Cosmology Discussion Forum

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Comment by Vlad Tarko
I've seen that some claim that the red shift may be due to Compton effect and not due to a Doppler shift caused by the "expansion of the universe".
I am uncertain about if this can really be a valid explanation: the Compton effect is also accompanied by elastic scattering (scattered light having the same wave length as the incident light). So, shouldn't the Compton effect just cause some smearing effect? I.e. a ray of light having a certain certain wavelength passing through plasma wouldn't just end up as a superposition of rays, one having the original wavelength and others with larger wavelengths?
How would the Compton effect produce a red shift similar to a Doppler caused red shift? From a star one receives a kind of spectral "fingerprint" (that's why we can determine what kind of atoms are there). The Doppler effect causes the entire spectral "fingerprint" to move left or right. Wouldn't the Compton effect cause just a smearing of the entire "fingerprint" (each spectral line of the "fingerprint" being smeared downwards)? I.e. doesn't the Compton effect explanation of the red shift ignore the existence of the elastic scattering of light on electrons?

Reply
Any scattering mechanism (if significant) should lead to a broadening of features, both spatially as well as spectrally (even for 'elastic' scattering you would get frequency shifts due to the Doppler effect). However, for any reasonable value for the intergalactic electron density, the scattering probabilities would be anyway much smaller than 1 (even over distance like 1010 lightyears), especially as the photon energy could only be reduced by a very small amount per scattering event (see the last equation on my page regarding the Photoelectric Effect (in the 'Particle Model' paragraph)). On the other hand, if one hypothetically assumes enough scattering particles to be present, what would happen is that the original feature would be surrounded by a 'halo' of scattered light (similar to the moon showing a halo when observed through a thin cloud layer) and it is only the light of this halo that would be redshifted, but not the direct light from the object (which would be merely reduced in its intensity). If the optical depth of the scatterers is much larger than 1 (which it would have to be if the Compton effect should lead to substantial changes of the wavelength), one would in fact not see the original object anymore at all, but just a diffuse background of scattered light.

But anyway, as mentioned on my home page entry regarding the Compton Effect , the usual interpretation of this phenomenon is flawed in my opinion i.e. it is actually not a scattering process at all, even for the standard experiments made with x-rays and solid targets (I am for instance not aware of any experimental confirmation of the Compton effect for actually free electrons i.e. in a plasma). Also the concepts of energy and momentum conservation should actually not be applied to light (see my corresponding pages regarding 'Photons' and Energy and Momentum Conservation).

Vlad Tarko (2)
What is the "reasonable value for the intergalactic electron density"?
Grote Reber, who made the hectometre radio telescope and detected radiation coming from the apparent void between the galaxies, said that based on his observation, and if one assumes that the radio waves are emitted by plasma existing between the galaxies, one can compute the amount of plasma (protons and electrons) existing between the galaxies. He said that more that 99% of all the matter in the universe in is this form!
So, maybe the light coming from galaxies and passing through this intergalactic plasma is faced with significant Compton effect (see for example "Compton Effect Interpretation of Solar Red Shift" by J.W. Kierein and B.M. Sharp (they also present a different interpretation of what a quasar is: just a star with a large atmosphere, not so distant from us after all)).

Reply (2)
I am actually aware of the theories of John Kierein and others, but as I said before, I can not accept this as a possible explanation as a) one would need intergalactic electron densities of the order of at least 102 cm-3 for a redshift of about z=1 (which would be about the plasma density of the solar wind or interstellar HII-regions), b) even if one tweaks the Compton scattering theory so that the effect becomes more efficient (as Kierein does I think), the obvious effects of the scattering mentioned above could not be avoided, and c) in my opinion the Compton effect doesn't exist anyway for free electrons.

