Below I respond to an inquiry about the cosmological model presented in my book and Carmeli’s Cosmological Relativity theory. I used Carmeli’s cosmology to create a biblical creationist model for the origin of the Universe, with a timeline which includes the 6 days of Genesis creation beginning about 6000 years ago. I took parts of Carmeli’s big bang cosmology and added biblically based hypotheses (and speculations) to make it conform to Scripture.
That means it is no longer Carmeli’s cosmology but a sort of hybrid cosmology. Carmeli only constructed a 4 dimensional (4D) space-velocity model for the Universe. He never found a full 5D model for the whole Universe which might be used to construct a history close to the creation epoch. I theorised on a new model–call it the Carmeli-Hartnett model if you like–which is 5D. I added the time dimension to Carmeli’s space and velocity dimensions, to create a linearised 5 dimensional model. That is shown in Appendix 6 of my book “Starlight Time and New Physics“. I then used that, making additional assumptions, to explore the idea of rapid time-dilation during Creation.
I do not claim it is the answer to the creationist starlight-travel time problem. If God did something like I describe it could provide us with an understanding of it. Adding new physics may be a simple way to avoid many fudge factors in cosmology but it does mean adding a new dimension that is very hard to even conceptualise.
Thanks for your inquiry. My comments below are inter-dispersed between your’s in the usual email manner. I am glad you have now read my book, Starlight Time and the New Physics.
In Appendix 6, you say v is changing. You make dv/dt huge in order to change the speed of light.
The speed of light in that Eq. (A6.17) is the constant c, and does not change. That is assumed constant throughout the history of the Universe.
(1a) Why is v changing according to you?
I make the assumption that acceleration dv/dt is large during the Creation Day 4. It is an assumption based on the idea that God created the host of heaven on that day. It is an additional assumption outside of Carmeli’s cosmology; it is introduced as an additional term/hypothesis. In Carmeli’s cosmology dv/dt is a universal constant a0 = c/τ. In my cosmology I suppose it was extremely large during Creation day 4. The acceleration (dv/dt) there is with respect to local atomic clocks. It is not v per se but dv/dt that changes greatly.
By your own axiom, v is a function of r (and is approximately linear for the visible universe),
That is Carmeli’s model — the Hubble law is an axiom in that model. That applies over the range of weak acceleration and large scales, after the universe has expanded to what we see.
and therefore a huge dv/dt implies a huge speed too.
That does not necessarily follow. I make the additional assumption here that in the unseen past at Creation God imposed on creation this rapid acceleration through the universe. The Hubble law does not have to apply then. And when you say ‘speed’, it is important to specify with respect to what. Everything is relative.
(1b) How can you approximate that speed that as zero?
Do you mean u, the parameter used to specify the speed of particles through space? That is not the speed of the expansion of space, v. They are not the same thing by any means. That is also understood in standard cosmology. It should be understood here, that I talk about two theories in physics. From the same set of equations one can derive an equation that applies to Special Relativity (SR) on the local scale where expansion of the cosmos is set to zero, and an equation that applies to Carmeli’s spacevelocity theory for the cosmos where particles, the galaxies, are fixed in space. I do not have a united theory to combine these, nor did Carmeli. In each theory different meanings are applied to the radial coordinate r. This means Carmeli theory is also incomplete.
If r vs v is almost linear, the contributions to time dilation from u2/c2 and a2 are equal, so neither dominates.
You might be conflating or confusing spacetime and spacevelocity. In theory applied to the universe (cosmology) we assume u = 0. The idea is that the galaxies are stationary in space, while the space expands. Besides there is no experiment that you can do to locally measure the expansion of space. Expansion of space, in my opinion, is a highly debatable subject, but that is a discussion for elsewhere.
For travel in the radial direction, they cancel and there is no time dilation. For travel is perpendicular to r you get the normal SR time dilation. (2a) Do you agree?
No. The coordinate r is the radial coordinate in a spherically symmetric universe.
(2b) If not, what do you get in the two directions?
