### Stand Back! I Don't Know How Big It Gets!

How mind-numbingly daft does an idea have to be before it's rejected outright by everybody? This is a question that keeps me awake at night, and is threaded through these disparate writings as the glue that holds them all together.

We've encountered some pretty batshit insane ideas over the course of my musings on the nature of thought, but few plumb the chasm of stupidity as deeply as our topic for today: Expanding Earth.

I first encountered this notion back in 2010, on the then newly-formed Ratskep forum. A certain user, a fairly egregious troll going by the appellation Brain man, presented it as ostensibly some sort of psychological experiment in one of the most horribly incompetent bits of experimental design I've ever come across, and that includes the creationists pouring water into a hole in the mud in some palsied effort to support the Noachian fludd. I'll link to the forum thread at the bottom of the page. It was debunked in fairly short order, yet I note that the thread is still going strong six years and five hundred-odd pages later.

The thread began with this video by cartoonist Neal Adams from 2000:

On the face of it, one might think this looks quite compelling, and that's not surprising, since the creator of this animation really wants to convince you that this 'theory' has merit. Unfortunately, it runs hard up against some deep empirical issues, issues that the proponents of EE models are generally keen to sweep under the carpet.

It's important to note before we begin in earnest that there are several flavours of expansion, and which particular problems are encountered depends largely on which of these flavours the proponent is defending. We should also be aware that which model the proponent is defending often depends on what objections are levelled at the ideas, and that they can often switch between models whenever it seems convenient in order to distance themselves from said objections.

I'd be remiss if I didn't also point out that the Earth is expanding, by virtue of a net energy gain due to in-falling matter and energy, but that this expansion is orders of magnitude below what any of the EE models require, and nothing like commensurate with the separation of the continents, meaning that expansion alone is insufficient to account for that separation.

In a previous post, DJ, Spin That Shit! we looked at the history of evidence that the planet we inhabit is an oblate spheroid. Among the pieces of evidence that we examined was the measurement of the Earth's circumference by Eratosthenes of Cyrene, and how he derived his figure of approximately 26,000 miles. Today, we've got a pretty robust figure of 24,901 miles at the equator. As we noted, there's a degree of uncertainty in Eratosthenes' measurement, not least because it was expressed in an archaic unit (stadia) that was far from standardised. He also assumed a perfect sphere, while we now know that the planet is oblate due to opposition of forces. This latter will become important for us before we're done, because there's an empirical law that underpins a huge amount of modern physics, and it's expressed neatly in the oblateness of the Earth.

In general, the idea of an expanding Earth has been with us for quite a while. What may come as a surprise to some is that one of the earliest advocates of an expanding Earth was Charles Darwin. Darwin, during the famed second Beagle voyage, was in Patagonia investigating stepped plains, which he hypothesised had been lifted up during a series of concentric elevations, suggesting expansion from a central point. He later revised his hypothesis, suggesting that the sea floor dropped while the plains were elevated.

In The Idiot's Guide to Relativity, we touched on the concept of translational symmetry, and in particular that Noether's theorem demonstrated that the translational symmetries discussed there were expressions of laws of conservation. It's worth looking a little more closely at Noether's theorem here, because it has consequences for all flavours of expanding Earth.

First, we should look at symmetry, because the common notion of symmetry, while a case of symmetry in the sense that we're discussing, doesn't reflect all symmetries as used in physics.

A symmetry in physics is any feature of a system that remains unchanged under a transformation. A transformation is basically a change in the conditions of the system in some respect. We might change the direction we're facing, or the location, for example, and there will be features that remain unchanged. Such features might be specific quantities, or the ratios between specific quantities. We'll look again briefly at those examples to make things clearer.

It's worth a small aside here to note an interesting point.

