The Start of Dark Energy and the limits of the Universe

[Positor]

Since 1968, the length of a meter has been defined by convention as the distance light travels in 1/299,792,458th of a second and the duration of a second is defined as the time it takes light to travel 299,792,458 meters and c is a constant ratio of 299,792,458 meters per second. The units of time, distance and c are all mutually defined so, if clocks tick faster, the length of a meter must grow shorter if the value of c remains is to remain the same.

Thank you for your comments. I have read your post carefully, and I understand the points about inertial frames and the constancy of c. However, while I can conceptually grasp the idea of expanding (or contracting) space, I have difficulty in understanding what it means for time to quicken (or slow). What does it mean to say that 'time itself' accelerates 'over time' (?) in the same inertial frame? Clocks give more ticks per – what? It cannot be 'per second' if the length of a second is the very thing that changes.

You say elsewhere in your post: "We have no universal reference for either one [space or time] that could tell us which one or both are changing". What would such a reference look like? What would its necessary properties be? What units, formulae etc would apply to it?

Here’s the rub. The WMAP data gave the universe an equivocal cosmic age of 13.766 billion years based on the Hubble rate of growth of 73.5 kilometers per second per megaparsec but the Hubble rate is a cosmological ratio of distance to time as is the constant c so the Hubble rate varies in sync with the expansion of the universe while remaining the same within each individual reference frame. The consequence of this is that the measured 13.766 billion year age of the universe will remain the same 10 billion years from now just as it was 10 billion years in the past.

Is there general agreement about this?

[doogles]

Bangstrom, your statement in your last post "Luminous objects resembling tiny galaxies have been created by passing high voltage electricity through a vacuum in glass spheres. The effect looks exactly like a galaxy in a bottle." aroused my curiosity.

Do you have a reference to such an experiment that I can follow up? Thank you.

[bangstrom]

I have difficulty in understanding what it means for time to quicken (or slow). What does it mean to say that 'time itself' accelerates 'over time' (?) in the same inertial frame? Clocks give more ticks per – what? It cannot be 'per second' if the length of a second is the very thing that changes.

Time and space are both identical in all inertial frames but they both vary from one frame to another. In any given frame, one second of time is defined as the time it takes light to travel 300,000,000 meters. To say that time accelerates means to say that clocks tick faster in recent reference frames than they did in the past.

You say elsewhere in your post: "We have no universal reference for either one [space or time] that could tell us which one or both are changing". What would such a reference look like? What would its necessary properties be? What units, formulae etc would apply to it?

We have no universal reference so there are no units or formulae. If we can imagine the universe expanding form the size of a golf ball to the size it is today we must imagine that there is some universal reference that we can use to measure the outside diameter of the universe. This would be an unchanging measure used by a godlike being outside our universe who could watch the universe expand or contract from a safe distance and tell us the radius from a golf ball on up.

Here’s the rub. The WMAP data gave the universe an equivocal cosmic age of 13.766 billion years based on the Hubble rate of growth of 73.5 kilometers per second per megaparsec but the Hubble rate is a cosmological ratio of distance to time as is the constant c so the Hubble rate varies in sync with the expansion of the universe while remaining the same within each individual reference frame. The consequence of this is that the measured 13.766 billion year age of the universe will remain the same 10 billion years from now just as it was 10 billion years in the past.

Is there general agreement about this?

I don’t know if there is a general agreement about this but it depends on how we measure distance. Distance can be measured as the length of a material object or the length of a light wave. Prior to 1968 the length of a meter was defined as the length of a platinum bar kept in Paris. We now have a more convenient measure for the length of a meter as 9,192,631,770 20 wavelengths of a microwave emission from a cesium atom.

If we assume a platinum bar never changes in length, that means that the universe is expanding relative to the length of a meter stick and we can calculate how many years it took to expand to its present size.

But, if we measure the length of meter as wavelengths of light, light waves lengthen (redshift) as space expands so the the universe never expands relative to a meter stick defined as a given number of wavelengths. Light years also expand as the universe expands so the universe measured in light years never expands meaning that we can’t calculate the age of the universe based on how long it took to expand because the observed radius is a constant.

