# Measuring the Hubble Constant

Attempts to measure the expansion of the universe have come in various forms. The recent Cosmology Crisis (https://www.space.com/why-is-there-a-cosmology-crisis) has me pondering the expansion rate as it relates to spacetime.

I am a rank amateur when it comes to astrophysics, and this train-of-thought could have all kinds of problems, but I do love to learn from the big IQs out there... so here is what I am thinking

Light, (and likely all other similar waves), as it travels from point A to point B, traverses “something”… our current best theory is that it traverses spacetime. We have proven that spacetime can bend and warp light due to influences originating from mass (the greater the mass, the greater the influence). Now, the shortest distance between two points is a straight line, but what if there are no straight lines in spacetime because mass is always bending it. I would suggest that even the smallest unit of mass bends spacetime and that influence can be measured however infinitesimally small and however infinitely distant from the photon. So, if there are no straight lines because spacetime cannot escape the influence of mass, then there cannot be a shortest distance between two points in our reality. The speed of light is constant, yes, however; light, moving at its constant speed between two points, is consistently being influenced by an infinite number of points of mass contained within the universe and as such cannot reliably used as a measuring tool to establish the distance between point A and point B. To me, this makes the Red Giant or Type Ia Supernovae technique problematic. This “error” in distance calculation can only be measured if you know every point of mass in the universe along with its density and its position in the universe relative to the photon it is influencing. The error result for short distances between two points would certainly be so small that it would lack relevancy in physics but consider how much error could exist between two points that are positioned in galaxies far distant from one another. This error could be enough that the Hubble Constant may not be a constant at all. I suggest that the Hubble Constant may actually be better defined as the Hubble Average Observation or Hubble Median Observation as there would always be a range due to error created by mass influence.

Could it be that photons follow the "path of least influence" on their trajectory?

Thoughts?

No.

You can compare that to what surveyors do: they measure the distance of an object by looking at it. Yes, there is air in between and yes, air currents influence the path or time the light takes, and yes every air molecule infinitesimally impacts that, and yes one can not calculate that exactly. But all those tiny influences are just that: tiny. And le voila, the surveyor can measure the distance from e.g. one building to another just fine.

If that doesn't convince you, one can repeat the same measurement. Another surveyor would fine the same distance between the two buildings, despite all those tiny influences being different the second time around. But they are still tiny and so simply don't matter.

Of course there might be large effects too. In the surveyor example, imagine on a hot summer's day a street with glimmering hot air above it. That might influence the surveyor's measurement and needs to be taken into account. The same is happening in cosmology, where gravitational lenses are being seen, are being measured repeatedly, and are taken into account.

what if there are no straight lines in spacetime because mass is always bending it

To date, experimental data (from WMAP, BOOMERanG, Planck projects) shows that the universe is flat within a 0.4% error. So it's safe to assume that light takes more or less straight paths in a universe, otherwise bending of universe would be detected globally and uniformly across all directions in the sky by above mentioned observations.

So, if there are no straight lines because spacetime cannot escape the influence of mass, then there cannot be a shortest distance between two points in our reality

Your conclusion does not follow. Even in the case of bending light path taken is simply shortest length curve along space-time. All curves (paths) has length, be it straight lines or not. Thus you can calculate a shortest one.

light, moving at its constant speed between two points, is consistently being influenced by an infinite number of points of mass contained within the universe and as such cannot reliably used as a measuring tool to establish the distance between point A and point B

Does not follow. The thing that light wave is bend by surrounding masses, does not say anything about it's reliability for measuring distance. Mass will adjust photon trajectory and it's energy (blue-shift or red-shift it), but still light travels at shortest path possible. And we can even detect the fact of light-bending (see gravitational lenses) from cross-comparison of multiple light sources.

• Thanks for the input. You and rfl both mentioned gravitational lensing which is kind of what I am getting at... I dont see how you could possibly account for every single influence on a photon that has traveled billions and billions of light years. The red-shift of such a journey should have an intrinsic margin of error however small it may be. That margin of error should grow as distances increase. Apr 7, 2022 at 18:45
• If anything, that error should average out. Also, note that gravitational lensing tends to make distant objects brighter. We observe supernovae type IA to be dimmer than expected.
– rfl
Apr 7, 2022 at 19:26
• @StevenAlsop You don't need to. Light escaping gravitational field is red-shifted and when approaching gravitational source, it is blue-shifted. So these additional energy fluctuations should cancel each other out over all photon travel trajectory and affecting masses. Given that gravity force drops according to inverse power law $F_G \propto 1/r^2$, and that photon only briefly flies in affecting stronger fields,- due to huge flight speed $c$, - you don't need to worry about that. It becomes only important when photon passes near-by of strong gravity fields,- black holes, neutron stars, etc. Apr 7, 2022 at 21:19

Hi Agnius Vasiliauskas:

Your quote: "To date, experimental data (from WMAP, BOOMERanG, Planck projects) shows that the universe is flat within a 0.4% error."

The Wikipedia article, Shape of the universe, says:

• Several potential topological or geometric attributes of the universe interest may be discussed. Some of these are:

• Boundedness (whether the universe is finite or infinite)

• Flat (zero curvature), hyperbolic (negative curvature), or spherical (positive curvature)

• Connectivity: how the universe is put together, i.e., simply connected space or multiply connected space.