Comment by N.
Your concerns with Hubble expansion affecting the size of galaxies, indeed
atoms themselves, are very misinformed. This is because the Hubble
parameter has an extremely small value. Whilst it's current value is around
75km/s per Mpc, in SI units this is only of the order of 10-18
metres per second, per metre. So that even *if* we assume a perfectly
homogeneous expansion, an object at a one metre distance will be receding
at the rate of around one atomic diameter *per year!*.
Now, let's see how fast one side of an *atom* is receding w.r.t the other
size - in other words how quickly it is expanding. Taking the diameter as
m, we have the astonishingly slow rate of 10-28
m/s. In 1 billion years this atom will expand by about 10-12
In other words by 1% of its original diameter in one billion years. How on
earth could this possibly produce any observable effects!
(And don't forget that all our measuring instruments, by your reasoning,
will similarly expand at a this unimaginably slow speed anyway!)
Check your facts - I recommend a few simple sums - they come in useful from
time to time!
Suggestion by Juan Casado
Unfortunately, your above calculation is wildly inaccurate. If you redo it without rounding everything to full decades, you will find that an atom would expand by about 10-11
m in 109
Anyway, it is easy to show generally that all objects would expand by the same fraction in a given time:
the Hubble expansion is given by v=Δx/Δt=H*x, i.e Δx/x=H*Δt. Since the latter ratio is independent of x, this means that all objects expand by the same fraction H*Δt within the time Δt. From rewriting the Hubble constant as H=0.8/(1010
years), you see that in fact all objects would roughly double their size in 1010
years, in agreement with the corrected calculation for the expansion of an atom in 109
years (which is an increase of 10% ). Looking 1010
years into the past would mean therefore that all objects should appear at about half its size and the emission frequency of atoms should increase correspondingly, but on the other hand the lines would be red-shifted by the same amount (you can check this by inserting a distance of x=1010
lightyears into the Hubble law, which yields a recession velocity v of the order of the velocity of light c and therefore a fractional redshift v/c=1 (non-relativistically)), i.e. overall one should not observe any frequency shift at all.
Apparently, cosmologists are assigning a different quality to the space between galaxies, the space between stars and the space between the electrons and the nucleus in an atom. What's more, corresponding surveys have even failed to detect any significant difference between the density of galaxies at high redshift and that in our local surrounding, i.e. there is no indication of a geometrical recession of galaxies whatsoever; nevertheless, cosmologists still cling on to their Big-Bang idea.
As indicated in the Cosmology
entry on my main page (and in my discussion with Todd Kelso on page 1
), the concept of an overall recession of galaxies is logically inconsistent and therefore flawed and the observed redshift has to be explained by other means (after all, it would be rather arrogant to assume that present physics can explain everything, and no further, so far unknown, physical processes exist in the universe; one just has to think a little bit harder than cosmologists do to figure out the actual cause of the galactic redshift).
An alternative cosmological model is summarized: light speed, c, slowly decreases as the cosmic time, t, increases and matches the expansion speed of the Universe itself, since c is the maximum speed at which any two particles can run away, i.e. the top escape velocity. This Universe has a radius, R, predicted by Schwarzschild equation at any time, which second derivative vs. t follows the simple equation:
(1) R'' = -GM/R2
where G is the gravitational constant, M is the mass of the observable Universe.
Combining Schwarzschild equation with (1) and integrating we can obtain:
(2) R =3ct/2
With this self-consistent set of equations, it can be deduced that the Hubble parameter is:
(3) H =2/3t
And, since the radiation temperature T is a measure of photon's energy, which is proportional to c2, we can obtain:
where subscript o indicate today's values. Equations 3 and 4 agree with Einstein-De Sitter model.
In our model, the redshift of distant galaxies has a gravitational contribution reflected in the decrease of light energy, E, since photons suffer the pull of the Universal mass as they travel from the past, more dense, Universe to the present state, in the same way other particles do.
(5) zG = (E-Eo)/Eo = (c2 – co2 )/ 2co2 = Ro-R/2R
As we can see this contribution has one half of the value of the nowadays-accepted expression for z, so that the total redshift would be the sum of both:
(6) z = (Ro/R)-1 + Ro-R/2R = 3r/2(Ro-r)
where r (=Ro-R) is the distance to the observed galaxy. From this equation and direct observational data good lineal fits are obtained, then Ro and M (assumed to be constant) can be estimated, and the time evolution of c, R, T and mass density can be predicted. Some preliminary results are:
Ro (m) = 2,0 * 1026
to (years) = 1,4 * 1010
(dc/dt)o (m/s2) = -2,2* 10-10 (a decay of 1 m/s would be observed in ca.140 years).
