# Superluminal recession speed is common

1. Apr 5, 2007

### marcus

A lot of objects are observed to have redshift z in range 2 - 6.
These would have been receding from us faster than c at the time the light which we are now receiving from them was emitted by them and began its journey to us.

Do you have any questions about this?

There is a popular misconception that if an object is moving away from us at superluminal, then light it emits cannot reach us.

If you are wondering about this, check out the Cosmo Calculator Tutorial thread. You'll find you don't even need redshift 2. It is already enough if an object's light has redshift 1.7.
That means that when the light was emitted the object was receding from us at 1.02c, just a wee bit over c.

Lately we've had a bunch of threads started by people who weren't sure about this or didn't understand it. So this is an attempt to address that directly and clear it up. I hope other people like hellfire and Wallace will help respond to questions, if people find superluminal puzzling and want help understanding how the light gets to us. (the key to it is that H changes over time, in fact it changes in a predictable way according to the Friedmann equation, but one can also say what happens in words without reference to the math, if necessary)

2. Apr 5, 2007

### cristo

Staff Emeritus
I'm not sure whether this fits completely in with the theme of the thread, marcus, but this (now rather old) paper gives quite a nice discussion of the topic, that might be worth pointing towards. (Of course, this has probably been cited here before, so apologies if I'm double posting it!)

Superluminal Recession Velocities
http://arxiv.org/abs/astro-ph/0011070v2

3. Apr 5, 2007

### marcus

Cristo, thanks so much for the reference! In fact I had not seen that paper and I'm a fan of Lineweaver---his explanations are some of the clearest writing around, and also he is a top cosmologist.
As you know, I think, the same authors (Lineweaver, Davis) as of your paper got asked to do a Scientific American article that appeared in the March 2005 issue called "Misconceptions about the Big Bang"

I'll copy the brief summary they give of the article you cited:
Superluminal Recession Velocities
Tamara M. Davis, Charles H. Lineweaver
4 pages, 2 figures, Cosmology and Particle Physics 2000 Conference Proceedings

Abstract: "Hubble's Law, v=HD (recession velocity is proportional to distance), is a theoretical result derived from the Friedmann-Robertson-Walker metric. v=HD applies at least as far as the particle horizon and in principle for all distances. Thus, galaxies with distances greater than D=c/H are receding from us with velocities greater than the speed of light and superluminal recession is a fundamental part of the general relativistic description of the expanding universe. This apparent contradiction of special relativity (SR) is often mistakenly remedied by converting redshift to velocity using SR. Here we show that galaxies with recession velocities faster than the speed of light are observable and that in all viable cosmological models, galaxies above a redshift of three are receding superluminally."

4. Apr 5, 2007

### MeJennifer

In the de Sitter space-time observers certainly have future event horizons.
As a consequence, light from certain stars will never reach these observers.

Equivalently, in Minkowski space-time, a uniformly accelerating observer has a future event horizon as well.

I think it is important here to distinquish between events that an observer cannot influence and events that an observer cannot detect.

Last edited: Apr 5, 2007
5. Apr 5, 2007

### Physics-Learner

i'll have to admit - that is one thing that i do still find puzzling. light reaching us, if it was emitted when the 2 places are moving away from each other at faster than c.

6. Apr 5, 2007

### marcus

Good for you! It is a sensible thing to find puzzling! Probably the professional cosmologists here (SpaceTiger, Wallace, maybe others I don't know) were each puzzled by it at one time. It is something you SHOULD ask about.

It has been explained repeatedly in various PF thread over the years. SpaceTiger gave an explanation in a thread here within the past few months.
If he or Wallace are around I wish they would take the question. I will make a stab and anybody else who wants to help me by adding words, thanks in advance.

One way to see it is that the Hubble parameter has always been decreasing with time since very early universe, and will continue decreasing (though gradually less rapidly) for many years to come.

