# Is Noether's theorem applicable to the expanding universe?

• quin dexter
In summary, Noether's theorem is not directly applicable to the expanding universe, as it is a theory that applies to systems with a fixed geometry. However, the underlying principles of conservation of energy and momentum described by Noether's theorem still hold true in the expanding universe, and have been used to study the evolution of the universe and the behavior of matter and energy within it.
quin dexter
is the BB theory no more ?.

and is my new thinking , which is taking me down a path of thought that,
if objects in the observable universe are 92 billion light years apart, how can the age of the universe be estimated at 13.5 billion years?

There was no big bang, the universe is constantly renewing itself. And is being created at the quantum level.??..

According to my understanding, there was a period of "inflation" in the first seconds after the big bang where space expanded at a phenomenal rate. See the wikipedia article here. http://en.wikipedia.org/wiki/Inflation_(cosmology )

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so why can we not find the location of the bb and why can we not find a general direction of where the big bang banged ??

Because when we look in every direction, it all looks relatively the same. All galaxies are accelerating away from us in every direction and the background radiation looks the same too. There isn't any way to tell.

The universe is expanding. A very similar topic was here recently regarding expansion of the universe: https://www.physicsforums.com/showthread.php?t=457550

This is how something can be further away from us now than it was just after the big bang and more importantly, further away than the 'size' of the universe after the big bang.

I don't believe the big bang was a point in space that we could find and nothing actually "banged".

The above post by JJ as well.

quin dexter said:
so why can we not find the location of the bb and why can we not find a general direction of where the big bang banged ??
Geometry implies the Big Bang happened everywhere.

quin dexter said:
and is my new thinking , which is taking me down a path of thought that,
if objects in the observable universe are 92 billion light years apart, how can the age of the universe be estimated at 13.5 billion years?

There was no big bang, the universe is constantly renewing itself. And is being created at the quantum level.??..

First question
It is because of the expansion of space that light from the edge of the observable universe that reaches us now, originated form an object that would now be at a 46 B Light years distance. See it like this. The light traveled 13.5 B years and in the mean time the distance grew "under its feet" to 46 B Light years.
Taking the 46 BLy as radius of the observable universe you could say that the diameter is 92 Bly.
I don't think the two object you observe in oposite directions would be in each others observable universe.

Second question
I'm not familiar with any models about creation of space on the quantum level.
Sort of phylosophical question: where does the "new" space come from?
I don't know.

Drakkith said:
Because when we look in every direction, it all looks relatively the same. All galaxies are accelerating away from us in every direction and the background radiation looks the same too. There isn't any way to tell.

The background doesn't look completely the same - there are CMBR anisotropies with visible structures of slightly different color temperature. These actually helped prove BB theory over the previously accepted explanation, that CMBR was forward scattered light from receding galaxies beyond the Hubble sphere. The Planck Spacecraft will reveal this CMBR in greater detail "next year" (I'm leaving the keyword name of that excitable year out for now). It's supposed to be a snapshot of the opaque universe at age 380,000 years. If the redshift of our peculiar motion can be correctly canceled out, it may be possible to use the image to estimate a position for the BB origin.

Drakkith said:
Because when we look in every direction, it all looks relatively the same. All galaxies are accelerating away from us in every direction and the background radiation looks the same too. There isn't any way to tell.

are all galaxies expanding away from each other as well? i read somewhere about nitrogen atoms in a vacuum becoming equidistant. maybe not the same process but, same effect? if so are they expanding at the same rate? is there gravity outside our universe pulling the expansion?

Subluminal said:
If the redshift of our peculiar motion can be correctly canceled out, it may be possible to use the image to estimate a position for the BB origin.

This is incorrect: the 'big bang' did not happen at one point in spacetime (as mentioned above by russ). The 'big bang theory' should simply be taken to mean a cosmological model in which the universe was once much smaller, hotter and denser than it is today, and which has expanded from that initial state.

I guess the initial question has been well and knowledgeably answered several times, so I just want to recap the main point.
quin dexter said:
if objects in the observable universe are 92 billion light years apart, how can the age of the universe be estimated at 13.5 billion years?
...