Today's mass density would be 4*10-27 kg/m3 , about 40% of ‘conventional' critical density. At any time the actual density should be equal to the critical density, i.e., the agreement of the critical density in the Einstein-De Sitter universe with the empirical determinations is not casual. The metric of this Universe is flat and the expansion would continue forever since its rate has exactly the value needed to equilibrate the gravitational pull at any moment. The entire Universe must be causally interconnected so that its maximum expansion rate must be c, since c is also the rate of gravity interactions. This was a problem in the frame of inflation theory, which assumes that, during an early period, the Universe was expanding faster than light. Now this inflation reveals to be not superluminical, although faster than today's speed of light. Finally the model predicts, without need of introducing an ad-hoc repulsive dark energy, that supernovae with z near 1 are farther away than previously expected, so that they will appear fainter, as recently observed. Within this model an object showing z=1 is at a distance of 8 * 1025 m; while in conventional models it would be at 6,7 * 1025 m. This difference would lead to about 30% less apparent luminosity.
Question by Ian
Unfortunately, your derivation, like the standard cosmological model, is already flawed by formulating Eq.(1) (I reduced therefore the font size for the rest of the text):
Even if you assume space to be curved (see however the corresponding entry on the main page
), the gravitational force on any object has to be zero for an isotropic and homogeneous universe, because equal and opposite forces cancel (if you compare the universe with the surface of a sphere, then gravitation acts on this surface and, if the latter is homogeneous, cancels to zero). In fact, as already indicated on the main page under Cosmology
, the concept of an expanding universe is a naive (and in fact conceptually inconsistent) interpretation of the Hubble- redshift of galaxies.
Your modification of the standard model is consequently not more than a cosmetic correction to a fundamentally flawed theory (whether a time-dependent value of the speed of light would be acceptable, is therefore merely of academic interest).
Juan Casado (2)
The gravitational force in an isotropic, finite and non homogeneous universe (as the above model assumes it is) should not be 0, since every mass attracts each other and is feeling the attraction of the rest of the Universe as it was in the past, since gravity propagation rate is not infinite but c. In other words if you consider a huge number of galaxies in a finite space and starting at rest, they will approach each other due to gravitation. The scientific community believes that they are not approaching each other because of Big Bang expansion.
In recent interpretations, cosmological redshift is not believed to be a Doppler effect anymore but a result of the expansión factor Ro/R, which does not presume any recession velocity, nor Hubble parameter and allows my model to be right.
Where can I find the equations describing your alternative cosmology? How does it fit with observational data?
It is you who has not justified the basic equation of the standard cosmological model (Eq.(1) above) and, as already indicated, it is indeed invalid as the gravitational force on a mass in an isotropic and homogeneous universe is
0, whether or not gravitation propagates instantaneously or with the speed of light: if you have the same mass distribution in one direction in the sky as in the opposite direction, the resultant gravitational force is obviously zero, whether you assume a finite or an infinite universe. This is just a basic consequence of the linear superposition principle for force vectors (I don't know by the way why you are saying 'non-homogeneous' above: the cosmological principle clearly requires homogeneity (and with it isotropy)
Also, I find you argument that the redshift of galaxies is not related to a recession but due to the expansion of the universe rather strange: you can not have an expansion without a recession, and if galaxies are receding you should certainly observe a Doppler effect. Big-Bang cosmology has in fact only been invented because
the redshift was interpreted as a Doppler effect. The logical paradoxes associated with an expanding universe show however that the redshift must
be caused by a different mechanism. I have made a suggestion for this on my site http://www.plasmaphysics.org.uk/research/#A11
, but I have unfortunately not been able yet to develop this any further.
Of course, for a static and infinite universe there are some other things to explain (e.g. the abundance of elements or the background radiation), but this can certainly be done, if not within the framework of known physics, then by postulating new physical processes (as long as these are, in contrast the the Big-Bang theory, logically consistent).
