SNe Ia, Implications, Interpretations, Lambda-CDM...

[bigsam1965]

I don't know all the difficulties involved, but a simple experiment might settle the issue. Choose a source of known absolute magnitude. Collect photon counts over a given time period. Also, measure the total brightness (energy flux) over the same time period. Sandage has done such an experiment and obtained a result that is about halfway between photon energy conservation and photon energy nonconservation. More work needs to be done in this area.

[modest]

The problem that you have with this google book source, is where does the photon energy go and what is the mechanism that causes the energy to be lost?

 

As a photon is redshifted it's energy is reduced by [imath]e=h\lambda[/imath]. Therefore the total energy of all the photons in the universe has decreased over time. This is true of all relativistic models and it's not a problem.

 

What changes the momentum of the light?

 

Its wavelength being stretched and frequency being reduced.

 

Are we bringing back the tired light theory in disguise, or some sort of unknown matter that is causing the light to scatter similar to Compton scattering. Since spatial expansion is stretching the wave length of the photon, it seem reasonable that the photon energy is also being stretched with the wave length. This makes more sense to me than just assuming that the photon energy is lost with no mechanism to explain the lose.

 

The energy is conserved in the system as a whole because it is expanding. This is analogous to a normal gas undergoing adiabatic expansion. The internal energy of the gas is lost; however, conservation is maintained in the system as a whole when considering the expansion itself.

 

This is consistent with relativity and consistent with the luminosity distance equation of the RW metric.

 

-modest

[modest]

I don't know all the difficulties involved, but a simple experiment might settle the issue. Choose a source of known absolute magnitude. Collect photon counts over a given time period. Also, measure the total brightness (energy flux) over the same time period. Sandage has done such an experiment and obtained a result that is about halfway between photon energy conservation and photon energy nonconservation. More work needs to be done in this area.

 

No - the only experiment that needs done is measuring the energy of photons at different wavelengths. This has of course been done and it has long been known that longer wavelength photons have less energy by [imath]e=h/\lambda[/imath] or [imath]e=hf[/imath]

 

-modest

[bigsam1965]

As a photon is redshifted it's energy is reduced by [imath]e=hlambda[/imath]. Therefore the total energy of all the photons in the universe has decreased over time. This is true of all relativistic models and it's not a problem.

 

 

 

Its wavelength being stretched and frequency being reduced.

 

 

 

The energy is conserved in the system as a whole because it is expanding. This is analogous to a normal gas undergoing adiabatic expansion. The internal energy of the gas is lost; however, conservation is maintained in the system as a whole when considering the expansion itself.

 

This is consistent with relativity and consistent with the luminosity distance equation of the RW metric.

 

-modest

 

It seems to me that your are treating a photon as if it is a hot billet similar to the tired-light theory. Your analogy of an adiabatic gas is a very weak one. It's lecture time. See you later.

[modest]

It seems to me that your are treating a photon as if it is a hot billet similar to the tired-light theory. Your analogy of an adiabatic gas is a very weak one. It's lecture time. See you later.

 

That’s not going to cut it bigsam1965

 

It seems to me that your are treating a photon as if it is a hot billet similar to the tired-light theory.

 

I am treating light exactly the same way Max Plank did more than 100 years ago.(1) The simple relationship he described is fundamental to physics, universally accepted, and has been verified thousands of times over. It is beyond criticism. There is no reason to compare a well-known fact about the nature of electromagnetic radiation to tired-light. Doing so demonstrates a lack of understanding - one that I should not be attacked for. Here are some sources explaining e=hf:

 

Planck's law - Wikipedia, the free encyclopedia

Photoelectric effect - Wikipedia, the free encyclopedia

Formulas - Planck's Law

http://www.iop.org/activity/education/Teaching_Resources/Teaching%20Advanced%20Physics/Astronomy/Cosmology/file_4978.doc

 

Your analogy of an adiabatic gas is a very weak one.

 

The Friedmann equations are based on an ideal fluid.(2)

 

From Wikipedia FLRW Metric:

 

The first equation can be derived also from thermodynamical considerations and is equivalent to the first law of thermodynamics, assuming the universe expansion is an adiabatic process (which is implicitly assumed in the derivation of the Friedmann-Lemaître-Robertson-Walker metric).