In the θ and φ angular directions? Those are the directions orthogonal to the radial cooordinate, r. You have Hubble expansion but in those coordinates you can set the total angular term in the metric dΩ2 = 0 for isotropy considerations. The coordinate r encodes the expansion then in all three directions, simply by the definition of isotropy. Isotropy is also assumed in the standard big bang model. The same solution of Einstein’s field equations in Carmeli’s spacevelocity can be found for cosmologies where the universe has a unique centre and bounded but finite, a finite number of local centres and without a centre, unbounded or bounded.
(2c) Why isn’t this ruled out by experiment, which measures time dilation in different directions as the same?
Because observations always see in the direction of the radial component only. In Carmeli’s cosmology we only look back in cosmic time or redshift. That is all we can ever measure anyway. Nevertheless there is no suggestion like you are trying to make. I think you have a real misunderstanding here.
For similar reasons, your model appears to predict different magnitudes of the speed of light in different directions.
No, that is absolutely not true. The speed of light c is constant and scalar. It is the only physical measureable parameter.
(3a) Why is this not ruled out by the Michelson-Morley experiment?
I don’t see how the MM experiment has anything to do with cosmology. It only measured local speeds (a null), not anything on the cosmological scale. Besides I believe that it is fundamentally impossible to devise any experiment that could, even in principle, measure the outbound and reflected inbound light signal in an expanding universe and get a non-null result.
(3b) Why is such a huge change of the speed of light you claim not ruled out by the measurement of an (to within a few parts in a million, at very most) constant fine structure constant?
Again, in this model c is constant for all observers. I don’t expect to see anything unusual in the fine structure constant. There is no huge change in the speed of light c. But if you are speaking about the one-way speed of light, not a physical property of spacetime, but something one could calculate, I suggest you read the following:
(3c) Why is your theory not ruled out by the decay times of elements measured in SN 1987a?
Actually Carmeli’s theory predicts a slight change in decay constants of radioisotopes but only at very high redshift. Since there is no change in the speed of light it is purely a relativistic effect. But since SN 1987a is extremely close to the Galaxy and at very low redshift, nothing unusual is expected.
Similarly, the energy of particles according to SR (and locally GR) whose velocity approach the speed of light tends to infinity. Not so in your model, which gives the similar energies for two directions perpendicular to r, but far less for the radial direction.
Do you mean in the θ and φ directions, orthogonal to the radial direction? The angular components? But as I said isotropy cancels any angular dependence. There is no such effect as you might be trying to suggest.
(4) In experiment we measure energies the same in all directions, so why doesn’t this rule out your theory?
No one measures energies in the θ and φ directions. All measurements in cosmology are in the radial (r) coordinate. And besides there are no cosmological measurements of energies of any sort that are not intrinsically conflated with an assumed cosmology.
(5) What intensity of starlight do you expect from your model, for both now and in the early universe, and why?
In chapter 6 of my book I briefly discuss expansion factors. I could only speculate that there are no unusual effects, as under that model we expect to see the universe as we do. Since we are dealing with spacevelocity not spacetime processes are a little different to what you might imagine.
I’ve given my straightforward calculation for the early universe, and your only response is that I was wrong, and that I was using GR (which I wasn’t, I was simply assuming conversion of energy and the geometry you described in words in your book). What do you actually get and why?
See page 96, I speculate about even a 10,000 fold increase in density (a net result due to volume reduction with expansion and the creation of new matter) would be no big issue. Remember, my model does not begin in the big bang. Carmeli’s did, but I have proposed other boundary assumptions. It is a Universe created by God who created form nothing, so it is then a question about how much can we understand with known physics.
(6) Why do you claim Carmeli is “secular” (even on the cover of your book)
On the introduction page before the Table of Contents Alex Williams wrote a recommendation where he wrote (inter alia),
There is no suggestion that Carmeli was a biblical creationist. He was ethnically Jewish, but was a big bang believer. I simply took his work, and added a new starting point.
when he, from his writings (both in his book, Cosmological Special Relativity, and on the arxiv), appears to be an old earth creationist at pains to square his cosmology with the Bible?
