# Cosmological redshift: how much energy has gone missing?

• marcus
In summary, the conversation is discussing the phenomenon of cosmological redshift and the question of what happens to the energy of photons in this process. Some suggest that the energy is lost, while others speculate that it may go somewhere, such as fueling dark energy. Rough estimates are provided for the amount of energy lost from the CMB due to redshift and it is noted that this is roughly equal to the current density of dark energy. The number of CMB photons per unit volume of space is also calculated.
marcus
Gold Member
Dearly Missed
[[I would like to hear some interpretations of this phenomenon, especially in regards to what happens to the energy of photons in cosmological redshift – where do YOU think it goes? Is it lost or is it conserved?]]

It is clear that a whole lot of energy has been lost by the stretching out of light over the course of billions of years and
in that thread some people were speculating that it had gone somewhere (instead of being simply lost) like into fueling the dark energy or something. I can't say just what the idea is, but I can try a rough estimate of how much energy has been lost.

(I don't think it is very much compared with the present amount of dark energy.)

Up to a factor of order one, the volumetric density of radiation at temp T is (correct me if I am mistaken) T4 times k4/hbar3c3

The temp of the CMB in absolute units is 2.0E-32
So raise that to the fourth and you get 16E-128

That is the current energy density in the space around us of the CMB (or about 2/3 that because of the order-one factor I omitted)

And the CMB is at redshift 1100. So, if the CMB had not been being redshifted all these billions of years since socalled "recombination" (estimated 300,000 years after bigbang) then its photons would each be 1100 times as energetic.

So the amount of lost energy (per unit volume of space) is about
1000 x E-127 which is E-124

But the dark energy density I have calculated a couple of times here (being 70 percent of critical) as 1.3E-123

So this redshift loss is only an order of magnitude smaller than the cosmological constant or dark energy density!

I did not realize that when I first calculated---and also made
a multiplication error I just corrected---so got a different conclusion.

Light from all the galaxies is a smaller density---it does not noticeably effect the temperature of space so I neglect it. So the energy lost from the CMB by space-expansion is (admittedly a huge huge amount of energy) is smaller but roughly comparable with Lambda, or Dark or "quintessence" whatever you call it.

(Q)'s question is provocative in that it tempts us to speculate that the energy lost by cosm. redshift as gone into something like expanding space and creating more dark energy.

I have no clue as to how that could happen and assume that the energy is simply lost.

Note that I calculated the CMB energy density in space simply by raising the temp to the fourth. (c=G=hbar=k=1) Would someone show how to calculate the joules per cubic meter of the CMB in metric terms? Probably not, but it would provide a check.

The actual CMB temp is 1.93E-32 absolute (corresponding to
2.725 kelvin) but for back-of-envelope I took it to be 2E-32.
E-32 of the Planck temperature is what corresponds roughly
in size to a kelvin, more accurately 1.4 kelvin.

Last edited:
Originally posted by marcus
[[I would like to hear some interpretations of this phenomenon, especially in regards to what happens to the energy of photons in cosmological redshift – where do YOU think it goes? Is it lost or is it conserved?]]

It is clear that a whole lot of energy has been lost by the stretching out of light over the course of billions of years and
in that thread some people were speculating that it had gone somewhere (instead of being simply lost) like into fueling the dark energy or something. I can't say just what the idea is, but I can try a rough estimate of how much energy has been lost.
No energy has been lost. Thermodynamics states that the amount of energy in the universe is constant. Its just spread out over a larger volume which decreases its DENSITY.

Originally posted by russ_watters
No energy has been lost. Thermodynamics states that the amount of energy in the universe is constant. Its just spread out over a larger volume which decreases its DENSITY.

Hello Russ, thanks for responding. what you say is a fascinating and novel idea. I never heard of thermodynamics being applicable to the universe as a whole.

Into what form do you suppose the energy of the CMB has gone?

By current estimates, the CMB that is observed today has lost 2999/3000 of its energy. Where could this have gone?

[[I would like to hear some interpretations of this phenomenon, especially in regards to what happens to the energy of photons in cosmological redshift – where do YOU think it goes? Is it lost or is it conserved?]]

It stikes me as an odd coincidence that the dark energy density calculated from MAP and supernova data is roughly equal to the amount lost from the CMB---within a factor of ten. I do not suppose that one feeds the other, it is just a curious coincidence.

