Can a redshift arise from expanding space?

[Rolando]

The spectral lines in the light we receive from distant galaxies are shifted towards the red. There is a “cosmic redshift”. The waves arrive stretched. We observe expanded waves in a static space.

The idea that space itself could expand or contract is not very common, but it is diffused by some cosmologists and their followers. These claim that space is expanding and that this is the cause of the cosmic redshift. But this is unintelligible to me. What do they mean? An expanded wave in an unexpanded space is equivalent to an unexpanded wave in a contracted space – not in an expanded one.

[Mordred]

Our universe is not static, it is expanding as a result we have the cosmological redshift. Expansion is also supported by thermodynamic reduction in temperature.

[Strange]

The idea that space itself could expand or contract is not very common

 

It has been common and generally accepted for most of my lifetime - ever since Wilson and Penzias discovered the CMB in the 60s.

 

These claim that space is expanding and that this is the cause of the cosmic redshift. But this is unintelligible to me. What do they mean?

 

The description of expanding space has a parameter called the "scale factor" which relates distances at one time to another. The scale factor now is greater than when the photons were emitted. This means that lengths, including the wavelength of the photon, are greater.

More here: https://en.wikipedia.org/wiki/Redshift#Expansion_of_space

[Rolando]

I meant that the idea that space itself could expand or contract is not very common outside the field of cosmology. Within cosmology, it is often claimed that space is expanding and that this is the cause of the cosmic redshift. In this context it is also often said that it is the "metric space" that is meant to expand.

When waves expand in an ordinary, static metric space, their wavelengths increase. Light will, thus, be redshifted.

The same observations would be made if waves remained unaffected in a contracting metric space.

If waves expanded or contracted in a metric space that evolved in proportion, there would be no observable shift in wavelengths. A unit of length such as the meter, which by definition is equal to a certain number of waves of a certain type of radiation, would expand in proportion with the observed light waves.

If waves remained unaffected in an expanding metric space, there would be a blueshift.

None of these alternatives describes the situation. Coherent objects up to the size of galaxy clusters are actually not assumed to evolve in proportion with the scale factor, which leaves just the voids between them to do that. My question is about the logic of those who claim that the redshift results from an expansion of metric space, when this applies to no coherent object at all (neither atoms nor galaxy clusters or anything in between). They must consider objects not to occupy space. Can you make this palatable to me?

Edited January 15, 2015 by Rolando

[Mordred]

It's easy if you don't think of space as having a substance its just a change in geometric volume.

 

As far as why only the voids are affected this is due to the energy density per volume of the cosmological constant.

 

This energy density is roughly 6.0*10^-10 joules per m^3.

 

Locally around gravitationally bound objects gravity can easily overpower the cosmological constant.

Cosmology is based on the ideal gas laws so the energy density relations per region is critical.

[Rolando]

It's easy if you don't think of space as having a substance its just a change in geometric volume.

 

I did not think of space having a substance. It is rather my belief that substance (objects) need a space that causes the trouble. How can one claim that space expands if the volume that is occupied by objects, even by whole galaxy clusters, is to be exempted?

 

Edited January 15, 2015 by Rolando

[Mordred]

In the case of expansion and in accordance with the ideal gas laws. The cosmological constant aka dark energy was at one time been thought of as being due to virtual particle production. Unfortunately the Heisenburg uncertainty principle aka quantum oscillator turned out to be 120 orders of magnitude too large.

 

Now as energy is a property of particles and does not exist on its own. The statement you made isn't inaccurate. Unfortunately we don't understand the mechanism that keeps the cosmological constant constant.

 

In terms of being a positive pressure influence with gravity being negative pressure as per the equations of state it isn't particularly mysterious.

 

What process causes it to remain constant is.

 

There has been some recent papers that are based on the Highs field interactions in the SO(10) standard particle physics model that may or may not solve the problem. The idea is still waiting for more data on the Higgs boson.

Here is some of the related material.

 

Higg's inflation possible dark energy

 

http://arxiv.org/abs/1402.3738

http://arxiv.org/abs/0710.3755

http://arxiv.org/abs/1006.2801

[Strange]

If waves expanded or contracted in a metric space that evolved in proportion, there would be no observable shift in wavelengths. A unit of length such as the meter, which by definition is equal to a certain number of waves of a certain type of radiation, would expand in proportion with the observed light waves.

 

That would be true if you measured the wavelength in the same frame of reference. So, for example, the Sun is emitting the same wavelengths of light (as measured by us) as it always has.

 

However, we measure the the light from distant stars in a different frame of reference from where they were emitted. Our "meter rule" is no longer the same as theirs.

I did not think of space having a substance. It is rather my belief that substance (objects) need a space that causes the trouble. How can one claim that space expands if the volume that is occupied by objects, even by whole galaxy clusters, is to be exempted?

