# Do we directly observe redshifted galaxies receding >c?

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## Main Question or Discussion Point

Sorry for a basic question but I keep reading conflicting information on this.

So, I know that there are distant galaxies that are being carried by the expansion of space faster than the speed of light relative to us. But were these objects actually receding >c when the light we are seeing was emitted, or are we extrapolating their redshift now given their current position in the observable universe?

As I understand it, it is possible for light to reach us from beyond the Hubble horizon due to the Hubble parameter slowing down over time. Allowing light to pass from a point in space expanding >c to a point expanding <c, thus it being able to eventually reach us. (I think that's how it works)

But I would have thought that would be a narrow band and couldn't account for us directly observing galaxies receding at 3c could it?

Bandersnatch
But were these objects actually receding >c when the light we are seeing was emitted
Yes, and with higher recession velocities than now. For points now observed as CMBR ($V_{rec_0} = 3.14c$) the recession velocity at emission corresponded to over 60c.

But I would have thought that would be a narrow band and couldn't account for us directly observing galaxies receding at 3c could it?
There is a band limiting the distance from which light can reach us (i.e. between the Hubble horizon and the event horizon), but it has to do with there being dark energy. If you apply the reasoning you described in the preceding paragraph to a universe where H always goes down towards zero, then there is no limit to how far an event initially ought to have been for it to be eventually observed (i.e. there is no event horizon). From this follows, that there would also be no limit to how fast the place of emission was initially receding.

For example, consider a hypothetical universe* in which all recession velocities of each particular galaxy or point in space remain identical throughout eternity, which corresponds to H going down as 1/a.
You can pick any initial recession velocity whatsoever, and have the light travel towards the observer. Since every point along its path towards the observer at emission will have lower recession velocity than the preceding point, and the velocities those points never increase, after each increment of time the light will always find itself in a region with lower recession velocity than before. Given enough time, it will have passed into a region with $V_{rec}<c$, and the rest is intuitively straightforward.

*this type of universe requires there being no matter, radiation or dark energy in it. In universes with matter and radiation H goes down faster. With dark energy in the mix, it goes down approaching a positive value.

kimbyd
Gold Member
Sorry for a basic question but I keep reading conflicting information on this.

So, I know that there are distant galaxies that are being carried by the expansion of space faster than the speed of light relative to us. But were these objects actually receding >c when the light we are seeing was emitted, or are we extrapolating their redshift now given their current position in the observable universe?

As I understand it, it is possible for light to reach us from beyond the Hubble horizon due to the Hubble parameter slowing down over time. Allowing light to pass from a point in space expanding >c to a point expanding <c, thus it being able to eventually reach us. (I think that's how it works)

But I would have thought that would be a narrow band and couldn't account for us directly observing galaxies receding at 3c could it?
This is largely correct, but one minor point:

Redshift is measured directly, usually via spectral lines from emission or absorption. It's the most precise distance proxy we have. Other estimates are typically inferred through complicated relationships and are much less certain as a result. The recession velocity, for example, is inferred using a cosmological model, not measured.

The rest of what you said is quite accurate. In short, many observable galaxies always have been and always will be receding at faster than the speed of light. But the light they emitted in the distant past eventually got close enough to start gaining ground against the expansion.

PeroK
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https://www.physicsforums.com/insights/coordinate-dependent-statements-expanding-universe/

Note especially the last section (pathological example) that demonstrates that it is a category error to compare recession rate with relative velocity in SR. Specifically, if one sets up a flat spacetime cosmological model, you end up with arbitrarily large recession rates that at the same time are unambiguous relative velocities < c. In curved spacetime, there is simply no well defined relative velocity (because to compare vectors, you need to parallel transport one to the other, but this operation is path dependent), but recession rate is certainly not analogous to one. One final note is that for any path you might use to parallel transport one 4-velocity vector to another, the resulting comparison after transport is always less than c. Thus, you can say that in GR, relative velocity is ambiguous but less than c.

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kimbyd
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https://www.physicsforums.com/insights/coordinate-dependent-statements-expanding-universe/

Note especially the last section (pathological example) that demonstrates that it is a category error to compare recession rate with velocity in SR. Specifically, if one sets up a flat spacetime cosmological model, you end up with arbitrarily large recession rates that at the same time are unambiguous relative velocities < c. In curved spacetime, there is simply no well defined relative velocity (because to compare vectors, you need to parallel transport one to the other, but this operation is path dependent), but recession rate is certainly not analogous to one. One final note is that for any path you might use to parallel transport one 4-velocity vector to another, the resulting comparison after transport is always less than c. Thus, you can say that in GR, relative velocity is ambiguous but less than c.
Slightly pedantic clarification: relative velocity at a distance is ambiguous. Relative velocity at the same point is not.

