult to wrap my head around.

I think the answer is necessarily: he does and doesn’t. Analogy is probably the only way to try and make these numbers concrete, but he can develop a stronger intuition and respect for the time scale with domain experience.

What exactly makes the light from these distant galaxies so “weak” that we need to point the telescope there for months to see it?

Like, isn’t there a constant stream of photons? How does just waiting longer for them make them show up if they wouldn’t have otherwise? Are things blocking most of the photons? Things from within the galaxies they’re coming from, or things in between the galaxy and the telescope?

edit: Ah, I suppose the further an object is the fewer photons from it are making it to the telescope, and so we need to wait longer for enough photons to arrive to be able to distinguish it from the random background noise on our end?

Yes, it's called NOISE!

But what specifically is it? Just random stuff in deep space between galaxies? I’d have thought most of the space between galaxies is mostly truly empty.

Isn't the paradox that if the universe is static in size or shrinking, eventually all the light would fill the sky into a blinding display, rather than dark. So it's a function of the universe expanding.

https://en.wikipedia.org/wiki/Olbers%27_paradox

The noise is inherent to our sensor technology... Very sensitive telescopes are cryogenically cooled to reduce the temperature of the focal plane, reducing the noise. As in an above comment, the light from distant objects is more spread out and appears weaker - fewer photos are arriving each second and hitting the focal plane than if the telescope were closer. At a certain point, the signal gets buried in the noise.

I worked on the BICEP Array telescope at the south Pole - the light we are observing is actually extremely low energy and we can't see it unless our detectors are colder than the light source we are looking at (which is about 2.7K). We cool our detectors to 0.3K!

Does the natural cold at the South Pole make it much easier to cool the instruments down that low? I know it's around 200K at its lowest, how does that make it easier and cheaper?

Yes, there are several factors that make that location particularly good, not only temperature. The cold and absence of sunlight for months at a time causes a relative absence of water vapor in the atmosphere during winter, which is extremely important for CMB observations. The high elevation (~10k ft) means there is less atmosphere to look through as well. During summers the sky heats up, contains more water vapor, and reflects so much more light that our telescopes become substantially less effective. Another advantage to the South Pole is the ability to continuously observe the same part of the sky, as the telescope is located on the earths axis there is no rising and setting of sky overhead. There is also a particularly 'dark' patch of sky in the southern hemisphere called the 'southern hole'. This is located up and away from the plane of our galaxy and contains very few objects standing in the 'path' of the CMB which also helps obtain better quality observations of the CMB.

Edit - it is as good as it gets on earth and way cheaper than a satellite! Other benefits are rapid upgrades and repairs with newer technology. A satellite, by the time it is deployed, is already pretty old! But the South Pole still isn't cheap!

As a sibling already mentioned, thermal noise occurs in the sensors. And there is also a range of cosmic background radiation coming in, including the cosmic microwave background which is just everywhere and is almost as old as the universe.

The noise is coming from inside the sensor: https://en.wikipedia.org/wiki/Johnson%E2%80%93Nyquist_noise

Cryogenically cooling helps, but since you can't hit absolute zero you can't entirely eliminate it.

Right, what I was missing was why how far the source of the light is effects how much the noise matters, but the inverse square photon concentration explains that.

There is read noise from downstream electronics converting photons to electrons, but the "shot noise" is a property of the photon stream and will be present regardless of how much we improve the electronics. Cooling the detector won't help there.

https://en.wikipedia.org/wiki/Shot_noise#Optics

The strength of light over a distance obeys an inverse square law[1], causing it to effectively lose power over long distances, since the same amount of energy is being spread over larger and larger spheres as it radiates out. For photons, I think this manifests as there being a lower rate of photons occurring in each section of the sphere since they’re “spread out”.

[1] https://en.wikipedia.org/wiki/Inverse-square_law

Doesn't this fail because we're looking at lots of stars spread out evenly, and so the farther you get away, the more stars fill the space?

Space is mostly empty.

As a sibling comment to yours says, Olbers’ paradox is that it doesn’t matter.

If we assume that the universe is homogeneous, infinite, and eternal and the density of stars (possibly averaged over a large but constant scale) is constant, then in any direction on the sky there is some (possibly very faraway) star, occupying a finite (possibly minuscule) solid angle in our field of view. The 1/r² falloff (aka conservation of energy) means that the energy received per unit of solid angle is independent of distance from the emitter, equal for example to that on its surface, so every piece of the sky containing a star means we should see stellar-surface amounts of energy shining upon us from every direction.

Assuming some sort of absorbing dust would obscure the stars doesn’t help: if the universe truly is eternal, every dust cloud, being unable to store arbitrarily large amounts of energy, will eventually heat up to the point that it radiates as much as it absorbs and so is as hot as the stars which it obscures (this is the insight behind Kirchhoff’s law and the existence of blackbody radiation).

What does help is either implementing “no point in space is special” through a device other than simply a constant stellar density (e.g. having stars distributed on a self-similar fractal of Hausdorff dimension < 3, our falloff argument having included what amounts to a definition of Hausdorff dimension) or abandoning “no point in time is special” (giving the universe a finite age or at least having no stars in the far past). Observations show the second possibility (named the “Big Bang” by its critics in what was meant to show its ridiculousness) to be true.

(Modern cosmology has much more direct arguments for a finite age of the universe, but they also require more advanced physics and/or observational technology, so the directness is in the eye of the beholder.)

But isn't space expanding? And the expansion is accelerating?