Juan Casado (3)
You did not get me right. When I said non-homogeneous I was refering to a Universe that has not the same properties, for instance the density, the temperature of the quasar abundances, today than in the past. Since we are observing an Universe as it was in different moments of its life, we are observing a non-homogeneous Universe, at least in time coordinates. If you take into account that the 3 apparent dimensions we observe are not single space dimensions, but have a time component, it is easier to understand how gravitation works opposite to the expansion of the Universe from an earlier more dense state to a later and less dense one. Taking the basic example of the balloon that increases in size, gravity (always coming from the past) slows down the expansion (in a similar way that tension of the balloon material does) even if for any 2-dimensional observer in the surface the situation all around him is isotropic. Only the 'perfect cosmological principle', postulated by Hoyle for his Steady State cosmology would be isotropic and homogeneous in any cosmic time.
On the other hand I pointed out that redshift is not related to any specific 'velocity' of recession, although obviously the galaxies are receding. However, within my model, they actually recede more slowly than it is thought when one interprets the redshift as a simple Doppler effect. I simply introduced a gravitational contribution due to the slowing down of photons (while trying to overcome the gravitational field of the Universe) and got a series of results that are in good agreement with observations, by means of equations much simpler than those in standard model. By the way Eq.(1) was already justified by Newton.
You know that a theory has to be confronted to observations in order to test it. What are the predictions of your's?
From my above arguments it is clear that I was referring to spatial homogeneity and if this holds the resulting gravitational force is zero whether or not the density changes with time (the gravitational force depends on the distance and direction between two masses in the real world but not on some fictitious space-curvature R as suggested by your Eq.(1); the balloon example is inappropriate and misleading as it requires the presence of the (isotropic) air pressure force in addition to the tension force of the material; only the combination of the two forces results in the curvature of the balloon surface; you would therefore have to assume that in addition to gravitation there is a corresponding unexplained force associated with the curvature of the universe if your Eq.(1) should hold; also, your analogy would require that the balloon material is infinitely thin, which is impossible).
Anyway, you should check out my discussion with Todd Kelso on page 1
regarding the sense and non-sense of non-euclidean geometries and the use of everyday objects to justify cosmological models by means of analogy.
Only a valid (i.e. logically consistent) theory can be compared to observations; your theory (as well as the standard Big-Bang theory) is not valid as it suffers from the error in logic pointed out by me. You can not say 'I realize that my theory contains an error in logic, but I don't bother about it because the end result fits the data'. Sooner or later the flaw in the theory will lead to discrepancies with observations which then forces you either to abandon it or to make further far-fetched and inconsistent assumptions to rescue it (the latter was the reason why the Ptolemaic theory of the universe could survive for so long, and one can only hope that the equally pseudo-scientific Big-Bang theory will become a subject of merely historical interest within a shorter time period.)
Anyway, what observational data are you referring to ? Those that until a few years ago proved that the expansion of the universe is decelerating, or those that now allegedly prove that the expansion of the universe is accelerating ? Cosmological data are so uncertain that they can be used to confirm almost any theory, especially if you don't care about the logical consistency of the latter ! If observations do not appear to agree with the assumption of an infinite universe, then only because the underlying physical model is inconsistent or incomplete.
The so called 'Olbers' Paradox' could for instance be explained through any of the following:
a) the 'paradox' inconsistently assumes that there is a permanent emission of radiation but does not account for absorption. In a steady state universe, these two processes have to occur at an equal rate, and the total radiation density is therefore necessarily finite.
b) the redshift of light (which could be produced by the intergalactic plasma; see http://www.plasmaphysics.org.uk/research/#A11
) reduces the frequency to such low values that eventually it becomes undetectable.
c) the interaction with the plasma could also reduce the coherency of the radiation (i.e. the originally sinusoidal wavetrain could gradually be scrambled to a random signal), which would also reduce detectability.
Whatever the explanation is, it is certainly not a finite universe (which is a logically inconsistent concept).
If the theory of "big bang" is true and this universe started as a quantum singularity, what was the quantum singularity existing in? There must have been something before the big bang in order for the singularity to exist. Now, you could make reference to the fact that our universes today is expanding and someday it will reach its maximum size and start to implode on itself to become a singularity once again, but then this is contradicted by the fact that that would mean the universes must have a center, and if the universe's boundary is infinite from any one point it is impossible to have a center... no?
Comment by Roger Ellman
As you noticed by yourself, the Big-Bang theory is full of logical contradictions and can therefore not be true (I addressed other inconsistencies in the above discussion for instance and elsewhere on this site). The elements of this theory are only mathematical constructs that can not possibly be applied to physical reality in a consistent manner:
the concept of a curved space is inconsistent because 'space' is what is left if you take all physical objects in the universe away, i.e. space is Nothing, and Nothing can not have a shape, nor can it have a center, a spatial boundary or a temporal beginning or end (or expand for that matter). The idea of the universe having developed from a singularity is therefore logically flawed (mathematical singularities can not possibly exist in reality anyway as they would be associated with infinite densities for instance, which is physically not possible).
