# How does the expansion of the universe stretch light?

Any galaxy that we can see, must have been travelling at less than light speed when the photons that we now see, departed from it. Therefore, the visible rate of galaxy separation is less than light speed. How then, could expansion "stretch" light? Particularly, if it is the expansion of space that is causing galaxies to separate, rather than their own movement, then between any two galaxies there would be pressure in both direction to effect separation. With perhaps hundreds of galaxies between us and the most distant views, light photons would have to overcome the resistance of the space that is pushing in the opposite direction from its own travel. One can understand that if a galaxy was receding from us at a high rate at the moment that the photons left, then the wave-length of the photons could be slightly stretched.
On the face of it, in order for space to move galaxies, it must have a high degree of viscosity. This, surely, would have the effect of slowing these hard working photons. Why then are they not compressed by, in the case of the most distant views, several billion years of resistance. And, (perhaps one for the physics guys), why do they weave from side to side, describing a wave motion?

Drakkith
Staff Emeritus
First, the expansion of space in no way puts "pressure" on anything inside. All it means is that the distance between ANY two points in space is always increasing. Light does not have any pressure to fight against as it travels. There is no resistance, no viscocity, nothing.

I believe the idea is that the expansion of space stretches the wavelength out, making the light redder. But I don't know the details of the phenomenon.

Also, light does not weave from side to side. The classic diagrame of a wiggly line merely represents the fact that the electric and magnetic fields that make up the photon are alternating back and forth from positive to negative. Light travels in a straight line, always.

Chalnoth
Any galaxy that we can see, must have been travelling at less than light speed when the photons that we now see, departed from it.
This is false. There is no unique way to define the velocity of a far-away object, and without a unique definition, the velocity of a far-away object clearly can't obey any hard-and-fast rules.

By the usual definition of recession velocity, most of the galaxies that we can see from Earth are now and always have been receding at faster than the speed of light.

The best way to think of the expansion I have seen is this.

t=0=the singularity

.

t>0

1234567890

...

1.2.3.4.5.6.7.8.9.0

...

1..2..3..4..5..6..7..8..9..0

....

1...2...3...4...5...6...7...8...9...0

Essentially all this says is time and space are the same size as they were at the singularity, the only thing that has changed is the graph itself of distance in terms of x,y,z,t or i even.

If you like.

First, the expansion of space in no way puts "pressure" on anything inside. All it means is that the distance between ANY two points in space is always increasing. Light does not have any pressure to fight against as it travels. There is no resistance, no viscocity, nothing.

I believe the idea is that the expansion of space stretches the wavelength out, making the light redder. But I don't know the details of the phenomenon.

Also, light does not weave from side to side. The classic diagrame of a wiggly line merely represents the fact that the electric and magnetic fields that make up the photon are alternating back and forth from positive to negative. Light travels in a straight line, always.
It's called doppler shift and is exactly the same for spacial attenuation as it is for sound, light or whatever.

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Drakkith
Staff Emeritus
It's called doppler shift and is exactly the same for spacial attenuation as it is for sound, light or whatever.
Doppler shift is a result of an object moving towards or away from you, and I thought I remember reading that the expansion of space can stretch the wavelength of light out in addition to the Doppler shift from an object. But I'm not 100% sure.

Doppler shift is a result of an object moving towards or away from you, and I thought I remember reading that the expansion of space can stretch the wavelength of light out in addition to the Doppler shift from an object. But I'm not 100% sure.
It's an analogy basically only space is moving and you aren't. It's probably best to think of it as a doppler shift in attenuations of space. Ok my brains now leaked out my ears, and will have to go sit down. :tongue2:

Drakkith
Staff Emeritus
It's an analogy basically only space is moving and you aren't. It's probably best to think of it as a doppler shift in attenuations of space. Ok my brains now leaked out my ears, and will have to go sit down. :tongue2:
I think we should leave doppler shift to moving objects and not try to relate it to the effect of expansion on light. Otherwise things just get messy!

I think we should leave doppler shift to moving objects and not try to relate it to the effect of expansion on light. Otherwise things just get messy!

Chalnoth
The simplest way I can think to say it is that you get some very specific total redshift for faraway objects due to the expansion. How much of that redshift is due to the doppler shift and how much is due to the expansion between us and the far away object is completely arbitrary.

PAllen
2019 Award
This is false. There is no unique way to define the velocity of a far-away object, and without a unique definition, the velocity of a far-away object clearly can't obey any hard-and-fast rules.