It tells the recession speed at any given distance. So if you, a photon, start from a galaxy which is receding at exactly c, then your speed exactly cancels and you STAY THE SAME DISTANCE FROM EARTH indefinitely (like a man on a treadmill or a fish swimming upriver at exactly riverspeed stays even)

but that is all it takes! since the H(t) is decreasing with time, eventually if you just stay at the same distance from earth, the recession speed where you are will decline to something substantially less and you will begin to make progress!

That can work out more generally, even if the photon starts from a galaxy receding considerably MORE than c---at first the photon will be swept back some but it still stays much closer to us than the emitter galaxy. Like you may have told your kid when they were having trouble in school or somewhere. If you can just hang in there and stay "within striking distance" even if you are swept back some just hang in there and IT WILL GET EASIER

Well oddly enough that happens with light. It doesnt happen in ALL cases. there is a place beyond which the photon always fails, is always swept away too fast for this effect to work. But it HAS worked a lot in the past and still continues to be workable (in spite of the "accelerating expansion" business which makes it harder) within a certain range.

Now I have heard other explanations that used more mental imagery and did not mention H(t) the hubble parameter. So there are explanations that are less mathematical. But that is what comes to mind for now.

Remember the Hubble law.

v = H(t) d

where d is the distance at time t, and v is the recession speed.
So if H(t) decreases and you stay the same distance d, then the recession speed v will decrease (and eventually you may get home safe )

does that make sense?

7. Apr 5, 2007

### Physics-Learner

hi marcus,

i think i am understanding what you are saying. but i thought that the rate of expansion was increasing ?

in other words, not only is the universe expanding, but it is expanding faster today, than it was yesterday ?

is that incorrect ?

it seems to me, that for your logic to be correct, that the rate of expansion would need to be decreasing, not increasing.

because it seems to me, that if the rate of expansion is increasing, then the rate at which we are moving away from galaxies is also increasing. which then would seem to lead to the conclusion that a photon sent in the past will continue to have a harder time reaching us, as opposed to a possibly easier time. (i.e. your explanation of it hanging in there until it can possibly start making progress).

i dont doubt that i am missing something. what is it that i am still not understanding about the theory ?

8. Apr 5, 2007

### marcus

problem with words. what I said is true namely H(t) is a decreasing function of time.

but H(t) should not be described at "rate of expansion".

the rate of expansion is increasing, but H(t) is decreasing and that is what we need for our explanation.

a full discussion involves some college calculus. I dont know if you want that or not.

9. Apr 5, 2007

### marcus

for people who enjoy simple freshman calculus

a(t) is the scalefactor (average distance between galaxies, something you solve the Friedmann equation to find, a size indicator of the universe often normalized so that it equals 1 at the present.)

da/dt is abbreviated a'

the second derivative d a'/dt is abbreviated a''

to say distances are increasing or expanding just means a' > 0

to say this expansion is accelerating simply means a'' > 0
(and all that is there in the mainstream model)

But the hubble parameter is something else! Mathematically it is defined as the ratio (a'/a)

As long as the denominator of that fraction (a, the size of the universe) is increasing really fast, then even if the numerator a' is increasing some, that RATIO can decrease.

So we can have a' increase (accelerating expansion, positive a'') AND at the same time have H(t) the hubble parameter decrease. It dependes on the relative sizes of the numbers and doesnt have to work out that way. Indeed in the distant future or beyond certain limits we can expect it to fail, but for now thats how the numbers work out.

My explanation, which I believe is correct and fairly standard, only talked about H. It did not involve the scale factor a(t) explicitly. So it is not bothered by that other stuff mentioned. It works in the present circumstances despite acceleration.