Let's calculate the number of CMB photons per unit volume in space. The observed temp is 1.93E-32 (in natural units c=G=hbar=k=1)

Stefan-Boltzmann says the volumetric density of radiation at temp T is (pi2/15 ) T4 times k4/hbar3c3. This last factor is just equal to one in natural terms, so the energy density is just

(pi2/15 ) T4 = 9E-128

The Planck blackbody curve says the average energy of a photon is 2.701 x 1.93E-32-----it is always 2.701 times kT. This is the energy of all the photons in a volume of space divided by the number of photons.

So the average photon carries 5.2E-32 of the natural unit of energy. The number of photons per unit volume of space has to be 9E-128 divided by the average. It works out to

1.75E-96

To look at that in human scale, use the fact that a mile is E38 and a cubic mile is therefore E114. so the density of CMB photons is
1.75E18 per cubic mile. Or about a quarter of that per cubic kilometer. On the order of a quintillion---don't know if that helps.

Anyway, each of those quintillion or so photons has lost
1100/1101 of its energy since the moment the light got loose
("recombination", a moment of clearing when the plasma cooled
to where it could condense to neutral hydrogen and the light which had been trapped in the plasma went flying in a suddenly transparent universe).

Pick a photon and look at it, the photon has lost 1100/1101 of its energy because it has been stretched out. Its wavelength is 1100 times longer than when it first got loose.

So we are surrounded by the concrete results of a huge loss of energy. In a cubic mile or cubic km of space there are roughly a quintillion things that have each lost 1100/1101 of their original energy. And no one, as far as I know, has suggested that the lost energy went into any new form. It did not "go" anywhere. It simply ceased to exist.

Energy is an idea, not a real substance. It is not conserved except in very specific types of models, of which apparently General Relativity, our prevailing model of space and gravity, is not one.

But it is eerie that the amount of energy which the CMB photons in a cubic mile have lost (since "recombination" some 13 billion years ago) should be roughly, within a factor of ten, the same as the amount of dark energy believed to be in the same cubic mile
volume.

Last edited:

Originally posted by marcus
Hello Russ, thanks for responding. what you say is a fascinating and novel idea. I never heard of thermodynamics being applicable to the universe as a whole.

Into what form do you suppose the energy of the CMB has gone?

By current estimates, the CMB that is observed today has lost 2999/3000 of its energy. Where could this have gone?
Is CMB the background radiation? I think the energy is either still in the background radiation or condensed into matter. Isn't this where the dark matter/energy question comes from? There is missing matter/energy, but I think cosmologists believe it exists.

The wording of the laws of thermodynamics is different for different situations, but they apply to all closed systems. The universe is (believed to be) a closed system.

Last edited:

Originally posted by russ_watters
Is CMB the background radiation? I think the energy is either still in the background radiation or condensed into matter. Isn't this where the dark matter/energy question comes from? There is missing matter/energy, but I think cosmologists believe it exists.

The wording of the laws of thermodynamics is different for different situations, but they apply to all closed systems. The universe is (believed to be) a closed system.

Hello Russ, so you are still around this morning!
Yes by CMB I mean CMBR cosmic microwave background radiation.
Get tired of long acronyms sometimes and write CMB for short.
You and I need a guru. the universe is believed to be infinite. I cannot think of it as a closed system, tho perhaps you can.
the energy in it would be infinite and so the conservation law would not seem to say very much. but perhaps it says something meaningful to you.

I don't think the conservation of energy applies, actually. The CMB has lost a huge amount and no one that I know has proposed any mechanism for the energy to have flowed into
any other form

Originally posted by marcus
the universe is believed to be infinite. I cannot think of it as a closed system, tho perhaps you can.
the energy in it would be infinite and so the conservation law would not seem to say very much. but perhaps it says something meaningful to you.
Our current understanding of the unvierse does indeed suggest that the universe is FINITE but without boundaries. This is what the Big Bang theory describes. It is analogous (but in 3d, not 2d) to an expanding balloon with dots on it - it has a finite surface area (that is increasing) but no boundary. So hypotetically, if you could travel fast enough in one direction, you'd eventually get back to where you started - just like on the surface of that balloon.

As such, there was also a finite amount of energy in the Big Bang.