Concerning your position on red shifts and the Hubble law, "....This does of course completely invalidate the interpretation of the redshift as a Doppler effect", there is a lot of evidence for an alternative. See my paper http://arxiv.org/abs/physics/9906031
Question by Jerry Freedman
First of all, your paper still uses the flawed Big-Bang concept in order to define your hypothetical temporal decay of the constants of nature. It would be more acceptable if you relate the decay to the signal propagation time or the corresponding spatial distance. In the latter case your theory would indeed become very similar to Milgrom's MOND theory. The questionable point about either theory is that they modify existing laws of physics without any physical justification (the 1/r2
dependence of the gravitational force is - like the 1/r2
dependence of the brightness of a light source - solely a geometrical factor (reflecting the fact that a surface has 2 dimensions) and any deviation from this would need a concrete physical cause (for the case of the light source this could be an absorbing medium)).
Anyway, there is neither a new theory needed for the 'Anomalous Acceleration' of the Pioneer space probes nor for the shape of galactic rotation curves. Both of these are simply the result of omissions and errors in existing theories (in the first case it is a wrong definition for the speed of light (see my page regarding the Speed of Light
), in the second the neglection of the effect of galactic magnetic fields (see my Dark Matter
I would not bother too much about the other issue mentioned in your paper, i.e. the supernova lightcurves. The data for these have very large error bars (due to the faintness of objects with large redshifts) and do not prove anything conclusively (apart from the fact that cosmologists must be really desperate if they try to support their flawed concept of an expanding universe with such bad data). One should note here that, contrary to the claim of cosmologists, any wavelength independent redshift mechanism should indeed lead to a dependence of the shape of supernova lightcurves on the redshift (I have recently emailed a proof of this to the author of a webpage which stated that only an expanding universe would show this effect; since then the page has apparently been taken off the web).
I have myself suggested a redshift mechanism in a static universe (see http://www.plasmaphysics.org.uk/research/#A11
) and it is well possible that this effect becomes non-linear for certain light intensities, which could explain the disproportionate redshift at larger distances. But again, I would consider the present evidence for this as rather inconclusive and there is consequently no need to explain this theoretically. In any case, the explanation would not be associated with an expansion of the universe as the latter is logically impossible (according to my reckoning, an accelerated expansion should anyway lead to brighter and not dimmer objects at larger distances: if an object has an initial velocity v0
and acceleration a, the velocity increases with time by a factor (1+a/v0.
t) but the distance only by a factor (1+1/2.
I believe that thinking of the big bang material as being 'sucked' into a region of absolute zero (rather than 'exploding' into it) could help model the expansion of the universe more accurately. Is there any inherent reason why this could not be the way it was?
This is a rather 'academic' question as the idea of an expansion is a flawed concept (see my main Cosmology
page), which is based on the mistaken assumption that the redshift of galaxies is due to the Doppler effect. As indicated on my page regarding the 'cosmological' Redshift
, different physical mechanisms have to be responsible for this.
But anyway, even in the framework of the Big-Bang theory, I can't see it making a fundamental difference as the physics behind it would be in any way speculative and it would not solve the theoretical problems inherent with the Big-Bang theory.
Jerry Freedman (2)
Thanks very much. I did wonder on reading through the various sections of your site whether you are promoting a static universe idea, or refuting the modelling methods of an expanding one - and your reply tells me which.
My own reason for supporting an expanding universe model is almost purely philosphical - the whole concept fits very well with how we experience our existence both physically and intellectually on earth. Basically we are used to large complicated systems evolving from smaller simple ones and it seems illogical to reason that our own way of coming into existence (at any level) could be anything other than a reflection or fractal of the system or mechanism that made us.
I fully understand where your are coming from with your philosophy regarding the universe. When I was 15 years old or so, I found the idea of an expanding (may be even oscillating) universe quite attractive as well, but since then I have convinced myself that this is merely children's philosophy which is conceptually and logically flawed. The point is that the universe is not a physical object itself, but merely a collective name for all objects (whether factual or potential). Because of this, it can by definition not have any limits, neither spatially nor temporally. If it had limits (which obviously would be implied by the idea of an expanding universe), it could by definition not be called the universe as it would have to be contained in something else.