By the usual definition of recession velocity, most of the galaxies that we can see from Earth are now and always have been receding at faster than the speed of light.
This is true, but to add to the point about no unique way to define this, an alternative definition:

parallel transport galaxy's 4-velocity (it doesn't matter what you measure it relative; it is a covariant geometric object) at time of emission along the null-path the light follows to reach earth (in *any* coordinate system you choose)

produces no superliminal speeds; in fact in produces a relative speed such that conventional SR kinematic doppler fully accounts for the red shift.

[EDIT: I should point out that the reason such an approach is not normally used is that it leads to a difficult distance scale. If you build a ladder of distances using reasonable measurements, extrapolate back to emission time, you find that relative speed by the parallel transport definition is inconsistent with such a distance scale; you would be required to use an adjusted distance scale.]

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Thank you for your replies. What I should have said is that the recession rate between us and any observed galaxy cannot have been greater than the speed of light, at the time that the light departed, proven by the simple fact that their light has reached us. How then can a sub-light speed expansion rate stretch light? With regard to "expanding space" these pages have many times stated that it is this phenomenon that is the cause of universal expansion. "Scientific America" states:-"The velocity in Hubbles law is a recession velocity caused by the expansion of space, not a motion through space." It also states that:- "as space expands, light waves get stretched, if the universe doubles in size during the waves' journey, their wavelength doubles and their energy halves."
As an aside, by how much can visible light waves be stretched before they are no longer visible light? How can we be sure that infra-red light from distant galaxies is not stretched visible light? Do ultra-violet rays and x-rays and gamma rays also get stretched? Or are they somehow immune?

i'm baffled by the confusion here.

the doppler shift is used to describe the expansion related red shift in light: the calculation used to determine the red shift z is simply the doppler formula, applied to measured galactic spectra with the standard scale of wavelength.

to say the red shift is possibly not a doppler shift is like saying a pound of feathers is possibly not really really a pound.

to say that the speed of an object can't be determined because there are many different answers is incorrect. what is your personal distance from the capitol of illinois? does that answer apply to everyone? does that mean the distance to chicago can't be determined?

special relativity theory merely requires the choice of inertial frames of reference. it doesn't say inertial frames become useless.

the oscillations of light are a behavior within an electromagnetic field, not a gravitational field. but i have not seen a clear answer as to how the phenomenon of cosmological red shift is produced.

it appears that when space is gravitationally dominated it keeps its dimensions -- the earth and our galaxy are not measurably physically expanding, because they are gravitationally bound -- while space that is not gravitationally influenced appears to be expanding, as it were underneath the electromagnetic fields carrying light from distant objects.

i've never seen a source state the minimal value of gravitation needed to produce the transition to a measurable red shift, e.g., as the minimum distance between two solar masses.

Chalnoth
Thank you for your replies. What I should have said is that the recession rate between us and any observed galaxy cannot have been greater than the speed of light, at the time that the light departed, proven by the simple fact that their light has reached us.
Yes, it absolutely can, and has, as given by the usual definition of recession velocity.

As I mentioned earlier, however, this definition is arbitrary and you can define far-away velocities however you choose. But the recession velocity is sort of the "obvious" velocity that you would write down: it's simply the Hubble expansion rate times the instantaneous distance to the object (the instantaneous distance is the distance given by the time it would take light rays to traverse the distance if you could instantly freeze the expansion to let those light rays do the bouncing).

The way this works is the following: you have a far-away universe emitting light in our direction in the early universe. At the time the light was emitted, the recession velocity of this galaxy was greater than the speed of light, and so as the light moved in our direction, the expansion of our universe carried it away faster than it could approach us.

However, our universe has an expansion rate (hubble parameter) that is slowing down. So, after some amount of time, after the light ray had traversed some distance, eventually the expansion rate slowed enough that the light ray started to make headway against the expansion, finally reaching us billions of years later. But the galaxy that emitted that light was further away still: it wasn't traveling towards us at the speed of light, it was just sitting where it always was among its local galaxies. So even though the expansion rate slowed enough that the light ray could eventually get to us, it didn't need to slow enough for that galaxy to stop receding at faster than the speed of light.

