While movement is expected in principle, the cosmic microwave background (CMB) is static over human time scales.

The light comprising the CMB last scattered at the same time everywhere, when the universe was about 370000 years old. The CMB that we see consists of the light that is just now reaching us. As time goes on, light from more and more distant regions is able to reach us. In this way, the CMB depicts a spherical slice of the 370000-year-old universe (the "last scattering surface") at an ever increasing distance as time goes on.

Over what time scale should we expect to see the CMB change, then? The smallest scales we can resolve, currently, are about 0.07 degrees on the sky, which corresponds to about 50000 light years (15 kpc) at the distance of the CMB. (This is actually remarkably small due to the angular diameter turnover!)

For a 50000-light-year structure, light from the far end takes 50000 years longer to reach us than light from the near end. Does this mean that we should expect CMB temperature fluctuations on those scales to change in about 50000 years? Well not quite. The CMB is redshifted by a factor of 1100, which means it's time dilated by the same factor. So we expect fluctuations on the (currently) smallest resolved scales to change over a (1100 times longer) time scale of about 55 million years.

Are these scales proportional such that we need to resolve the CMB to a scaled one million times smaller to see changes in a lifetime? Can the CMB even be resolved to a scale that small?

How simultaneously did the universe go from opaque to transparent? I'd imagine that the different CMB temperatures correspond to different densities and therefore different temperatures, so is "at the same time" just more or less the same time on a cosmic scale?

Right, found this myself after a quick Google search, correct me if I'm wrong. It's not the density or temperature of the plasma that really affect transparency, rather, it's the fact that this plasma is opaque only because there exist photons of high enough energy to rip apart nuclei and electrons again (the electrons can then scatter incoming photons galore). As the expansion of the universe redshifts the photons, at a certain point there will be no photons of sufficient energy to ionise atoms, hence simultaneity.

Follow up question: assuming we're talking about a Boltzmann distribution, at what timescales do we expect to go from e.g. 1% to 99% of photons falling below ionisation energy?

That's right, the scales are precisely proportional in that way.

With respect to whether such resolution is possible, I can't say much about the instrumentation side, but I can point out a major physical challenge. According to our calculations, there simply wasn't much structure on very small scales in the early universe, due to diffusion damping. Photons were able to gradually diffuse between hot and cold regions, allowing their temperatures to equalize. This effectively smoothed out the early universe; due to photon travel times, it affected small scales more than large scales.

According to this paper, the last scattering surface has a comoving thickness of about 19 Mpc, which corresponds to a physical thickness of (19 Mpc)/1100 ~ 17 kpc or a duration of (17 kpc)/c ~ 56000 years.

Edit: The above concerns how thick the last scattering surface is at any given point on the sky (which is connected to how long recombination -- the process by which the universe became transparent -- took, as well as how opaque the universe was before recombination). I just realized that you are instead asking how the recombination time varied between different patches of the sky. Temperature variations in the CMB are around the 10^-4 level (one part in ten thousand), which implies that the recombination time varied to a similar degree. 10^(-4) of 370000 years is 37 years, so the spatial variation in the recombination time is of order tens of years.

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if 0.07 degrees of arc goes to 50k year time scales, then 0.00007 degrees of arc goes to 50 year time scales, wavelength of 1.9 mm, rayleigh criterion of angle ~= 1.22*lambda/diameter.

I must have done something wrong because I came out to an effective diameter of only 35 meters, we've totally built radio dish networks bigger than that, heck, the EHT made such a big hubbub about planet scale scopes.

I agree that we would not expect much change over human lifetimes.

Another problem, not yet mentioned, is that each time astronomers take a "picture" of the CMB, camera technology improves the resolution creating a much different picture. Improved resolution is easy to see. I don't think changes in the CMB between 1989 and 2013 would be easy to see.

Here are images from COBE (1989), WMAP (2001), Planck (2013).

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Missing the redshift factor (should be ~55 million years), so I guess that would be ~40 km diameter?

Why has it taken light 13 billion years to reach us?

Wouldn't that indicate that, for 13 billion years, the distance between us and that light source has been expanding at almost the speed of light since the very beginning?

The Andromeda galaxy is expected to collide with the Milky Way in approximately 4.5 billion years. Does this time take into account the expansion of space in between the two galaxies?

Mpc? Kpc?

Not an abbreviation I'm familiar with.

I'm going to guess millions or thousands of parsecs, which are each about 3.26 light years.