 

Therefore expansion in FLRW cosmology is perfectly analogous to adiabatic expansion. It is a good analogy because it addresses your misunderstanding directly and simply. Your question has to do with expansion, conservation of energy (thermodynamics), and the even distribution of a relativistic gas. There is no better analogy than adiabatic expansion. Once again you attack what I say even though it's commonly understood in physics rather than address it. Here are some links for adiabatic expansion:

 

http://www.astro.uu.se/~nisse/courses/kos2006/lnotes/ln6.pdf (equation 132 and surrounding text)

Friedmann-Lemaître-Robertson-Walker metric - Wikipedia, the free encyclopedia

Adiabatic process - Wikipedia, the free encyclopedia

 

Since spatial expansion is stretching the wave length of the photon, it seem reasonable that the photon energy is also being stretched with the wave length. This makes more sense to me than just assuming that the photon energy is lost with no mechanism to explain the lose.

 

The energy loss of photons traveling through expanding space is very-well known and the mechanism needed to explain it was described as early as the 1890's. It's now well-verified. Relativity is based on (or at least supports) Planck's law. I'm honestly sorry if this is devastating to your model but I don't believe there is any way around it. A photon that has traveled through expanded space has lost energy.

 

-modest

[bigsam1965]

The energy is conserved in the system as a whole because it is expanding. This is analogous to a normal gas undergoing adiabatic expansion. The internal energy of the gas is lost; however, conservation is maintained in the system as a whole when considering the expansion itself.

 

This is consistent with relativity and consistent with the luminosity distance equation of the RW metric.

 

-modest

 

Let's take your adiabatic analogy and look at it. First of all normal gas has coefficients of specific heats. It puzzels me how anyone can obtain coefficients of specific heats for a photon. Also, particles expanding with space is not the same as particles expanding through space in an adiabatic process. If photon energy is conserved then as space expands radiant energy density goes down by [math](1+z)^{-3}[/math] and the total radiant energy of expanding space is conserved. However if we assume that the photoelectric effect applies in expanding space as it does in the static-space of a laboratory then an additional reduction of energy density by the scale factor [math](1+z)^{-1}[/math] occurs and the total radiant energy of the system becomes [math]E=(1+z)^{-1}E_0[/math], where [math]E_0[/math] is the radiant energy emitted from a source. This means that the system has lost a total of [math]E_{lost}=z(1+z)^{-1}E_0[/math]. I would like to know where this lost energy went. I propose that the energy is still there because it is stretched with the photon wave length. In your adiabatic process with photons losing energy, you claim that the total energy is still there, show me where it is.

[modest]

Let's take your adiabatic analogy and look at it. First of all normal gas has coefficients of specific heats. It puzzels me how anyone can obtain coefficients of specific heats for a photon.

 

The ratio of specific heats for a relativistic gas (e.g. photon) is 4/3. Therefore:

[math]\Gamma=4/3[/math]

[math]T_{\gamma}{\propto}V^{-(\Gamma-1)}\;=V^{-1/3}{\propto}a^{-1}[/math]

 

FLRW is based on this analogy Sam, it's fine.

 

I'm leaving to get some serious dental work done - would anyone like to agree/disagree with my last few posts and continue the conversation as I may well be out of commission for a few days.

 

-modest

[bigsam1965]

No - the only experiment that needs done is measuring the energy of photons at different wavelengths. This has of course been done and it has long been known that longer wavelength photons have less energy by [imath]e=h/lambda[/imath] or [imath]e=hf[/imath]

 

-modest

 

That has been demonstrated only in local-space labrotories, not in the expansion of space where we are seeing the past Universe in dilated time. The wave lengths are dilated by the expansion of space. This is not the same as observing the spectrum of a hot object as it cools and the wavelength of the maximum intensity of the spectrum moves toward the red end of the spectrum.

[bigsam1965]

 

I'm leaving to get some serious dental work done - would anyone like to agree/disagree with my last few posts and continue the conversation as I may well be out of commission for a few days.

 

-modest

 

modest, I wish you well and get well soon. I am not attacking you, so stay calm. We are having some fun here. Let's keep it that way. You said that the radiant energy of expanding space is conserved even though photon energy is reduced as space expands. I showed above that total radiant energy is not conserved under your explanation. Please demonstrate where the lost photon energy is to conserve radiant energy.

