Estimating Mass of Universe Within Horizon

[wolram]

How can we estimate the mass of the Universe if we can only see
the part that is within our horizon?

 

[mapper]

How can we estimate the mass of the Universe if we can only see
the part that is within our horizon?

I imagine cause we are only estimating what's known to us. Its an educated guess.

 

[Chronos]

Based on the current rate of expansion, the critical mass density of the universe is about 1.06E-29 grams per cc [roughly 6 hydrogen atoms per cubic meter]. Our best measurements indicate the universe is flat, hence extremely close, if not exactly at the critical density. To get the total mass of the universe, you need only multiply the average density by the volume. If you assume, as most do, that to be the Hubble volume, you arrive at a total mass of around 6E52 kg.

 

[SpaceTiger]

I imagine cause we are only estimating what's known to us. Its an educated guess.

Or perhaps, more precisely, what's knowable to us. This is basically the correct answer, though. The mass of the "universe" usually refers to the mass of the observable universe and that has a definite size.

 

[Crosson]

Figures for the total mass of the universe are infered from the expansion rate of the universe.

 

[SpaceTiger]

Figures for the total mass of the universe are infered from the expansion rate of the universe.

You need more than that. Hubble's constant is part of the problem, but the full formula (for a flat universe) is:

$$M=\frac{4}{3}\pi r_p^3 \rho$$

$$r_p=\int_0^{t_0} \frac{c}{a}dt$$

$$\rho = \Omega_M \rho_{crit}=\frac{3\Omega_M H_0^2}{8\pi G}$$

where r_p is the particle horizon, $$\rho_{crit}$$ is the critical density, $$\Omega_M$$ is the matter density parameter, and $$H_0$$ is Hubble's constant.

In other words, you need Hubble's Constant, omega matter, and the dependence of the scale factor on time, something which itself depends on the other density parameters (such as dark energy). We have good measurements of these things from WMAP, but it's not as simple as you seem to be suggesting.

 

[hellfire]

Or perhaps, more precisely, what's knowable to us. This is basically the correct answer, though. The mass of the "universe" usually refers to the mass of the observable universe and that has a definite size.

If we want to compute the mass of the universe which is knowable to us, we should restrict to a size which is empirically proven (at least with some assumptions). For example, based on Neil Cornish work searching for intersections of circles in the CMB, we could assume the universe is at least 24 Gly in diameter (comoving distance). This is less than 46 Gly in radius (comoving distance) for the particle horizon in the standard model. Thus, we should use 12 Gly as the ‘known’ radius, but not more. However, this makes actually no sensible difference, since we do not expect to know the mass with such an accuracy. I assume that only orders of magnitude are relevant.

 

[SpaceTiger]

However, this makes actually no sensible difference, since we do not expect to know the mass with such an accuracy. I assume that only orders of magnitude are relevant.

If it weren't for this last point, I imagine we could get into a long and healthy debate on the issue, but the measurements really are too crude for it to be worth it. I have a lot of trust in the standard model beyond the CMB, though certainly not all the way to t=0, as my equations above would indicate. The point was mainly to illustrate what was needed for the calculation. To get the answer that you're suggesting, one need only change the lower limit of the integral to the time of recombination.

 

[hellfire]

To get the answer that you're suggesting, one need only change the lower limit of the integral to the time of recombination.

You are right if we were sure that there is no matching at all between any of all possible circles which can be drawn in the CMB. In such a case, we would reach the comoving distance at which the last scattering surface is located without noticing any topological effect and we could take this as the known radius (actually 45.5 Gly for z = 1100, instead of 46.3 Gly for the particle horizon). However, this is not the case, as it seams that Cornish did only put some minimum constrainst on possible matchings of circles obtaining 12 Gly for the radius. I agree with you that it is and interesting theoretical discussion, but it is not relevant for the calculations givent the current data.