Originally posted by russ_watters
Our current understanding of the unvierse does indeed suggest that the universe is FINITE but without boundaries. This is what the Big Bang theory describes. It is analogous (but in 3d, not 2d) to an expanding balloon with dots on it - it has a finite surface area (that is increasing) but no boundary. So hypotetically, if you could travel fast enough in one direction, you'd eventually get back to where you started - just like on the surface of that balloon.

As such, there was also a finite amount of energy in the Big Bang.

http://xxx.lanl.gov/PS_cache/astro-ph/pdf/0202/0202008.pdf
It is the accepted view. Professional journal article Feb.2002.
The universe is not like a balloon for gods sake!
It is flat----infinite in other words.
You do not come back to the same place by going in a straight line in the real universe.

That was the pretend universes of 10 years ago. Wake up. Cosmology has changed.
Please do not use the balloon analogy any more!

The field has changed radically because there are finally sufficiently accurate observations to check models
and exclude the finite (positive curvature) balloon-type case
and stuff. Observations are what count, finally.

Last edited by a moderator:
That link isn't working for me. I'll try again later. This is related to that poll you just posted I'm sure, but in any case, I don't think you are correct. The expansion of a finite universe is central to the Big Bang theory. The Big Bang theory is still valid. Certainly there are a few people who disagree, but the vast majority of Cosmologists still consider the Big Bang to be valid.

Originally posted by russ_watters
That link isn't working for me. I'll try again later. This is related to that poll you just posted I'm sure, but in any case, I don't think you are correct. The expansion of a finite universe is central to the Big Bang theory. The Big Bang theory is still valid. Certainly there are a few people who disagree, but the vast majority of Cosmologists still consider the Big Bang to be valid.

the prevailing idea of the big bang is not something that begins at a single point with a finite amount of energy

you are mistaken about what the majority of cosmologists think.

the big bang is generally accepted by the great majority
but has no assumption of finiteness
(the finiteness and the balloon analogy is a popular misconception stemming from deceptive analogies used to
explain things mathlessly

it is like the "rubber sheet" analogy for general relativity that has
damaged so many people by making them think that spacetime is somehow like a rubber sheet

journalists and science writers have a lot of sins to atone for)

the point is that as close as anyone can measure, the universe is flat (has curvature zero). It might still be curved some, pos or neg, a tiny tiny bit. But there is no evidence of it. The simplest thing is just to take it as flat. And this fits the inflation scenario.
A flat universe is infinite. Lines do not curve around to the starting point. It never recollapses. It has infinite energy. And its big bang is not localized in a bounded region.

There was an article in sci am recently based on the infiniteness of the universe and people made a long thread about it here at PF. It had several versions of "multiverse" of which the first and simplest was elaborated merely from the idea of infinite extent.
Because of observed flatness it would be hard to find a professional cosmologist who would quarrel with the infiite extent business. Intellectual fashions change in every field of research and sometimes it is to the better---I think in this case it certainly is.

If the Big Bang is correct, doesn't that mean that at one time the universe was extermely small? Thats what the Big Bang Singularity was. And after the Big Bang it expanded. And it continues to expand. So when did the expansion of a finite universe cause it to go from finite to infinite? Further, since the Big Bang started with a singularity, there is a maximum size to the universe - with an age of about 15 billion years, the universe could not possibly be more than 30 billion light years across as that would require the expansion to be faster than the speed of light.

Last edited:
Originally posted by russ_watters
If the Big Bang is correct, doesn't that mean that at one time the universe was extermely small? Thats what the Big Bang Singularity was. And after the Big Bang it expanded. And it continues to expand. So when did the expansion of a finite universe cause it to go from finite to infinite? Further, since the Big Bang started with a singularity, there is a maximum size to the universe - with an age of about 15 billion years, the universe could not possibly be more than 30 billion light years across as that would require the expansion to be faster than the speed of light.

Bravo! these are just the right questions to ask!
I was asking them myself not long ago!
I cannot reply as an authority---only as a fellow student.
It is really interesting.
the current view of the universe is that it is flat which means
infinite

(or if not precisely flat and positively curved then thousands of billions of LY, for all practical purposes infinite, huge----might as well take it as infinite which is the simplest way to interpret the data)

do you trust Ned Wright of UCLA astro and physics dept?
Teaches cosmology and has a website that other physicists
like to link to. A member of the team that owns MAP (the microwave
anisotropy probe observatory orbiting the sun out at the Lagrange point L2) Do you trust him? I do he has excellent credentials and in my judgement is careful and rigorous. Plus
other experts confirm what he says.