[bigsam1965]

Also, you claim that by transforming dilated time and dilated distance in the Friedmann-Lemaitre metric, without the cosmological constant, to proper time and proper distance, a coasting-universe solution should be obtained. Why should proper time be used in an expanding universe?

 

Last, but not least, you write that there is a density of 3.65 equivalent proton masses per cubic meter. I thought there was only one atomic hydrogen mass per cubic meter. Where does this discrepancy come from?

 

 

 

 

CC

 

CC, you use a shotgun approach. Keep your powder dry and reload. I will answer these two questions first and get back to the others later.

 

The Friedmann_Lemaitre metric in it's expanded form has both dilated distance and dilated time. It is difficult to integrate over dilated time. Proper lookback time is the the normal flow of time from the present toward the beginning of the expansion. As redshift approaches infinity proper lookback time approaches Hubble time or the age of the Universe. Proper time in my model is the distance between observer and source when the photons we observe were first emitted from the source. So I use a simple trick of calculus called the chain rule to transform dilated time to proper time, so I can integrate with a linear independent variable which is proper time.

 

I think the 1 hydorgen atom per cubic meter is a crude estimate of the density of space between galaxies. The density I use is the mean density of space, which includes all matter in space.

[coldcreation]

I am not convinced either that an expanding universe is an adiabatic process, or that is can even be related to one (far from it). Nevertheless, it is "implicitly assumed in the derivation of the Friedmann-Lemaître-Robertson-Walker metric." [My bold]

 

An expanding universe is certainly not an adiabatic process where the temperature of a fixed volume of air changes even though no heat is exchanged between air and the environment.

 

To assume such a relation (adiabatic expansion of gas in air, and an adiabatic expansion of the universe) seems like a last ditch effort to find some kind of corroborative physical evidence (or package deal) to support the notion that space can 'in fact' expand (along with that which fills space) and yet stay true to the natural laws (particularly the conservation laws).

 

The fact is, as modest wrote, "there is no better analogy than adiabatic expansion." But that unfortunately doesn't make it a good analogy.

 

 

It is not yet checkmate.

 

 

:phones:

 

 

CC

[Erasmus00]

I am not convinced either that an expanding universe is an adiabatic process, or that is can even be related to one (far from it). Nevertheless, it is "implicitly assumed in the derivation of the Friedmann-Lemaître-Robertson-Walker metric."

 

What the derivation of the FLRW metric shows is that an expanding universe CAN be related to an adiabatic process. If the universe is modeled as a perfect fluid, we arrive at the FLRW metric. i.e. certainly it is possible for a universe to expand adiabatically.

 

If you are at all familiar with GR/thermodynamics, might I suggest playing with both Einstein's equations and the equations of motion for such a system. Deriving the FLRW and doing calculations (probably numerical) of the fluid flow can create a lot of insight. When in doubt- do it yourself.

-Will

[bigsam1965]

The ratio of specific heats for a relativistic gas (e.g. photon) is 4/3. Therefore:

[math]Gamma=4/3[/math]

[math]T_{gamma}{propto}V^{-(Gamma-1)};=V^{-1/3}{propto}a^{-1}[/math]

 

FLRW is based on this analogy Sam, it's fine.

 

I'm leaving to get some serious dental work done - would anyone like to agree/disagree with my last few posts and continue the conversation as I may well be out of commission for a few days.

 

-modest

 

This is interesting since there is no coefficient of specific heat at constant pressure for a photon gas.

[bigsam1965]

What the derivation of the FLRW metric shows is that an expanding universe CAN be related to an adiabatic process. If the universe is modeled as a perfect fluid, we arrive at the FLRW metric. i.e. certainly it is possible for a universe to expand adiabatically.

 

If you are at all familiar with GR/thermodynamics, might I suggest playing with both Einstein's equations and the equations of motion for such a system. Deriving the FLRW and doing calculations (probably numerical) of the fluid flow can create a lot of insight. When in doubt- do it yourself.