There is no contradiction because no physical law prevents distances from expanding more rapidly than c. The "speed limit" many people talk about is a feature of Special Rel that applies to ordinary motion, defined at ordinary distance scales where curvature can be neglected. I think the limited applicability of SR has been pointed out already.

Drakkith raised an interesting question by mentioning inflation.

Does anyone have an estimate of the size at the end of the hypothetical inflation of what we now call the observable universe?

I have the impression that in ordinary inflation scenarios the observable chunk was still quite small. Maybe Cristo or Russ knows a ballpark figure?

The Wikipedia link that Drakkith offered has this plot:

http://en.wikipedia.org/wiki/File:Horizonte_inflacionario.svg

According to this, the scalefactor at end of hypothetical inflation was roughly 10-25 to 10-30.

If you take a figure like 40 billion lightyears and scale it back by 1025
you get very roughly around 10-15 of a lightyear.
That's only around 9 meters.
I'm being really sloppy just to get a rough idea. That seems like hardly any distance at all.

In linear terms, in a conventional inflation scenario most of the expansion occurs AFTER inflation ended, if we go by this.

I think many people do not realize this and have the idea that the reason the observable portion is so large is somehow because of inflation.
One could, I suppose, challenge the inflation scenario and provide some alternative discussion of the initial conditions at the start of normal expansion---and still have a large universe due to normal (non-inflationary) expansion.

Any comment? I expect some of us have thought this through more thoroughly than I have.

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quin dexter said:
and is my new thinking , which is taking me down a path of thought that,
if objects in the observable universe are 92 billion light years apart, how can the age of the universe be estimated at 13.5 billion years?

FAQ: Why is the radius of the observable universe in light-years greater than its age in years?

The radius of the observable universe is about 46 billion light years, which is considerably greater than its age of about 14 billion years. Since the radius of the observable universe is defined by the greatest distance from which light would have had time to reach us since the Big Bang, you might think that it would only lie at a distance of only 14 billion light years, since x=ct for motion at a constant velocity c. However, a relation like x=ct is only valid in special relativity. When we write down such a relation, we imagine a Cartesian coordinate system (t,x,y,z), which in Newtonian mechanics would be associated with a particular observer's frame of reference. In general relativity, the counterpart of this would be a Minkowski coordinate frame, but such frames only exist locally. It is not possible to make a single frame of reference that encompasses both our galaxy and a cosmologically distant galaxy. General relativity is able to describe cosmology using cosmological models, and this description is successful in matching up with observations to a high level of precision. In particular, no objects are observed whose apparent ages are inconsistent with their distances from us.

One way of describing this difference between special relativity's x=ct and the actual distance-time relationship is that we can think of the space between the galaxies as expanding. In this verbal description, we can imagine that as a ray of light travels from galaxy A to galaxy B, extra space is being created in between A and B, so that by the time the light arrives, the distance is greater than ct.

quin dexter said:
so why can we not find the location of the bb and why can we not find a general direction of where the big bang banged ??

FAQ: Where did the Big Bang happen? Would that be the center of the universe?

According to standard cosmological models, which are based on general relativity and are found to agree well with observations, the Big Bang was not an explosion that happened at a particular point in a preexisting landscape of time and space. Time and space did not exist before the Big Bang -- or even *at* the Big Bang, which is a point where the theory breaks down because things get infinite. The high temperatures and high densities associated with the early universe existed everywhere at once and were very nearly uniform. In these models, which are constructed so as to be perfectly uniform, no point in space has different properties than any other. This is in good agreement with observations of the universe, which shows that that there is a nearly complete lack of structure on very large scales.

marcus said:
Drakkith raised an interesting question by mentioning inflation.

Does anyone have an estimate of the size at the end of the hypothetical inflation of what we now call the observable universe?

I have the impression that in ordinary inflation scenarios the observable chunk was still quite small. Maybe Cristo or Russ knows a ballpark figure?

The Wikipedia link that Drakkith offered has this plot:

http://en.wikipedia.org/wiki/File:Horizonte_inflacionario.svg

According to this, the scalefactor at end of hypothetical inflation was roughly 10-25 to 10-30.

If you take a figure like 40 billion lightyears and scale it back by 1025
you get very roughly around 10-15 of a lightyear.
That's only around 9 meters.
I'm being really sloppy just to get a rough idea. That seems like hardly any distance at all.

