Dear Boris,

The expanding cosmological space-time, the Friedmann-Lemaître-Robertson-Walker model, is only a valid description of the geometry on cosmological scales. It is an averaged geometry. On the other hand, the geometry in gravitationally bound objects like atoms, stars, star clusters, galaxies and galaxy clusters is described by very different space-times that are not expanding, but are embedded in the expanding cosmological space-time. In other words, bound objects do not expand.

As for the expansion velocity, interpreting the observed recession velocity due to cosmological expansion as a physical velocity is a misconception. It is an apparent effect coming from the expansion rate of the scale factor, the Hubble rate. The scale factor completely characterises the cosmological space-time and it tells us how the size of the ruler of the metric changes with time. There's nothing wrong with this apparent velocity being larger than c, as there is nothing travelling with that velocity.

Best,

Lukas

Dear Baryshev,

that's a really intriguing topic, and the reference that you give seems interesting in this regard.

What is usually told is that, in cosmological models involving an expanding universe, it's the spacetime itself which is expanding. This means that, even in the case in which the "matter content" of the universe has no proper motion, it is nevertheless co-moving with the metric and the net effect is the relative motion that we can observe between galaxies.

The usual example that we encounter is this: a number of small dots are drawn on a balloon at fixed distances; then we inflate the balloon and observe the dots move away from each other as time passes. The surface of the balloon represents a 2-dimensional version of our universe and the dots are the galaxies.

Clearly, two of those dots can be found to be moving apart from each other at a speed greater than the speed of light: that's the reason for the presence of the cosmological horizon.

But the main point is that there is no violation of the speed of light as the upper limit for velocites, because in this case the "points of space" are moving faster than c with repect to each other: the limit is imposed to objects moving in the spacetime and not to spacetime itself.

Thanks, I will read the reference on the arxiv.

My best regards,

Giovanni

Dear Giovanni !

Yes, the relative velocity of "points of space" can be larger then the velocity of light. But the question is: why the elementary particles and atoms do not expand together with space? If we have expansion of space itself, we have to have expantion of atoms too (like expansion of dots drawn on the balloon). It means the size of atoms and corresponding radiation wave length would increase. Therefore the emission lines which we use for expansion measurements would change too. And thus this space expansion would be unobservable.

So now we have an expansion of void space itself and have no expansion of matter in this space. This go against modern concept of physical vacuum. This is the main problem to my opinion.

Best regards,

Boris

Dear Boris,

good point there!

I think that the solution (which actually I don't have) could reside in the different scales of the phenomena we are considering. In the models of expanding universe, such as Friedmann-Robertson-Walker, the characteristic scale is given by the Hubble parameter H (and its derivatives, if it's time-dependent), which in turn is related to the curvature scalar characterizing the spacetime we are considering; on the other hand, the charatecteristic scale of elementary particles is very small compared to the scale of curvature of the universe. I think that here resides the answer.

In fact, one of the best theoretical frameworks that we have in general relativity is the "inflationary model" which gives an explanation for the present state of our universe (homogeneous, flat and isotropic, at least on a rough approximation). The mechanism of inflation involves an exponential expansion of space, which in turn translates in a constant and intense curvature: in this scenario the quantum fluctuations, that are initially very small compared to the dimension of the universe, are atually "stretched" towards the classical scale and eventually form the density fluctuations that we observe: clusters of galaxies.

see e.g. http://ned.ipac.caltech.edu/level5/Sept02/Kinney/Kinney4_5.html

But this happens only in inflationary stages: in the non-exponentially expanding universe, we should not be aware of the expansion in our "local neighborhood", and this is exactly what you say. But when we observe distant galaxies (which is no longer a "local neighborhood" and thus involves larger scales) we are able to see the expansion. In this sense I think that the answer resides in the different scales of the phenomena.

But I don't understand why you say that this goes against modern concept of physical vacuum: can you explain to me?

My best regards,

Giovanni

Dear Boris,

The expanding cosmological space-time, the Friedmann-Lemaître-Robertson-Walker model, is only a valid description of the geometry on cosmological scales. It is an averaged geometry. On the other hand, the geometry in gravitationally bound objects like atoms, stars, star clusters, galaxies and galaxy clusters is described by very different space-times that are not expanding, but are embedded in the expanding cosmological space-time. In other words, bound objects do not expand.

As for the expansion velocity, interpreting the observed recession velocity due to cosmological expansion as a physical velocity is a misconception. It is an apparent effect coming from the expansion rate of the scale factor, the Hubble rate. The scale factor completely characterises the cosmological space-time and it tells us how the size of the ruler of the metric changes with time. There's nothing wrong with this apparent velocity being larger than c, as there is nothing travelling with that velocity.