One way of understanding this is to recall from GR how clocks tick slower in a strong gravitational field while distances grow shorter but clocks tick faster as the gravitational field lessens and lengths grow longer. This is how events appear to a remote observer but, to an observer entering or leaving a gravitational field, clocks and space remain the same.

There is no remote observer from outside the universe to tell us how it looks from their point of view. We can only observe the universe from the inside where locally space and time are defined as constant relative to c.

[bangstrom]

Bangstrom, your statement in your last post "Luminous objects resembling tiny galaxies have been created by passing high voltage electricity through a vacuum in glass spheres. The effect looks exactly like a galaxy in a bottle." aroused my curiosity.

Do you have a reference to such an experiment that I can follow up? Thank you.

I have seen more more scientific references than this but here is an anecdotal account from Eric Dollard who has been creating galaxies in a bottle since his high school days. He said when he tried it in high school the lights in the neighborhood would dim and someone would have to pull the plug on the transformer before they had an explosion. Later he joined the Navy as an electrical engineer and he was told that about the same time the radar screens at the nearby naval base would go blank and the Navy never understood why.

https://video.search.yahoo.com/yhs/sear ... tion=click


Here is a 3 ½ hour lecture by Dollard explaining the history of the theories behind his work. It starts slow and elementary but picks up speed later.

https://video.search.yahoo.com/yhs/sear ... ction=view

[BurtJordaan]

You say elsewhere in your post: "We have no universal reference for either one [space or time] that could tell us which one or both are changing". What would such a reference look like? What would its necessary properties be? What units, formulae etc would apply to it?

Here’s the rub. The WMAP data gave the universe an equivocal cosmic age of 13.766 billion years based on the Hubble rate of growth of 73.5 kilometers per second per megaparsec but the Hubble rate is a cosmological ratio of distance to time as is the constant c so the Hubble rate varies in sync with the expansion of the universe while remaining the same within each individual reference frame. The consequence of this is that the measured 13.766 billion year age of the universe will remain the same 10 billion years from now just as it was 10 billion years in the past.

Is there general agreement about this?

Positor, it seems to me that Bangstrom is a scholar of pseudo-science and dissident scientists. Hence it seems to me that he has lost sight of what is going on in real science (for relativity and cosmology at least). So while he writes quite entertainingly, my advice would be to not take it too seriously.

The age of the universe is based on the Hubble constant today and observations of how it has changed over time - we can look billions of years into the past. Even if some of the parameters used in age determination, like the density parameter and the cosmological constant is off by some margin, the age that we arrive at would be different, but we would still conclude that the time since the BB is increasing by one earth-year per year.

If you are interested and mathematically inclined, I can show you how the precision calculations are done.

PS: While the age changes by one year per year, the size of the observable universe must change by just over 3 light-years per year.

[bangstrom]

Positor, it seems to me that Bangstrom is a scholar of pseudo-science and dissident scientists. Hence it seems to me that he has lost sight of what is going on in real science (for relativity and cosmology at least). So while he writes quite entertainingly, my advice would be to not take it too seriously.

I resemble that remark. I am always seeking new sources of interest and when encountering a novel idea I look for what might be right about the idea before looking for what might be wrong. I am a major skeptic about everything I encounter and enjoy the shopping more than the buy.

I see little value in discovering something wrong about a novel idea but discovering what might be right is golden. In high school, I discovered some concepts in Newtonian physics that failed under close scrutiny and, once I saw the problems, I was able to visualize possible solutions only to discover that Einstein had done the same long before and much better that I ever could. He also provided the math.

If you are interested and mathematically inclined, I can show you how the precision calculations are done.

Getting back to our matrix models, I see a problem with Escher’s drawing that would not work for contemplating expansion or contraction. A model with red spheres connected by lines work better but that problem is easily overlooked.

That said, I see my model with the red blocks shrinking in size while the blue bars remain the same length to be equivalent visually and mathematically to your model where the red blocks remain the same size while the blue bars lengthen. One is the simple inverse of the other so any conclusion drawn from one model should be precisely reproduced by the other if all the variables are properly considered.

Why should that not work?