 

[SpaceTiger]

However, this is not the case, as it seams that Cornish did only put some minimum constrainst on possible matchings of circles obtaining 12 Gly for the radius.

If the topology is non-trivial on those scales, I'll eat my hat.

 

[wolram]

By Space Tiger.


In other words, you need Hubble's Constant, omega matter, and the dependence of the scale factor on time, something which itself depends on the other density parameters (such as dark energy).

Dark energy, seems such a thorn in the side, is there a model that comes
even close without it?

 

[SpaceTiger]

Dark energy, seems such a thorn in the side, is there a model that comes
even close without it?

I would say no, but it depends on who you ask. There's one about super-horizon modes that's been making the rounds on astro-ph, but it's too early to say anything definitive about it.

 

[wolram]

http://arxiv.org/abs/gr-qc/0503099

A quick search of arxiv has come up with this paper

A new model of the observed universe, using solutions to the full Einstein equations, is developed on the basis of the suggestion of Kolb, Matarrese, Notari and Riotto [hep-th/0503117] that our observable universe is an underdense bubble in a spatially flat bulk universe. It is argued that on the basis of Mach's principle, that true cosmic time is set by the bulk universe. With this understanding a systematic reanalysis of all observed quantities in cosmology is required. I provide such a reanalysis by giving an exact model of the universe depending on two measured parameters: the present density parameter, Omega_0, and the Hubble constant, H_0. The observable universe is not accelerating. Nonetheless, due to systematic factors in the luminosity distance relation the inferred luminosity distances will very closely mimic models with a cosmological constant, in accord with the evidence of distant type Ia supernovae. The measured Hubble constant is found to differ from the present physical Hubble parameter by a systematic offset. The predicted age of the universe agrees well with observation. For a universe with only baryonic matter, the expansion age can easily account for structure formation at large redshifts. It is also predicted that the low multipole (large angle) anomalies seen in the cosmic microwave background anisotropy spectrum might be resolved by the new model.

 

[SpaceTiger]

There are a lot more and they all take different sides. Look for recent papers that have Kolb as an author or reference his recent work.

 

[Chronos]

The Kolb et al paper [http://www.arxiv.org/abs/hep-th/0503117] has drawn a great deal of attention [there is a related thread on Wiltshire & Kolb on the string board]. Kolb has been taking a pretty fierce beating, for the most part.

 

[wolram]

By Chronos

The Kolb et al paper [http://www.arxiv.org/abs/hep-th/0503117] has drawn a great deal of attention [there is a related thread on Wiltshire & Kolb on the string board]. Kolb has been taking a pretty fierce beating, for the most part.

I think that any paper that attempts to do away with dark energy is worth
a look at, it seems to me that it is," bandage", for a theory that does not
quite work, how can it be that our U is made of 75% of stuff we know
nothing about, and how can we make predictions about any thing if all this
mass is just not there? Kolb may be wrong, but no more than a theory with
a huge unknown chunk thrown into make it work i guess a theory like
that would not pass peer review now.

 

[Chronos]

Nobody is going to be happy with dark energy, or dark matter, until we know what it is and how it came to be. As distasteful as it is to insert huge chunks of 'unknowns' into the equation of state, there just has not been a better alternative to date. While it is possible our basic theories are either wrong or have gaping holes. People like Kolb continue exploring that possibility, and they do this knowing full well, and expecting their peers to jump all over it. Science is a cruel mistress.

 

[turbo]

Nobody is going to be happy with dark energy, or dark matter, until we know what it is and how it came to be. As distasteful as it is to insert huge chunks of 'unknowns' into the equation of state, there just has not been a better alternative to date. While it is possible our basic theories are either wrong or have gaping holes. People like Kolb continue exploring that possibility, and they do this knowing full well, and expecting their peers to jump all over it. Science is a cruel mistress.