However, scattering is not the only process by which matter can affect light. For instance, a magnetic field can rotate the polarization vector of light. In this sense, I have suggested on my website plasmaphysics.org.uk under Plasma Theory of Hubble Redshift of Galaxies page that the irregular electric field due to the electrons and ions in intergalactic space causes the redshift. Even though this is a statistical effect as well, this is very much different from scattering but could probably be compared to a refraction effect (albeit one independent of wavelength): the point is that here the effect of the plasma field in the direction of propagation of the wave always has the same sign, that is the stretching of the wave (and thus the redshift) is additive (i.e. it is a scalar effect) and will, despite the random nature of the field, result in a very sharply defined redshift.
On the other hand, the transverse deviation of the direction of propagation caused by the plasma field has vector properties and thus a random walk character given the isotropy of the medium. So there will be some blurring due to this circumstance, but this should be very small and negligible: first of all, if one assumes the intergalactic plasma field to have a scale of about 1m (corresponding to a plasma density of 1m-3) then, over a distance of 1010 lightyears = 1026m, one has 1026 additive redshifts. Now this leads to a redshift of the order of z=1, i.e. in the space of 1m the redshift change is about dz/ds=10-26/m. Assuming that the direction of propagation is changed by the same amount (compared to 360 deg) within 1m, this results over the total distance of 1010 lightyears in a statistical angle of deviation (i.e. a blurring) of Δα=10-26.√1026 .360 deg = 4.10-11 deg, which is negligibly small (for comparison, the angular width of our own galaxy from a distance of 1010 light years would be about 6.10-4 deg , i.e. about 7 orders of magnitude larger; it would take a distance of 7.1014 lightyears until the blurring would become comparable to the apparent size of the galaxy (which would then only be about 10-8 deg; of course, this would be not observable anymore as it is beyond the 'horizon' at about z=104 caused by the spatial scale of the intergalactic plasma field (see the page Plasma Theory of Hubble Redshift of Galaxies at at my site plasmaphysics.org.uk).
Furthermore, as indicated on my page regarding Galactic Redshifts and Supernova Lightcurves, the apparent delay in the light curves of supernovae could also be explained by this effect.

Regarding quasars: it is possible that the redshift is caused by their atmosphere, but again this cannot be due to the Compton effect (for similar reasons as above). In my opinion it could be caused by a strong electric field surrounding the object (e.g. a plasma polarization field associated with strong plasma density gradients). I am not sure however if the very strong electric fields required could be produced in this way, so may be the redshift of quasars is indeed due to the same mechanism as for normal galaxies, and that thus their intensity is really so enormous.

Comment by Stefan
I am glad to have stumbled on your page, because it shatters the illusion that every theoretical physicist knows exactly what they are talking about. In fact, there are many issues that I have with mainstream physics, and I would like to discuss a few of them with you, in hopes of getting a professional and adequate answer.

First of all, I'd like to ask about black holes. I was surprised that I did not see it mentioned any times on your physicsmyths.org.uk page. As far as I see it, they are nothing more than a mathematical over-extension of general relativity. While effects of the so-called black holes have been observed, no direct evidence has confirmed their existence. Not only have they been mathematically contrived, but hawking himself dropped his claim that no information can escape from a black hole, an idea which is purely theoretical and lacks any truth other than in the minds of physicists.

Cutting to the chase, my question is this. What direct evidence has confirmed the existence of black holes, such that the definition can be accepted for truth? To be perfectly clear, I am not doubting the presence of "something", because "something" is clearly causing a huge gravitational pull at the center of galaxies. What is in question is how the assumption can be made that an object whose presence depends on mathematics alone to exist could possibly be proposed as galactic nuclei.

The effects observed such as radiation emissions, gravitational lensing, and accretion disks are in no way direct conclusive proof of the existence of a black hole.

Reply
I do largely agree with your remarks, but so would actually in this case also quite a few 'mainstream scientists' (at least as far as the evidence for black holes is concerned). First of all, the presence of a large central mass in the centre of galaxies (or at least in our own) is obviously unquestionable as proven by the observations of stars very close to the galactic center. However, although there is no direct visible evidence of such a large central mass, this does of course not prove the existence of 'black holes' in the proposed theoretical sense that it is an object with an 'event horizon' (i.e. from which no information can escape). There have been claims based on the observations of other objects (X-ray binaries) that the 'event horizon' would have been 'detected' given the unexpected dimness of the observed radiation (see this NASA article) but this claim is very much contested by other scientists (see for instance this reference) who indeed claim that a direct proof of the 'event horizon' by means of observation in the electromagnetic spectrum is fundamentally impossible.
I can actually suggest my own theoretical explanation of the dimness of the radiation from these massive objects here: in gravitational equilibrium, their gravitational energy and thus their temperature increases proportionally to the mass and inversely proportional to the radius (see the page regarding Coronal Heating on my site plasmaphysics.org.uk); so one would expect extremely high temperatures for these objects (a supermassive object of 1 million solar masses and with solar density would have a temperature of about 1011K, corresponding to particle energies of 107eV), and the point is that the collision cross sections of all radiative processes decrease very strongly with energy E (between E-2-E-3; see for instance my page regarding the Radiative Recombination Cross Section), which simply means that such a hot object becomes virtually invisible as it only emits a very small amount of radiation at very high frequencies (in the gamma ray region). This could explain the absence of any observed radiation from such massive objects without involving black holes at all.
Regarding the alleged effect of masses on light in the form of 'gravitational lensing', you may want to have a look at my page Plasma Theory of 'Gravitational Lensing' of Light which suggests that this is also a plasma effect rather than directly related to gravity.

