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We have previously seen that observations of distant galaxies using the James Webb Space Telescope (JWST) are contrary to the predictions of the big bang but match predictions of biblical creation.  Now, new observations of the angular sizes of distant galaxies challenge one of the essential underlying assumptions of the big bang – that the “fabric” of space is expanding as galaxies recede.  Without an expanding space, a big bang is impossible.  These observations support a new creation-based model of cosmology – the Doppler model – which makes specific quantitative predictions about future observations.

Introduction

In the early twentieth century, Albert Einstein discovered the equations that describe how matter “bends” the fabric of space, which causes the phenomenon we call gravity.  These equations allow us to predict how mass moves through space.  By making certain assumptions and approximations, physicists attempted to apply these equations to the entire universe.  In the 1920s, four physicists independently realized that Einstein’s equations imply that the entire universe could be expanding or contracting, like the surface of a balloon as it grows or shrinks in size.  The mathematical structure of space is called a metric.  And the particular metric that describes an expanding or collapsing universe (under the aforementioned assumptions and approximations) is named after these four physicists: the Friedmann-Lemaitre-Walker-Robertson metric (FLRW metric).

In 1929, astronomer Edwin Hubble published a new discovery he had made which we now call the Hubble law.  Hubble had been measuring the distances to galaxies along with their velocities by measuring the spectral shift of their light.  He found that almost all galaxies are moving away from us; their light had been shifted to longer wavelengths.  The shift of light to longer wavelengths we call redshift.  Amazingly, Hubble found that there was a relationship between a galaxy’s distance from us and its redshift.  The farther a galaxy is, the larger its redshift.  This is the Hubble law.  It basically means that farther galaxies are moving away from us faster than nearby galaxies.  Hubble interpreted the redshifts as being due to the Doppler effect.  The faster a galaxy is moving away from us, the more its light is stretched to longer wavelengths.

One of the physicists who had discovered the FLRW metric, Lemaitre, realized that the Hubble law could be explained if the fabric of space is expanding (just as the FLRW metric allows) rather than being caused by a Doppler shift.  Consider points on a balloon.  As the balloon expands, points that are nearby slowly move away from each other; but points that are already far away from each other move apart much faster.  If galaxies are like points on the surface of a balloon, then an expanding universe would naturally produce a Hubble law.  Most astronomers came to accept the expansion of space as the explanation for the Hubble law and as confirmation that the FLRW metric was correct.

In 1931, Lemaitre speculated that if the universe is expanding like a balloon, then perhaps that balloon started from a size of zero.  This was the first version of what would later be called the big bang.  The big bang assumes that space is expanding according to the FLRW metric and that it started from a size of zero.  Most creation astronomers have accepted the FLRW metric as the correct explanation for the Hubble law but reject the notion that the universe started from a size of zero.  An expanding space does not require or imply that space started with no size at all.  It just means that space was smaller in the past.  How much smaller depends on how old the universe is.

Expanding Space vs Doppler Effect

An expanding space according to the FLRW metric is a fundamentally different explanation for the Hubble law than Edwin Hubble’s original interpretation.  Hubble interpreted the redshifts of galaxies as being due to the Doppler effect as galaxies move through space.  We are all familiar with the Doppler effect in sound waves.  When a car is approaching us, its pitch is higher than when the car is moving away.  Light also does this, although the effect is harder to detect partly because light is so much faster than sound.  But when an object is moving through space away from us, the light waves are stretched to longer wavelengths, and we detect a redshift.

On the other hand, the same effect could be achieved by galaxies that are essentially stationary in a space that expands like a balloon.  Dots painted on a balloon do not move relative to the balloon’s surface.  But these dots will all move away from each other as the balloon expands.  If galaxies are more-or-less stationary in an expanding space, then they will move away from each other.  This also causes a redshift of their light because the light gets stretched to longer wavelengths as it travels through space that is being stretched.  Light from the most distant galaxies has been traveling longer through expanding space and is thus more redshifted than light from nearby galaxies.  So, the expanding space of the FLRW metric naturally results in a Hubble law.

These are two fundamentally different explanations for the Hubble law.  On the one hand, the galaxies could be basically stationary, but the expansion of space carries them away from each other over time.  This is the FLRW metric and can be thought of as dots painted on an expanding balloon.  Alternatively, the Hubble law could be due to the Doppler effect.  Galaxies move away from each other through non-expanding space such that the farthest ones move the fastest.  Let’s call this the Doppler model.  It can be thought of as pocket billiard balls after a break.  The farthest balls move away the fastest, but the table does not expand or contact.

Nearly all astronomers embrace the latter model because it naturally explains why the most distant galaxies should be the most redshifted.  However, the Doppler model could also explain this from a Christian theistic perspective.  Namely, God may have imparted the most velocity to the farthest galaxies for reasons of stability – it prevents the galaxies from all collapsing into a black hole.