Best,

Lukas

If a physical theory is applicable to the universe as a whole, but not to parts of the universe, at least we have three observations. The first is that behind the explicit theory, there are no explicit constraints (only valid for the whole and not for the parties). The second is that there is no argument for such constraints, except that the reality is that there is no local expansion, and then the theory have unreliable basis, and adjusted to match the reality known but have not a priori serious justification. There are arguments ad-hoc. The third is that if the expansion rate is not a physical velocity, what is it? It's a trick to get expand coordinates to and fit as measured by Hubble? Within this approach we can define the temperature T as the LN (T'), T' a thermodynamic temperature, (Temperature is any continuous function of T', it's only a change of coordinates). It is easy to see that T = 0 is mathematically inaccessible, because – ∞ is unreachable. However, does this solve the physical problem of inaccessibility? It seems to confuse the tool –mathematics- with the physical reality is unclear, and although apparently "resolves" the inconsistencies, this makes more difficult to obtain better solutions.

Dear Giovanni,

The old classical picture was: there is a void space (vacuum as empty box), and there is a matter placed this space. That is we had 2 quite different entity. In this case we naturaly have different behaviour for space and matter and may be different scales for them.

The modern concept of physical vacuum means that vacuum is rather physical media than empty box. Void space is just lowest energy state of this media, while the different particles are the excited states of this media. In this case we have only one natural scale - Planck length = 10−35 m, which is very small value. We have no other natural scale length from first principles of physics. Hence it looks strange to have different space (media) expansion on different scales.

Even more, the redshifts of emission lines now in expansion model are not regarded as a Doppler shift but rather the expansion of space. In that case the redshift means just the expansion of photon!

You must admit it is very strange situation - some elementary particles (photons) expand while other particles not?

Best regards,

Boris

Our discussion of the PHYSICS of the expansion of space in FLRW cosmological model of GR clearly demonstrate that there is a strong confusion in physical understanding this process which lead to paradoxical situation in interpreting observational astrophysical data.

Lukas and Giovanni present the usual point of view (V1 picture) that receding galaxy actually do not moving, distance between galaxies increase but they are at rest, truly new situation of the creation of space. While Jorge , Armen and Boris present physical arguments (V2 picture) that see receding galaxies as a real velocity because the distance between galaxies is increase with increasing time (natural view on velocity). I like Jorge view that “if the expansion rate is not a physical velocity, what is it? It's a trick”, also Boris emphasized that now physical vacuum consists of particles, exist everywhere and can not be static in one place and expanding in another place.

Dear colleagues , thanks for your comments. In my opinion the V2 picture is physically true. The essence of the problem is that one should not accept an analogy as the true physical explanation of an actual physical process. Balloon analogy was invented just for display the possibility of galaxy receding with having no the center, it can not explain the space expansion of the general relativity and actually it really deceive a researcher:

1) To measure the distance between two points on the inflating balloon one should have an measuring rood, which in the case of balloon surface is the 2 nearby points on the same balloon. The result is that distances between any two points relative to measuring rood is unchangeable, it is also clear if instead of points we have spots of finite size on the surface of the balloon.

2) Mathematically it was demonstrated already by Robertson that the EXACT relativistic formula of the FLRW model for the velocity of space expansion is identical to the Newtonian velocity expression : V_exp = H R = c (H/c) R = c (R/R_H), so for a galaxy at a distance larger than the Hubble R_H = c/H the galaxy recede with velocity larger then velocity of light!

3) Concept of inflation only make stronger this paradox, it based on the expansion velocity equals to 10^{120}cm/sec (Allan Guth)!

4) So observed cosmological redshift may be interpreted as a global gravitational redshift without motion (as in the first paper by de Sitter in 1917, see discussion in the recent book http://www.springer.com/astronomy/book/978-94-007-2378-8).

Best regards,

Yurij.

Dear @Boris,

I don't think it is so strange to have different expansions on different scales. Given the fact that every small region of space can be locally approximated by a Minkowski flat patch (disregarding possible singularities), you can easily have a particle which is locally unaware of the expansion of the universe (again, if you are not near a singularity of the metric).

What I don't understand is this: if you claim that the velocity of recession of the galaxies is due not to expansion of space, but to a real motion of the galaxies departing from each other, are you implying that the universe is not expanding? (please, take this question as a sincere one: I'm just concerned about understanding your point)

With regard to photons, you say that redshift in expanding models is just the expansion of photons. I agree that the net effect that you register is an expansion of the wavelength of light. If the space is expanding, the photons coming from far away are spending more energy to reach us than the energy required if the space was not expanding. But this effect cannot be registered in a "local scale" experiment: you need a photon traveling "cosmological scales" in order to see the effect. So the difference is not between some particles that seem to expand and others that does not: it is a matter of local and global observations.