Yes, and with higher recession velocities than now. For points now observed as CMBR (Vrec0=3.14cVrec0=3.14cV_{rec_0} = 3.14c) the recession velocity at emission corresponded to over 60c.
Wow, that blows my mind. So had we been able to observe at the time of recombination, photons emitted next to us would have receded at 60c, but due to the fall off in H0, the Hubble horizon eventually caught up to them? And those first photons made their way to us sometime in our history? (also 3.14 sounds a bit too close to pi, just saying)

a universe where H always goes down towards zero, then there is no limit to how far an event initially ought to have been for it to be eventually observed
So, in that scenario, the Hubble horizon would eventually catch up to the event horizon, and so eventually all light could reach us?

In universes with matter and radiation H goes down faster. With dark energy in the mix, it goes down approaching a positive value.
So, we believe it will stop slowing at a positive number, and that is why some of the universe will never be viewable?

I apologise if I am misunderstanding what you are saying, I have no background in the sciences or in mathematics. So I am right at the edge of what my brain can get itself around.

Thanks for the reply by the way. Google is only so much help!

Other estimates are typically inferred through complicated relationships and are much less certain as a result. The recession velocity, for example, is inferred using a cosmological model, not measured.
So now I am confused again. We use cosmological models like Planck and the CMB or standard candles to model H0, but does that mean we infer >c redshifts, or do we observe them? As you can tell I am having trouble understanding how we can directly observe light that is being carried away by space faster than c. I get that there is a band where light can escape super luminary expansion, but I don't get how it can 2 or 3 or now 60c?

Thanks again for the reply and bearing with me.

PeroK
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So now I am confused again. We use cosmological models like Planck and the CMB or standard candles to model H0, but does that mean we infer >c redshifts, or do we observe them? As you can tell I am having trouble understanding how we can directly observe light that is being carried away by space faster than c. I get that there is a band where light can escape super luminary expansion, but I don't get how it can 2 or 3 or now 60c?

Thanks again for the reply and bearing with me.
You can't observe anything other than light that reaches your receiver (always at the speed of light) and with a given frequency and wavelength. Redshift, if you think about it, is not measurable but only inferred (*). For example, you know the spectrum of light emitted by a common atom, such as hydrogen. You measure the light from a distant star and find it matches the spectrum of hydrogen, except it is more red than it should be. You infer that the light was produced by a hydrogen atom and that somehow the wavelength you receive is not the wavelength at the time of emission. You infer that the light has been redshifted.

Note: what you do not get is light that you can directly measure as redshifted. You only measure the one frequency and only indirectly can you calculate how this has changed. Light doesn't come directly with the information "I was frequency $x$ at the time of emission and now I'm frequency $y$"!

Then, you have a cosmological model (based on General Relativity) that predicts that light is redshifted in an expanding universe. There is then a complicated mathematical model that tells you the redshift of light from various distances based on changing expansion rates over the history of the universe. By measuring the redshift (as inferred from spectrometry), from many light sources, you can build up a picture of the expansion rate of the universe over time.

(*) You can, of course, directly measure redshift in a local experiment. E.g. light moving through the Earth's gravitational field.

Bandersnatch
So had we been able to observe at the time of recombination, photons emitted next to us would have receded at 60c, but due to the fall off in H0, the Hubble horizon eventually caught up to them? And those first photons made their way to us sometime in our history?
The 60+c is for regions which at recombination emitted light currently observed as CMBR. These were hardly next to us, as the distance to those regions then was ~ 44 million light years.
At recombination the Hubble law was just as valid as today, albeit with a different value of H. So if you imagine the regions at 44 Mlyr receding at 66c, regions then at 22 Mlyr would be receding at 33c, and so on. If you were present at recombination, you'd see photons emitted from just next to you, with little recession velocity to speak of.
So, in that scenario, the Hubble horizon would eventually catch up to the event horizon, and so eventually all light could reach us?
In this scenario there is no event horizon whatsoever. The event horizon is defined as the distance from beyond which no light can ever reach an observer, regardless of how much time passes.
So, we believe it will stop slowing at a positive number, and that is why some of the universe will never be viewable?
Yes, because in this case there is an event horizon.

I'd encourage you to read the Insights article linked above by PeroK. Even if you gloss over the maths, the figures and explanations should be of much help in visualising the interplay between the changing scale of the universe, light travelling through it, and various horizons.

So now I am confused again. We use cosmological models like Planck and the CMB or standard candles to model H0, but does that mean we infer >c redshifts, or do we observe them? As you can tell I am having trouble understanding how we can directly observe light that is being carried away by space faster than c. I get that there is a band where light can escape super luminary expansion, but I don't get how it can 2 or 3 or now 60c?
Just to add a simple clarification to what was said by others, so that this doesn't get lost. You definitely do see the light. It has reached you to be observed after having travelled through the expanding universe. But all the properties of the emitter, such as its recession velocity, must be inferred. The point in kimbyd's post was that recession velocity is not the direct observation.

Bandersnatch
Redshift, if you think about it, is not measurable but only inferred (*). For example, you know the spectrum of light emitted by a common atom, such as hydrogen. You measure the light from a distant star and find it matches the spectrum of hydrogen, except it is more red than it should be.
I kinda get the point you're making, but don't you think that the last sentence above is exactly what one would call measuring redshift? One measures the distance between some observed lines and their laboratory reference. That's the redshift. One certainly needs some physics to give a meaning to what the lines are and why it makes sense to identify the observed ones as a shifted reference, but the observation of a shift is a direct one.