 

Galaxies, etc. do not expand because they are held together by galaxy. In the absence of any such force, objects will tend to move apart. (For exactly the same reason, by the way, that objects with mass will tend to get closer together - aka gravity).

 

Light is not an "object" and so is affected by the scale factor. Hence we see a different wavelength for distant light.

[Rolando]

However, we measure the the light from distant stars in a different frame of reference from where they were emitted. Our "meter rule" is no longer the same as theirs.

This is what I meant. While the light is on its way, our ”meter rule” and the light waves expand in proportion. Hence no redsdhift.

 

 

Galaxies, etc. do not expand because they are held together by galaxy.

This is how most astronomers think about it. In an ordinary, static metic space, galaxies etc. are held together by gravity, while the universe as a whole is said to expand. There is no problem with the logics of this reasoning, but on a very large scale, it leads to velocities > c, which are considered as unphysical. I think that this is the reason why the expansion has come to be attributed to space itself.

 

The logical problem arises if the metric space is assumed to expand. In this case, it needs to be explained why meter rules and galaxies etc. contract within this space. i.e., why their comoving linear size shrinks by the inverse of the scale factor, i.e., just as much as necessary to keep their sizes constant in a non-expanding metric space.

Edited January 15, 2015 by Rolando

[Strange]

This is what I meant. While the light is on its way, our ”meter rule” and the light waves expand in proportion. Hence no redsdhift.

 

Except the ruler doesn't expand because it is held together by electrostatic forces.

 

This is how most astronomers think about it. In an ordinary, static metic space, galaxies etc. are held together by gravity, while the universe as a whole is said to expand. There is no problem with the logics of this reasoning, but on a very large scale, it leads to velocities > c, which are considered as unphysical.

 

There is no problem with (apparent recessional) velocities greater than c. You are applying something dervied from special relativity (a subset of GR that only applies to inertial frames) to a problem that requires GR.

 

The "speed limit" only applies locally; i.e. wher SR is can be used as an approximation.

 

 

The logical problem arises if the metric space is assumed to expand. In this case, it needs to be explained why meter rules and galaxies etc. contract within this space.

 

They don't contract they stay the same size. Because they are bound by various forces.

 

In the absence of any force, objects will tend to move apart - which is what expanding space means.

[Rolando]

 

Except the ruler doesn't expand because it is held together by electrostatic forces.

Sure, in the real world, the ruler (= the meter) does not expand, but to my understanding this blatantly contradicts the claim that the metric space expands.

 

There is no problem with (apparent recessional) velocities greater than c. You are applying something dervied from special relativity (a subset of GR that only applies to inertial frames) to a problem that requires GR.

 

The "speed limit" only applies locally; i.e. wher SR is can be used as an approximation.

Then, what is the reason for ascribing the expansion of the universe to an expansion of metric space?

 

[about meter rules]

They don't contract they stay the same size. Because they are bound by various forces.

Sure, but in order to stay the same size in their non-expanding metric space, meter rules need to contract in the assumed expanding metric space (which stays the same size in comoving coordinates).

[elfmotat]

Sure, in the real world, the ruler (= the meter) does not expand, but to my understanding this blatantly contradicts the claim that the metric space expands.

 

Then, what is the reason for ascribing the expansion of the universe to an expansion of metric space?

 

Sure, but in order to stay the same size in their non-expanding metric space, meter rules need to contract in the assumed expanding metric space (which stays the same size in comoving coordinates).

 

Put a coin on a rubber sheet and stretch it. The space of the sheet is expanding, but it is not nearly enough to overcome the molecular bonds in the coin and rip it apart. This simulates galaxies, clusters, and other gravitationally bound objects. The force of expansion is not enough to overcome their gravity.

 

If you put two coins on the sheet and stretch it, the coins will move apart from each other. This is because the coins are not bound to each other. It simulates two galaxies which are very far apart, such that their gravitational interaction is too small to overcome expansion. Also notice that the coins on the sheet reproduce Hubble's Law: if they are twice as far apart they will move twice as fast away from each other.

[Strange]

Then, what is the reason for ascribing the expansion of the universe to an expansion of metric space?

 

This is a relatively non-mathematical explanation: http://math.ucr.edu/home/baez/einstein/einstein.html

[Rolando]

Elfomat & Strange,

 

thanks for your replies, in which you explain how an expansion of the universe can be understood and why galaxies do not expand. This may be valuable for newcomers, but I am quite familiar with it already.

 

My question concerned, instead, the claim that metric space expands. How can one reasonably claim this when any standards of comparison for length that are shorter than the diameter of a galaxy cluster have to be exempted from the expansion? (Otherwise, there would not either arise an observable redshift.) I am not either quite sure about why this idea has come to be diffused.