So true. The standard model needs both dark energy and dark matter (in monstrous quantities!)to keep it from self-destructing. The universe is complex, but it must arise from simple consistent rules. The implications of the possibility that rules of the universe can change or even smoothly evolve include non-homogeneity, non-uniformity, and prehaps inadequate time for life to evolve. Let's pretend that the rules of the universe are relatively stable, and that they are the same here for me as they are for you.

Perhaps there is a model by which light loses energy through its interaction with the EM fields through which it passes, negating the need for DE, because the universe is NOT expanding at all. Perhaps that same model can model gravitation on galactic and cluster scales better than GR, and can explain the optical effects of "gravitational' redshift without the need for DM. Would you even entertain considering the relevance of such a model? I have constructed such a model, and it is logically consistant throughout, with no weird constants, infinities, etc.

 

[Chronos]

... Perhaps there is a model by which light loses energy through its interaction with the EM fields through which it passes, negating the need for DE, because the universe is NOT expanding at all. Perhaps that same model can model gravitation on galactic and cluster scales better than GR, and can explain the optical effects of "gravitational' redshift without the need for DM. Would you even entertain considering the relevance of such a model? I have constructed such a model, and it is logically consistant throughout, with no weird constants, infinities, etc.

I would not seriously entertain such a model. It rubs against the grain of QED - another theory that is not imminently imperiled. It is well known that the vacuum polarization effect alters the 1/r-nature strength of Coulomb's law by a factor of 0.1% at a distance scale of the electron-Compton wavelength. The VP effect is based in the response of the vacuum to field strength inhomogenities and interpreted as a dielectric particle-hole (electron-positron) photon polarizibility. Due to its limited range, VP potential can only be detected in the vicinity of the atomic nucleus. The VP effect does not violate the superposition of electromagnetic fields, hence anomalous, and unobserved interactions, such as photon-photon scattering, or photon-electromagnetic field interactions are highly improbable.

 

[wolram]

http://xxx.sf.nchc.gov.tw/PS_cache/gr-qc/pdf/0503/0503107.pdf
Understanding our universe T Padmanabhan.

Although i do not have the level of mathematic skill to understand all of
this paper, I can see it as fair reference as to understanding our U, and
the problems that have to be solved.
It seems to me that this paper high lights the voids of present understanding
and leaves us with only a 2% portion that is knowable.

 

[turbo]

I would not seriously entertain such a model. It rubs against the grain of QED - another theory that is not imminently imperiled. It is well known that the vacuum polarization effect alters the 1/r-nature strength of Coulomb's law by a factor of 0.1% at a distance scale of the electron-Compton wavelength.

Can you supply any citations for this? Who did this experimental work?

The VP effect is based in the response of the vacuum to field strength inhomogenities and interpreted as a dielectric particle-hole (electron-positron) photon polarizibility. Due to its limited range, VP potential can only be detected in the vicinity of the atomic nucleus.

Do you have any citations to support your claim of effects being observable only on the nuclear scale? Who did the experimental work, or is this claim merely theoretical?

The VP effect does not violate the superposition of electromagnetic fields, hence anomalous, and unobserved interactions, such as photon-photon scattering, or photon-electromagnetic field interactions are highly improbable.

Improbable or just really uncomfortable to the status quo? There is a huge difference. Light has to propagate throught the EM fields of the vacuum energy. The denser these fields are, the higher their refractive index, and the slower light will go, and the more light will be refracted (bent, just like in a lens). Light is not a shower of little balls of energy traveling through a vacuum (photons). Light is wave phenomenae propagating through a transmissive medium, and its speed is inversely proportional to the density of the medium, just like in classical optics.

Here is a review paper that touches on some of the work being done in this field. As you can see, there are lots of people who take vacuum energy very seriously. When something as pervasive and energetic as vacuum energy is entirely left out of General Relativity, we should expect that modifying GR to encompass vacuum energy might solve some of the mysteries facing the standard BB theory. We are repeatedly told by BB cosmologists that normal baryonic matter makes up only about 4% of the universe. It's high time we balanced the books with something more believable than DE, DM, and fairy dust.

http://arxiv.org/PS_cache/hep-th/pdf/0012/0012062.pdf

 

[Chronos]

Can you supply any citations for this? Who did this experimental work?