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Expansion is a big factor but you can think of the light of the CMB as having originated from everywhere. The part of the CMB we observe is a growing bubble. The light is traveling uninterrupted after having been emitted in the early universe.

To the second question, the expansion of space is not that significant between nearby galaxies.

Remember the CMB light originated everywhere. So there will always be a distance such that light originating from that distance is just reaching us now. Cosmic expansion doesn't come into play here.

> The Andromeda galaxy is expected to collide with the Milky Way in approximately 4.5 billion years. Does this time take into account the expansion of space in between the two galaxies?

Space expanding doesn't physically do anything. It's just a convention that's useful in some contexts. (It represents a choice of coordinates on spacetime.)

Since the misconceived reification of expanding space is pretty deeply ingrained in the public consciousness, here are some articles discussing the point further.

(1) A diatribe on expanding space. This is pretty technical, but it's the most direct attack on the idea of expanding space. One key quote is that

> there is no local effect on particle dynamics from the global expansion of the universe: the tendency to separate is a kinematic initial condition, and once this is removed, all memory of the expansion is lost.

For example, the Milky Way-Andromeda system is no longer expanding, so cosmic expansion is simply no longer relevant to it.

(2) The kinematic origin of the cosmological redshift. Very well written and less technical, although there are mathematical arguments. The main point of this article is that the cosmological redshift -- often framed as a consequence of space expanding -- is more precisely viewed as just a Doppler shift.

(3) On The Relativity of Redshifts: Does Space Really "Expand"? The least technical of the batch. This article is also focused on the interpretation of the cosmological redshift. It includes the choice paragraph:

> While it may seem that railing against the concept of expanding space is somewhat petty, it is actually important to set the scene straight, especially for novices in cosmology. One of the important aspects in growing as a physicist is to develop an intuition, an intuition that can guide you on what to expect from the complex equation under your fingers. But if you assuming that expanding space is something physical, something like a river carrying distant observers along as the universe expands, the consequence of this when considering the motions of objects in the universe will lead to radically incorrect results.

On average, yes, but in reality the recession velocity is neither constant nor linear. Points at the distance of the CMB scattering surface are currently receding from us at more than three times the speed of light.

The Milky Way-Andromeda system is bound together by gravity, and so is unaffected by expansion. Newtonian mechanics is all you need to calculate the time until the two galaxies collide (notwithstanding the uncertainty in the current distance and relative velocity of Andromeda).

Tens of years... Wow, so short. Really puts the temperature uniformity in a new perspective for me.

Are this and this still about right for how we think it would have looked?

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Sorry, I typed "reionization" but meant "recombination"... I've fixed that.

To clear things up:

• Recombination is a process that occurred at a time of around 370000 years. At this time, the universe cooled enough that all of the free protons and electrons condensed into neutral hydrogen. Without all of the free electric charges, the universe became transparent. (The "re" in "recombination" is a complete misnomer.)

• Reionization is a process that occurred at a time of around 200 million to 1 billion years. This is what those videos are showing. When the first galaxies formed, the light emitted by their stars and black hole accretion disks ionized essentially all of the neutral hydrogen in the universe. (The universe didn't become opaque again, though, just because the hydrogen was far too sparse by this time.)

What's 0.07° (4.2 arcmin) based on? It's somewhat close to Planck's FWHM at its highest frequencies (the main CMB frequencies are more like 5-7 arcmin), but Planck isn't the state of the art at small scales - that's the South Pole Telescope (SPT) and Atacama Cosmology Telescope (ACT) with resolutions of about 1 arcmin.

Though as you say in another comment, there's hardly any CMB left at those scales. ACT has published a foreground-cleaned CMB temperature power spectrum with significant signal detection up to l = 3700 which corresponds to roughly 0.10° = 5.4 arcmin 0.05° = 2.9 arcmin.

I think I read a paper at some point about the feasibility of detecting the time-derivative of the CMB. If I remember correctly, it was actually the largest scales that were considered the most promising there, not the smallest. Those scales change extremely slowly, but the signal is also much brighter there, and from what I remember that won out.

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I just lazily took pi/l for l=2500, the largest l that Planck papers plot. Indeed, the ground-based telescopes push to somewhat higher l.

Hmm, around 1 degree (where the fluctuation power peaks), the time scale for the CMB to change would be of order a billion years, or one part in ~10^(9) per year. I wonder how far off that kind of sensitivity is.