While the age changes by one year per year, the size of the observable universe must change by just over 3 light-years per year.

If a star is 1 billion light years away today (or pick any other number of light years) how many light years away will the same star be in one year? A billion years?

[Positor]

If you are interested and mathematically inclined, I can show you how the precision calculations are done.

Yes please. I cannot guarantee that I will understand all the mathematics, but hopefully I will grasp the main points.

[Positor]

If we can imagine the universe expanding form the size of a golf ball to the size it is today we must imagine that there is some universal reference that we can use to measure the outside diameter of the universe. This would be an unchanging measure used by a godlike being outside our universe who could watch the universe expand or contract from a safe distance and tell us the radius from a golf ball on up.

According to my understanding, there is no 'outside' to the universe. Any godlike being would have to be inside!

If there is no 'universal' frame of reference inside the universe, therefore, there cannot be one at all. In that case, the question of whether space is 'really' expanding or time is 'really' accelerating (or both) is meaningless; the two kinds of change are simply equivalent.

The idea of time 'accelerating' universally (rather than relatively, in different frames) still seems incoherent to me.

If we assume a platinum bar never changes in length

Can we assume that? If the universe is expanding, wouldn't the space between the two ends of the bar expand?

the measured 13.766 billion year age of the universe will remain the same 10 billion years from now just as it was 10 billion years in the past.

If that is so, how is it possible to conclude that the Big Bang took place?

[bangstrom]

If we assume a platinum bar never changes in length
Can we assume that? If the universe is expanding, wouldn't the space between the two ends of the bar expand?

In particle theory, the short range nuclear force and gravity hold the bar and all other material together. Galaxies have far more space than solid matter and lack the strong nuclear force between stars so galaxies should expand as the universe expands but at a slightly slower pace. There doesn’t appear to be a sharp divide between expansion rates of galaxies and solid matter so the gravity explanation appears weak and we need to look for a better explanation.

the measured 13.766 billion year age of the universe will remain the same 10 billion years from now just as it was 10 billion years in the past.

If that is so, how is it possible to conclude that the Big Bang took place?

The statement doesn’t necessarily rule out the Big Bang but it implies that the distance of a light year is the same in all inertial reference frames just as c is a constant in all reference frames. If we measure the distance of a light year now, it should be shorter than a light year measured a billion years from now if the universe is expanding but the radius of the expanded universe should be calculated to be the same as it appears today because the length of a light year expands in sync with the expansion of space. This makes the calculated radius of the universe a constant so the estimated age of the universe based on how long it took the universe to reach its present size is also a constant.

The old balloon analogy applies here. If the circumference of the balloon is marked by ten equally spaced dots on its surface the circumference of the balloon will always be ten dots no matter what the size of the balloon.

... how is it possible to conclude that the Big Bang took place?

The proof for the Big Bang that ruled out the alternatives was the discovery of the 2.7 K cosmic background radiation left over from the big bang when the universe had cooled enough so that matter and energy could go their separate ways.

Early radio engineers knew the 7cm band was unusable because of the interference on that part of the radio spectrum and they attributed the interference to the presence of dust and gases in space being heated by stars and re-radiating their energy at an extremely low equilibrium temperature which Arthur Eddington had called the “temperature of space.”

Penzias and Wilson rediscovered this radiation and explained it as residual energy left over from the Big Bang. I think the paper below is important in understanding the source of the background radiation.

History of the 2.7 K Temperature Prior to Penzias and Wilson
https://www.ifi.unicamp.br/~assis/Apeir ... 79-84(1995).pdf

[BurtJordaan]

If you are interested and mathematically inclined, I can show you how the precision calculations are done.

Yes please. I cannot guarantee that I will understand all the mathematics, but hopefully I will grasp the main points.

The starting point for cosmic age determination is to get present values for some cosmic parameters and then plug them into the first Friedmann equation, which in its most digestible form is

This is already a mouthful, so let me explain briefly.
H is the time variable Hubble value (essentially the changing expansion rate over cosmic time) and Ho is the present observed Hubble expansion rate.