How weak is the vacuum polarization effect? Weak enough that it has never been directly detected:
http://arxiv.org/abs/physics/0402073
Ultrafast Resonant Polarization Interferometry: Towards the First Direct Detection of Vacuum Polarization
Or you can try looking where the background field is a billion trillion times stronger than the ground state:
http://arxiv.org/abs/astro-ph/0502351
The High-Energy Polarization-Limiting Radius of Neutron Star Magnetospheres II -- Magnetized Hydrogen Atmospheres

Do you have any citations to support your claim of effects being observable only on the nuclear scale? Who did the experimental work, or is this claim merely theoretical?

It has only been detected indirectly in colliders:
http://www.ihep.ac.cn/data/ichep04/p_paper/4_ew/411-cushman-p/ichep04_g2new.pdf.

Improbable or just really uncomfortable to the status quo? There is a huge difference. Light has to propagate throught the EM fields of the vacuum energy. The denser these fields are, the higher their refractive index, and the slower light will go, and the more light will be refracted (bent, just like in a lens). Light is not a shower of little balls of energy traveling through a vacuum (photons). Light is wave phenomenae propagating through a transmissive medium, and its speed is inversely proportional to the density of the medium, just like in classical optics.

What transmissive medium are you referring to? Asserting that light [an EM field] requires the EM field of the vacuum as a medium to propogate is not very satisfactory. It raises the question of what medium the vacuum EM field relies upon for its propogation. And how do photons, in the absence of matter, interact with each other causing refraction? That sounds like new physics to me. Have any references to that gound breaking paper? I probably wouldn't be the only one to question that experimental result, assuming there is one.

Here is a review paper that touches on some of the work being done in this field. As you can see, there are lots of people who take vacuum energy very seriously.

Of course people are interested in vacuum energy. But few think it has important macroscopic effects other than imparting a small cosmological constant. I'm curious why you would cite that source. This excerpt from the abstract does not appear to be a ringing endorsement of your position:

"The solution suggested here to the nature of the vacuum is that Casimir energy can produce short range effects because of boundary conditions, but that at long range there is no overall effect of vacuum energy, unless one considers lagrangians of higher order than Einstein's as vacuum induced."

When something as pervasive and energetic as vacuum energy is entirely left out of General Relativity, we should expect that modifying GR to encompass vacuum energy might solve some of the mysteries facing the standard BB theory.

If vacuum energy is responsible for the cosmological constant, you could make the case it was not left out of GR. But Einstein added it ad hoc because he couldn't reconcile the implications of GR with his preconceived notion of a steady state, stable universe. Just how would you go about modifying GR to include vacuum energy that is not ad-hoc? What about the Maxwell equation? It does not factor in vacuum energy. Does it too need modification? On the other hand, they both work quite well - despite being approximations. I suspect once we figure out how to quantize GR things will be clearer.

We are repeatedly told by BB cosmologists that normal baryonic matter makes up only about 4% of the universe. It's high time we balanced the books with something more believable than DE, DM, and fairy dust.

http://arxiv.org/PS_cache/hep-th/pdf/0012/0012062.pdf

And they have some pretty good reasons for telling us these are the most reasonable explanations to date. Believability? Where would quantum physics be if believability was part and parcel to the scientific method? Believability is for magicians, not scientists.

 

[misskitty]

This might sounds stupid, but if we can measure the curvature of the universe could we measure the mass of the universe as well? Then again that would be very difficult since the universe is more vast then we can imagine.

 

[Chronos]

This might sounds stupid, but if we can measure the curvature of the universe could we measure the mass of the universe as well? Then again that would be very difficult since the universe is more vast then we can imagine.