Last edited: Apr 5, 2007
10. Apr 5, 2007

### Physics-Learner

at this point, college calculus wouldnt help me.

i understand what you are saying.

i can understand from the theory of H decreasing with time, that it would lead to varying degrees for the photon.

but that seems inconsistent with the increasing rate of expansion.

in a nutshell, i guess what i am saying is that it SEEMS that the theory of H and the photon AND the increasing rate of expansion are contradictory.

if you had told me that the expansion rate was at least decreasing some, then i think i can somewhat understand how the photon could still get here, even if it was receding faster than c when emitted. because at some point, the recession would be slower than c, and the photon, still travelling at c, would eventually get here.

but it the rate is expanding, then it seems to me that it would continue to lose ground, instead of gaining ground.

i appreciate your help. but i think my logic would seem very logical to most people interested in the topic - which at least gives you an understanding as to why it would seem confusing to people.

i am not saying that i am correct, by any means. just giving you my thought processes from someone who is interested, but no longer deeply involved in it.

i will read your last paragraph. i still understand what velocity and accelleration are. i thought you were gonna go deeper than that. LOL.

Last edited: Apr 5, 2007
11. Apr 6, 2007

### Physics-Learner

hi marcus,

lets talk classical physics. with constant accelleration, accelleration stays the same, but velocity will continue to increase. so certainly accelleration divided by velocity decreases with time. with expanding accelleration, it seems like there would also be at least times where the accelleration increase would not keep up with the velocity increase, and once again the accelleration divided by velocity would decrease over time.

i really was not aware of the mathematical definition of the hubble (are constant and parameter the same thing here ?). from what you said, am i correct to think that the hubble parameter is simply the accelleration divided by the velocity ?

i can see how there can be an increase in accelleration, but where the product of acceleration divided by velocity gets smaller.

so i can see how the expansion rate can be increasing, but at the same time, the hubble parameter can be decreasing.

i guess what i am failing to see then is what the hubble parameter has to do with it all.

i think one thing that is confusing is that when we speak of the velocity, or lets just say speed, and forget about the direction part of the velocity vector, of the photon, we are speaking about the speed of an object.

when we talk about the speed at which galaxies are receding from one another, we are talking about relative motion, not the motion of an actual object.

according to relativity, c is the limiting speed for an object in our universe. however, there is no limiting speed for relative motion.

somewhere in all of this - perhaps there lays an answer. LOL.

12. Apr 6, 2007

### Garth

If you understand it is possible for objects to move away from us a speeds greater than light speed because they are being carried along with the cosmological expansion of space, then understand too that photons, en route to us from those objects, are also carried along with that same expansion and can reach us even when the emitting object is super-luminal in the Earth's frame of reference.

Garth

13. Apr 6, 2007

### marcus

That's a good picture! in a figurative way one can imagine the photon being "pushed along" or aided by the expansion of the space behind it, so that at the end of the day it seems to have covered a lot more distance than it thinks it did.
Physics-Learner, I'd recommend Garth's picture too. There are several ways to picture what is going on and any of them can help build up your intuition. they dont necessarily contradict each other.

Last edited: Apr 6, 2007
14. Apr 6, 2007

### Physics-Learner

hi marcus,

do we actually measure this photon as moving faster than c ? if so, does this not contradict the notion that no object is measured to go faster than c ? if not, then it seems like our measurement of the photon's speed is not consistent with us saying that the photon, i.e object, is being carried along at faster than c ?

the problem i have with garth's picture is that the universe is expanding, and that in general, everything is moving AWAY from everything else. so space carrying along its objects away from us, would SEEM to make things harder to get to us, not easier.

for example, lets say that there is no expansion. the universe is at a standstill. space is not carrying objects along at all. this being the case, it would SEEM to me that all photons could eventually get here, given enough time, because they are continually getting closer.

if the universe was contracting, then it would SEEM that this might bring the photons closer to us, even sooner.

but with the universe expanding, i dont see how that is an advantage to the photon, if its goal is to reach us here in some other galaxy from its emission ?