So yeah-----if you start reading his site it will contradict a lot of what you think now.

In GR (as opposed to SR) things CAN move faster than light and most of the universe IS moving away from us at speeds faster
than light.

thats surprise number one.

SR is all true but only in the neighborhood of a point
you can't have two things moving relative to each other
faster than light IN THE SAME LOCALE
or, as some people say, you can't have somebody pass by
somebody else at greater than c.

Also in cosmology there is a rest frame. a special preferred frame
that is used out of all the billions of possible frames, to define the
preferred distance scale.
this is the frame which is at rest with respect to the CMB
and distance defined in that frame is called the "comoving distance" and is considered to be measured AT THE PRESENT MOMENT
The Hubble parameter is only defined in terms of the comoving
distance. (this is a key fact, should be emphasized, when it says 71 km/sec per megaparsec of distance that megaparsec is of
comoving distance at the present instant of time)

Even tho the age of the universe is only 14 billion Y the radius of the observable universe is almost 42 billion LY (comoving distance)----which is much more than just the age of the universe multiplied by the speed of light. Surprising as it seems, this is stuff everybody in beginning cosmology learns. don't blame me Russ I am just reporting.

cosmology is the most amazing mindboggling field!

And yes, somehow the big bang was not confined to a bounded finite region-----this is devlish hard to understand, I know.

And yes, there are galaxies out there that are receding from us
at twice the speed of light and it is real easy to say what the
comoving distance to them is. It is 28 billion LY-----that is, twice the Hubble length.

Ned Wright has a calculator at his website that I can use to'
turn that 28 billion LY into redshift or "z" terms. Maybe I will
just to see what comes out.

check this out:
http://www.astro.ucla.edu/~wright/cosmolog.htm

and from there go to the "cosmology FAQ" and the
"cosmology tutorial"

Good luck, it is a hard subject to stretch yer brain around

Last edited:
redshift z= 6.4
corresponds to distance 28 billion LY
and to something receding at the present moment
from us at twice the speed of light

I went to
http://www.astro.ucla.edu/~wright/CosmoCalc.html
the cosmology calculator page
and did the calculation

to check it, enter z = 6.4 and press the "flat" button.
there is no finite universe button, that would say "closed"
but there is a button that says "open" which is
another option----also infinite

the calculator also gives "light travel time" of 12.8 billion years
from an object with redshift 6.4
astronomers do not like to use light travel time as a measure
of distance because it is not a good measure and hard to use
and does not fit into the Hubble parameter definition etc
but it is still legit to ask "how long was that light traveling on its way to us?" and the answer is 12.8

BTW a quasar with redshift 6.4 has been observed and Bob Becker of UC Davis
bob@igpp.ucllnl.org
is one of the people who has studied its spectrum.
If you don't believe me write email to Bob Becker and ask
"did you really see a z=6.4 quasar and is that mother
really 28 billion LY away and receding from us at twice c?"

Last edited:
Heh, I don't know if this is true .. I just read it one time in a place far-far away. Can't remember where.

What happens to the energy of a photon on redshift, or by transformation of coordinates, is that we see it as the energy redirected from the electric component to the magnetic component of the photon.

This seems like a repeat of another post, but the case is that when z=infinity, v=c. So no quasar that we can see is receeding faster than c, or by definition we wouldn't be able to see it. The energy from light emmitted at near the beginning of the universe is redshifted because there is more SPACE now than there was then. It does not violate conservation of energy.

... The energy from light emmitted at near the beginning of the universe is redshifted because there is more SPACE now than there was then. It does not violate conservation of energy.

This might be a minor point, but strictly speaking, energy is not a conserved quantity. From "Space Time and Quanta" by Robert Mills (of Mills/Yang fame), page 170:

"... Note that energy conservation alone is not consistent, because the energy in a new frame depends, by the Lorentz transformation law (eq. 14), on the momentum in the old frame; thus momentum nonconservation in one frame leads to energy nonconservation in the other. The point is that the energy and momentum in the new frame depend only on the energy and momentum in the old frame, and nothing else. If they're both conserved in one frame, then they're both conserved in the other, even though momentum and energy get mixed together by the transformation."

Originally posted by marcus

Energy is an idea, not a real substance. It is not conserved except in very specific types of models, of which apparently General Relativity, our prevailing model of space and gravity, is not one.