Indeed, measuring the curvature of the universe, as did WMAP, tell us something about its mass density. If you extrapolate that density to the volume of the observable universe, you can derive the total observable mass - of course most of it is not luminous [e.g., dark matter].

 

[wolram]

One thing occurs to me, and that is could we define the U, if gravity is
"emergent" and not the primal "energy", in the Universe?
If gravity is a secondary "energy" emerging from matter spectra, then the
only way to "weigh" the U is to add all the possible energy states," emissions",
of the matter "field"..

 

[turbo]

How weak is the vacuum polarization effect? Weak enough that it has never been directly detected:
http://arxiv.org/abs/physics/0402073
Ultrafast Resonant Polarization Interferometry: Towards the First Direct Detection of Vacuum Polarization
Or you can try looking where the background field is a billion trillion times stronger than the ground state:
http://arxiv.org/abs/astro-ph/0502351The High-Energy Polarization-Limiting Radius of Neutron Star Magnetospheres II -- Magnetized Hydrogen Atmospheres

As you well know, it is my contention that the vacuum fields are polarized by the presence of matter due to a differential in the gravitational infall rates of matter vs antimatter. You have cited non-detections of vacuum polarization in the presence of electromagnetic fields. These non-detections are not surprising to me. If we put a Casimir device in Earth orbit and orient it with the plates perpendicular to the Earthward direction for a number of orbits then orient it with the plates parallel to the Earthward direction for a number of orbits, I believe we will see differences in the Casimir force that will demonstrate the vacuum polarization and density differences caused by the Earth, the Moon, and the Sun.

It has only been detected indirectly in colliders:
http://www.ihep.ac.cn/data/ichep04/p_paper/4_ew/411-cushman-p/ichep04_g2new.pdf.

How does this support your assertion that vacuum polarization can only be detectable on nuclear scales? Just because someone looked at nuclear scales does not constrain the effects of vacuum polarization to nuclear scales. People are looking for dark matter candidates at nuclear scales. If one were detected at that scale, would you refuse to believe that the particles could have a combined effect on galactic scales? As for scales of detection, I believe we see the optical effects of vacuum polarization in every instance of astronomical lensing.

What transmissive medium are you referring to? Asserting that light [an EM field] requires the EM field of the vacuum as a medium to propogate is not very satisfactory. It raises the question of what medium the vacuum EM field relies upon for its propogation. And how do photons, in the absence of matter, interact with each other causing refraction? That sounds like new physics to me. Have any references to that gound breaking paper? I probably wouldn't be the only one to question that experimental result, assuming there is one.

The transmissive medium through which EM waves propagate is the EM field of the vacuum (ZPE field). It's funny how many people cling to Einstein and his GR without understanding his motivations. I urge you to cite even one paper or letter in which Einstein characterized light as "photons". He always treated light as EM waves, and waves propagate though fields. Einstein believed in an aether because it is needed to transmit EM waves, however he could not reconcile it with GR, so he modeled it as it if it had no other properties beyond being a transmissive medium. For purposes of GR, he stripped the aether of any sensible properties, including sensibility of proper motion. This might not have been a good idea, as illustrated by the Unruh effect.

There is a misunderstanding relating to detector sensitivity that causes some people to believe that light travels in discrete quanta. Light travels in waves of indeterminant, continuously decreasing energy. When the energy is absorbed by an atom, the REACTION of the atom is that one or more of its electrons will momentarily assume a higher energy state, then cascade back to its ground state. The detector has reacted in a quantized manner to an energy input that is non-discrete and continuous. This makes some folks think that the light arrives in discrete quanta. It does not. An analagous situation occurs with photographic film in astrophotography. To get the silver salts in the emulsion to change state (register an image) you have to concentrate enough light waves on the salts to provide the energy to make them change state. This is very easy with bright images, and the f:stop/exposure time relationship operates very smoothly in this domain. When you get to very faint objects, however, an effect called reciprocity failure kicks in. No matter how long you expose your film, you never manage to accumulate enough energy from faint objects to trigger the phase change in the silver salts, so faint objects are not captured in your image. The only way around this (assuming you don't use more sensitive film) is to gather more energy from the faint source, leading to what astromoners call "aperture fever".