-Will

 

Will, I missed your post earlier. I have been through tensor analysis, differential geometry, general relativity, the Swartzchild solution, and the derivation of the Friedmann-Lematre metric. I must admit that I have not studied the details of the theory in the last few years. I am using the matter-dominated part of the Friedmann-Lemaitre metric. Most of my work over the last four years has been concentrated on a solution of the FL metric. I do not use the Robertson-Walker shell. Space-time is modeled as a perfect fluid. modest was refering to light as an adiabatic process. I was familiar with the equation about the ratio of specific heats, and it has always struct me as curious that one of the specific heats is not real. I don't disagree with the the equation that he presented.

 

What I do maintain is that the question of whether photon energy is conserved or not conserved is an open question. Sandage conducted experiments on Tolman surface brightness and inferred that the substantial difference in his results with Tolman surface brightness is due to luminosity evolution of the source, which may be true. I have shown elsewhere from the dilated-source image and dilated time due to expansion of space that the Stephan-Boltzmann constant is not invariant in the relativistic transformation and is dilated by the stretch factor (1+z). This has an effect of (1+z) on the observed energy flux of a black body source at dilated distance from an observer.

[coldcreation]

Let's take your adiabatic analogy and look at it. First of all normal gas has coefficients of specific heats. It puzzels me how anyone can obtain coefficients of specific heats for a photon. Also, particles expanding with space is not the same as particles expanding through space in an adiabatic process. If photon energy is conserved then as space expands radiant energy density goes down by [math](1+z)^{-3}[/math] and the total radiant energy of expanding space is conserved. However if we assume that the photoelectric effect applies in expanding space as it does in the static-space of a laboratory then an additional reduction of energy density by the scale factor [math](1+z)^{-1}[/math] occurs and the total radiant energy of the system becomes [math]E=(1+z)^{-1}E_0[/math], where [math]E_0[/math] is the radiant energy emitted from a source. This means that the system has lost a total of [math]E_{lost}=z(1+z)^{-1}E_0[/math]. I would like to know where this lost energy went. I propose that the energy is still there because it is stretched with the photon wave length. In your adiabatic process with photons losing energy, you claim that the total energy is still there, show me where it is.

 

Since we are dealing photons as opposed to a gas, perhaps an answer to this can be found here: Quantum harmonic oscillator: Wiki.

 

Of course, in the case of an expanding manifold the photon energy loss would be associated with an adiabatic decrease in spring constant (not an increase: see illustration).

 

It would seem that energy is conserved... :huh:

 

 

 

PS. I hope everything went well modest.

 

 

CC

[bigsam1965]

A test of Tolman surface brightness (Lubin&Sandage 2001) has been conducted. Perfect Tolman surface brightness uses [math](1+z)^4[/math] which includes non-conservation of photon energy. Galaxies in three clusters were tested. The test concluded that the exponent was 2.59 for the R band and and 3.37 for the I band with [math]q_0=1/2[/math]. The sensitivity was shown to be less than 23% between [math]q_0=[/math] 0 and 1. Without lookback luminosity evolution, this result supports surface brightness using [math](1+z)^3[/math] and conservation of photon energy. The authors of the paper use a theoretical lookback luminosity evolution model to explain away the difference in the test and perfect Tolman surface brightness. The authors may be right. There are many lookback luminosity evolution models for galaxies.

[Erasmus00]

This is interesting since there is no coefficient of specific heat at constant pressure for a photon gas.

 

The mistake isn't the adiabatic relation, merely identifying [imath]\gamma[/imath] with the ratio of specific heats, which isn't necessary.

 

Consider for an adiabatic process all change in energy is due to PdV work. Combine this with the relation for a photon gas U = 3PV. Hence

 

[math]

-PdV = dU = 3VdP +3PdV

[/math]

[math]

-\left(\frac{3+1}{3}\right)\frac{1}{V}dV = \frac{1}{P}dP

[/math]

[math]

ln \left(\frac{V}{V_0}\right)^{-\frac{4}{3}} = ln\left(\frac{P}{P_0}\right)

[/math]

[math]

PV^{-\frac{4}{3}} = Const.

[/math]

 

We can do the same thing with the other adiabatic relationships. [imath] \gamam = \frac{4}{3} [/imath] for a photon gas, with no ambiguity. Hence, Modest's point still stands. For an adiabatic expansion, photon temperature drops like one over the scale factor, which is exactly what is observed in FLRW.

-Will