Marcus, why are you often talk what you have no idea about (say, energy, or conservation laws)? Piling a mistake over another.

Energy can't be lost. In expansion of photons their kinetic energy (color) went into their potential (spread in vast gravitational field), same way as a kinetic energy of atoms of supernova goes into their gravitational potential energy when a star expands.

Last edited by a moderator:
Originally posted by Nacho
This might be a minor point, but strictly speaking, energy is not a conserved quantity. From "Space Time and Quanta" by Robert Mills (of Mills/Yang fame), page 170...

I'm with you on this Nacho
It is simplistic to imagine that energy conservation holds
in contexts where it is not proven.

I don't have a copy of Mills book so I cannot tell exactly what
he is talking about----it may be in a context of Special Relativity---I'm not sure what the quantities are and can't comment specifically.

I had in mind a General Relativity context where space is expanding and there I believe it is simply a fact that energy is not conserved. I never heard of someone proving an energy conservation law for GR.

People seem to have tried and have apparently invented a formulay of "pseudo-tensors" in their attempts---but this is marginal, I understand, not generally accepted. In mainstream cosmology, according to my understanding, there is no energy conservation.

Of course, there is. Flatness of universe is the consequence of energy of universe conservation.

Originally posted by Alexander
Marcus, why are you often talk what you have no idea about (say, cinservation laws)? Piling a mistake over another.

Energy can't be lost. In expansion of photons their kinetic energy (color) went into their potential (spread in vast gravitational field), same way as a kinetic energy of atoms of supernova goes into their gravitational potential energy when a star expands.

this is a beautiful idea but it sounds like your own fantasy, Alex.

If it is not just your own imaginings, please cite an online reference where some expert is asserting this.

The CMB is distributed roughly uniformly throughout space and the loss from it (by expansion) is occurring as we speak uniformly throughout space

where is the energy going, where is the gravitational potential, in your picture, in what direction does the field point?

I understand the conversion of energy in a supernova explosion from kinetic (outward motion) to potential (distance from center). but in the expansion of space there is no center. It is not a useful analogy as far as I can see. Or would you like to explain?

Marcus, everybody knows that gravitational potential energy is icreasing with spread. Gravity is attractive, dude.

I'm with you on this Nacho
It is simplistic to imagine that energy conservation holds
in contexts where it is not proven.]

Yabut, as I said, a minor point. From what I can get out of what I read (I'm not a real good mathmatician), one thing that leads to non-conservation of energy is velocity. But we are talking here about particles that travel only at the speed of light .. so the velocity is a constant, and in essense is not a factor in transformation.

If they're both conserved in one frame, then they're both conserved in the other,
It is conserved. If you have some mass with grav energy GM2/r. Then explode it mv2/2 (=GM2/r). The small increase in m by factor gamma is paid for by whatever force exploded the mass in the form of a little extra acceleration needed to explode the mass.

Originally posted by Nacho
From "Space Time and Quanta" by Robert Mills (of Mills/Yang fame), page 170:

"... If they're both conserved in one frame, then they're both conserved in the other, even though momentum and energy get mixed together by the transformation."

This does not appear to be talking about global energy conservation, does it?

One fundamental reason often cited for why GR has no energy conservation law is that you DO have conservation at a single point but to get global energy you have to do an integral and the integral is not defined.

People have constructed concrete counterexamples to conservation in GR.

Adding a 4-vector in the tangent space at a point x
to a 4-vector in the tangent space at a different point y
is like adding apples to oranges. So the process of integration
does not work and the usual method of proof breaks down.

I don't have Mills so I can't say what the context is. But it seems
likely that he is not talking about global energy cons in GR.
Otherwise he wouldn't quibble about energy and momentum getting mixed. In GR the problem with defining it goes much deeper than that.

I don't have Mills so I can't say what the context is. But it seems likely that he is not talking about global energy cons in GR.
Otherwise he wouldn't quibble about energy and momentum getting mixed. In GR the problem with defining it goes much deeper than that.

You're right there .. it was on a section about Special Relativity. Also, as I said, one of the things that lead to the non-conversation is velocity, so it would have to be a particle, like an electron, that travels at less than the speed of light.

Adding a 4-vector in the tangent space at a point x
to a 4-vector in the tangent space at a different point y
is like adding apples to oranges. So the process of integration
does not work and the usual method of proof breaks down.
I think you should check this.