Furthermore, big bang advocates must embrace the FLRW metric because the Doppler shift interpretation does not allow for a big bang.  The big bang requires that all space was contained in a singularity billions of years ago.  But in the Doppler model, space does not expand; thus, there never was such a singularity.  If galaxies are simply moving away from each other through space, then you might initially think that they all came from a common central explosion.  But this cannot be the case because galaxies have tangential (“sideways”) motion in addition to their recessional motion.  That is, running time backward, they would “miss” each other and would not converge to a common center.  Thus, big bang advocates must embrace the FLRW metric and cannot consider the Doppler model without abandoning their own origin story.

You might think that it would be impossible to observationally distinguish the Doppler model from the standard model that assumes the FLRW metric.  After all, both models can account for the redshifts of galaxies (although their explanations differ).  Both can make sense of the Hubble law even though the reasons for the Hubble law differ.  Observationally, the two models are nearly indistinguishable.  However, there are two observational effects that differ between the two models.  And recent data from the JWST now allow us to test which model is correct.

Angular Diameters

From everyday experience, we know that a distant object appears smaller in size than a nearby object whose actual size is the same.  The size of an object as it appears to the eye is called the angular size.  The moon, for example, as seen in Earth’s sky, has an angular diameter of ½ degree.  The sun also has an angular diameter of ½ degree, so it appears about as large as the moon in angle.  In reality, the sun is 400 times larger than the moon.  But since it is also 400 times farther away, its angular size is nearly identical to the moon.  This is what makes solar eclipses possible.  The angular diameter of an object is inversely proportional to its distance.  That is, if I double the distance to a given object, it will look ½ the angular size in each dimension.

This applies to galaxies as well.  Consider two galaxies of identical (actual) size.  If one galaxy is twice as far away as the other, it will appear half the angular diameter.  If space is non-expanding, then this effect works at all distances.  Galaxies will continue to look smaller and smaller as we look to increasing distances.

However, in an expanding FLRW universe, things are more complicated.  As light travels long distances in an expanding universe, this will affect the angular diameter we perceive for any distant object.  It will cause its angular diameter to be larger than it would be in a non-expanding space.  The expanding space of the FLRW metric acts a bit like a magnifying glass, causing distant galaxies to appear larger than they would otherwise.  I will not attempt to go through the mathematical details on why this happens.  These are given in the corresponding technical paper.  But it is a well-accepted and mathematically proven principle that expanding space causes distant objects to appear magnified.

The upper panel shows how galaxies appear smaller with distance in a non-expanding space. The lower panel shows that galaxies will appear larger after a certain distance in an expanding space.

This magnification effect is negligible for nearby galaxies.  They indeed look smaller and smaller as their distance increases.  But the effect becomes large for more distant galaxies.  At a distance corresponding to a redshift of 1.6, the magnification effect becomes stronger than the diminishing angular diameter due to geometry.  In other words, if we could move a galaxy to a distance where its redshift is 1.6, the galaxy would have the smallest angular diameter it could have.  Moving it even farther would cause the galaxy to look larger.  Thus, galaxies beyond a redshift of 1.6 should look larger with increasing distance, not smaller!  This result is counterintuitive, but it is a well-established principle in the FLRW metric.

Figure 1. The angular diameter of a 4.5 kpc galaxy at various redshifts according to three different models.

The red curve in Figure 1 shows the angular diameter of a typical (4.5 kpc) galaxy as it should appear at various redshifts according the FLRW metric.  For redshifts less than 1.6, the galaxy looks smaller as its distance increases, as our intuition expects.  But beyond a redshift of 1.6, the galaxy should look larger with increasing redshift.  Notice that the effect becomes quite strong at redshifts approaching 20.  Thus, the most distant galaxies seen in JWST observations should look quite large if the FLRW metric is correct.

However, this magnification effect can only exist in an expanding space.  If the Doppler model is the correct explanation for redshifts of galaxies, then no such effect will occur.  Galaxies will continue to look smaller with increasing distance even beyond a redshift of 1.6.  In fact, their angular diameter will continue to be inversely proportional to distance.  The angular diameter of a typical (4.5 kpc) galaxy at various redshifts according to the Doppler model is shown in the black curve in Figure 1.  The difference between the predictions of the Doppler model (black) and the standard model assuming the FLRW metric (red) become substantial at redshifts approaching 20.  Therefore, it should be possible to distinguish between these models by looking at the actual angular diameters of galaxies in the JWST deep field.  Galaxies come in a range of sizes.  But the average or median size should fall along the curve of the correct model.