Therefore, there are many galaxies that we can see which always have been and always will be receding at faster than the speed of light.

marcus
Gold Member
Dearly Missed
i'm baffled by the confusion here.
It is confusion on your part. Chalnoth's discussion is clear and correct.

the calculation used to determine the red shift z is simply the doppler formula, applied to measured galactic spectra with the standard scale of wavelength.
You sound confused. The redshift is not "determined by a calculation" using doppler formula, as you seem to believe. The redshift z is measured directly from the spectra. z+1 is the ratio by which all wavelengths are expanded. (Answer to Peter Watkins)

to say that the speed of an object can't be determined because there are many different answers is incorrect...
You are mistaken Drollere. There are several different measures of distance. Recession speed (better called recession rate) is the rate that distance to something is increasing. Before specifying a recession rate one should really say WHICH measure of distance one is using. As Chalnoth pointed out the natural measure when discussing Hubble Law expansion is the instantaneous distance (where you imagine freezing the expansion process at a particular moment so you can measure it, by bouncing a radar signal or however you like, and so measure the distance at that moment). The Hubble Law v = HD is stated in terms of that distance. For the law to apply, D is understood to be the distance "now" (at some moment) and v the current rate that distance is expanding.

Thank you for your replies. What I should have said is that the recession rate between us and any observed galaxy cannot have been greater than the speed of light, at the time that the light departed, proven by the simple fact that their light has reached us. How then can a sub-light speed expansion rate stretch light? With regard to "expanding space" these pages have many times stated that it is this phenomenon that is the cause of universal expansion. "Scientific America" states:-"The velocity in Hubbles law is a recession velocity caused by the expansion of space, not a motion through space." It also states that:- "as space expands, light waves get stretched, if the universe doubles in size during the waves' journey, their wavelength doubles and their energy halves."
As an aside, by how much can visible light waves be stretched before they are no longer visible light? How can we be sure that infra-red light from distant galaxies is not stretched visible light? Do ultra-violet rays and x-rays and gamma rays also get stretched? Or are they somehow immune?
Chalnoth gave a very clear answer already. As he pointed out the natural definition of distance to use in discussing Hubble Law. It's sometimes called the "proper" distance. I will use that distance and just amplify by saying that:
1. most of the galaxies we observe have redshift z bigger than 1.7.
2. with any such galaxy, the distance to it was already growing > c when the light was emitted. And the distance to is growing faster than c today.

In answer to your question, all wavelengths are expanded by the same ratio z+1. the visible range is .4 to .7 and .5 is green. Suppose z = 4 so that the expansion ratio z+1 = 5 then some invisible UV with wavelength .1 gets stretched to .5, which is visible as green.
and green .5 would be stretched to 2.5 which is infrared.

And some infrared would be stretched out by a factor of 5 and become microwave etc.

should have said is that the recession rate between us and any observed galaxy cannot have been greater than the speed of light, at the time that the light departed,
Yes, it absolutely can, and has, as given by the usual definition of recession velocity.

As I mentioned earlier, however, this definition is arbitrary and you can define far-away velocities however you choose. But the recession velocity is sort of the "obvious" velocity that you would write down: it's simply the Hubble expansion rate times the instantaneous distance to the object (the instantaneous distance is the distance given by the time it would take light rays to traverse the distance if you could instantly freeze the expansion to let those light rays do the bouncing).

The way this works is the following: you have a far-away universe emitting light in our direction in the early universe. At the time the light was emitted, the recession velocity of this galaxy was greater than the speed of light, and so as the light moved in our direction, the expansion of our universe carried it away faster than it could approach us.

However, our universe has an expansion rate (hubble parameter) that is slowing down. So, after some amount of time, after the light ray had traversed some distance, eventually the expansion rate slowed enough that the light ray started to make headway against the expansion, finally reaching us billions of years later. But the galaxy that emitted that light was further away still: it wasn't traveling towards us at the speed of light, it was just sitting where it always was among its local galaxies. So even though the expansion rate slowed enough that the light ray could eventually get to us, it didn't need to slow enough for that galaxy to stop receding at faster than the speed of light.

Therefore, there are many galaxies that we can see which always have been and always will be receding at faster than the speed of light.

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You sound confused. The redshift is not "determined by a calculation" using doppler formula, as you seem to believe. The redshift z is measured directly from the spectra. z+1 is the ratio by which all wavelengths are expanded.
nope. the wavelength of a specific absorption or emission line in the receding galaxy spectrum is measured. the wavelength of the matching absorption or emission line is measured in a terrestrial laboratory. the ratio is taken, using the 19th century doppler formula. this is called a calculation by most people. what do you call it?

You are mistaken Drollere. There are several different measures of distance.
and therefore? because there are many different measures of distance (z, light years, parsecs, etc.) from many different inertial frames does not mean that the distance "cannot be determined".