(In a mathematical framework, you could say that Christoffel connections are trivial in a local Minkowski patch, while they act fully on cosmological scales)

As a last remark, I address @Yurij:

I don't think that superluminal expansion for R>R_H constitutes a real paradox. Usually, when one talks about paradox of superluminality actually implies that the paradox resides in "causality violation", because a superluminal signal could affect regions outside the causal cone of the observer and lead to "effects preceding the cause" and stuff like that. In the case of expanding universe I see no causality violation, no signal reaching an observer in faster-than-light way. So, apart from the terminology "faster than light", where is the paradox?

(this also happens in optics with the group velocity of a wave packet, which can exceed speed of light: the solution of the paradox is that group velocity does not represent the velocity of propagation of energy or information)

Best regards,

Giovanni

Dear Giovanni,

I am not professional in this field (cosmology) and not familar with corresponding mathematics but I am interesting and would like to understand it at least at the qulitative level.

What I see:

1) The weak experimental basis of theory. The main experimental fact - redshifts could be explained by very different reasons without such global (sorry - Universal) conclusions like Universe expansion.

2) Nevertheless I like this conception. I indeed think the space expand. But we have to clarify some questions:

- Expandind relative of what? We have to have some rigid scale to measure such expansion. Otherwise it is unobservable as I mentioned above.

- Let the atoms, particles etc. provide you with such rigid scale. Then you have to admit they are embedded in some another rigid space because their wave functions depends on the space-time parameters of this rigid space.

- Then we have 2 options: either this rigid space is global and the "soft" expanding space is embedded in (like 2 dimensional surface of balloon is a subspace of our 3-D space), or this rigid spaces are local and there are some boundaries between expanding and not expanding areas of space (which is very strange to me and ask more questions than give answers).

To solve these problems (to my opinion) one need to abandon the present approach when the properties of matter (wave functions etc.) are described in some predetermined space-time. On the contrary, the space should be derived from the physics. To me instead of geometrization of physics (interactions) one needs "physicalization" of geometry. In this view I like the theories with discrete space-time (loop quantum gravity as example). At the beginning we have some objects (nodes) and links between them. The topology of this net could be very different. Then you have to introduce the interactons, dynamics (physics) on this net. The continual space in this case is just the large scale approximation of discrete net. In such theories the "softness" of space area could depend on the matter in ithis area.

Best regards,

Boris

Dear Giovanni, we are speaking not about mathematical abstract exercise (with known answer), but about the physical cosmology which consists of the experiments/astronomical observations and the theory of gravitational interaction which is used for certain interpretation of the observational facts. So the aim of physical cosmology is not a believe in some mathematical interpretation of the observed phenomenon but to prepare and perform a crucial experiment/observation which can distinct between different physical interpretations based on different gravitation theories and hence help to choose the right theory (now there are dozen relativistic quantum theories of gravitational interaction).

As a specialist in extragalactic astrophysics (about 40 years in the fields of radio astronomy, active galactic nuclei, relativistic astrophysics, large scale structure of the Universe, crucial cosmological tests, which have been published in about 100 papers) I do not believe in the expansion of the Universe because up to now there is no astrophysical observation which proved the reality of the expansion space phenomenon.

By the way, Edwin Hubble in his classical paper “A relation between distance and radial velocity among extra-galactic nebulae” (1929) also do not “believe” in the expansion of space interpretation of the Redshift – Distance relation. He wrote that discovered redshift law “may present the de Sitter effect” and that “In the de Sitter cosmology , displacements of the spectra arise from two sources, an apparent slowing down of atomic vibrations and a general tendency of material particles to scatter”. It means that the observed cosmological redshift in de Sitter model is due to global gravitational redshift (g_00 components dipend on the distance) together with peculiar velocities of galaxies. Up to his death Hubble do not believe in the expanding space interpretation of the discovered him “redshift-distance” relation.

Modern technology of astrophysical observation allow to perform the crucial test on reality of the space expansion. This is the Allan Sandage test on the dependence on time the redshift of distant sources. For static space the cosmological redshift is constant with time, while in the standard Friedmann model it should change with time. ESO 40 m telescope is planned for this cosmological test by using spectra of quasars.

In 1922 Alexander Friedmann was a professor of theoretical mechanics department at our university (St.-Petersburg State University), and he changed existing at that time cosmology, so, as a joke I can say that here at SPbU we have “rights” to be especially critical for development of contemporary cosmology too.

Regards, Yurij.