Yes, they typically plot out to l=10000, but all the power out there comes from point sources (if one doesn't clean those away). I used 360°/l, but if I use 180°/l the ACT foreground cleaned spectrum becomes too faint to be detectable at 2.9 arcmin.

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These are great explanations, thanks

The total surface area doesn't need to be that big, we're definitely in radio wave territory, so synthetic aperture techniques are readily usable. As long as several telescopes are more than 40km apart and have good enough clocks, we can stitch the data together to get interesting things.

I'm guessing the hurdle is most of these measurements need to be space based since all the flag ship data sets are from satellites.

is the JWST able to/going to take a shot of the CMB? would be neat to have it alongside the others

JWST is tuned to detect infrared light. Microwaves, the 'M' in CMB, are just too long of a wavelength for JWST unfortunately. It might be able to do a similar survey and find other data but it won't see the same CMB.

JWST infrared filters can't see the CMB microwave radiation.

• JWST infrared filters range from 0.6 to 28.5 micrometers wavelength

• CMB microwave radiation = 1.9 millimeters wavelength.

• 1.9 millimeters = 1,900 micrometers

Sorry

Redshift is equivalent to time dilation? So early galaxies at high redshift appear basically frozen in time from our perspective? I've never heard of this... wouldn't nova events (or other time dependant events) in distant galaxies last way longer than close ones, from our perspective?

>While movement is expected in principle, the cosmic microwave background (CMB) is static over human time scales. > >The light comprising the CMB last scattered at the same time everywhere, when the universe was about 370000 years old. The CMB that we see consists of the light that is just now reaching us. As time goes on, light from more and more distant regions is able to reach us. In this way, the CMB depicts a spherical slice of the 370000-year-old universe (the "last scattering surface") at an ever increasing distance as time goes on.

I just had a stupid thought, since different wavelengths take different amounts of time to reach us does that mean the speed of light varies based on its frequency?

One of the reasons we know the universe had to have been much smaller and closer together in the past is that to have that uniform temperature over such a large scale (the entire cmb) those parts needed to be close together at some point to "coordinate" on what temperature they should all be.

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> The light comprising the CMB last scattered at the same time everywhere

Out of curiosity, what is "the same time"? Was this over the course of a few milliseconds? Years? Millenia?

In fact, they do. It's very useful for us, allowing us to get a lot more data from them.

https://www.newscientist.com/article/dn13792-cosmic-time-warp-revealed-in-slow-motion-supernovae/

Nice. Just learned another something weird and cool about our universe!

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See this comment! About 56000 years.

(Actually, come to think of it, shouldn't the formula be sqrt(4pi)/(lmax+1)? Alms from 0 to lmax have (lmax+1)² degrees of freedom (sum_0^lmax (2l+1)). This is enough information to split the full sky into (lmax+1)² pixels, which would then have a side length of sqrt(4pi)/(lmax+1). This works out to 1.13*pi/l, so very close to your formula and far from the 2pi/l I had been using.)

Thanks for these useful links.

Tens of years shift in a process that took tens of thousands of years.

No, the time light took to reach us only correlates with the amount that the light's frequency is shifted and not with the light's absolute frequency. For example, the CMB is actually a whole spectrum of frequencies. Those frequencies don't take (significantly) different amounts of time to reach us; if they did, the CMB spectrum wouldn't be such a perfect blackbody spectrum.

How did all the light scatter at the same time? All photons in the CMB just bounced off a particle somewhere and haven’t touched any particles since?

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What happened is that the universe cooled enough that all of the free protons and electrons condensed into neutral hydrogen. Neutral atoms interact with light much more weakly than do free electric charges, so this process made the universe transparent to light.

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Redshifting slows down the frequency of light. But the total amount of oscillations of the light signal isn't affected.

Suppose a far away galaxy sends a 1 second long burst at 1 GHz, 1 billion cycles. At Earth it arrives redshifted to twice the wavelength, and a frequency of 0.5 GHz. We still receive 1 billion cycles, they're just spread over 2 seconds of time now. So we effectively see the signal - and everything else from that distant galaxy - at 0.5 speed.

Wow that's incredible! If I understand correctly that means the light being emitted from an object is one long stream and we can access different segments of it by tuning into different frequencies?

The "light" emitted at the end of the "dark ages" occurred in an instant? 370,000 years after the big bang. Did that mean it happened "everywhere " at the same time? Also, since all other celestial light sources have their distances calculated by their red shift, what is the distance to the universe at that time? Thanks

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