Comment by Chris Bennett
I was interested in your "Flawed Concept" summary of the Big Bang Theory which is based on the observed red-shift being due to the Doppler Effect. You based your objections on various scientific principles being violated. But there are some rather amusing consequences that arise by assuming that the Big Bang which occurred about 13.7 billion years ago is correct.
Due to the finite velocity of light, observation of distant light sources must be of past events, and the most distant galaxies were formed at a time only just after the Origin. Yet these galaxies occur in all directions near our horizon. If these distant galaxies were all near the Origin, an increased density of matter and light would have been expected. But this high density has been dissipated into the whole universe by expansion, and our own galaxy would have been there originally. So light is just reaching this Earth from galaxies that were near us about 13 billion years ago, though we have been travelling (at less than the velocity of light) to our present position during the whole of that period. Further, consider what could be observed from any planet in each of the distant galaxies in all directions on our horizon. Each could observe the Milky Way near their horizon as a primitive galaxy, and would wonder how it had formed so quickly after the Big Bang. Their combined conclusions would be that the Origin of the Big Bang occurred very close to the position of the Milky Way.

The logical conclusion to all these obvious paradoxes is that the theory that the universe originated from a Big Bang event at a point is untenable and should be abandoned. This dispenses with Inflation and Dark Energy, and leaves the way open for an entirely new theory which does not depend on the red-shift being caused by the Doppler Effect.

Reply
The point is that at the moment when the light of the other galaxy was emitted, we would have been much closer to it than we are now if we would have been receding from it since then. So if we had just a distance of 0.7 billion years at that time, then, in view of the constancy of the speed of light (the travel time of the light signal should be independent of the recession velocity of the light source), we should thus have observed the corresponding redshift already 0.7 billion years later i.e. 12.3 billion years ago, but not now. So if the universe was expanding, we would not be able to look back so far into the past in the first place.

If all the galaxies had been created at about the same time, one should also generally see galaxies with high redshift in a state very different from nearby galaxies. However, there is no conclusive observational evidence for this. The universe at high redshift looks pretty much the same as that at low redshift (apart from the fact that it has a larger redshift (and maybe some biases associated with this)).

For an alternative redshift theory see my page Plasma Theory of Hubble Redshift of Galaxies on my other site plasmaphysics.org.uk.

Question by Jay
If you must insist that dark matter is a myth can you please address the contradiction to your theory that this observation provides?

Reply
First of all, with my page regarding Dark matter, I am primarily referring to the conclusions drawn in this respect from galactic rotation curves. And I quote from the Wikipedia entry for the 'Bullet Cluster' (which displays essentially the same phenomenon you addressed) : Despite its importance, the Bullet Cluster provides no insight into the galaxy rotation curve problem. Dark matter has not yet been observed on galactic scales, where (if dark matter exists) the high frequency of collisions should produce phenomena similar to the Bullet Cluster. No such phenomena have been observed. Moreover, critics of dark matter have cautioned that astronomers expect sizable quantities of non-luminous baryonic matter to reside in large galactic clusters, so the Bullet Cluster phenomenon can be explained without appealing to exotic dark matter. Until dark matter is observed in more mundane circumstances, it cannot be assumed to be ubiquitous.
Secondly, I have also addressed on my page the point that the mass-luminosity relationship (from which the 'normal' mass is usually derived), can be quite inaccurate, especially for low mass (i.e. low luminosity) stars. So it is just possible that the mass is simply being underestimated in these cases.