Dear Giovanni, we are speaking not about mathematical abstract exercise (with known answer), but about the physical cosmology which consists of the experiments/astronomical observations and the theory of gravitational interaction which is used for certain interpretation of the observational facts. So the aim of physical cosmology is not a believe in some mathematical interpretation of the observed phenomenon but to prepare and perform a crucial experiment/observation which can distinct between different physical interpretations based on different gravitation theories and hence help to choose the right theory (now there are dozen relativistic quantum theories of gravitational interaction).

As a specialist in extragalactic astrophysics (about 40 years in the fields of radio astronomy, active galactic nuclei, relativistic astrophysics, large scale structure of the Universe, crucial cosmological tests, which have been published in about 100 papers) I do not believe in the expansion of the Universe because up to now there is no astrophysical observation which proved the reality of the expansion space phenomenon.

By the way, Edwin Hubble in his classical paper “A relation between distance and radial velocity among extra-galactic nebulae” (1929) also do not “believe” in the expansion of space interpretation of the Redshift – Distance relation. He wrote that discovered redshift law “may present the de Sitter effect” and that “In the de Sitter cosmology , displacements of the spectra arise from two sources, an apparent slowing down of atomic vibrations and a general tendency of material particles to scatter”. It means that the observed cosmological redshift in de Sitter model is due to global gravitational redshift (g_00 components dipend on the distance) together with peculiar velocities of galaxies. Up to his death Hubble do not believe in the expanding space interpretation of the discovered him “redshift-distance” relation.

Modern technology of astrophysical observation allow to perform the crucial test on reality of the space expansion. This is the Allan Sandage test on the dependence on time the redshift of distant sources. For static space the cosmological redshift is constant with time, while in the standard Friedmann model it should change with time. ESO 40 m telescope is planned for this cosmological test by using spectra of quasars.

In 1922 Alexander Friedmann was a professor of theoretical mechanics department at our university (St.-Petersburg State University), and he changed existing at that time cosmology, so, as a joke I can say that here at SPbU we have “rights” to be especially critical for development of contemporary cosmology too.

Regards, Yurij.

For a pedagogical discussion see the paper: "A comparison between the Doppler and cosmological redshifts" by M.L.Bedran; American J. Physics 70, 406-408 (2002) .

Dear Maria, if you send me pdf file of this your article (M.L.Bedran; American J. Physics 70, 406-408 (2002) ) I will be glad to see it.

Yurij.

Dear Yu. Baryshev, there is a link to my article at

http://www.df.uba.ar/users/sgil/physics_paper_doc/papers_phys/cosmo/doppler_redshift.pdf

Maria Luiza Bedran

Dear Maria, thank for the reference, your paper is very good presentation of the principal difference between Doppler and Lemaitre effects. But the question is what does it mean for the physics of the space expansion? Why expansion velocity is just adds to the true peculiar velosity as Newtonian law? Actually receding galaxy is not moving and the distance increase just due to Creation of space/vacuum.

Regards, Yurij.

Odd, as the photon has zero spin.

Dear Mike, in principle, it easy to distiguish beween static and expanding spaces. In static space the distances between galaxies do not change while cosmological redshift exists. The observational programs exist for convincing proof of the change/not-change of the distance between galaxies, e.g. decrease of flaxies, variation of redshift and so on (see discussion in http://www.springer.com/astronomy/book/978-94-007-2378-8) .

Note for Jose: dear Jose, poton has zero rest mass, and spin equals 1.

Thanks Yurij. I stand corrected.

Dear Mike Smith, the question about physical understanding of the space expansion in modern FLRW cosmology is really fundamental and it hides many surprises/paradoxies for cosmological physics.

In recent astrophysical literature there are splash of acute discussions on the interpretation of the observed cosmological redshift: is it space expansion, Doppler effect or cosmological gravitational effect. The paper http://arxiv.org/abs/1202.0775 by F. Melia and references in this interesting paper is just an example of this discussion. The problem was formulated by Edward Harrison in his book “Cosmology”, Cambridge Univ. Press, 1981 (second ed. 2000). Now there are more than ten papers which argue the different possibilities. Abramowicz et al.(2007; 2008) demonstrate that only space expansion can be used for understanding the cosmological redshift, while Chodorowski (2007; 2011), Bunn & Hogg (2009), Melia (2012) insist on the interpretation as the sum of Doppler effect plus gravitational effect (of cosmologically distributed matter).

However in general relativity space / space-time itself have the same level of existence as matter (Einstein equation joins them) so the space can be curved, stretch, spread (as GW) and so on. And this also can be considered as an argument in favor of the expanding space interpretation, though the problem is still opened.