PAllen
2019 Award
nope. the wavelength of a specific absorption or emission line in the receding galaxy spectrum is measured. the wavelength of the matching absorption or emission line is measured in a terrestrial laboratory. the ratio is taken, using the 19th century doppler formula. this is called a calculation by most people. what do you call it?
This ratio is just redshift. The doppler formula is what relates this to velocity. There are two versions: pre-relativity and relativistic. They give different answers. Neither is normally used for cosmologic reshift because a given expanding universe model directly relates redshift to distance instead of velocity. The resulting recession rates are often superluminal.

As I mentioned in an earlier post, there are ways to use use the geometry of given universe model with parallel transport of 4-momentum along a null path that allow treating the recession non-superluminally, and consistent with relativistic doppler formula. This is a mathematically valid but non-standard approach.

and therefore? because there are many different measures of distance (z, light years, parsecs, etc.) from many different inertial frames does not mean that the distance "cannot be determined".
What people are telling you is not about units or frames, but that nobody has billion light year rulers. We measure things like liminosity, redshift, and there is no choice but derive distance in the context of (hopefully well motivated) model. You need a model of standard candles, and of dynamics of spacetime, or you can do nothing with the actually measured quantities. Different assumptions or definitions lead to different distances.

Within GR, even over modest distances, using a distance defined in terms of bouncing light (multiplying time by c) versus proper distance (metric computation) do not yield exactly the same result in the presence of curvature.

marcus
Gold Member
Dearly Missed
and therefore? because there are many different measures of distance (z, light years, parsecs, etc.) from many different inertial frames does not mean that the distance "cannot be determined".
I wasn't talking about distance UNITS. In a world with changing geometry, or spacetime curvature, there are different definitions corresponding to different ways of measuring. PAllen said it.

What people are telling you is not about units ... Different assumptions or definitions lead to different distances.

Within GR, even over modest distances, using a distance defined in terms of bouncing light (multiplying time by c) versus proper distance (metric computation) do not yield exactly the same result in the presence of curvature.
Thanks for taking this one up! Here is an example that might help in the case of someone else confused on this point, if they are willing to learn. Just ask them to google "cosmo calculator" and they will get:

http://www.astro.ucla.edu/~wright/CosmoCalc.html

They immediately see various versions of distance! This is for a galaxy with redshift z=3.
Measuring by light travel time the distance to the galaxy is 11.476 billion lightyears. Say 11.5 not to put too fine a point on it.

==quote==
...
The light travel time was 11.476 Gyr.
The comoving radial distance, which goes into Hubble's law, is 6460.6 Mpc or 21.072 Gly.
The angular size distance DA is 1615.1 Mpc or 5.2678 Gly.
...
==endquote==

The estimated proper distance, if you think of freezing the expansion process at this moment and measuring by radar or whatever usual means, is 21 billion lightyears.

And judging by the angle it makes in the sky, the distance is would be only a little bit over 5 billion lightyears. That is the proper distance the thing was when the light was emitted and started on its way to us. (If you had frozen expansion then, instead of now.)

It's obvious you know all this PAllen, I'm just thinking how we can explain things to a confused newcomer, like that there are different meanings of measure, not just different units. There is also that essay by the Princeton guy about the various different measures of distance used in cosmology. Ask them to google "Hogg distance" and they will get the essay titled "Distance Measures in Cosmology". It explains the different measures which the calculator illustrates like "travel time", proper, angular size etc. I suspect you are already familiar with that essay.

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Thank you for your replies, baffling though some of them may be for a rapidly fossilising brain. The problem I have is understanding why light is stretched. All regularly observed galaxies will have a set of co-ordinates so that astronomers can find them. These co-ordinates do not show where the galaxy currently is but rather, where it was when the light that is now arriving here, left there. If we were to draw an instantaneous picture of the light path, we would see them reaching our galaxy, and behind the point marked by our co-ordinates would be a light path leading back to the galaxy of origin, however far away that may now be. My point is, what possible influence could that receding galaxy, and the others all around it, above, below, to the side, in front and so on, have upon the departed photons? Stretched by a high recession rate at the moment of leaving I can understand, but how the moving apart of galaxies elsewhere can cause light waves to stretch seems to make no sense.
Nice to see that Coldman now agrees with me that the expansion rate is slowing,(#14), something that I have been saying for 2-3 years now. Also that "expanding space" is simply the increase in distance between galaxies, rather than a mechanism that is causing the separation, (#2).