All the Omegas are today's best observed density parameters, so they are essentially constants. The omegas in order of appearance are: Lambda (vacuum energy) density; overall energy density; matter energy density and finally radiation energy density. They are all expressed as fractions of the critical energy density, which is the total energy density that, given the present Ho, will balance the expansion rate with the energy density. More about that later.

The z's are cosmological redshifts, ranging from z=0 at present, to z approaching infinity just after the BB. They are used to scale the relative densities of the various components over the full range of the possible redshifts. Note the power 0.5 at the end, which is just way simpler than putting a square root sign around the outer brackets of the equation.

I will break the post here and continue in the next one, because some or other bug in the system doesn't allow me to upload another attachment for the final equation.

[BurtJordaan]

If you are interested and mathematically inclined, I can show you how the precision calculations are done.

PART 2

In order to make the the final equation a little more convenient to write (and read), I usually define s=z+1 and also use the Hubble time, which is just T_H=1/H. Then the time since the BB is just this rather simple-looking integral:

Unfortunately, once you have substituted the flesh of T_H = 1/H back in, it is not simple and as a matter of fact, only a super-computer doing numerical integration (small step-by-small-step summation) can spit out a precise value.

Fortunately, since the parameters are not known with very high precision, any numerical integration software, running on a laptop or even on a cell phone can today do it to adequate precision. With Ho=68 km/s/Mpc, the vacuum energy about 69%, matter energy about 31% of critical density (radiation energy is a very small fraction) and with flat space, my laptop spits out a time of about 13.8 billion years. Now we can talk a lot about how these parameters are determined, but they are our best-buy from all available data that has been processed up to 2015. More about that in a later post.

Let me know if you have any difficultly reading the math and let's clear that up before continuing down the parameter road.

[Positor]

Let me know if you have any difficultly reading the math and let's clear that up before continuing down the parameter road.

Thanks very much. I will need some time to digest this, as the math is a little above my level. But I will look at it carefully and let you know if I have any questions before you continue.

[Positor]

The statement doesn’t necessarily rule out the Big Bang but it implies that the distance of a light year is the same in all inertial reference frames just as c is a constant in all reference frames. If we measure the distance of a light year now, it should be shorter than a light year measured a billion years from now if the universe is expanding but the radius of the expanded universe should be calculated to be the same as it appears today because the length of a light year expands in sync with the expansion of space. This makes the calculated radius of the universe a constant so the estimated age of the universe based on how long it took the universe to reach its present size is also a constant.

It would be illogical to say that the universe has always 'really' been 13.8 billion years old. The expression "13.8 billion years old" necessarily implies that it was 12.8 billion years old a billion years ago.

If we say that the universe is always measured (or calculated or estimated) to be 13.8 billion years old, that means there is something wrong, or incomplete, in our measurement. If you are correct that the length of a light year expands, then that needs to be factored in when comparing two (hypothetical) measurements a billion years apart. Then we would get two different values for the age of the universe, and any contradiction would be avoided.

[BurtJordaan]

If a star is 1 billion light years away today (or pick any other number of light years) how many light years away will the same star be in one year? A billion years?

The Hubble rate (converted from km/s/Mpc to Giga-year units) is 0.07 Gyr^-1. The proper distance increases at the Hubble rate, so in a billion years the 1 billion light years will become 1.07 billion, roughly. Actually a little bit more, because the Hubble expansion works like compounded interest.

[bangstrom]

It would be illogical to say that the universe has always 'really' been 13.8 billion years old. The expression "13.8 billion years old" necessarily implies that it was 12.8 billion years old a billion years ago.

If we say that the universe is always measured (or calculated or estimated) to be 13.8 billion years old, that means there is something wrong, or incomplete, in our measurement. If you are correct that the length of a light year expands, then that needs to be factored in when comparing two (hypothetical) measurements a billion years apart. Then we would get two different values for the age of the universe, and any contradiction would be avoided.

I am saying the observed and calculated distances within the universe measured in light years remain the same. The length of a light year is a dimensional constant just as c is a dimensional constant. Both are units of distance divided by time.

If space expands, the light waves within expand and the distance of a light year also expands so distances measured in light years are like an infinitely stretchable rubber ruler. This makes the light year unreliable as a measure of either distance or time. The “year” part allows us to use the light year as a measure of time but, like a flat map of a curved surface, it works locally but not at the extremes.