That is very strange to hear. I knew him quite well. Though his wife was a liberal believing Jew he had no religion. One time he wrote a paper (The First Six Days of the Universe) for a conference of Hebrew rabbi’s where he tried to relate his big bang universe timeline to the 6 Days of Genesis creation. That got him a lot of bad press but there was never any indication from him that he believed in God, let alone was a long age creationist. The paper he told me was for the rabbi’s who had invited him to the conference. So what you say is news to me.
(7) How is “cosmological special relativity” (CSR) distinguishable from lying?
Carmeli published his model in secular theoretical physics journals, as he developed it. I think it is really bad form to accuse him of lying, when he was doing what he had done his whole academic career, which I would say was quite distinguished. I would add though his CSR theory did not work well. It was more of a demonstration of ideas. Only when he developed his General theory was there anything that was useful for the real Universe.
If in a future “frame” we deny what we measured today, how is that not simply being dishonest?
What Carmeli suggested was simply based on the observations at hand. He was not calculating what would be measured in a future frame. His special theory only applied to past epochs and hypothetical observers at past epochs. Because it is not measureable, his concept of addition of cosmic times is curious but not something to be taken too seriously. In fact, this is one reason his CSR theory is invalid.
Carmeli, for example, says that the first day was 11 billion years long. The number of times a clock has ticked is an *objective fact*. If “day 1” was 11 billion years long, a clock would tick off 11 billion years. Surely someone who comes along later and claims the clock ticked any other number of times is simply lying.
No, he is explaining what one would measure from a relativistic effect according to his theory. Such effects often seem to defy common sense. As already explained I would not take this aspect of his CSR theory too seriously. But much the same was faced by Einstein for the first 30 years after he published Special Relativity. If you calculate the speed of a very fast-moving particle and you do so from different moving frames of reference, you will get a different answer each time. That is not lying. If you change coordinate frames, from one to another, a sequence of events in one frame can occur in opposite order to that in the other frame. That is not lying. It is relativity. What you can do in a laboratory you cannot do to the whole universe. In his CSR theory Carmeli constructed the analogue to SR and summed cosmic times instead of particle speeds.
(8) If, from the beginning onwards, we looked at a clock on a local star which ticks once a year (in that star’s local time), approximately how many times would we (here on earth) have actually seen it tick, according to your model?
According to that model, it would tick at the same rate as we measure locally. Of course, it cannot be measured. We assume that it is so before we make measurements about related things in the cosmos.
Similarly, if as Carmeli says that his own theory says, the first “day” is 11 billion years long, and the second 4, then the amount of time which has passed is 11+4=15 billion years. That is what a clock would measure. The total amount of time which has passed is not 11+4=11 billion years, and nor is it one day. There is no clock anywhere which measures that.
The correct analogy is the special relativistic addition of velocities formula. You could add the velocities of spacecraft in a similar fashion and get 1+1 not equal to 2 but 1.8. That is well established in SR.
(9a) Do you deny that 1+1=2 (when it comes to time) and (9b) say that the amount of time passed is *not* what is actually measured?
Quite obviously it is not that simple. Applied to the universe, well, we could never test Carmeli’s idea. What we measure is the answer. It is the amount of time that has passed.
I hasten to add, I do not hold too tightly to anything in cosmology, Carmeli’s or any other. Carmeli’s has several unsolved problems. Even the concept itself of a velocity dimension. Does that make any sense? Maybe there is another theory that contains some aspects of Carmeli’s cosmology, like a universe where time is not scalar, but a vector. Maybe the universe is not even expanding, then the Hubble Law, which seems to be valid for normal galaxies, must be due to some other process, not expansion of the cosmos. Can we find a cosmology where the Hubble law is valid but involves a static universe? Maybe?
In my view, this is all scratchings on pieces of paper compared to the Word of God, which is true and trustworthy down to the very first word in Genesis, “In the beginning God …”