Edited January 15, 2015 by Rolando

[Mordred]

The metric term was probably added to point out space is geometric volume. Aka metric expansion. How often do you hear people ask what is it in space that expands. Orb if space expands what is it made of?

 

The term metric implies geometric volume distance.

Lol I wouldn't be surprised if the term originated from some forum frustrated with answering those questions. Oh but GR says space stretched it must be some form of fabric. Lost track number of times I heard that one

[Rolando]

 

Put a coin on a rubber sheet and stretch it. The space of the sheet is expanding, but it is not nearly enough to overcome the molecular bonds in the coin and rip it apart. This simulates galaxies, clusters, and other gravitationally bound objects. The force of expansion is not enough to overcome their gravity.

 

If you put two coins on the sheet and stretch it, the coins will move apart from each other. This is because the coins are not bound to each other. It simulates two galaxies which are very far apart, such that their gravitational interaction is too small to overcome expansion. Also notice that the coins on the sheet reproduce Hubble's Law: if they are twice as far apart they will move twice as fast away from each other.

 

OK. The stretching rubber sheet represents the expanding universe as described by Friedmann, Robertson-Walker, the ΛCDM concordance model, etc. These models have been derived on the basis of GR, assuming that the mass of the universe is distributed uniformly. They assume that there are no coherent objects (neither small ones nor larger ones, such as galaxy clusters etc, which probably house nearly all the matter in the real Universe). Further, they describe the possible evolution of the universe in a system of reference that is not itself affected by this evolution, like that in which a coin on the rubber sheet is static. However, coins on the rubber sheet are not within the universe. If anything, they represent separate, metrically static worlds outside the universe.

 

In order to model the actual Universe, to which there is no outside, it would be necessary to have the coins embedded within the rubber sheet. But this would make it clear that the Universe could never have been smaller than the volume of the coins and that the mentioned models and the big bang are grossly unrealistic.

[Mordred]

One shouldn't take analogies too far.

 

The rubber sheet and the coins are mere visualization tools to represent coordinate changes only.

Edited January 16, 2015 by Mordred

[elfmotat]

 

OK. The stretching rubber sheet represents the expanding universe as described by Friedmann, Robertson-Walker, the ΛCDM concordance model, etc. These models have been derived on the basis of GR, assuming that the mass of the universe is distributed uniformly. They assume that there are no coherent objects (neither small ones nor larger ones, such as galaxy clusters etc, which probably house nearly all the matter in the real Universe). Further, they describe the possible evolution of the universe in a system of reference that is not itself affected by this evolution, like that in which a coin on the rubber sheet is static. However, coins on the rubber sheet are not within the universe. If anything, they represent separate, metrically static worlds outside the universe.

 

In order to model the actual Universe, to which there is no outside, it would be necessary to have the coins embedded within the rubber sheet. But this would make it clear that the Universe could never have been smaller than the volume of the coins and that the mentioned models and the big bang are grossly unrealistic.

 

Because the FLRW metric is obviously just an idealization which makes for useful approximations, just like most anything else in physics. At large enough scales the universe is approximately homogeneous, meaning the FLRW metric approximates our universe at large scales.

You also shouldn't take analogies too seriously: space isn't 2-dimensional either! I only provided the analogy because it makes visualization easier, which is sometimes helpful for people who aren't well-versed in this stuff.

[Strange]

In order to model the actual Universe, to which there is no outside, it would be necessary to have the coins embedded within the rubber sheet. But this would make it clear that the Universe could never have been smaller than the volume of the coins and that the mentioned models and the big bang are grossly unrealistic.

 

That would be true if the galaxies had always existed. But we know (even if we don't understand all the details) that they formed from clouds of gas. And that gas was once denser and hotter. So the "coins" analogy only works for the universe as it s now.

[Rolando]

 

That would be true if the galaxies had always existed. But we know (even if we don't understand all the details) that they formed from clouds of gas. And that gas was once denser and hotter. So the "coins" analogy only works for the universe as it s now.

Even now, the mass of galaxy clusters consists mainly of gas clouds (and, supposedly, of even more dark matter), and the size of the clusters (”coins”) is given by the mass enclosed within the envelope at which the gravitational attraction balances the expansion of the universe. It makes no difference to the size of the ”coins” whether the mass enclosed by the envelope is condensed into stars or present in form of gas and dark matter.

At large enough scales the universe is approximately homogeneous, meaning the FLRW metric approximates our universe at large scales.

This approximation may be acceptable at present, when most of the volume of the universe consists of voids, but it becomes grossly inadequate when we go back in time, e.g., to z=10 (of the most distant galaxy that has been observed). The scale factor a(t) was then roughly 0.05 and the volume of the universe about a factor of 10^-4 smaller than it is now. There was not much room for expanding voids then.