A while ago, I started a post about the unsung heroes of science. I talked to a lot of friends and acquaintances in the scientific community, as well as asking for a broader list of candidates of scientists I might not be aware of. I already had Emmy Noether as one of the inspirations for that post, but it's noteworthy that her name was touted by almost everybody, especially the physicists, including well-known names, such as Lawrence Krauss. In the event, just in researching Emmy Noether for the purpose of that post, I realised that there's an entire book to be had. Watch this space.

In the broadest terms, Noether's first theorem tells us that each differentiable symmetry of the action of a physical system, where the action is the integral over time from which the behaviour of the system can be calculated from the principle of least action, corresponds to some conservation law.

In our earlier outing, we talked about rotational symmetry, and how Noether's theorem applies, showing that it corresponds to conservation of angular momentum. If I conduct an experiment facing West, it should yield the same result as an identical experiment conducted facing East, or indeed any other direction. We also looked at how conducting the same experiment in different locations should yield the same results, and how this corresponds to conservation of momentum. There are many such symmetries, and Noether showed that all of them correspond to some law of conservation.

As another brief aside, there's a common misconception that, if the constants of the universe were even slightly different, life would not be possible. I won't belabour this point here, as fine-tuning is to be comprehensively addressed in a future post, but Noether's theorem, properly applied, tells us that this is simply false, because it isn't the constants themselves that are important, it's the ratios between them. For instance, the masses of particles can be changed radically but, if the gravitational constant is altered commensurately, the relationships remain unchanged. This is setting aside the theoretical prediction that one of the fundamental forces of the universe could be removed in toto, and it would result in life arising with even greater probability.

So, let's look at the different flavours of EE:

Here's our first flavour, and we'll call it the 'constant mass' hypothesis. In this model, the Earth expands without acquiring any new mass. This presents several problems that should be reasonably obvious to anybody with any competence in physics, or who's been following this blog from the outset. Even for those joining the show already in progress, the foregoing discussion should provide some pause. Here's a critical equation, one of the most easily recognisable in physics.

$F=G \dfrac {m_1 m_2} {r^2}$

This is Newton's famous equation detailing the inverse-square law for gravity. It's known to be inaccurate, but it serves well enough for our purpose here. F is force, G is Newton's gravitational constant, m1 and m2 are our two masses, and r2 is the square of the radius between their centres. What it tells us is that, as the distance between two centres of mass increases, gravity falls off as the square of the distance. In other words, if you double the distance, the gravitational attraction is one quarter. If you triple the distance, the attraction is one ninth.

This has some obvious consequences. The first is that we should expect to see that surface gravity on Earth was considerably stronger in the past. Let's pick a couple of snapshots from Adams' video above and try to work out what that might mean. Look at the point in the video at seventy million years ago, and let's put it alongside a snapshot from today.
Now, even allowing for the fact that I may have been less than entirely precise in my snipping of these captures (although you can see by the size of the text at the top that I can't be a million miles away), this is a significant difference in size. It's almost, but not quite, double the size today that it was 70 million years ago on Adams' view. This means that the gravity at Earth's surface would have been almost four times what it is today. This should have observable consequences.

One simple and obvious consequence is that the organisms of the time would have left much deeper trackways. There's an entire field of study on this topic, known as ichnology, and there are examples of dinosaur trackways all over the world. What do we find? Yep, they're exactly commensurate with gravity at the surface remaining unchanged, and this goes back considerably further than a mere seventy million years. Here's a particularly nice example from Cal Orcko in Bolivia of a baby T. rex flanked by two adults*.
Look for contributions in the Ratskep thread by palaeontologist and former museum director Theropod.

Of course, higher gravity would have other consequences for organisms of any time. Most notably, even single-celled organisms are directly affected in size by the strength of the gravitational field they inhabit, with a direct inverse proportionality to their size. We have examples of microfossils going back three and a half billion years, and all consistent with no change in the strength of gravity.

In larger organisms, the effects are even more pronounced, affecting circulation, internal fluid dynamics and musculoskeletal development. In fact, if gravity were even a fraction of the strength implied by a constant-mass expansion model, organisms the size of humans would have been a stretch, let alone 30 metre sauropods weighing in at 60-100 metric tons.