In linear terms, in a conventional inflation scenario most of the expansion occurs AFTER inflation ended, if we go by this.

I think many people do not realize this and have the idea that the reason the observable portion is so large is somehow because of inflation.
One could, I suppose, challenge the inflation scenario and provide some alternative discussion of the initial conditions at the start of normal expansion---and still have a large universe due to normal (non-inflationary) expansion.

Any comment? I expect some of us have thought this through more thoroughly than I have.

The image that stuck in my mind from a Scientific American article is that the presently observable universe was about the size of a dime at the end of inflation. I think this is in excellent agreement with your estimate of 9 m. In any case, we don't know whether inflation is even correct.

I don't think inflation has anything to do with the fact that the radius of the observable universe in light years is greater than the age of the universe in years.

bcrowell said:
The high temperatures and high densities associated with the early universe existed everywhere at once and were very nearly uniform. In these models, which are constructed so as to be perfectly uniform, no point in space has different properties than any other. This is in good agreement with observations of the universe, which shows that that there is a nearly complete lack of structure on very large scales.

My hope was that since exceptions to homogeneity and isotropy are observable all the way back to the surface of last scattering, perhaps there is a way to look at other structural clues in CMB temperature variation that could point to a BB origin position. The models that assume no structure say that decoupling happens everywhere all at once. But there is structure, so maybe there was a frontal boundary of sorts, as decoupling took effect from one side of our little speck of observable universe to the other at that time. It would be slight, possibly small enough to be lost in the redshift correction we make to account for our own peculiar velocity. What if this redshift correction has caused us to ignore a slight large scale structure where one side of the sky is a hot spot and the opposite side is a cold spot - would this point to the origin, at least a vector that a "frontal boundary" followed?

It seems probable that the BB origin is outside the region of the universe we can see. If after inflation this region was the size of a dime or the Epcot ball, it seems pretty small for a universe 0.38 BY old, and pretty small for photons to take 13.5 BY travel from the edge to us in the center. Something I get from Einstein is that c does not change, only time. So back then, a second had to seem really really big compared to what we think of a second. At the same time (or instead?), a meter would be really really tiny compared to what we think of as a meter. This whole expansion idea makes me think of spacetime as a conserved quantity. I know that's not right, but it might help me sleep tonight!

Subluminal said:
My hope was that since exceptions to homogeneity and isotropy are observable all the way back to the surface of last scattering, perhaps there is a way to look at other structural clues in CMB temperature variation that could point to a BB origin position...

Have you by any chance watched the balloon model animation at Ned Wright's UCLA site?
It's short, just 4 or 5 minutes, and informative. If you haven't, and want to view it, just google "wright balloon model".

It is a 2D analogy of our expanding 3D geometry. The 2D creatures in that world (all existence concentrated on the balloon surface) would not be able to point in the direction of the origin of their BB. In their space---at any given moment, once the balloon has begun to expand---there is no point of origin.

From your line of questioning it seems like you are asking about something that logically does not exist in today's universe. A non-existent location. Perhaps I don't understand your question.

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Subluminal said:
It seems probable that the BB origin is outside the region of the universe we can see.
In that case, we would not be able to observe its afterglow, which is the cosmic microwave background.

There are cosmologists working with models that are not perfectly homogeneous. The CMB anisotropy is a big subject in current research. It's not as though everybody has just assumed isotropy and never considered what happened when the approximation was broken.

bcrowell said:
In that case, we would not be able to observe its afterglow, which is the cosmic microwave background.

bcrowell you are orders of magnitude smarter than me and I know it, but bear with me on this:

There's another decoupling event for neutrinos, about 1 second after the BB (http://en.wikipedia.org/wiki/Decoupling#Physical_cosmology). Call it the CNB, with its own radius to us analogous to our CMB radius. One day we'll be able to measure it, but maybe not in our lifetimes. Think of the CMB as a cloudy "eye of the hurricane" wall with lightning going off inside, and we are at the center of the eye - we can see the illuminated cloud wall two miles away but can't see any further details of the storm. Say the CNB is ring of radio stations 30 miles from the storm center. I can observe those only because they send "particles" that can penetrate the cloud. Along this idea, our CNB radius of the neutrino afterglow (radio stations in range) is greater than our CMB photon radius (to the cloud wall). So, I think it's a higher probability that the BB origin falls within the larger CNB sphere than the smaller CMB sphere.