15. Apr 6, 2007

### marcus

Garth used some well-intentioned WORDS intended to make the notion more friendly and intuitive to a generic layman. In some folks case they might be helped and satisfied by those words but in your case not.

It looks like we slipped down from discussing the main topic and got into discussing what are the least confusing words to use with a nonmathematical layperson The main topic is not that, but is light getting here from superluminally receding sources. As for that, not only does the math show it, but I find I can visualize the model clearly in my head and see how the photon manages to get here (even tho swimming upstream so to speak). So I am guessing that you can too.

I think that if you forget Garth's well-intended words and focus on my original explaination that involved decreasing H(t) that you now understand it. But you are not a generic layman because you took a calculus course some years back---or the equivalent. IIRC.

The side issue we slipped over to discussing seems to be WHAT WORDS TO USE with a generic layman. Translating stuff into words is very very tricky. It can make things worse. maybe a lot of the charming science popularization writings of for example Brian Greene or Stephen Hawking just ultimately makes things more confusing for people. Their wonderful literary metaphors maybe ultimately just give people more stuff to misunderstand and doubt.

But that is a separate issue. Our real issue which I will emphasize with caps, is SUPERLUM RECESSION SPEED IS COMMON and a lot of what we see in the sky (all the redshift z > 1.7 stuff) was RECEDING FASTER THAN c WHEN IT SENT OUT THE LIGHT WE ARE NOW RECEIVING FROM IT.

and furthermore it's not really all that hard to mentally visualize how a photon would eventually reach us AS LONG AS H(t) IS DECREASING and it starts the trip not too far away and receding not too much faster than c.

And finally, what you brought up, that H(t) CAN BE DECREASING even though a'(t) is increasing. that is even though we have a kind of acceleration in the picture-----a(t) is the size, a' is the time rate of increase, a'' positive means acceleration.

I put that in caps to emphasize that we have a lot on our plate in this thread.
Like that cap stuff is written on the blackboard and if you have any questions please ask.

But this side issue of whether one should or shouldnt use certain words to try to make the business palatable to a generic layman--that might just be too much for our slender thread. It might snap

If you had some calculus or equivalent, as I think I recall, then you might be interested to know that the main equation in cosmology is the Friedmann and the Friedmann equation (look it up on Wikipedia if you want) is actually ABOUT the way H(t) changes.

the LHS of it has the term (a'/a) which you may remember is how H(t) is defined! so the most basic cosmology equation is giving us a handle on this quantity H(t) and how it evolves with time.

there is a second Friedmann equation that gives us a handle on a"

both are remarkably simple equations considering how powerful or fruitful of results they are.

but that is definitely a By-the-Way. I just thought you might be interested to check out some cosmology fundamentals sometime.

Last edited: Apr 6, 2007
16. Apr 7, 2007

### Garth

Hi Physics-Learner!

Yes, I am trying to put into laypersons words difficult mathematical concepts. Please bear with me.

To see the diagrams describing that mathematics download the pdf file of cristo's link.

Remember it is the emitting object whose speed seems to be greater than that of light.

That object emitted a photon towards the Earth billions of years ago when the universe was smaller and its relative recession speed then was less than the speed of light.

The photon was 'adrift' on the sea of space-time and carried along with the expansion of space.

Now those diagrams in the link paper were drawn for the standard (h,$\Omega_M$, $\Omega_{\Lambda}$) = (0.68, 0.3, 0.7) model in which Dark Energy causes the expansion to accelerate.

And if the universe accelerates during the photon's journey towards us then, as it is being carried along with the space-time, it is still able to continue and complete that journey even when the emitting object has been accelerated beyond light speed away from the Earth.

The apparent paradox is due to the acceleration of the universe's expansion.

I hope this helps.

Garth

17. Apr 7, 2007

### Chronos

Photons traveling through stretching space are stretched as a consequence. It's called cosmological redshift. In that sense, photons in expanding spacetime also travel superluminally.
 In otherwords, what Garth just said.

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