Question by Tom Conner
I have no scientific or mathematical background, as I'm sure you will realize when I ask my question. Rather I am just trying to wrap my head around some of what I understand to be 'established truths' about the universe.

So, the further away we look, the further back in time we are seeing, right? Everything is said to be rushing away from us (the universe expanding in all directions). I have also heard it said that the further away the objects, the faster they are observed to be moving (greater red-shift), which has been used as evidence that the rate of expansion is increasing (hence bringing things like dark energy into the conversation to explain how this is possible).

But if the above observations are true, doesn't it suggest the opposite: that the most distant objects (the oldest (i.e., closer in time to the beginning) moving fastest means that things are actually slowing down over time? What am I missing?

Reply
What you are describing above are not the observations. The observations merely show that the redshift of galaxies is proportional to the distance (Hubble law). It is then only assumed that the redshift is related to a corresponding velocity. But this assumption is not only completely unsubstantiated but can be shown to contradict fundamental physical concepts, i.e. this interpretation must be incorrect (see my page The Expansion of the Universe Debunked).

Question by Tom Jelinek
Assumptions: The velocity of an object relative to another object cannot exceed, or even meet, the speed of light. It is necessary to compare objects because velocity does not exist in relation to a void, where dimensions do not exist.
Question: Is there a limit to the size and separation of two objects under which this constraint holds? If there is, then what is the physics behind that? If there is no limit, then it means that a sub-atomic particle at one end of the increasingly expanding universe is limited in its acceleration by the farthest sub-atomic particle at the other end of the universe, accelerating in the opposite direction. Is this factored into calculations of the expansion of the universe?

Reply
Yes, in the Big-Bang theory the speed of light limitation is factored in (the usual linear distance/velocity relationship is assumed to hold only for small distances), but the point is that a) such a limitation does in fact not exist (not as far as I am concerned anyway, see my page regarding the Speed of Light and Relativity), and b), the universe is in fact not expanding (see my page The Expansion of the Universe Debunked).

Question by Bruce Harvey
With regard to your theory of red shift of light from distant galaxies: how does plasma exist in deep space without the charged particles combining to form uncharged particles such as hydrogen atoms?

Reply
The answer is that there are always sources of ionization in a gas (e.g. radiation or auto-ionization). In equilibrium, the ionization rate must be equal to the recombination rate, and this determines a steady-state plasma density (the plasma would only fully recombine to a neutral gas if there are no ionization sources anymore).

Comment by John Hardy
In regards to the initial formation of space-time and the Big Bang, I found it most interesting to proceed from Hawking's idea of "a quantum fluctuation with literally no pre-existing state".
My surmise is that, the key to the creation of the universe was the evolution of the Second Law of Thermodynamics (i.e. entropy) as a result of that quantum fluctuation. In short, perhaps the introduction of the arrow of time (i.e.entropy) from a quantum fluctuation (of some sort) was the catalyst for the Big Bang and our otherwise highly improbable existence.
In the very beginning, therefore, in our (this) nascent universe, a complex of events led to the second law of thermodynamics/entropy and off-shoot - the arrow of time within those very narrow confines. The instantaneous appearance (evolution) of the arrow of time gave rise to a 'new reality' and in that system, the entropic process itself provided the new system with enormous amounts of potential energy which would then evolve in concert with quantum gravity to a 'Big Bang' (with or without inflation).

Reply
There are several issues with your suggestion:

First of all, the Big-Bang theory is a flawed concept based on the erroneous interpretation of the galactic redshifts as being due to recessional velocities (see my Cosmology Page and links from there for more).

Secondly, entropy is not a fundamental physical law, but only a law of macroscopic physics that depends on certain initial conditions. Even in macroscopic physics, there are situations where for brief periods of time the law of entropy would appear to be violated in certain respects or would not be applicable at all (see my page regarding the Collisional Relaxation of Gases). So in this sense, it would be logically wrong to say that entropy (i.e. a concept from macroscopic physics) could have some underlying relevance in microscopic physics.

The fact that processes in macroscopic are largely irreversible have nothing to do with the arrow of time. It is merely a practical consequence of the complexity of the system. Time goes forward in any case (see my reply to the first discussion entry on this page). Even 'reversible' processes are reversible only in forward time (so strictly speaking nothing is reversible as you can't reverse time), but this has nothing to do with entropy (nor even with physics) but with the framework of our existence as such.