For completeness, the predictions of the tired light model are shown in the green curve.  This model, proposed by Fritz Zwicky in 1929, assumes that galaxies are nearly stationary in a non-expanding universe, and that their light becomes redshifted due to energy loss over time by whatever mechanism.  The tired light model was not widely accepted.  It predicted a blurring of light in images of distant galaxies – a blurring which is not seen.

The Observations

With the James Webb Space Telescope, we can now detect and image galaxies at distances up to a redshift of 20 and beyond.  By measuring the angular sizes of these galaxies, we can see which model best matches the typical size of galaxies at any given redshift/distance.  Although galaxies come in a range of sizes, their median angular size should fall along the curve of the correct model.

Figure 2. The median angular diameter of galaxies at each redshift compared with three models.

In Figure 2, the median angular size of galaxies are plotted at various redshifts, as seen in the Hubble Space Telescope (HST) for low redshifts or JWST for high redshifts.  These are the black squares.  The vertical bars are the standard deviation, which is indicative of the range of galaxy angular diameters for that redshift.  But the squares are the median size – indicating a typical angular diameter for a galaxy at that redshift.  And these line up almost perfectly with the predicted angular diameter according to the Doppler model.  Furthermore, none of the data fit the standard model based on the FLRW metric.  In fact, none of them of are even within one standard deviation of the standard model.  This is extremely compelling evidence that the FLRW metric is wrong and the Doppler model is right.  Furthermore, since the big bang is predicated on the FLRW metric along with additional assumptions, it too is wrong.

What Figure 2 shows is that the magnification effect required by the FLRW expansion of space is simply not there.  Galaxies continue to look smaller with increasing distance, which is just how they should look if the fabric of space is not expanding.  Assuming the Doppler model is correct, then distant galaxies are very similar to nearby galaxies in terms of their actual size.  Thus, there is no evidence of substantial galaxy evolution that would be expected by big bang advocates.[1]

Galaxy Brightnesses

If space were expanding according to the FLRW metric, then this would also affect the perceived brightness of a distant galaxy.  For a stationary object in a non-expanding space, the apparent brightness diminishes with the square of the distance.  So, if you move a lightbulb twice as far away, it will appear one-fourth as bright.  This is called the inverse square law.  This approximation works very well for distances within our own galaxy.  However, if space is expanding, then the distance between particles of light in a beam constantly increases, which reduces the number of particles per unit time seen by the observer, making the source appear fainter.  Thus, distant galaxies will appear fainter in an expanding universe than what is predicted by the inverse square law.

On the other hand, if galaxies are moving through non-expanding space at high speed, this also affects their perceived brightness due to an effect called Lorentz beaming.  This effect is explained in the book The Physics of Einstein and is also covered in the corresponding technical paper.  Lorentz beaming also causes galaxies to look a bit fainter than they would if they were stationary according to the inverse square law.

So, both FLRW expansion of space and the Doppler model predict that galaxies will look fainter at a given distance than what the inverse square law predicts.  But the equations are different between the two models.  So, they predict a different amount of dimming.  Basically, according to the Doppler model, galaxies at a redshift of 13 should appear roughly 2.5 times fainter than they would if the FLRW metric were true.  Astronomers report brightness according to the magnitude system, where a magnitude of 1 represents a brightness ratio of about 2.5.  So, galaxies at redshift 13 should appear about 1 magnitude fainter according to the Doppler model than the standard (FLRW metric) model.

Figure 3.  The estimated brightness of distant galaxies.

Galaxies come in a variety of brightnesses.  But there is an effective upper limit on brightness.  So, presumably, the brightest galaxy seen at each redshift should be about the same true brightness as the brightest galaxy at other redshifts.  Therefore, if we plot the estimated true brightness of the brightest galaxy at each redshift in JWST images, then this should reveal which model is correct.  The FLRW metric predicts a flat line shown in red in Figure 3, whereas the Doppler model predicts a downward slope shown in black in Figure 3.  The actual brightnesses of the brightest galaxy in each redshift bin is indicated by the black squares.  The blue line is a best (least-squares) fit to the data.  It shows the downward trend predicted by the Doppler model.  This confirms that the apparent brightnesses at various redshifts best match the Doppler model and do not match the standard model.  This is further confirmation that the Doppler model is correct and the big bang is wrong.

Objections

How can a big bang advocate refute such powerful evidence?  He or she could challenge an assumption made in the above analysis.  The curves in Figure 2 show the apparent size of a typical 4.5 kpc diameter galaxy at various redshifts for three different models.  The assumption is that distant galaxies have the same range of sizes as nearby galaxies, and therefore that 4.5 kpc is the typical diameter of distant galaxies as well.  A big bang advocate could challenge that assumption.