The idea that we should be a kind of mirror image of the system that made us is wholly religiously motivated and is in fact turning the situation completely on its head. In reality, you are actually projecting your own physical properties into something that is not a physical object itself but merely an abstract concept.
Again, such an approach has everything to do with religion but nothing with science and is as such not acceptable as a physical theory.
Jerry Freedman (3)
To reiterate, my main intention is not to support BB and an expanding universe as such; it's more concerned with presenting a way of modelling any of it's mechanisms that we observe directly or indirectly more simply.
You mentioned religion so I should say this: I have not believed in a single creative entity i.e. God in any form since being a young teenager Therefore I can assure you that any connection that's made to religious motivations on my part is not justified or true. If I were driven by religion I think I'd be arguing against more accurate modelling.
How is your belief that we live in a static universe a physical theory? Or, how do you know personally that the universe isn't expanding; and what are the forces that keep the universe in equilibrium?
I probably did not phrase my 'religious motives' argument correctly above. What I wanted to say is that the Big-Bang idea is born out of similar motives as religious ideas, i.e. in order to have some convenient ad-hoc explanation for certain facts or events disregarding the logical or scientific rationality of this idea. Of course, believing in the Big Bang theory does not imply believing in God but it can make a good substitute for some people.
Having said this, it may probably be of interest that Georges Lemaitres (the 'inventor' of the Big Bang theory) was himself an ordained catholic priest. Also, the previous pope publicly supported the Big-Bang idea as being acceptable to the Catholic faith, and the very fact that the pope would support a scientific theory is in my view almost a guarantee that it is scientifically flawed (not that this guarantee would be needed for me).
In this sense, the quest for simplicity that you mentioned may be a dangerous route to go, as it may go at the expense of the scientific accuracy and consistency. If you look at the history of models of our universe, then the Ptolemaic model could be described as being very simplistic originally, but all the complications that had to be introduced later in order to model observations made it eventually collapse under its own weight. A similar process is presently going on with the Big-Bang theory as more and more hypothetical concepts have to be added in order to make it consistent with observations. What makes the Big-Bang theory actually even less acceptable than the Ptolemaic model is the circumstance that the latter did actually not claim to be a strictly scientific theory whereas the Big-Bang theory masquerades as such.
I answered you question how I know that the universe is not expanding already above: if it would be expanding, it would have to be finite (otherwise the notion of 'expansion' could not be defined) and could thus by definition not be called 'universe' (as it would have to be part of something larger).
It does therefore not take any observational data to come to this conclusion, but it can be done on the grounds of the logical consistency of conceptual definitions alone.
Let me give a simple example to illustrate my point: how do you know that there are no cube-shaped spheres in the universe? The fact that you haven't seen any does not prove they don't exist. If you have a theory for their existence, you might want to put it forward and apply for a research grant to better model your theory (I reckon you might even get money for this). But seriously, of course you know that cube-shaped spheres don't exist because the notion itself is a contradiction in terms, and likewise is the notion of an expanding universe. In a static infinite universe there actually no overall forces (the gravitational force is zero because the amount of mass is identical in all directions) and so the problem of equilibrium does not arise.
Jerry Freedman (4)
The problem I have at the moment is that your ideas on the definition of the universe as a word seem to me to be just that: defining a word.
So far, I believe you have basically said that the universe cannot be expanding and therefore finite because that's what the dictionary says. That, if you don't mind me saying, is not very scientific.
In the model of a static infinite universe, where did all the material come from? How did it get there? How old is it? How can evolution be a mechanism of our solar system but not of the universe? The homogeneity and isotropy you write of which is needed to maintain equilibrium is on a large scale - how are local variations of density dealt with in a static universe?
It is the concept of an expanding universe which is unscientific as it is a logical paradox. This is therefore just a question of conceptual consistency and not of physical theories. Nobody questions the existence of the redshift of galaxies, but logical paradoxes like an expanding universe are not be acceptable as scientific explanations for this. As I have mentioned on my page regarding the Redshift of Galaxies
, there are other physical mechanism that could produce be responsible. This may be difficult to prove theoretically or experimentally, which should however not be an excuse to adopt ad-hoc theories that are logically flawed.
Obviously, the question where all the material in the universe comes from and how old it does not apply to a universe infinite in space and time. The matter was always there and will always be there. It is only on smaller scales that variations occur due to local and temporary imbalances of the various physical processes acting. On the average however, all physical processes are in equilibrium with each other and the universe looks thus basically the same everywhere and anytime (which is by the way also what observations confirm (in contradiction to the Big-Bang model)).