When the universe was one light year in diameter relative to our light years, it was nearly 14 billion light year in radius measured from the inside. The amount of spacetime within the universe remains constant over time but it stretches out and becomes less crowed as time goes on.

[bangstrom]

The Hubble rate (converted from km/s/Mpc to Giga-year units) is 0.07 Gyr^-1. The proper distance increases at the Hubble rate, so in a billion years the 1 billion light years will become 1.07 billion, roughly. Actually a little bit more, because the Hubble expansion works like compounded interest.

These comments logical but I find the implications contrary to General Relativity where time should quicken as the universe grows older and less gravitationally dense.

My question is What is changing?

If the newer light year is longer, that means that light has traveled faster to cover a greater distance or time has slowed to make the year longer. Something must be wrong with this picture.

[BurtJordaan]

These comments logical but I find the implications contrary to General Relativity where time should quicken as the universe grows older and less gravitationally dense.

My question is What is changing?

I take it that you mean "what makes GR work differently for cosmological cases, versus around stars and black holes"? The relative difference in time in GR depends on difference in gravitational potential, not difference in density. The universe at large is at the same gravitational potential, with only minor "gravitational dents" at the bound galaxies and bound clusters. Think about the balloon analogy: where on the surface of the balloon will the gravitational potential differ - only in the dents of course.

But the universe is largely voids, so we take the whole as at uniform gravitational potential. Hence LCDM is an approximation, but it is a very close one. For some observations, cosmologists take into account the paths that light rays follow through and around the "minor dents". Think about gravitational lensing, but there are other effects as well that are taken into account.

If the newer light year is longer, that means that light has traveled faster to cover a greater distance or time has slowed to make the year longer. Something must be wrong with this picture.

For the gravitational potential reasons of above, the light year does not get longer. A billion years into the future, the 1 Glyr proper distance will simply become 1.07 Glyr, as measured by the same light-year metric as today. That's what Einstein's GR says and that's how his own original cosmological model worked. Recall that he found that his model either expands or contracts and could not be static - hence he chose a non-zero cosmological constant in a futile effort to keep it static.

[bangstrom]

These comments logical but I find the implications contrary to General Relativity where time should quicken as the universe grows older and less gravitationally dense.

My question is What is changing?

I take it that you mean "what makes GR work differently for cosmological cases, versus around stars and black holes"? The relative difference in time in GR depends on difference in gravitational potential, not difference in density.

That isn’t what I was asking or what I had in mind but since you answered. I am not interested in the little bumps of gravitational density (potential may be a better term) around stars or black holes or galaxies. I am interested in the larger changes in gravitational potential. If the universe was once the size of a golf ball, that is what I would call a high gravitational potential. Today we have a far weaker gravitational potential because the mass of the universe is highly dispersed to a larger volume. That is a big jump downward in gravitational density- perhaps the biggest.

As I understand GR, a move from an environment of high gravitational potential to an environment of low gravitational potential involves an expansion of space and a quickening of time. Another way of describing this is to say we are moving from a universe of highly curved spacetime to one of barely curved spacetime. So the universal trend is from an environment of dense space and slow time to one of expanded space and quicker time.

Here is my question and it doesn't necessarily have anything to do with GR.

I asked, "What is changing? If the newer light year is longer, that means that light has traveled faster to cover a greater distance or time has slowed to make the year longer?

What is the change that makes a light year longer in the future than it was in the past? Faster light, slower time, quicker time, or something else?

[Faradave]

"What is changing? If the newer light year is longer, that means that light has traveled faster to cover a greater distance or time has slowed to make the year longer?

If you're driving at constant speed on a rubber road and the road gets stretched to twice its length, you have farther to drive (and taking a longer time) to get to the end but that does nothing to change your speed. So it is with expansion of space.

[BurtJordaan]

What is the change that makes a light year longer in the future than it was in the past? Faster light, slower time, quicker time, or something else?

But who said the light year gets longer? They stay the same as what they always were and the distance between clusters gets larger - as would be measured by radar (or standardized meter sticks), if we could 'freeze' the expansion somehow.