Comment by Gerry Francisco
First of all, fantastic site. Well done. Bravo.

I was thinking about spiral galaxies lately. Some quick mental math suggested that there is no need for dark matter at all. To be sure, I got out calculator, paper, and pen, and went to work:

Diameter of Milky Way: 100,000 L.Y.
Radius of Sun's Orbit: 25,000 L.Y.
Sun's Orbital Period: 250,000,000 Y.
Mass of Milky Way: 100,000,000,000 Solar Masses.

The dark matter people say that one star in the Galaxy has pretty much the same orbital speed as any another, regardless of distance from the center of the Galaxy. Therefore, a star at the edge of the Galaxy should have the same orbital speed as the Sun.
Since the orbital radius of said star is twice that of the Sun, it should take the edge star twice as long to travel the circumference of the Galaxy, since its speed is the same. Using Newton's form of Kepler's 3rd Law (M = A^3/P^2), and knowing that only the mass within the confines of an orbit is effective, it should be possible to calculate the size of the Galaxy. Then, we could see if the resulting diameter is anywhere close to that of the real Galaxy. If it is, then that would suggest that the mass of the stars in the Galaxy alone is sufficient to control the motion of them all. When I do the calculation, I get a diameter of 93,000 L.Y., which seems pretty close to the accepted value. Being such a gigantic structure that extends through both time and space, the diameter of the Galaxy could easily be off by 10%, which makes the fit even better.

My question is why we need dark matter at all? If the stars in a spiral galaxy are distributed uniformly throughout the disk, as I have assumed for the sake of simplicity, then stars at greater and greater radii would be able to "call on" more and more mass, thus keeping orbital speed constant, despite the increasing distance from the center. Putting "dark matter" in a huge halo surrounding the Galaxy isn't necessary and doesn't make sense anyway, since that dark material is outside the orbital radius of any star, and is therefore ineffective at influencing any aspect of orbital motion. The globular, lenticular, and elliptical galaxies could be handled in the same way, the only difference being that now the stellar orbits are no longer confined to a plane.

I could be misunderstanding something, yes, but the above ideas would explain why dark matter hasn't been detected yet (it doesn't exist).

Really, the problem could be that, in the Solar System, objects orbit the exteriors of other objects. We really don't have much direct experience with systems, such as galaxies, where objects orbit the center of mass within the exterior surface of another. I have heard that gigantic stars, such as Betelgeuse and Antares, may have companion stars that do this very thing, so this situation, which is so foreign to us in the Solar System, may not be that rare in the Universe at large.

Reply
Thank you for your comment.

The crucial factor for the traditional calculation of galactic rotation curve is the density distribution of the matter. In general, the rotation velocity v at radial distance r is given by v=sqrt(G*M/r) where G is the gravitational constant and M the total mass inside r (this can easily be shown by equating the centrifugal force with the gravitational force). This means that for M=const. (i.e. outside the primary mass) the velocity decreases ~ 1/sqrt(r), which is Kepler's law. On the other hand, if M increases ~r, then v=const. Since the latter is what is (by and large) observed in the outer regions of galaxies, it is therefore concluded that M~r. However, as this does not coincide with the numbers of stars seen in this region, it is speculated that there must be dark matter. It is important to note though that the velocity v is not the velocity of stars at all here, but the velocity of gas clouds (simply because in those outer regions there are practically no stars; see this link for more). Even though, if gravity would be the only force, then the argument would hold for gas clouds as well as stars, so "dark matter" would be the conclusion, but as I have pointed out on my page regarding galactic rotation curves, gas can be crucially effected by magnetic fields (during periods where it is ionized) in a way that would result in a constant rotation velocity without any dark matter.

Comment by Sebastian Sundvik
I have no problem with the notion that the dimensions of space are infinite, and so the notion of the universe (understood as encompassing all space) 'expanding' is nonsensical.
I have no problem with the notion that the dimensions of time are infinite, and so the notion of time 'beginning' with the Big Bang is nonsensical.
However, I do have a problem with your apparent claim that the mass conservation law (which debunks the 'expansion of the universe') shows that the Big Bang Theory is a flawed concept.
As Todd Kelso said in his first comment, 'as long as matter is not created or destroyed, pieces of matter are free to move away from each other.' You responded with an explanation of the mass conservation law, and concluded that 'it is therefore logically impossible that the matter density decreases simultaneously everywhere in the universe'.
However, this response is not satisfactory. It is logically possible for there to be an overall recession of galaxies without there being a corresponding decrease in matter density. This is provided that we assume that the dimensions of space are indeed infinite. Herein, there is no violation of the mass conservation law.

