The Problem

Finding the right value for Hubble's Constant has been difficult.

No One Can Agree How Fast Universe Is Expanding. New Measure Makes Things Worse.

https://www.livescience.com/hubble-c...s-deepens.html

Hubble Trouble: A Crisis in Cosmology?

https://www.aps.org/publications/aps...805/hubble.cfm

Best-Yet Measurements Deepen Cosmological Crisis

https://www.scientificamerican.com/a...ogical-crisis/

To visualize the problem, imagine you shoot a laser beam into space, and it passes a series of targets placed 200 million light years apart.

In a simple universe, the laser beam will reach the first target in 200 million years, the second target in 400 million light years, and so on.

But we don't live in such a simple universe. We observe cosmological redshifts. These are an observed fact, and you can learn more about cosmological redshift here.

The redshifts are interpreted as the expansion of space. In this universe, the targets will be moving away from us according to Hubble's Law:

where v is the velocity of the target, H is Hubble's Constant, and D is the starting distance of the targetv = H × D

According to observations of relatively near phenomena, H is measured to be 74 km/sec / Mpc.

But according to measurements at our most distant observable range, H is measured as 67 km/sec / Mpc.

Yet another measurement based on the curvature of space puts H at 54 km/sec / Mpc.

(blue = static, white = expanding, fastest on the left, slowest on the right.)

As the measurements become more accurate, they remain in disagreement.

Hypothesis

Edwin Hubble said that it was convenient for the redshift to be interpreted as a Doppler-like effect, leading to the expanding universe theory. He also said redshifts might be interpreted as how nature actually works. In other words, the redshifts aren't caused by some other phenomenon; cosmological redshift is a new phenomenon in-and-of itself. However, he cautioned, if there are existing ways to explain the redshifts, adding a new principle of nature should be avoided.We may state with some confidence that red-shifts are the familiar velocity-shifts, or else they represent some unrecognized principle of nature. We cannot assume that our knowledge of physical principles is yet complete; nevertheless, we should not replace a known, familiar principle by an ad hoc explanation unless we are forced to that step by actual observations.

E. Hubble, The Observational Approach to Cosmology, pg. 22, 1937

But choosing the path of the familiar principles over a new principle has forced us to propose several new principles anyways, including dark energy and inflation. It is also unclear, despite many accurate measurements, how fast space is expanding.

Let's back up then and ask: if cosmological redshifts do represent a new principle of nature, what is that principle? Consider the following premises:

- A decrease in frequency is observed
- The speed of a wave is v = frequency × wavelength

Therefore, if these premises are taken literally and plainly (and somewhat naively):

- the observed decrease in frequency should result in a decrease in speed.

To examine this literal interpretation of redshifts, I considered possible models where the speed of a photon begins at c and decreases as the distance from its source increases.

The simplest of these models is one where H × D is just subtracted from c.

Hypothesis 1: the speed of light = c - H × D

This hypothesis achieves something interesting. Even though the targets are stationary, the time it takes to reach the next target increases in a way that is similar to the time it would take to reach a moving target.

Unfortunately, this doesn't seem to help with the issue of Hubble's constant. Observations say there is a faster rate of redshift in the nearby universe and a slower rate of redshift in the farthest parts of the observable universe. Compared to the standard expanding model, Hypothesis 1 makes the problem worse.

To match observations, more redshift is needed in the first half, and less is needed in the second half.

I thought about dividing H × D by an increasing number, but H × D itself increases as the photon travels. So how about dividing c by that?

Hypothesis 2: the speed of light = c / (1 + H × D)

This hypothesis results in a much higher rate of redshift for nearby objects and a much lower rate of redshift for far away objects, compared to the expanding models.

In this hypothesis, the units of H are independent of the units of c. The units of H are inverse length, which means (1 + H × D) is unitless.

On the graph, hypothesis 2 makes more of a straight line than a curve. By making it an inverse square law, a more pronounced curve can be made.

Hypothesis 3: the speed of light = c / (1 + H × D)^2

Squaring just H × D makes an even more interesting curve.

Hypothesis 4: the speed of light = c / (1 + (H × D)^2)

(1 = green, 2 = magenta, 3 = purple, 4 = red)

These models and others can be examined on the Testing Page.

In these models, the laser beam shows delays in reaching the targets even though the targets are stationary. In such a universe, space is not expanding.

This conclusion raises questions that must be addressed that include:

- Doesn't this predict redshifted stars in our own galaxy?
- Isn't the expansion of the universe a fact?
- Doesn't the Cosmic Microwave Background confirm an expanding universe?
- Isn't this the discredited Tired Light theory?
- Is this a Varying Speed of Light theory?
- Doesn't this conflict with special relativity?
- Doesn't this violate the Conservation of Energy?
- Shouldn't we be able to measure a drop in a photon's speed?

Doesn't this predict redshifted stars in our own galaxy?

That depends on which hypothesis is used.

To see the differences between them, a better view of the graph is needed. Let's put the ratio between time in the hypothesis and time in a static universe on the y-axis.

From this view, the expanding models (white) are a straight line. Hypothesis 1 (green) lags behind the expanding models, while hypotheses 2 and 3 (magenta and purple) jump out a ways ahead initially before tapering off.

Hypothesis 4 (red) does something different. It lags behind for hundreds of millions of years, then jumps out ahead, and then flattens out.

https://mikehelland.github.io/hubble...aph_ratios.png

So what do the models predict for redshifts in our own galaxy?

- Hypothesis 1: Yes
- Hypothesis 2: Big Yes
- Hypothesis 3: Big Yes
- Hypothesis 4: No (almost none)

Hypothesis 4 shows a staggering difference from what's predicted by any of the other models, including the expanding ones. There is almost no expansion for hundreds of millions of years, which fits with observations very closely.

Shown by itself and the main measurements behind the disagreement in values for Hubble's constant, we get the following picture:

The space between the white lines represents the Hubble tension, and the red line is the suggested solution.

There is a 12,000 character limit to a post on the message board, so the rest of the questions are answered here:

https://mikehelland.github.io/hubbles-law/

Thanks for your time.