PeroK
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I kinda get the point you're making, but don't you think that the last sentence above is exactly what one would call measuring redshift? One measures the distance between some observed lines and their laboratory reference. That's the redshift. One certainly needs some physics to give a meaning to what the lines are and why it makes sense to identify the observed ones as a shifted reference, but the observation of a shift is a direct one.
It's getting towards semantics, but the point is that in cosmology you aren't able to observe the emission wavelength. I was only trying to emphasise this point in response to the OP's question.

In particular, if light was emitted by a source receding at $>c$, then there is no problem or contradiction eventually measuring the light that reaches you. The superluminal recession at emission is irrelevant to the process of measuring the wavelength of the light you receive. And, in this case, you are definitely not measuring a $>c$ redshift.

You guys are really helpful, thank you.

One last clarifying question and I'll move on to another topic in a new thread.

So, we don't directly observe redshift, due to the different emission spectrum of atoms (I think). It is calculated through a process I don't really understand, but the point is it isn't directly observed.

But the crux of my question is do we see/infer/calculate redshifts of bodies that are greatly above c, or do we see a redshifted body slightly above c, and say 'given it's current position in the observable universe, this redshift we see, is now in fact 2 or 3 or 60 times the speed of light'.

Bandersnatch
You see a redshifted object, and you can say that for it to have this redshift in our model of how the universe behaves, it needed to have such and such recession velocity at emission, and by now it should have such and such recession velocity. These velocities may be well over c, depending on the observed object.
Similarly with positions - you observe the redshifted body and can infer something about where it was at emission and where it should be now.

PeroK
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But the crux of my question is do we see/infer/calculate redshifts of bodies that are greatly above c, or do we see a redshifted body slightly above c, and say 'given it's current position in the observable universe, this redshift we see, is now in fact 2 or 3 or 60 times the speed of light'.
In a simple scenario, the redshift would depend on a relative velocity. This is called the Doppler effect. For example, leaving aside universal expansion, if you receive light from a source that is moving away from you it is redshifted and moving towards you it is blueshifted. The red or blueshift depends on the relative velocity. A relative velocity of $\ge c$ is not possible, so there is no redshift associated with $\ge c$.

In the expanding universe, however, the scenario is not this simple - especially once you start thinking about light that was emitted by a source that was receding superluminally. In this case, something more than the recessional velocity at emission is relevant. The eventually measured wavelength is a function of the expansion of the universe across all the time that the light has been travelling to you. So, it's a sort of averaging out. But, of course, since there is no redshift associated with a simple $> c$ recessional velocity, it's not possible to view the problem from the point of view of recessional velocity alone.

The best explanation, unfortunately, takes it beyond a B level. Basically, you model spacetime over the relevant duration of the universe; you describe the light as a thing called a four-vector; the properties of this four-vector include a measurable wavelength at the source at the time of the emission and a measureable wavelength at the receiver at the time it's received. The difference is the redshift!

To understand this to any extent you definitely need some maths. But, in a nutshell, it's not simply about recessional velocity. It's about the evolution of spacetime from the emission to reception.

Clearly I have a lot to learn. Starting with Math, and maybe, you know actual physics, and then maybe some Astrophysics.

Not being flippant, I have a genuine interest but sadly not the education. I do appreciate you taking the time to try to explain it to me.

PeroK
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Clearly I have a lot to learn. Starting with Math, and maybe, you know actual physics, and then maybe some Astrophysics.

Not being flippant, I have a genuine interest but sadly not the education. I do appreciate you taking the time to try to explain it to me.
You have learned quite a lot already and there is plenty more you can learn. But, fundamentally, the real understanding in physics does require some mathematics. Also, studying mathematics in a way is like physical training: it changes the way your mind works and gives you the capability to look at problems in a new way.

That said, as long as you are prepared to stretch your mind conceptually and trust that mathematics gives you the calculations, you can get a lot out of physics studies.

kimbyd
Gold Member
So now I am confused again. We use cosmological models like Planck and the CMB or standard candles to model H0, but does that mean we infer >c redshifts, or do we observe them? As you can tell I am having trouble understanding how we can directly observe light that is being carried away by space faster than c. I get that there is a band where light can escape super luminary expansion, but I don't get how it can 2 or 3 or now 60c?

Thanks again for the reply and bearing with me.
Redshifts are measured. They are almost entirely independent of the cosmological model.

It's the other properties that are inferred, such as recession velocity.

For a breakdown on how redshifts are observed:

1) For galaxies (near and far) the most reliable method is by observing their spectra and measuring emission/absorption lines.
2) For galaxies, it's also possible to use photometric redshifts (basically, where you just measure the color of the galaxy). Photometric redshifts are error-prone, but it's vastly faster to do this kind of redshift, so you can measure many, many more galaxies.
3) For the CMB, the redshift is measured using the black body spectrum and comparing it against the temperature at which a hydrogen-helium mixture turns from a plasma to a gas.