Reply
I appreciate your comment, but I wonder whether you fully read my page regarding the concept of an expanding universe. As explained there, if the number of galaxies in each volume cell (as defined physically by some lattice grid) decreases, the mass conservation would be violated (whether you have a finite or an infinite grid).

Sebastian Sundvik (2)
Apologies if I have misunderstood your explanation on http://www.physicsmyths.org.uk/expansion.htm.
However, could you clarify how a general recession of galaxies violates the mass conservation law if you have an infinite grid?
So long as you have an infinite grid, it would seem that a general recession of galaxies means that when the number of galaxies decreases in any one volume cell, it correspondingly increases in another (so, case B rather than case C, meaning no violation of mass conservation).

Reply (2)
A general recession of galaxies implies that the number of galaxies decreases in all cells of the lattice grid that lines out your universe (be it a finite one or an infinite one), so mass conservation is violated as constantly mass disappears from your universe.

Sebastian Sundvik (3)
Thanks for the response once more, however I'm still perplexed by your logic. Consider this scenario:
You and I are standing next to one another in a hall. Next, we start walking away from one another in opposing directions. If this hall has infinite length, there is no limit to the distance we can walk away from one another. As time goes by, we will be further and further away from one another...
Do you agree that the above scenario is physically possible? Do you agree that there is no violation of mass conservation? Do you agree that you and I do not need to keep getting larger and larger (in terms of mass) as we move away from one another?

Reply (3)
Of course mass is conserved in your example, but here the mass density does not decrease in all cells: when you leave one cell, the mass density decrease there, but it increases in the neighbouring cell that you enter. The assumption of a homogeneous expanding universe however implies that the mass density decreases in all cells, which would thus violate mass conservation. This is a trivial logical consequence.

Sebastian Sundvik (4)
Of course the assumption of a homogeneous expanding universe implies that the mass density decreases in all cells. However, my assumption was always that of an infinite universe, rather than an expanding one. With this in mind, there is a clear parallel between my example of the two of us moving away from one another in a (infinite) hall, and the example of multiple galaxies moving away from one another in the (infinite) universe. Mass is conserved in both examples, precisely for the reasoning you have given: when you leave one cell, the mass density decrease there, but it increases in the neighbouring cell that you enter.
The point of all this, then, was to explain how an expanding universe is not synonymous with a general recession of galaxies, contrary to the impression given on http://www.physicsmyths.org.uk/expansion.htm. While you can use basic (or even 'trivial', as you say) logic to debunk an expanding universe, you cannot use it to debunk a general recession of galaxies (within an infinite universe). In the case of the latter, we have to resort to the evidence obtained via observation, which of course you go into here http://www.physicsmyths.org.uk/cosmology.htm.

Reply (4)
Note again that when you are saying "when you leave one cell, the mass density decrease there, but it increases in the neighbouring cell that you enter" this logically contradicts the assumption of a homogeneous universe: at no point in time (whether you assume a finite or infinite universe) can the mass density increase in one cell when it decreases in others, because in that case the universe would not be homogeneous anymore.
Note anyway that there can not be a difference between the finite and infinite case:   mathematically 'infinite' means nothing more than 'for arbitrary large finite numbers', so if I show that something is true for an arbitrary finite size, then, by definition, it is also true for an infinite size.

Sebastian Sundvik (5)
The non-mathematical definition of infinite is 'unlimited in size or extent'. It is the antonym of finite. It does not make sense to use the mathematical definition of infinite ('arbitrary large finite') when referring to the universe. Doing so necessarily implies that the universe has a 'cosmic edge', which implies that there exists something that is not contained within the universe. This is logically inconsistent since, by definition, the universe must contain everything.
It is logically impossible for something that is infinite ('unlimited in size or extent') to be 'expanding'. Hence the 'expansion of the universe' is debunked. However, a 'general recession of galaxies' is not debunked.