Back to your point, if the BB origin fell outside our special CMB or CNB radii, why should we not be able to observe the decoupled particles or photons of either background?

bcrowell said:
There are cosmologists working with models that are not perfectly homogeneous. The CMB anisotropy is a big subject in current research. It's not as though everybody has just assumed isotropy and never considered what happened when the approximation was broken.

I'm thankful the universe is not in fact isotropic! Thanks for all your input.

marcus said:
Have you by any chance watched the balloon model animation at Ned Wright's UCLA site?

I've heard of the spherical rubber sheet analogy but never saw this animation, thanks. Why do the galaxies themselves not get bigger with expansion, does gravity effectively cancel out expansion in the near field? Extending to the strong force, is the volume of a helium nucleus also not affected by cosmological expansion over billions of years?

Subluminal said:
... Along this idea, our CNB radius of the neutrino afterglow (radio stations in range) is greater than our CMB photon radius (to the cloud wall). So, I think it's a higher probability that the BB origin falls within the larger CNB sphere than the smaller CMB sphere...

What do you mean by "the BB origin"?

Subluminal said:
I've heard of the spherical rubber sheet analogy but never saw this animation, thanks. Why do the galaxies themselves not get bigger with expansion, does gravity effectively cancel out expansion in the near field? Extending to the strong force, is the volume of a helium nucleus also not affected by cosmological expansion over billions of years?

So did you in fact watch it? If so that's great! then you saw the galaxies (white) and also the photons of light (colored wigglers, that gradually get longer wavelength and redder color).

You guessed right about galaxies and helium nuclei not being affected. They are bound structures.Do you understand why I say the BB point of origin does not exist today? that there is no location that we can point to?

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Subluminal said:
My hope was that since exceptions to homogeneity and isotropy are observable all the way back to the surface of last scattering, perhaps there is a way to look at other structural clues in CMB temperature variation that could point to a BB origin position.

People have looked for this. For a while they were seeing things that *might* be interesting but with more data none of those weird things turned out to be significant.

http://arxiv.org/abs/1001.4758

What if this redshift correction has caused us to ignore a slight large scale structure where one side of the sky is a hot spot and the opposite side is a cold spot - would this point to the origin, at least a vector that a "frontal boundary" followed?

At that point you start crunching numbers and seeing what the limits are for "weird" stuff.

Subluminal said:
Call it the CNB, with its own radius to us analogous to our CMB radius. One day we'll be able to measure it, but maybe not in our lifetimes.

I wouldn't say that. People are trying...

http://arxiv.org/abs/hep-ph/0703075

Back to your point, if the BB origin fell outside our special CMB or CNB radii, why should we not be able to observe the decoupled particles or photons of either background?

Don't understand the question. If you are coming up with an alternative theory of cosmology, you tell me what you expect to see.

marcus said:
So did you in fact watch it? If so that's great! then you saw the galaxies (white) and also the photons of light (colored wigglers, that gradually get longer wavelength and redder color).

You guessed right about galaxies and helium nuclei not being affected. They are bound structures.

Do you understand why I say the BB point of origin does not exist today? that there is no location that we can point to?

The balloon example appears to suggest that spacetime is not a conserved quantity, it just keeps oozing out of nothing forever. I couldn't sleep, thinking that galaxies and helium atoms have to obey the same laws of physics today and 13 BY ago because c has always been the same. And that got me thinking about those stretchy wigglers in between. Where does the energy go that changes them to longer wavelengths? We have spontaneous generation of spacetime and the disappearance of a lot of photon energy all happening in the same place. What is going on? I chose my handle based on thinking maybe photons from a receding galaxy really were slower but since signing up have learned that can't be.