Another thing that you have wrong is that the universe started out as a tiny thing - it is only the observable universe that started out tiny, simply because light could only have moved a short distance in the first nanosecond after the BB. As far as we can establish, the universe itself started out infinitely large and obviously then still is...

I understand that you find it difficult to accept, but then, we are talking mainstream science, not opinions or preferences. The mainstream is backed by a century of insights into Einstein's theory and an enormous amount of observations supporting it.

[bangstrom]

"What is changing? If the newer light year is longer, that means that light has traveled faster to cover a greater distance or time has slowed to make the year longer?

If you're driving at constant speed on a rubber road and the road gets stretched to twice its length, you have farther to drive (and taking a longer time) to get to the end but that does nothing to change your speed. So it is with expansion of space.

I understand the example to be more like an enormous circular racetrack where all cars are not moving but the track is stretching to twice its circumference. The question remains as to why the road is expanding. Is it faster light, slower time, older whiskey, younger women, faster horses…?

[bangstrom]

But who said the light year gets longer? They stay the same as what they always were and the distance between clusters gets larger - as would be measured by radar (or standardized meter sticks), if we could 'freeze' the expansion somehow.

I understand the light year remains constant in every reference frame but it must be growing longer with every reference frame if the universe is said to be expanding. Expansion “stretches” out the distance of a light year just as it stretches out light waves.
Our units of measure are now standardized by measurements involving light so the units of distance, time, and the value of c are all mutually defined. This makes the meter a constant fraction of a light year.

Another thing that you have wrong is that the universe started out as a tiny thing - it is only the observable universe that started out tiny, simply because light could only have moved a short distance in the first nanosecond after the BB. As far as we can establish, the universe itself started out infinitely large and obviously then still is...

I understand that you find it difficult to accept, but then, we are talking mainstream science, not opinions or preferences. The mainstream is backed by a century of insights into Einstein's theory and an enormous amount of observations supporting it.

I have a problem with an infinitely large universe and, if light in the primal universe could only move a short distance, a light year must have been much shorter then.
As I understand the mainstream view, the entire universe started out tiny and expanded from there. My personal preference favors an enormous universe that remains the same size while all matter within grows smaller so I am asking about about what I consider to be the mainstream view.

I don’t find your view consistent with any mainstream opinion where the universe is infinite and the only thing that expands is our observable radius. That model would invalidate some of the markers of early universal evolution such as nucleosynthesis.

[Faradave]

an enormous circular racetrack where all cars are not moving

"not moving" is just another speed (of zero magnitude relative to the race track or even the cosmic background). To the extent you suggest it remains constant during expansion, so do all the other possible speeds.

The question remains as to why the road is expanding.

That's a good question! But keep in mind that we could be misperceiving this. A beauty of 4D spacetime is that it lays out all of space and all of time (a deterministic perspective). Worldlines, such those of our own particles, extend from the past to the future. From this view, space doesn't need to actually stretch, rather a worldline emerges into larger and larger spatial layers. In a flat geometry this is referred to as expanding blocks (like keystones) but I prefer the larger circular arcs of curved-space, radial-time (like a worm eating its way out of an onion).

Is it faster light

No. Speed limit c remains as steady with respect to expansion as any other speed. c is special for numerous other reasons discussed earlier. But your cars, while motionless with respect to the racetrack, are still separating (or "receding") from each other. That recessional speed is among the class phenomena unrestricted by speed limit c.

[Positor]

Let me know if you have any difficultly reading the math and let's clear that up before continuing down the parameter road.

Thanks very much. I will need some time to digest this, as the math is a little above my level. But I will look at it carefully and let you know if I have any questions before you continue.

Where do the exponents 2, 3 and 4 in the first Friedmann equation come from? And why is 1 added to z?

It is a long time since I did calculus at school, so I am not clear about all the details of the integral.

But I think I understand the gist of the procedure you are describing, so please continue with your explanation.