One fundamental reason often cited for why GR has no energy conservation law is that you DO have conservation at a single point but to get global energy you have to do an integral and the integral is not defined.

Which integral?

Hello Schw.

Try this---its a page from Baez introduction to his tutorial on GR

http://math.ucr.edu/home/baez/einstein/node2.html

The picture might help. If it doesn't help here's a kind of
rumination on my part.

Im summarizing here what I get from reading what experts have to say about the failure of energy conservation in GR.

Do you ever go to Usenet?
Its a good place to learn stuff
John Baez is the moderator on sci.physics.research
which is kind of the best from my point of view.

they have discussions about why no energy cons in GR
and give reasons like
no way to integrate globally
cant add tangent vectors in two different tangent spaces
(apples and oranges idea)

Also Usenet has a physics FAQ and

You have to find access at a level you understand.

I summarize expert mainstream views that I gather and
if you don't trust my boiling it down and giving you my take
on it then you have to go to the horse's mouth.

These are not my pet ideas---they're what I get from the smartest people I can find who have something to say about it.
I don't have a stake in it either way. I'd be delighted if it DID have an energy conservation theorem that somebody could prove.

Einsteins GR does not have energy conservation as it stands but it could always be modified someday with some new mathematical gizmo
and the new theory could have a mathematical proof of a conservation theorem and then they would test the new theory experimentally and MAYBE it would be more accurate and people would gradually accept it.

But as it stands the plain vanilla GR does not have it.
"pseudotensors" which have problems and turn many people off are a gizmo invented to get energy conservation but so far
not generally accepted as workable.

A QUOTE FROM PHYSICS FAQ at Baez site":
"The Cosmic Background Radiation (CBR) has red-shifted over billions of years. Each photon gets redder and redder. What happens to this energy? Cosmologists model the expanding universe with Friedmann-Robertson-Walker (FRW) spacetimes. (The familiar "expanding balloon speckled with galaxies" belongs to this class of models.) The FRW spacetimes are neither static nor asymptotically flat. Those who harbor no qualms about pseudo-tensors will say that radiant energy becomes gravitational energy. Others will say that the energy is simply lost."

they are standing around scratching their heads and saying how can we fix it so there will be energy conservation, what extra assumptions do we need, what tools must we invent etc etc.

I believe to understand the tangent spaces on a differential manifold and the ambiguity of transporting vectors from one point to another you need a course in differential geometry. But someone may be able to explain it---not I tho.

http://math.ucr.edu/home/baez/einstein/node2.html

Baez draws The Picture that goes with the explanation in his
GR tutorial at his website, maybe that would help. But maybe it wouldnt.

Last edited:
Don't take offense. That's a nice website you posted. I read through it but didn't see the problems that you're talking about. The only major problem they mentioned was the condition that t=0, physics breaks down, because you have possibly infinite density in zero space.
The FAQ is not maintained by Dr. Baez.

This seems like a repeat of another post, but the case is that when z=infinity, v=c.

Where are you getting this? Give a reference.
On Usenet people get laughed at for saying this about the Hubble law v.
It is a confusion between SR and GR.
In SR there is indeed a doppler formula for z according to which v=c corresponds to infinite z.
But that is not the same v as in the Hubble law

So no quasar that we can see is receeding faster than c, or by definition we wouldn't be able to see it.

Dont you see the fallacy in what you are saying? This is covered in cosmology FAQ at Wright's site. Lots of the quasars we can see are at the present moment receding faster than c.
What is the "by definition" you are talking about? We see the quasar at a moment a long time ago when it was not receding so fast.

The energy from light emmitted at near the beginning of the universe is redshifted because there is more SPACE now than there was then. It does not violate conservation of energy.

This is covered at the Physics FAQ at Baez site. The simplest thing is to view the energy as lost---what do you mean "violate". It sounds as if you are under the misconception that there is a law of conservation of energy (in GR) to violate. Energy conservation laws are mathematical theorems which it is possible to prove in some contexts and and not in others.

I don't like arguing about generally accepted matters, even with people who have Hitchcock sigs and believe the US is governed by a Kleptocracy. Please bring your viewpoint up to date.

Don't take offense. That's a nice website you posted. I read through it but didn't see the problems that you're talking about. The only major problem they mentioned was the condition that t=0, physics breaks down, because you have possibly infinite density in zero space.
The FAQ is not maintained by Dr. Baez.