Staying with the balloon idea, I understand if you collapse the hollow balloon in reverse time all points converge to one infinitesimally small point, so there can be no point where the BB didn't happen. I am focusing on the time when matter and energy are decoupled - the universe had a radius R (assuming it is a sphere) with a center at r=0 and an edge at r=R, and the center of what will be our observable universe is at some r<R*. I guess all I just proved is that YES, we are INSIDE the universe. Whether we were at r=0 or r=.999R at a certain time, it makes no difference. It's like being a crumb in the unburnt part of a cake and wondering if your were originally in the center of the pan or not as a drop of batter - it makes no difference, nothing new is gained, it's all the same delicious cake. *OK, I understand now as opposed to at the beginning of writing this paragraph up to "r<R", and I have you to thank. Now I am definably going to sleep well.

Subluminal said:
Where does the energy go that changes them to longer wavelengths? We have spontaneous generation of spacetime and the disappearance of a lot of photon energy all happening in the same place.

At cosmological scales, energy isn't conserved.

Also at some point you the answer to "why?" is "I don't know why it is, but that's what we see."

What is going on? I chose my handle based on thinking maybe photons from a receding galaxy really were slower but since signing up have learned that can't be.

Tired light...

One problem I think with most physics textbooks is that they give you the current ideas of what is going on. One thing that would be cool is "an encyclopedia of failed ideas". That would speed up the "have you thought of... Yes, we thought of that, and here is why it didn't work..."

Something else that would be interesting is to go back to an old textbook and mark it up. Something that I like doing is reading old books to see what's changed.

Subluminal said:
Back to your point, if the BB origin fell outside our special CMB or CNB radii, why should we not be able to observe the decoupled particles or photons of either background?
The observable universe consists of everything from which information has had time to get to us since the big bang, traveling at the speed of light. If something happened outside of that, then we wouldn't have been able to receive any information about it by now.

twofish-quant said:
At cosmological scales, energy isn't conserved..

Do you think a Theory of Everything is attainable?

I may have another "have you thought of... " but I'm going to read a few hundred more posts first on GR, expansion, this Tired Light loss, and dark energy & matter. Also, my calc and diff eq skills need a major refresher. I apparently suffered a "use it or lose it" event.

twofish-quant said:
One thing that would be cool is "an encyclopedia of failed ideas". That would speed up the "have you thought of... Yes, we thought of that, and here is why it didn't work..."

I'm working through Edward Wright's website at UCLA that marcus pointed me to. It's well written and often recaps old ideas and how new observations forced people to come up with new ideas.

I came across a recap of Tired Light in his "fads and fallacies" section and wondered if it was the same theory you mentioned: http://www.astro.ucla.edu/~wright/tiredlit.htm

In the tired light theory, redshift was due to photons losing energy but not momentum, but not due to expansion since the theory (as Wright explains it) did not support expansion as the cause of the "tiredness". Are you talking about a tired light explanation that also allows for expansion?

Some observe redshifted light and say it's due to space expanding. I am thinking (no doubt incorrectly) that maybe we are observing space expanding due to photons there losing energy. The correlation between distance and redshift is already observed, so this is a question to me of which is causing what, and does what's happening now jive with what was happening when the universe was 3000K. Does anyone know the energy density of photons in the vacuum between galaxies relative to CMB temperature?

Subluminal said:
Do you think a Theory of Everything is attainable?

It's unclear to me on what basis I would use to answer that question, so I'd have to answer with "I don't know."

twofish-quant said:
One thing that would be cool is "an encyclopedia of failed ideas". That would speed up the "have you thought of... Yes, we thought of that, and here is why it didn't work..."

I have read and respected many of your comments, but i must disagree here. It can actually be educational for people to make the mistake for themselves, and not all discarded ideas are without merit.

Cosmo Novice said:
I have read and respected many of your comments, but i must disagree here. It can actually be educational for people to make the mistake for themselves, and not all discarded ideas are without merit.

As much as I agree that making mistakes yourself is a good way to learn, there's just not enough time. And to have too many people working on already failed ideas just wastes even more time.

If an idea is shown to be a complete failure, I don't see what would be wrong with having it listed somewhere for people to 'check on' when they come up with something.

twofish-quant said:
It's unclear to me on what basis I would use to answer that question, so I'd have to answer with "I don't know."