It still depends on their contribution right? If you said all lights are equal in strength, then being on top of one gives a strength of 1. Being x units away from it gives a some value less than 1, based on the sqrt of distance

Being close & between two lights would take the sum of their strengths, say .75 each so 1.5, giving a value greater than 1 (more light than either individually produces)

Being far from the two lights, each contributes .25 strength, so .5 total — half the light of standing on top of one

And of course if you get really far, a ridiculously large number of light sources are contributing a ridiculously small amount of light, which may still sum to something fairly small

I’m imagining it works like an influence map: https://www.gamedev.net/tutorials/programming/artificial-int...

This is Olbers' Paradox[1] and is one piece of evidence that the universe isn't static.

1 https://en.wikipedia.org/wiki/Olbers%27_paradox

Pretty nifty how the example images of things like the sand grains (but make it Deep-Field-y) were made. I was hoping for an explanation, and the author didn’t disappoint.

If you're interested in AI art, I've made a few more things built out of a series of generated images around a theme.

https://moultano.wordpress.com/2021/08/23/doorways/

https://moultano.wordpress.com/2021/07/20/tour-of-the-sacred...

I need this in my life; it would be great to create engaging lectures. Is there anything like MidJourney but public?

Nothing super user friendly. Most of the things people make right now are via various Google Colab notebooks.

https://twitter.com/rivershavewings/status/14275803546515865...

https://colab.research.google.com/drive/1go6YwMFe5MX6XM9tv-c...

GP, the links above are far out of date, you want reddit.com/r/discodiffusion and the Disco Diffusion v4.1 (note: I'm specifically saying 4.1 instead of 5.0, focused more on animation and trades off quality for speed of frame generation)

They're very, very, easy to use if you have any familiarity with coding. The hard part is patience.

Midjourney is (hand-waving) a Discord UI on top of that. Again, hand-waving, there's some secret sauce Midjourney does that makes it more likely to recognize your prompt. I assume they swapped out a model somewhere with one they trained on a wider variety of images

I don't think we should try, when scale is this large we should wonder and marvel in the numinous of this existence.

Why not both?

Just a century ago, people thought there's infinitely many stars. Any real number of stars pales in comparison. It's not hard to think of a criteria where only a handful of stars in observable universe will fit. Or even none at all (but non-zero chance of).

Deep field was pointed at an "empty" piece of space, what would the number be in the most populous piece of space?

Space at the scale being discussed here is uniform, so no one direction should be "more populous" than another. The "empty" here designates an area without stars easily visible from Earth. Our local area is denser in our galactic plane, in the direction of our supercluster, etc. But 13 billion lightyears in ANY direction should look about the same.

One of the key findings of astronomy / cosmology of the modern age is that the universe is exactly so uniform in all directions, at the largest scales. In a way this is support for the notion of the big bang itself. There are density differences at some distance scales which have to do with clumping of matter (galaxies) as it began forming, but those differences are not a notion of "the universe being different depending on where you look".

Funny how every subdivision / suburb looks kind of the same in the shape of the roads, density of houses. It is the nature of the laws that govern how these things get built.

Btw, you could see a lot more stars (not galaxies) if you pointed the telescope in certain directions, but likely that would be because you're just looking at the direction of our own galaxy (which we're at the relative edge of), instead of looking out of our galaxy to see the rest of the universe, which is made up of the kinds of places shown in these images.

These images are chosen to be taken in a direction far from our galaxy's disc (thing of us as sitting on the edge of a frisbee), because if you aimed at the disc, your image would be full of the giant overwhelming circles with spikes rather than tiny grains of sand, each of which is a galaxy far far away.

What causes that particular starburst pattern in the James Webb telescope image?

Search 'diffraction spikes' IIRC

The struts of the secondary mirror cause diffraction spikes on all 18 segments which combine to give the final pattern seen, the horizontal spikes are caused specifically by the top strut in particular. This video mostly covers how JWST was focused but from 01:15-04:00 it has an excellent of how the pattern is formed.

https://www.youtube.com/watch?v=cWXTy_GeCis

What does "understanding" mean in this context?

Being able to visualise, and thereby.....comprehend?

But "comprehend" and "understand" mean the same thing.

eh, maybe? I understand that a quadrillion dollars is a large number, but I don't comprehend exactly how large of a pile of cash that would be (assuming Benjamins and not Jacksons).

I think, at least in common vernacular, they are indeed different when placed side by side, much like “listen” vs “hear”.

or "hear" and "comprehend" being the same.

Take the phrase "they don't hear that well". Does that mean they cannot actualy hear based on volumes and noise or some sort of hearing problem? Or does that mean they can "hear" just fine but don't comprehend what they are being told? Or that they do comprehend it just fine, but just don't like it being told to them?

Now we're getting into idioms territory and less about definition of words and why have two words with the same, but different, meanings.

When people actually talk about quadrillion dollars, I no longer listen, I only hear.

I hear that's common in the world of the peasants. Those of use in the 5 Commas club enjoy those reminders, as we try to comprehend what it would be like to have so little. It's beyond our understanding though

And that was my point. I understand those numbers better as i have a better visualisation of them. We are going to a beach tomorrow. There are trees behind us. My kid, and his friends, have a better idea of the stars than ever before - they'll be even more impressed at the beach.

I always liked the idea of "Look at all of the land you can see around you. That's just a fraction of the land. Of all of the land on Earth, it is just a fraction of the surface. The rest is water." From a kid's perspective, water just got huge.

It means distinguishing intuitively between these particular large numbers and other large numbers.

Once you get into the trillions, quadrillions, etc., it can be tricky to get a sense of the scale vs other large numbers that may sound similarly impressive but differ by orders of magnitude.

These examples show that a quadrillion is smaller than I would have imagined without thinking about it, and I found they helped to get an intuitive sense of the scale.

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