In other words, the FLRW metric could still be correct if distant galaxies are actually much smaller than nearby galaxies.  The big bang advocate could argue that the reason we don’t see any obvious magnification (due to expansion of space) is because distant galaxies are actually five to ten times smaller than nearby galaxies.  So, they are really magnified but do not appear to be magnified because they are actually much smaller.  And, in fact, this seems to be the default assumption of secularists.  But this rescuing device is not realistic for several reasons.

First, there is no physical mechanism that should cause a galaxy to somehow increase in linear size (by a factor of ten) without gaining mass.  We already know that these high redshift galaxies are essentially as massive as nearby galaxies (based on the light from their stars).  No computer simulations of galaxy evolution has predicted such a strange enlarging phenomenon.

Second, we already know that high redshift galaxies are similar to nearby ones in most other respects that are independent (or nearly so) of the cause of the redshift.  For example, distant galaxies are about as massive as nearby galaxies, have similar morphology (shape), and have similar metallicity (fraction of heavy elements).  The observational evidence indicates that there is no substantial difference between these distant galaxies and nearby ones.  Therefore, it is unreasonable to appeal to galaxy evolution over time to explain away the data when we see no evidence of significant galaxy evolution.

Third, and most significantly, to salvage the FLRW metric, galaxies would have to enlarge over time (without gaining significant mass) in precisely the right way to make the Doppler model look right even though it supposedly isn’t.  That is, galaxies at a redshift of 1 would have to be about 60% the size of nearby galaxies, and galaxies at a redshift of 10 would have to be nearly five times smaller!  The Doppler model not only predicts the correct median angular diameter of galaxies at a specific redshift, but at all redshifts.  Is it reasonable to suppose that galaxies magically grow in precisely the right way to eliminate all evidence of FLRW expansion?  Furthermore, galaxies would have to increase in brightness in just the right way to also miraculously eliminate any evidence of expansion of space – as in Figure 3.

So, to suppose that galaxy evolution over time amazingly cancels out all evidence of an allegedly real expansion of space would be absurd.  Yet, this is probably the option ardent big bang supporters will take.  However, Occam’s razor suggests that the reason the Doppler model looks right according to all the data is because it is right.

Predictions

The Doppler model also allows us to make predictions in regard to future JWST observations that differ from the predictions of the big bang based on the FLRW metric.  As shown in Figure 1, the median angular diameter of galaxies beyond a redshift of 20 should continue to be smaller than galaxies at low redshifts.  In particular, the Doppler model predicts the median diameter of galaxies beyond a redshift of 20 to be around 0.2 arcseconds.  This is roughly ten times smaller than the predictions based on the FLRW metric.  Furthermore, The Doppler model predicts that such galaxies will be fainter by a bit more than one magnitude.  Time will tell which model is correct.

Note that these are specific, quantitative predictions.  Successful specific predictions are the hallmark of good science.  I suggest that the big bang is not good science as it does not make specific successful predictions.  Furthermore, it is not consistent with the latest JWST observations of galaxy sizes and brightnesses.  In addition, the big bang has difficulty accommodating the existence of galaxies at such high redshifts since they have had so little time to form according to secular assumptions.  I predict that galaxies will continue to be discovered at higher redshifts, up to the detection limit of the JWST.

Conclusions

The angular sizes and apparent brightnesses of distant galaxies are consistent with the Doppler model and not with the big bang.  To be clear, the universe is indeed expanding because the average distance between galaxies increases with time as these galaxies move through space.  But apparently, the fabric of space is not expanding.  The FLRW metric is wrong.  This affects the estimated sizes of distant galaxies because the FLRW metric predicts a magnification effect that is simply not seen.  The implication is that distant galaxies are about the same size and brightness on average as nearby galaxies.  Thus, there is no evidence of galaxy evolution over the supposed billions of years.  Thus, the Doppler model fits the natural expectation of a “recent” (thousands of years ago) supernaturally created universe.  The Doppler model is compatible with the ASC model that explains how distant starlight reaches Earth within the biblical timescale.

This creation-based Doppler model makes specific quantitative predictions about the angular diameters and brightnesses of galaxies that will be discovered in future JWST images.  Namely, these will have an average angular diameter of 0.2 arcseconds, roughly ten times smaller than the big bang model predicts.  And such galaxies will be fainter than big bang predictions by a little over 1 magnitude (2.5 times).

This is a very exciting time to be a biblical creationist.  All the observations coming from the JWST confirm biblical creation models, and none are supportive of a big bang.  In fact, these latest observations are absolutely devastating to big bang interpretations.  And since models like Doppler and ASC make specific predictions about future observations, creation scientists are now leading the way in cosmology research.

[1] In the standard model, light takes billions of years to travel from these distant galaxies to Earth.  Thus, we see such galaxies not as they are today, but as they were billions of years ago.  Big bang advocates expected such galaxies to be low mass, clumpy, “baby” galaxies.  But this is not what was found.  There is no evidence of substantial galaxy evolution in JWST images.