Part III: The GLV Building Blocks as a Philosophical Framework. Layer 1. Cumulative Path Deviation

The biggest mistake we make in cosmology is painfully simple. We act as if light behaves like a laser beam in a dark room, one clean line from source to detector. We measure how red the light is, how bright it is, how long it takes, and we put a straight distance and a corresponding mass next to it. Anything that deviates, we push onto missing matter, dark matter, or dark energy. Layer 1 of GLV begins exactly there. It says, wait, what if the error is not in the mass, but in the route the light has travelled.

In earlier chapters I explained that space is never empty. The zero point field is everywhere, and what we call empty space is in reality a fine grained structure of gas, dust, halos, filaments, and gravitational wells on all scales. Add to that the three spherical shape of the universe, in which there is no outside and no truly far away place that does not lead past structures, and you get a world in which every photon, without exception, travels through a kind of cosmic obstacle course. Layer 1 gives that a name, cumulative radial distance bias, the systematic overestimation of distances because we smooth the winding route of light into a straight line.

The mountain road is again a useful image. Imagine two villages with a winding road over the mountain between them. The car drives at constant speed, you measure only the travel time. You multiply time by speed, you draw that distance as a straight line on the map, and you are done. But the map lies. Geographically the village is closer than your straight line suggests, because the car took a detour. The optical route, the driven kilometres, is longer than the geometric distance, the straight line. In cosmology we do exactly that with light. We see a photon from a distant supernova, we measure its redshift and brightness, we divide the travel time by the speed of light, and we assume the result is the straight distance. But if the photon took a substantial detour through lens fields, we place the source too far away on the cosmic map. I call that error radial distance bias.

In GLV I summarise that effect in one simple number, δ. That number says by what percentage the straight distance on our map is overestimated compared to the true geometric distance in spacetime. If δ were zero, the light path would be perfectly straight, and optical and geometric distance would coincide. As soon as δ is larger than zero, you know the light path was longer than we assume, and that we place sources systematically too far away. In later parts of the book I will show that δ is about 11%, here it is enough to realise that δ is not zero, and that this small deviation has enormous consequences once you apply it on cosmic scales.

In the language of GLV, this means the optical path is longer than the geometric distance. A photon travelling through the cosmos does not take a billiard straight route, it takes a road full of hairpin turns past gravitational wells of every kind and size, from dwarf galaxies to massive clusters. Each of those small lenses bends the trajectory by a tiny amount, lengthens the path a little, and shifts the arrival phase by a fraction. These are small effects per encounter, but the number of encounters is enormous. The net outcome is that the photon, in the zero point field, has travelled a longer route than we assume when we simply divide its travel time by the speed of light. When we project that too long optical route back onto a straight map, we place the source systematically too far away. That is the radial distance bias.

The same error shows up in almost all our cosmic measurement methods. If we use standard candles, supernovae whose intrinsic brightness we think we know, we infer a distance from the measured flux. But that distance is based on the idea of a straight path in an FRW space, not on a zero point field full of small lenses. If we use standard rulers, such as baryon acoustic oscillations, we interpret the measured angular size of structures as if the underlying geometry is smooth. If we link the angular position of the first peak in the background radiation spectrum to a particular horizon length at decoupling, we do something similar. Each time we put a straight ruler next to a winding trajectory. The universe you get on paper that way looks larger, younger, or more rapidly expanding than it really has to be.

The irony is that we already recognise part of this misdirection in gravitational lensing itself. We know that massive clusters distort the light from background galaxies, they stretch it, they pull it into arcs. We even use that effect as a magnifying glass to look farther than our telescopes directly allow. But in our mental picture it remains an exception, a few recognisable lens systems in the middle of an otherwise fairly empty space. In my worldview it is exactly the other way around. The exception is the perfectly straight light ray. The normal case is a path that constantly makes small kinks, without us seeing them individually. We take the smeared out optical route, we smooth it, and we act as if we are drawing a straight line back. At every step, something goes wrong.

The result is a misleading universe, but the misdirection is not in nature, nature simply does what it does. The misdirection is in our translation from light to reality. When we find that stars at the edges of a galaxy rotate faster than you would expect based on the visible mass, we conclude that there must be an extra source of gravity, dark matter. But rotation speed is derived from light, through Doppler shifts and through a distance estimate that can be radially too large. If the effective light path wound more than we assume, then the true radius is smaller, and the required mass is smaller too. Then less dark is needed to support the same speed.

With clusters we see the same pattern. We measure how strongly they bend the light of galaxies that lie even farther away, and we combine that with the visible mass in gas and stars. We attribute the difference to a dark halo structure. But here too we reconstruct a lens from deviations in the light field, without fully accounting for the fact that the light has already passed through a web of smaller lenses before it even reaches the cluster. The cluster then appears to lens more strongly than it really does as a local mass, simply because we do not calculate the full lens stack along the line of sight, we attribute it to one visible object. The universe looks like a larger weak gravity lens than it is.

On cosmic scales the same game repeats. When we look at supernovae in distant galaxies, we see that they appear fainter than you would expect from a simply expanding universe. The standard interpretation is that the expansion of the universe accelerates, fuelled by a mysterious dark energy. In the GLV picture I question the optical route instead. If space is nowhere empty, if the zero point field has small structures everywhere, then the light cones between those supernovae and us are not pristine. Photons have followed bent routes, their optical path is longer than the shortest distance. If we convert that extra length incorrectly into how far away the supernova is, and how much space has grown in the meantime, then part of what we see as accelerated expansion can be misleading geometry.

That does not mean that every deviation can be explained away with the thought that light winds. It is not that simple, and I do not want to make it that simple. But it does mean you first have to take optical paths seriously, and actually calculate them, before you introduce new entities. In my GLV framework that idea becomes concrete through an optical correction term, an extra piece in the story of the geodesic, the light path, that indicates how much the radial distance has been systematically overestimated compared to a calculation that does not account for all the small lenses. That correction grows with distance, precisely because distant photons encounter more structures and therefore accumulate more kinks. The misleading universe does not suddenly become honest, but we do get a more honest map.

You could say that the first light paths of the universe carry two different stories. The first is physical, they tell what the young phase of the zero point field looked like, how hot and how dense it was, which quantum ripples lived at the beginning. That story sits in the spectral distribution and the fine structure of the cosmic microwave background. The second story is optical, they tell how winding the route of each photon towards us has been, which structures it passed along the way, how much extra path length was added. That story sits in subtle deviations in brightness, in small shifts of angles, in the statistics of lensing. Up to now we mostly read the first story, and we act as if the second hardly matters. My claim is that you are not allowed to separate them.

So the misleading side of the universe does not arise because the zero point field is fooling us, it arises because we confuse one kind of information, the intrinsic content, with a mixture of content and route effects. It is like trying to infer how far apart two cities are from the kilometres on a car’s odometer, without knowing that the driver took detours, sat in traffic, and drove back a little. You can measure precisely how much fuel was used and how long the engine ran, but if you ignore the shape of the route, you get a distorted map. In cosmology, light is our odometer, and the cosmic web is the hairpin turns.

In the next chapters I will unpack this misleading universe further. How, with a zero point field, a three spherical shape, and winding light paths, you can understand the behaviour of gravity without dark matter as an extra substance. How rotation curves, clusters, background radiation, and supernovae can be reread in that light. And how the combination of quantum mechanics and relativity, supplemented with an optical lens, can lead to a universe that is still complex, but less mysterious than it seems at first glance. Because if there is one lesson in these first light paths, it is this, it is not the universe that lies, it is our assumptions about how we look at it that do.