[bangstrom]

But keep in mind that we could be misperceiving this. A beauty of 4D spacetime is that it lays out all of space and all of time (a deterministic perspective). Worldlines, such those of our own particles, extend from the past to the future. From this view, space doesn't need to actually stretch, rather a worldline emerges into larger and larger spatial layers. In a flat geometry this is referred to as expanding blocks (like keystones) but I prefer the larger circular arcs of curved-space, radial-time (like a worm eating its way out of an onion).

That makes sense to me. Taking a clue from E. Abbott’s “Flatland,” expanding spacetime is like a 4D hypersphere passing through our 3D Sphereland. We are in that sphere that appeared from nowhere and now appears to be expanding in 3D space but remains unchanged in 4D space.

The speed of this expansion is governed by the rate at which 4D spacetime becomes apparent to us in 3D space and not by the inertia of galaxies given a boost of energy from the Big Bang so the observed redshifting of distant galaxies is due to global changes in space and time misinterpreted as the galaxies being driven by inertia.

Speed limit c remains as steady with respect to expansion as any other speed. c is special for numerous other reasons discussed earlier. But your cars, while motionless with respect to the racetrack, are still separating (or "receding") from each other. That recessional speed is among the class phenomena unrestricted by speed limit c.

Speed limit c is a constant but I don’t like to think of it as the speed of light since it appears to be a dimensional constant of spacetime rather than the speed of anything. c appears to be a constant limit resulting from the combined rates of the magnetic permeability and electro permittivity of free space as found in Maxwell’s equations.

Some refer to c as the “rate of creation” and it may be the rate at which 4D “curved-space-radial-time” geodesics become apparent to our 3D senses which appears to us as the creation of more space.

[Faradave]

c appears to be a constant limit resulting from the combined rates of the magnetic permeability and electro permittivity of free space as found in Maxwell’s equations.

I think we're moving in a similar direction. As you note, Maxwell's ingenious derivation, it relies on the electric (ε₀) and magnetic (μ₀) constants. Like the related fine structure constant, these are measured values. From them, Maxwell clearly identified light as an electromagnetic phenomenon. However, in terms of explaining speed limit c, his result is not fundamentally different than measuring it.

Further, one should realize that by the same reasoning, Maxwell also implicated gravity (which also propagates at c) as electromagnetic!

Speed limit c … appears to be a dimensional constant of spacetime

I agree that speed limit c arises fundamentally from the underlying structure of the continuum. I derive this briefly from first principles in this post and published more completely here.

[BurtJordaan]

I understand the light year remains constant in every reference frame but it must be growing longer with every reference frame if the universe is said to be expanding. Expansion “stretches” out the distance of a light year just as it stretches out light waves.

I still do not know where you get that from - you may be mixing reference frames in your conviction. The number of light years fitting in between two clusters are simply more in the future - why do the light years need to stretch? The speed of light is the same for all wavelengths - that's been observationally proved over and over. And if we talk 'light years' we use a uniform (cosmic) time coordinate, otherwise a light year becomes an undefined measure.

I have a problem with an infinitely large universe and, if light in the primal universe could only move a short distance, a light year must have been much shorter then.

False logic, probably based on your "expanding light year", which may be the source of the errors in thinking.

I don’t find your view consistent with any mainstream opinion where the universe is infinite and the only thing that expands is our observable radius.

I think it is time that you learn the mainstream view properly. These arguments are going nowhere and this is surely not a course in cosmology. You must also understand the way that the radius of the observable universe, the Hubble radius and the distance between distant clusters all expand together, but are not in unison at a 1 to 1 expansion rate.

For example, here are some important present cosmic radii: the Hubble radius is 14.4 Gly, the cosmic event horizon radus is 16.5 Gly, the CMB radiation radius is 31.5 Gly and the radius of the observable universe is now 46.3 Gly. This is the distance that a particle emitted at time zero (and could get through to us without being absorbed by the original plasma) would have covered traveling at the speed of light.

The minimum size of the total universe, if it is not spatially perfectly flat and taking the maximum uncertainty towards the positive curvature side, is more than a trillion light years in radius. This is difficult to imagine, but the balloon analogy might help - the circumference of the balloon must be more than 2 trillion light years, practically infinite. The observable universe is just a small patch on the surface.