What website do you mean? I have posted several.

In the my post immediately preceding yours there was a link
to an essay by Baez himself.

http://math.ucr.edu/home/baez/einstein/node2.html

I know that the Physics FAQ is not maintained by Baez and each article is signed. He writes some of them. But the FAQ is just a small part of what is at Baez site. he has a lot of his own essays.
the one I referred you to was one of this.

It addresses the "apples and oranges" problem (incomparability of tangent vectors at different points on manifold) which tends to stymie global theorems. The picture is there on the page. It is a ball.
It shows parallel transport of a vector from one point to another depends on path----so the correspondence is not uniquely defined. This is why in GR stuff can recede at greater than light speed. (velocities only compare rigorously at a single point, or less rigorously in a small neighborhood of a single point)

I don't recall seeing anything there about "t=0" and the beginning of the universe and "physics breaking down"

http://math.ucr.edu/home/baez/einstein/node2.html

I don't recall seeing anything there about "t=0" and the beginning of the universe and "physics breaking down"
he says that right on the web page.

quote:
--------------------------------------------------------------------------------
I don't recall seeing anything there about "t=0" and the beginning of the universe and "physics breaking down"
--------------------------------------------------------------------------------

he says that right on the web page.

Er...I will post the URL for the fifth time in a row.
There are ten paragraphs on the page and a picture which
gives the key to why energy conservation is not proven in GR.
It's a sphere showing parallel transport of tangent vectors.
There is nothing on the page about "t=0" and "physics breaking down".

What I believe I'm testing is what happens when you ask a question and request a link, and then I give you a link bearing on the question. The issue is trolldom, I believe.

http://math.ucr.edu/home/baez/einstein/node2.html

In which of the ten paragraphs does it talk about "t=0"
and "physics breaking down"?

We two are certainly burning up the wires with all this communication aren't we?

Now a miracle occurs...
so, true it doesn't say the words "physics breaks down."

My link was to page 2 because of the bearing on your question

http://math.ucr.edu/home/baez/einstein/node2.html

http://math.ucr.edu/home/baez/einstein/node7.html

On page 7 Baez says: [[...Now a miracle occurs. By all rights, this equation should only hold at t = 0 for a small ball of initially comoving particles in free fall. However, in the special situation we are considering, it holds at all times for arbitrarily large ball of galaxies, even though the galaxies are not comoving! I wish I knew a simple reason why this works...]]

He is not saying "the physics breaks down" but that the model continues (fortunately and unexpectedly) to hold for all time than only around a specific moment t = 0.

What he is doing is deriving a form of the first Friedmann equation from the simplified GR equation that he started with.
The whole essay is "GR made simple" and at some point one wants to get the Friedmann equation from the main Einstein one---he is doing this and saying "the physics works here remarkably well and I can't explain why it does in a simple way but just take it on faith that the equation works for all time under assumptions of homog and isotropy."

I don't think one can understand this out of context. Indeed you have misunderstood the passage with a complete 180 degree twist! Although it says Big Bang in the title on page 7 this does not mean that t = 0 refers to the very beginning of the universe and he is saying that the equation does NOT break down.

At issue for me is I need to learn what happens when you ask a question and I find something on web that bears on it and give you a link to a specific page (in this case with a specific picture).
Then is it likely to happen that you get to talking about something that is not on the page and misinterpreting other stuff on the wrong page and, as in this case, making up "physics breaks down" phrases that arent even there and arent part of the authors meaning even on the wrong page! If that happens it means discussion by means of shared web-pages is not workable in this case. For whatever reason---maybe you don't like me, or you are feeling ornery or whatever. It doesn't matter what the reason is, the point is I should not try to share web pages and discuss them with you cause it doesn't work. No hard feelings however

as long as you have no problems with infinite energy existing in an infinitely small volume, then physics has no problem describing the conditions of t=0.

• Astronomy and Astrophysics
Replies
13
Views
1K
• Astronomy and Astrophysics
Replies
1
Views
784
• Introductory Physics Homework Help
Replies
1
Views
805
• Cosmology
Replies
92
Views
4K
• Beyond the Standard Models
Replies
32
Views
746
• Special and General Relativity
Replies
14
Views
1K
• Cosmology
Replies
4
Views
1K
• Cosmology
Replies
14
Views
2K
• Cosmology
Replies
37
Views
3K
• Cosmology
Replies
5
Views
1K