Edited January 17, 2015 by Rolando

[Mordred]

Yes but even then the distribution of matter followed a homogeneous layout at large enough scales. Homogeneous does not mean just voids.

 

Today the scale we consider homogeneous is 100 Mpc. When the universe was smaller that scale is also smaller.

 

Prior to the CMB roughly at the time the universe was roughly 150000 years old the temperature was too hot for galaxies to form. This period of time and prior is when particles are in thermal equilibrium. Any reactions were unstable and the reverse reactions occurred.

 

Any period after inflation has been shown to be homogeneous and isotropic.

 

Prior to inflation no one knows for sure due to the dark ages. Time period when the mean free path of photons is too short for light to reach us. This changed when atoms started to form. Hydrogen deuterium some lithium primarily.

 

The term homogeneous occurs at sufficiently large enough scales that anistropies become irrelevant.

 

much like a lake with waves. Look close it is definitely anisotropic measure a larger volume and those waves become negligible.

For that matter it is easier to show uniformity shortly after inflation.

 

The universe started at a hot dense low entropy state. In thermal equilibrium. As a result the number of degrees of freedom of particles not in thermal equilibrium was greatly reduced.

For that matter it is easier to show uniformity shortly after inflation.

 

The universe started at a hot dense low entropy state. In thermal equilibrium. As a result the number of degrees of freedom of particles not in thermal equilibrium was greatly reduced.

http://arxiv.org/pdf/hep-th/0503203.pdf"Particle Physics and Inflationary Cosmology" by Andrei Linde

http://www.wiese.itp.unibe.ch/lectures/universe.pdf:"Particle Physics of the Early universe" by Uwe-Jens Wiese Thermodynamics, Big bang Nucleosynthesis

 

These two articles go into detail on nucleosynthesis.

[Strange]

It makes no difference to the size of the ”coins” whether the mass enclosed by the envelope is condensed into stars or present in form of gas and dark matter.

 

Except that gas can be compressed more than stars and planets can.

 

This approximation may be acceptable at present, when most of the volume of the universe consists of voids, but it becomes grossly inadequate when we go back in time, e.g., to z=10 (of the most distant galaxy that has been observed). The scale factor a(t) was then roughly 0.05 and the volume of the universe about a factor of 10^-4 smaller than it is now. There was not much room for expanding voids then.

 

The universe was more homgeneous then. The current "clumpiness" was magnified by areas of fractionally higher density collapsing under gravity.

[Rolando]

Yes but even then the distribution of matter followed a homogeneous layout at large enough scales. Homogeneous does not mean just voids.

 

Today the scale we consider homogeneous is 100 Mpc. When the universe was smaller that scale is also smaller.

I agree, but I think we also agree that it is only the voids that expand, since the rest is gravitationally bound, and that this inhomogeneity is crucial. If the universe was completely homogeneous, there would be no redshift, because the standards of comparison would expand in proportion to the light waves.

 

The universe can never have been smaller than the total volume of the gravitationally bound regions within it, and, to my understanding, this volume cannot have been smaller in the past than it is now.

 

Except that gas can be compressed more than stars and planets can.

Sure, but it makes no difference to the size of the gravitationally bound regions whether the mass in them is present in form of gas, stars or planets.

 

The universe was more homgeneous then. The current "clumpiness" was magnified by areas of fractionally higher density collapsing under gravity.

One can also say that the universe was more homogeneous in the past, since a smaller fraction of its volume was void (gravitationally unbound).

Edited January 17, 2015 by Rolando

[Mordred]

Gravitational bound regions can be infinitely dense. You can have homogeneous and isotropic expansion. Redshift has nothing to do with homogeneity its a change in volume from one homogeneous point in time to another..

 

So I'm not really sure what your implying. The observable universe started in a region less than an atom in volume. That's the start of our region of causality.

One must keep in mind stars and galaxies aka baryonic matter is only 3% the mass/energy budget. Galaxies is considered as mere dust. Our universe dynamics is controlled by dark matter and the cosmological constant as they are the two largest contributors.

 

Dark matter formed shortly after inflation. No one knows precisely when but research leads to roughly when the universe was in its first few seconds.

 

radiation both relativistic and non relativistic is the third main contributor.

 

Matter has negligible contribution to pressure not so with radiation and the cosmological constant.

 

You have three major time periods after inflation.

 

Radiation dominent

Matter dominant

Lambda dominent

 

Were in the latter

[Strange]

One can also say that the universe was more homogeneous in the past, since a smaller fraction of its volume was void (gravitationally unbound).

 

Which is exactly what I said. The voids and the denser regions (stars and galaxies and large scale structures) were created by gravity causing matter to collapse together. This has been pretty accurately modelled.