[BurtJordaan]

Where do the exponents 2, 3 and 4 in the first Friedmann equation come from? And why is 1 added to z?

Let me start with with z. It is the classical redshift, i.e. a fractional change in wavelength, e.g. if a signal's transmitted wavelength is 100 and the received wavelength is 200, the fractional change is z=(200-100)/100 = 1. In cosmology we do not want the fractional change, but the actual ratio between the wavelengths, 200/100=2, which is the same as z+1.

The exponents in the equation indicate how the energy densities change with wavelength ratio change due to expansion of the universe, e.g. curvature energy density changes with a 2nd power, matter density with a 3rd power and radiation energy density with a 4th power of the wavelength ratio, which is the z+1 above.

Another way is to note that curvature is a 2-dimensional and matter a 3-dimensional energy entity. Radiation is is 4-dimensional energy entity, because it is like matter, but with the redshift of the radiation, it loses another factor (1+z) of energy. Note that the Lambda (vacuum energy) density does not get influenced by the expansion. In other words, vacuum energy density is just a constant, like Lambda

You are welcome to ask more questions. As I said to Bangstrom, this cannot be a tutorial on cosmology, but Q&A on mainstream science is cool.

[bangstrom]

All I see are a lot of unsupported assertions about your mainstream views that make little sense to me and I don’t even find them to be mainstream.

I understand the light year remains constant in every reference frame but it must be growing longer with every reference frame if the universe is said to be expanding. Expansion “stretches” out the distance of a light year just as it stretches out light waves.

I still do not know where you get that from - you may be mixing reference frames in your conviction. The number of light years fitting in between two clusters are simply more in the future - why do the light years need to stretch?

I assume you are referring to distant star clusters. If there are more light years between the star clusters in the future than there are now, where are the additional light years coming from?

The mainstream answer is that the galaxies are moving farther apart because the space between them is expanding. Light waves in transit between the clusters are also “stretched out” which is why we have redshifting and why light years, just as light waves, are stretched out by the expansion of space..
This is basic elementary cosmology.

https://www.scientificamerican.com/arti ... 999-10-21/
“Distant galaxies are not traveling at a high speed through space; instead, just like our own galaxy, they are moving relatively slowly with respect to any of their neighboring galaxies. It is the expansion of space, between the time when the stars in these distant galaxies emitted light and our telescopes receive it, that causes the wavelength of the light to lengthen (redshift). Space is itself infinitely elastic; it is not expanding into anything."

The speed of light is the same for all wavelengths - that's been observationally proved over and over.

I know c is the same for all wavelengths. Why do you assume I don’t know elementary physics?

And if we talk 'light years' we use a uniform (cosmic) time coordinate, otherwise a light year becomes an undefined measure.

The uniform (cosmic) time coordinate is a mathematical devise used in models that sets time as a constant similar to the use of comoving coordinates. It does not operate in the natural world or in relativity where time dilations are involved. It is not real and it does not make the light year a constant anywhere except on paper.

[BurtJordaan]

I assume you are referring to distant star clusters. If there are more light years between the star clusters in the future than there are now, where are the additional light years coming from?

In the mainstream it comes from the metric expansion of the universe. Now this is elementary cosmology.

Light waves in transit between the clusters are also “stretched out” which is why we have redshifting and why light years, just as light waves, are stretched out by the expansion of space..
This is basic elementary cosmology.

As far as the "stretching" light years are concerned, you have your elementary cosmology wrong.

The increase in wavelength happens gradually, as the light from distant sources travels through successive small local inertial frames at speed c, en route through the void. If you could use a radar locally in such a frame to continuously measure the distance between its "ends", you will find two things: there is a small redshift in the return signal and the distance measured by the radar gets progressively larger, both rather slowly due to the smallness if the frame. This is metric expansion of space. More light years, not "longer light years".

One can actually add up all the small redshifts and end up with the redshift of a cosmologically distant source. It can be adapted for large distances through the void as well, but then it becomes more technical.

This is only slightly more than elementary cosmology, but if you want a proper treatment of this, consult any modern cosmology textbook. e.g. by Prof. Peebles, "Principles of Physical Cosmology", or Prof. Peacock, "Cosmological Physics".