Aristotle said that a body in motion always eventually comes to rest. It took people like Newton and Galileo to find and convincingly show otherwise. The current belief (I understand not held by all) that photons simply lose energy in extragalactic vacuum reminds me of that time before energy was determined to be a conserved quantity, so I can't see how it's true. I admit this is intuition, and I apologize for that. It just seems to me that we lack the capacity to observe what's really happening, as Aristotle lacked the instruments available to later scientists. Or maybe we can see it but we're not looking in the right place.

If we could integrate all the photon energy lost to expansion redshift within our CMB sphere since decoupling, how would that compare that to WMAP readings of how much dark energy we see now? The Planck spacecraft is due to send us much better data than WMAP next year, the "year that dare not speak its name". The WMAP gave such solid confirmation of BB theory that it's hard to deny (http://map.gsfc.nasa.gov/universe/bb_tests_exp.html). Planck will measure the amount of dark matter & energy 10x more accurately. Are there any theories that predict the ratio of these 2 things?

Subluminal said:
If we could integrate all the photon energy lost to expansion redshift within our CMB sphere since decoupling, how would that compare that to WMAP readings of how much dark energy we see now? ...

I remember making a similar comparison back in 2003-2004, just for fun. It was something like this: we don't know that "dark energy" is actually an energy. It behaves like a constant in the equation, whose dimensions is curvature. Interpreting as energy is optional

but if you do choose to do that the energy density is about 0.6 nanojoules per cubic meter.

And correct me if I am wrong, anybody, but I recall the CMB energy density is about 4.2 x 10-5 nanojoules per cubic meter. It should be lookable-up somewhere.

Now those CMB photons have "lost" (by a succession of little doppler shifts as they progress from frame to frame--if you choose to think of the expansion process that way) about 1090/1091 of their original energy, so the energy of each photon now in this frame is 1/1091 what it was when it started in its emission frame.

So the energy of those photons used to total about 1000 times larger. that is about
4.2 x 10-2 nanojoules per cubic meter.

So 0.04 compared with 0.6

It doesn't match. It is nearly within an order of magnitude, which is kind of cute. But it does not match. And there is no physical reason it should.

So Subluminal, to answer your question in a rough sort of way, if you take a cubic meter out in space, if you like to quantify the cosmo constant as an energy density and like to think of it that way, then that cubic meter has 0.6 joules of DE in it. And if you look at all the CMB photons in it, and add up all the energy they have "lost" since they started their travels, then that cubic meter of CMB photons has lost a total of 0.04 joules.

If I recall correctly. It's quite a bit less. You wanted a comparison like that, I think.

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The concept of energy is meaningful within a given reference frame. I guess most of us, to define energy, would require a Newtonian frame, or the frame of a Special Rel observer.
Just, for instance, to be able to say clearly what "work" is.

Conservation of momentum and energy are proven using time and space translation symmetry. In the real world (where symmetry is only approximate) they are only approximately true. In general, there is no global frame of reference. There is no global definition of energy. You cannot prove conservation globally. There is no reason to believe it in general

We have all met people who suffer from excessive credulousness. They don't critically examine their beliefs. Some one told them "energy is conserved" and "things cannot move faster than c relative to other things". They swallow that naively without asking "in what context?" and "under what assumptions?"

Without assumptions about symmetry you cannot define our motion relative to something that existed in the past. Without a reference frame there is no unambiguous definition of motion or speed. As a general rule, curved spacetimes do not admit global frames.

I'm no great expert or authority in these matters, but I'm pretty sure that over cosmological distances you can't unambiguously say what distance is or motion is without making some explicit definitions first. That would go for energy also, to the extent that it can be defined.

BTW I recall reading years ago that in a curved space an amoeba-like creature could travel by successively changing its shape. I've lost the reference. It was in arxiv.org as I recall, maybe about the same time 2004? Do you happen to remember seeing something like that? It appears to violate intuition---the think is moving without rockets, without any "equal and opposite" reaction mass. Anybody remember seeing that?

I found some links!
Something from Science, February 2003:
http://www.sciencemag.org/content/299/5614/1865
Free article from Physical Review D
http://arXiv.org/pdf/gr-qc/0510054v2
also more recent popularization in Sci Am.
http://www.scientificamerican.com/article.cfm?id=surprises-from-general-relativity&page=2
Some animations (scroll down)
http://physics.technion.ac.il/~avron/

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