Of course people are interested in vacuum energy. But few think it has important macroscopic effects other than imparting a small cosmological constant. I'm curious why you would cite that source. This excerpt from the abstract does not appear to be a ringing endorsement of your position:

"The solution suggested here to the nature of the vacuum is that Casimir energy can produce short range effects because of boundary conditions, but that at long range there is no overall effect of vacuum energy, unless one considers lagrangians of higher order than Einstein's as vacuum induced."

I cite the source for several reasons, not the least of which is to show you that a brief review reveals hundreds of papers regarding the nature of vacuum energy. The quote illustrates a common logical disconnect that often accompanies discussions of vacuum energy. The fact that locally we have only detected it via "short range effects due to boundary conditions" cannot be logically extended to support a claim that the effects of vacuum energy are therefore limited to "short range effects". This is a very illogical conclusion, as anybody who deals with experimental selection effects and detector insensitivity can tell you. For instance, physicists are looking for dark matter candidates on scales ranging from solar mass to sub-atomic, although the required cosmological effect is purely gravitational, and on galactic scales and larger. The gravitational properties of the theoretical Dark Matter are not constrained by the scales at which the detections are sought.

If vacuum energy is responsible for the cosmological constant, you could make the case it was not left out of GR. But Einstein added it ad hoc because he couldn't reconcile the implications of GR with his preconceived notion of a steady state, stable universe. Just how would you go about modifying GR to include vacuum energy that is not ad-hoc? What about the Maxwell equation? It does not factor in vacuum energy. Does it too need modification? On the other hand, they both work quite well - despite being approximations. I suspect once we figure out how to quantize GR things will be clearer.

We will not be able to quantize GR as long as we ascribe physical reality to the the model of gravitation=curved space-time. This curved space-time idea is only a mathematical approximation with no underlying mechanical cause and effect. If we describe gravitation as an attractive force resulting from polarization and densification of the vacuum fields, we will have a real mechanical model for gravitation in FLAT space-time. Quantum theory works really well in flat space-time, but not in the curved space-time fields of GR. As for the Maxwell equations, they describe FIELDS, and include terms for the permeability and permissivity of space. These are terms that apply to fields, not to "empty" space. Without an EM field, EM waves cannot propagate. The potential energy of the ZPE fields need not be addressed in the Maxwell equations, as this energy is the ground state of our universe, and EM waves are sensed relative to this ground state. The existence of the EM field in "empty" space is essential for transmission of EM waves. The theoretical energy of that field (according to quantum theory) is irrelevant to Maxwell's equations.

And they have some pretty good reasons for telling us these are the most reasonable explanations to date. Believability? Where would quantum physics be if believability was part and parcel to the scientific method? Believability is for magicians, not scientists.

Dark matter and dark energy are not reasonable entities. They are placeholders that are inserted into the standard cosmology to keep it somewhat predictive. In the SLAC lectures I linked elswhere, lecturers frequently used the word "epicycle" to describe these concepts, and these guys are not crackpots. By convention, cosmologists use these entities because they are convenient. There is no independent evidence (apart from the failings of BB cosmology to explain anomalous gravitation and redshift, etc) to suggest that they exist. Decades of very diligent searching for dark matter has turned up no detection at all. I propose that we can keep the general concept of Dark Matter if we model it in terms of effects of something that we know exists - the ZPE fields of the vacuum. The particle/antiparticle pairs of the ZPE are everywhere, and according to quantum theory the ZPE field is highly energetic, yet these fields are barely detectable to us because they are the ground state of our universe. Hmmm, lots of energy potential, hard to detect... Doesn't that make you just a bit curious?