So what about other consequences? An excellent example is lunar recession. It's well-established that the moon is tidally locked to the Earth. It's the reason that we always see the same side of the moon. This tidal locking manifests in a really interesting way. Firstly, it's responsible for the two marine tides per day that we encounter here on Earth. Here's what it looks like:
This is obviously quite exaggerated, but it highlights the principle quite nicely. Despite the fact that Bull O'Really thinks this is something we can't explain, we have an extremely coherent model of tidal forces. As you can see, the moon is gravitationally tugging on the oceans. That's why there's always a high tide on the side of the planet facing the moon. It leads the moon by approximately ten degrees. There's also a high tide on the opposite side of the planet, because the moon is also pulling on the planet, and tugging it away from the water on the opposite side, which is why you end up with that cigar-like shape.

One of the consequences of these tides is that, because the water is exerting drag on the rotation of Earth, the period of rotation is slowing over time. This has been empirically demonstrated over many millions of years via studies of strata of sedimentary rock laid down with a diurnal periodicity known as tidal rhythmites, as well as by observations of fossil stromatolites. There' a wonderful paper drawing all this evidence together by George E. Williams, which I'll link at the bottom.

This brings us nicely back to the wonderful Ms Noether, because the Earth's rotation is a manifestation of angular momentum. Angular momentum is a quantity that is conserved, which means that the angular momentum has to go somewhere. It can't simply dissipate. So where does it go? It gets transferred to the moon! The net effect of this conservation is that the moon's orbit recedes over time, so that the angular momentum in the Earth-moon system remains constant. Thus, symmetry is maintained, and all is well.

Now, look again at Newton's equation above, and put this all together, and we can see that there's a deep problem here, namely that, if Earth is expanding, then rotational velocity should be slowing purely as a result of the expansion in order to conserve angular momentum, meaning that tidal transfer would be reduced, resulting in a lower rate of lunar recession. All our observations are entirely consistent with the strength of gravity on Earth having remained constant.

So do other models fare any better? How about if we let the mass grow?

Afraid not. Many of the reasons are similar to those detailed above. First, of course, we'd still be dealing with significant changes in the strength of gravity, although this time it would be in the opposite direction. Dinosaurs would leave shallower tracks, tidal effects would be reduced, which in turn would reduce the past effects on Earth's rotational period and the moon's recessional velocity, tidal rhythmites and stromatolites would be affected.

And all of that is, of course, setting aside that there's no discernible mechanism for the addition of this mass. One tweep last night suggested a white hole inside the planet. This suggestion smacks of desperation, not least because a) a white hole is a purely theoretical construct - basically the opposite of a black hole, that spews matter out rather than sucking it in - with no observational evidence and b) that such an entity, were it to exist inside our planet, would have significant and measurable consequences, not least of which would be wild fluctuations in the mass of the planet. This is complete nonsense, regardless of the existence status of white holes.

The same user also suggested a white dwarf inside the planet, but this is even more silly. A white dwarf wouldn't provide any additional mass than it started with. A white dwarf is simply a low-mass star that has run out of all fuel, and is composed mostly of electron degenerate matter. All white dwarfs are formed from stars with mass lower than the Chandrasekhar limit of approximately 1.4 solar masses. Although they have low mass, because of electron degeneracy, these stars are held up against gravity only by the Pauli Exclusion Principle, which we discussed in Give Us A Wave! This means that they're extremely dense (the only things we know of that are denser are neutron stars and black holes, although there are postulated to be quark stars, which would be intermediate between the two). For example, a white dwarf with the mass of the sun would be approximately the same size as Earth. Ultimately, the mass of the Earth is known, and it's nothing like sufficient to have a white dwarf in its interior. It is, however, entirely consistent with a core of molten iron, which also explains the planet's magnetosphere.