Reply (5)
You can in practice never prove that something is 'unlimited in extent', so this definition does not work. The only thing you can do is to prove that it extends to a certain finite size. And only if you can do this for any finite size, does this mean the extent is 'infinite'. This is the only possible definition.
But as I said above already, it does not make a difference whether you have a finite or an infinite (in the above sense) lattice grid: if there is a general recession of galaxies, this implies that the number of galaxies in each cell gets smaller. So if, let's say, each cell of your infinite grid contains originally 100 galaxies, and then after a while, due to the general recession of galaxies, only 50, mass conservation is violated, as 50 galaxies in each cell have simply disappeared. You could only have mass conservation, if in some cells the number of galaxies decreases but in others increases. But this would be inconsistent with a general recession of galaxies. So a general recession of galaxies is a priori impossible, whether you have a finite or an infinite lattice grid.

Sebastian Sundvik (6)
You cannot prove that the universe is 'unlimited in extent' a posteriori, but you can prove that the universe is 'unlimited in extent' a priori.
If you have a posteriori proven that the universe 'extends to a certain finite size', you have not a posteriori proven that it does not, in fact, extend beyond this certain finite size. In fact, we know a priori that it does extend beyond this certain finite size; it is logically impossible for there to be something 'outside' the universe (as the universe must, by definition, contain everything).
Similarly, you cannot prove that the set of integers is 'unlimited in extent' a posteriori, but you can prove that the set of integers is 'unlimited in extent' a priori.
If you have a posteriori proven that the set of integers 'extends to a certain integer' (e.g. by counting), you have not a posteriori proven that the set of integers does not, in fact, extend beyond this integer. In fact, we know a priori that the set of integers do extend beyond this certain integer; it is logically impossible for there to be an integer 'outside' the set of integers (as the set of integers must, by definition, contain all integers).

You can (dis)prove a general recession of galaxies a posteriori, but you cannot (dis)prove a general recession of galaxies a priori.
The mass conservation law states that the total amount of mass must be conserved. If you believe that the universe is 'unlimited in extent', then you accept that mass is conserved with a general recession of galaxies, and also that mass density (across all of the universe) is conserved. If you believe that the universe 'extends to a certain finite size', then you accept that mass is conserved with a general recession of galaxies on the condition that the universe itself has 'extended beyond its prior certain finite size', and that mass density (across all of the universe) falls.
To reiterate, if the size of a container of mass increases, ceteris paribus, the total amount of mass remains constant, while the total mass density falls. Imagine a balloon with grains of sand inside it. As it inflates, the total mass of the grains of sand remains constant, while the total mass density of sand inside the balloon falls. The key point is that the physical law is 'mass conservation', not 'mass density conservation'.

Reply (6)
When you are saying 'infinite' means 'unlimited in extent' then this in fact the same as 'extending beyond any finite size'. It is just a matter of phrasing it. And in both cases, I agree, the concept of a 'universe' as such requires that it is infinite. But your balloon example does not represent an infinite universe. The balloon has a finite size, and the density of the matter inside only decreases as it expands into empty space. An infinite universe can not expand however, only a finite sized object can. So an infinite universe must have constant density if mass conservation should hold.
So as a) the universe must necessarily be infinite, and b) the density must be constant with time, it follows (a priori) that there is no general recession of galaxies, so the observed redshift must be due to other processes. And the only conceivable one, as far as I am concerned, is the Intergalactic Plasma Redshift Mechanism suggested by me.

Sebastian Sundvik (7)
The balloon by itself does not represent an infinite universe, true. Instead, the balloon is a finite sized object expanding within an infinite universe. So while the mass density inside the balloon falls as it expands, the mass density across the universe as a whole remains constant.
So while we appear to agree on premises a) and b), I remain unconvinced that these premises necessarily lead to the (a priori) conclusion that there can be no general recession of galaxies.

Reply (7)
If you assume that the universe consists of a finite expanding volume of matter in an otherwise empty and infinite space, then of course you would have a recession of galaxies without violating mass conservation (as the finite volume is always increasing). But this is not the 'standard' model for an expanding universe, which assumes that the matter density is different from zero everywhere in the infinite space (so the volume of matter is infinite to start with). And in this case it is not possible that the matter density decreases everywhere without violating mass conservation.

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