I think the Lambda-CDM model may have a number of different distance scales, such as "Comoving Distance" and "Proper Distance" and perhaps "Hubble Distance". And within those there may be some ambiguity about which you would measure with a tape measure. This ambiguity allows the freedom to point to a graph showing a common "proper time"; that is a "true" simultaneity of the universe, for objects that either are or aren't moving toward and away from each other.

Some people find this idea to be more palatable than the idea of a minkowski spacetime. In the Lambda-CDM model, there is all sorts of warping of space, depending on how you define it, but the universe has one universal clock, ticking forward, one tick at a time. In Minkowski spacetime, though, you have a big lightcone, so between the past light-cone, and the future lightcone, there are events that are not in your definite future or history, and they can slant backward and forward in time.

I made a simulation of some of the SN1a data a few years ago with the Minkowski idea in mind, and posted my results in a youtube video.

https://www.youtube.com/watch?v=UuGX2_aReew

When I modeled things, I did not use your idea that you get a different value of distance depending on whether you use redshift or luminosity. Instead, I modeled that the distance as a function of luminosity alone, and the velocity a function of redshift alone.

From those two values I extrapolated to find *when* the supernova material departed from the "origin", that is; our galaxy's world-line, in minkowski spacetime.

The model has material spraying out from the origin, starting 50 billion years ago, and ending about 14 billion years ago.

I put some oversimplifications into my model... For instance, I know they used red and (maybe) indigo filters to view the supernovae and measure their magnitude... I presume that they dealt with how the filters interact with redshift to get a good measure. Another issue is aberration. A star moving away at a high proportion of the speed of light would not have the same magnitude vs. distance relationship as a stationary star. In calculating the distance to a high-z star, one could, in principle, decide to correct for aberration or not. (In the video linked above, I did not, though in the context of the Minkowski model, it should certainly be present.)

I imagine that measuring redshift and magnitude of a supernova takes some expertise and specialized equipment, as it would involve identifying some signature emission line(s) that are not located in the correct bandwidth.

The whole point of studying type Ia supernovae is that it was thought that they all had the same intrinsic luminosity, so that their luminosities, when compared to their redshifts, could be used to calibrate the redshift scale, and make up for the otherwise unknown change in the Hubble Constant over time (it was very large early on, rapidly reduced because of the high density of the early Universe, but as the Universe got bigger the density decreased, so the Hubble Constant's decline slowed, until about 6 billion years ago there was so much more empty space than mass that the expansion of empty space-time predicted by Einstein began to win the battle between gravity and expansion, and the Hubble Constant (constant only in the sense that it is about the same everywhere at a given time) has been increasing ever since. It was hoped that using the difference between the luminosity graph for type Ia SN would allow an accurate correction for the changing value of the Hubble Constant over time.

Unfortunately, it now appears that although most SN1a do have nearly the same luminosity, they do not all have the same luminosity. This may be similar to the problem faced by Hubble early on, in which he compared 'normal' Cepheid variables in our galaxy to a slightly different type of far brighter Cepheid variables in other galaxies (not noticed in ours because they are rare, but more noticeable in other galaxies because they are easier to see than normal Cepheids). This gave Hubble an early estimate for the Hubble Constant that was a factor of 4 or 5 too large and would have made the Universe younger than the Earth. If that is the sort of problem involved, it should eventually be easy to find out how to correct the apparent discrepancy between luminosity and redshift-based distance estimates. Or it may turn out that the mechanism involved in type 1a supernovae is not as simple as was thought and correcting for errors in the luminosity in order to properly calibrate the redshift values will be more difficult than had been hoped. At the moment, the answer is not obvious; but hopefully most of us will live long enough to see its solution.

Dear Robert Shour,

".....Might the situation instead be that the universe has two reference frames, so the same object is measured at different distances depending on which reference frame applies? "

Concerning type 1a supernova and cosmic distances, I and an associate wrote and published a research paper on this subject, as seen below:

Article An Alternative Universe-Scale Analytic Metrology and Related...

The conclusion of the paper was that the Hubble distance formula calculates cosmic distances wrong, and for this reason, dark energy probably does not exist. At cosmic distances with a redshift of .6 the Hubble formula overestimates distances by about 10%. This is why they proposed dark energy. At redshifts greater than z-1.2 distances are progressively underestimated by this formula by more than 10%.

But the inverse square law of gravity also fails at calculating cosmic distances greater that z=.5 by 5%,, and underestimates distances after that.

Our formula to calculate cosmic distances using both corrected factors can be seen below. Also the comparison between the Hubble formula and our formula is also shown.

http://www.pantheory.org/HF.htm

regards, Forrest Noble

Hi Robert,

I am not sure if you are interested in alternative physics, but I completed a paper in which I reference your paper on 4/3 entropy.

Preprint A Classical Description of Black Body Radiation and the CMBR

In this paper I give theoretical values for the two reference frames you mention. Let me know what you think.

Regards

Randy

In my simulation, (see YouTube video link in previous answer) I assumed that the redshifts and magnitudes were "standard candles"

Making that assumption, I found that some of the stars didn't follow hubble's law. In particular, the nearby stars followed Hubble's Law, and those outside 5 or 6 billion light years did not.

If, instead, one assumed that the SN1a followed Hubble's Law, they would have to conclude they weren't standard candles. I think, though, to make this conclusion, in the absence of other differences would amount to confirmation bias.

@Courtney Seligman, you said ", it now appears that although most SN1a do have nearly the same luminosity, they do not all have the same luminosity."

I wondered how the determination is made which ones are nonstandard? Is it the ones who don't fit Hubble's Law, or is there something distinctive in the spectrometry?

How is "redshift distance" determined? Via Hubble's law, by inferring radial velocity from the (supposed) Doppler redshift, and then calculating distance D via V = HD? We should keep in mind that Hubble's law applies only to galaxies and therefore to stars inside them, but not to isolated , exotic astronomical objects.

My own sense says that you're justified in inferring velocity from redshift, but then calculating D via V = HD is only valid if the object under consideration is part of the Hubble flow.

The part I think is lacking from Hubble's Law is to consider an epoch of immense pressure 40 to 13.7 billion years ago.

Hubble's Law assumes that from the moment of the big bang all bodies were immediately free to move with their initial inertia. It does not account for the possibility (quite likely) that the masses jiggled back and forth at high pressure for some time before having the freedom to expand outward at constant velocity.