Chalnoth
Thank you for your replies, baffling though some of them may be for a rapidly fossilising brain. The problem I have is understanding why light is stretched. All regularly observed galaxies will have a set of co-ordinates so that astronomers can find them. These co-ordinates do not show where the galaxy currently is but rather, where it was when the light that is now arriving here, left there. If we were to draw an instantaneous picture of the light path, we would see them reaching our galaxy, and behind the point marked by our co-ordinates would be a light path leading back to the galaxy of origin, however far away that may now be. My point is, what possible influence could that receding galaxy, and the others all around it, above, below, to the side, in front and so on, have upon the departed photons? Stretched by a high recession rate at the moment of leaving I can understand, but how the moving apart of galaxies elsewhere can cause light waves to stretch seems to make no sense.
Nice to see that Coldman now agrees with me that the expansion rate is slowing,(#14), something that I have been saying for 2-3 years now. Also that "expanding space" is simply the increase in distance between galaxies, rather than a mechanism that is causing the separation, (#2).
Well, yeah, the far away galaxy has no influence whatsoever upon the light once that light is emitted. That's sort of the point. This is what allows us to see some galaxies that are now and always have been receding at faster than light (according to the usual definition of recession velocity).

Anyway, the simplest possible way to look at this is to define your coordinates in such a way that each galaxy is nearly stationary but with the distances between galaxies increase with time. In this view, when the light traverses the universe, it gets stretched right along with the expansion, and that accounts for the redshift. There may be some redshift due to the local motion of the galaxy, but most of it comes from the stretching of space that also stretches out the wavelength of the light as it travels.

marcus
Gold Member
Dearly Missed
The problem I have is understanding why light is stretched. the separation...
Good question. I want to reinforce what Chalnoth just said, with some more mental imagery.
You could picture it as a chain of "infinitesimal" doppler shifts all along the way. Chalnoth's picture of a long chain of stepping stones, each one stationary relative to background, which are drifting apart.

At each stepping stone galaxy, an observer can approximate the local situation by a standard "flat" framework that includes the next galaxy and in which the next galaxy actually appears to be moving away, and there is a standard doppler effect.

So the overall redshift is seen as the cumulative effect of many many many standard doppler shifts each calculated in an approximately flat locale.

If this doesn't help, please ignore it

Thank you again. One last problem; looking at the full e/m spectrum it would seem that gamma rays are something like a million time shorter than visible light rays. If a galaxy is far enough away to have it's visible light rays stretched by 25% by the time they arrive here, wouldn't this stretch gamma rays from the same source by a factor of 250,000, meaning that they are no longer gamma rays. And yet they can be seen coming from distances approaching 13 billion light years.

PAllen
2019 Award
Thank you again. One last problem; looking at the full e/m spectrum it would seem that gamma rays are something like a million time shorter than visible light rays. If a galaxy is far enough away to have it's visible light rays stretched by 25% by the time they arrive here, wouldn't this stretch gamma rays from the same source by a factor of 250,000, meaning that they are no longer gamma rays. And yet they can be seen coming from distances approaching 13 billion light years.
Any wavelength is shifted (expanded) by the same factor. A z factor of 1 converts blue light to red light and a gamma ray to a somewhat less energetic gamma ray. A z factor of 9 (around the biggest observed) still only converts most gamma rays to less energetic gamma rays or x-rays (a 10 mev gamma becomes a 1 mev gamma).

The simplest way I can think to say it is that you get some very specific total redshift for faraway objects due to the expansion. How much of that redshift is due to the doppler shift and how much is due to the expansion between us and the far away object is completely arbitrary.
Quite.

i'm baffled by the confusion here.

the doppler shift is used to describe the expansion related red shift in light: the calculation used to determine the red shift z is simply the doppler formula, applied to measured galactic spectra with the standard scale of wavelength.

to say the red shift is possibly not a doppler shift is like saying a pound of feathers is possibly not really really a pound.

to say that the speed of an object can't be determined because there are many different answers is incorrect. what is your personal distance from the capitol of illinois? does that answer apply to everyone? does that mean the distance to chicago can't be determined?

special relativity theory merely requires the choice of inertial frames of reference. it doesn't say inertial frames become useless.

the oscillations of light are a behavior within an electromagnetic field, not a gravitational field. but i have not seen a clear answer as to how the phenomenon of cosmological red shift is produced.

it appears that when space is gravitationally dominated it keeps its dimensions -- the earth and our galaxy are not measurably physically expanding, because they are gravitationally bound -- while space that is not gravitationally influenced appears to be expanding, as it were underneath the electromagnetic fields carrying light from distant objects.

i've never seen a source state the minimal value of gravitation needed to produce the transition to a measurable red shift, e.g., as the minimum distance between two solar masses.
Yeah but the point is you can understand the question even though you might not understand why it was asked: perspective wise.

No doubt when you were learning this these questions ran through your mind, unless you were a genius, is what I mean.

They might of done genius or not. But meh you get my point.