@hackenslash1 I have made a video about. I researched it for 3 years and concluded EE is a fact.
I put it to this researcher that he really needs to research some physics, because there are major issues here.

There's one more model, namely one suggesting that the gravitational constant - the G in Newton's equation - has changed over time. This idea fails for all the same reasons as above, as well as having other major observable effects on the history of the universe, most notably in the formation of stars and galaxies. Observations of galaxies and stars going almost all the way back to the last scattering surface show that gravitationally-bound objects have behaved in exactly the way that our models predict for the entire history of the universe, let alone the time that the EE models cover.

Another interesting discovery that isn't explained by any of the EE models, probably because the 'researchers' haven't even considered it, is Neil Shubin et al's discovery of Tiktaalik roseae on the Southern end of Ellesmere Island in the Arctic. This discovery detailed in Shubin's magnificent Your Inner Fish, required a prediction that is entirely incompatible with any of the expanding Earth models, and is only explained by modern plate tectonics. Now, you might think that this discovery has nothing to do with any of this, except when you note one thing:

The prediction leading to the location of this discovery was entirely rooted in modern plate tectonics. Ellesmere Island, in the deep past, was actually in equatorial regions. On an EE model, it could only have been in polar regions.

Another notable consequence of expansion would be obvious buckling, and this would definitely be observable. In DJ! Spin That Shit! we looked at the consequences of having a plane of a fixed size on different spherical surfaces. If Africa, for example, originated on a much smaller sphere, there would be measurable buckling as a consequence of the flattening of Africa to inhabit a larger sphere. This is not conclusive, not least because, as hard as we thin k rocks are, they're actually quite plastic under pressure. However, this is still a line of evidence that would indicate expansion.

One last thing before my final comments, namely that we've been monitoring the planet for several decades by various means, including by satellites. Indeed, our GPS system relies on the size of the planet being roughly constant, because the relativistic correction for rate of orbital motion and differential gravity is reliant on it. This correction is to the tune of 38 microseconds per day. Now, this doesn't sound like a whole lot but without it, as discussed in the previously-linked post on relativity, GPS systems would drift by about 10 kilometres per day. Even very small changes in the size of the planet would have noticeable effects in fairly short order. Aside from that, we have geomonitoring satellites whose job is to record everything from fluctuations in climate and temperature to the advance and retreat of glaciers. To within very small margins of error, no expansion is observed, and these margins of error are again orders of magnitude below what would be expected from any of the above models.

In short, there are plenty of good reasons to suppose that ALL expanding Earth models are complete nonsense. What they most definitely all are is pseudoscience. In Onus Probandi, Assertionism and Peer-Review, we talked about how science is conducted. One of the key elements in the conduct of good science is that we work as hard as we can to show that our ideas are false. If that's not what you're doing, then not only are you setting yourself up for a fall, what you're doing is really not science. I've yet to encounter an EE proponent who wasn't working extremely hard to show that his ideas were correct. This is exactly the sort of behaviour we see from Intelligent Design advocates, alien visitation/UFO advocates, and science-deniers of all stripe.

There's a famous saying in physics circles: If you're going to be against Emmy Noether, you'd better be prepared to lose your shirt. There is no model for expansion that doesn't fall afoul of Noether's first theorem. This is complete drivel, and not to be entertained by a thinking person.

Nits, crits and comments welcome as always.

*Tyrannosaur remains haven't been found outside Western North America (Laramidia). The information concerning the nature of these trackways accompanied the image at the source, the Smithsonian magazine's website. Trace fossils such as trackways utilise a different classification system than skeletal fossils, and the latter would be required to confirm the presence of T rex outside Laramidia.Even were these found, such trace fossils would be unlikely to be attributed to the T rex without direct robust evidence. It's entirely probable that these were made by another theropod entirely. Thanks very much to He_Who_Is_Nobody for the heads-up and to Theropod for the additional clarification.