In GR, space expands and clocks run faster in a background of declining gravitational density. For example, if you take an enormous cube of expanding space with galaxies moving apart in all directions, the expansion of space should also result in a quickening of time because of the declining gravitational density.
Meters don’t participate in expansion here because of two opposing effects. The expansion of space "stretches" the space of a meter but the acceleration of time reduces the length we define as a meter. The length of a meter is defined as the distance a beam of light can travel in a given length of time so the acceleration of time shortens the standard length of a meter. The two effects cancel so meters remain meters. Both meters and our observation of Einstein’s c remain unchanged because both are the same space/time ratio.
No, light traversing the expanded distance from A to B would take longer because our clocks are running faster and the distance would appear greater when measured in meters. In both models, light takes longerto traverse increasing distances but you need to remember that the misnomer "expanded" time means accelerated time, quickening time, faster running clocks, etc. It is also important to remember that this is more of a GR model than FLRW where time is largely static so the comparisons with FLRW don't match.

Hi Bob,

I hope you can help me out, because I'm having trouble understanding your proposal that on a universal scale, if space "expands", time must accelerate as well so as to keep "c" a constant.

Yesterday, while "parked" in unaccelerated motion in deep space, I performed an EVA to check the oil level on my Toyota rocket ship using my dipstick. For some light relief, I switched on my torch and decided to measure the distance that light travelled in 1/299792458th of a second, and found that it had travelled exactly the length of my dipstick. With a great sense of satisfaction, I conclude that my dipstick is one metre in length (mine's bigger than most).

Today however, I'm a little afraid to measure my dipstick again. Yesterday, someone told me that space is constantly expanding and that time runs faster and faster to compensate. Being a scientist, I gather that if this was true, then sure, "c" would remain constant. But what about my dipstick?

On the one hand, maybe my dipstick has grown a little from yesterday because space has expanded and expanded my dipstick with it. Oh, happy days! But it still measures one metre because time is running a little faster than yesterday. Ok, I can live with that.

But, on the other hand, despite space expanding, and time running a little faster than yesterday (to keep "c" a constant), I realise those pesky atomic and electromagnetic forces are just far too strong to let my dipstick stretch with the "expansion" of space-time. So, even though a "metre" is still a "metre", I'm afraid my dipstick will now measure less than a metre long - it will have appeared to have shrunk!

In space, no-one can hear you scream... So, how long is my dipstick?

It would appear that this enormous cube is already close to its maximal time rate overall (since it contains large volumes of space which are effectively flat, and others which are effectively dominated by local mass), but is unbounded in its capacity to increase in size.
So I wonder, in this cube, how the neat ratio of space and time "expansions" that you describe is maintained. Am I missing something cosmological?

So there isn't really any "offsetting" effect going on at all. We're seeing space get larger (acquiring more metres), while metres retain their proportional relationship with lightspeed. Any increased value of time rate, many decreased values of time rate, and no change in time rate would all produce this same picture (with different measured rates of expansion for observers inside the Universe). So maybe you don't need that precise space/time ratio, after all.
Like mc^2, I do wonder how you fit metre-sticks into this business, though. Do they expand with space (in which case light will take longer to travel along them); not expand with space (in which case light will still take longer to traverse them); or somehow contract in proportion to time, so as to keep aligned with lightspeed?

In which case you should readily be able to compare your model with FLRW and tell us which best matches observation. Or are they indistinguishable?

Grant Hutchison

One of us has got Bob Angstrom's thesis reversed.
The simple story that space and time lengthen together to preserve c seems to what tommac was saying. Bob, I think, has time going faster, making the distance travelled by light in a given time shorter, and therefore shortening the metre as defined by the flight of a photon. In effect, it packs even more (light travel-time) metres into expanding space. So its seems, under Bob's arrangement, that a physical dipstick would get longer, as measured by light travel-time.
I think.

Whatever: it seems that tweaking time to adjust the metre (via lightspeed) creates problems unless physical objects can react to the change in time rate and adjust their length to maintain consistency with the flight time of the photon.

Grant Hutchison

Oh.
I can't remember on which of the umpteen related threads I've said this before, but I guess it might bear repeating at this point:

To what extent is it meaningful to maintain that the rate of cosmological time changes? Relative to what observer? Under GR and SR we have separate observers who disagree about simultaneity and elapsed time. Under universal expansion, we have a cosmological time which is defined by the agreed elapsed time of comoving observers. So who is it who is stepping outside this metric with a clock in order to observer changes in the rate of elapsed time for the whole Universe, relative to their own elapsed time?
If we can't identify such an observer, then it seems we need to just accept that cosmological time elapses at a second per second, and that's all we know about it.

Grant Hutchison

Wrong on both accounts. Tommac has said repeatedly that "stretched" time is faster time. He most recently made this clear in post#56. And a physical dipstick held together by electrostatic forces would grow shorter than a standard meter measured by light travel time.

You have a great account of what happens to the length of a meter. Electromagnetic forces have not allowed your dipstick to keep up with changes in space-time so it has grown too short. Dipsticks tend to rust out every few million years anyhow so it sounds like you need a new dipstick calibrated to the proper length of a meter.

Light reaching us from distant sources is lengthened "redshifted" relative to light from our "now" reference frame so we have a valid comparison. There is no godlike observer with a standard time to tell us if the redshifting is strictly a recessional Doppler effect or due to changes in time or some combination of the two. We can only say with certainty that there is a change.

My point exactly.
So in what way is your description "necessary"?

Grant Hutchison

I have reviewed a number of alternative cosmologies and they all agree about one thing. There are too many space-time variables in cosmological redshifts to use them as precise measurements for distance or velocity so the exact size and extent of the universe is unknown. The FLRW model is the only one that can gives us any precise values by interpreting galactic redshifts as Doppler recessional values with space expanding but not time. The cosmologist Edward Harrison once picked three plausible density values for the universe out of thin air and compared them within the FLRW model. He found that a universe that is older and more massive than our universe is presently thought to be would fit observations better than the standard model. By better, I mean it would not require an inflationary period or dark energy to conform to observations so the standard model itself is telling us there is something wrong.

Well, it's good to know that you and tommac agree.
But you just told us that:That seems to imply that matter, unaffected by the spatial expansion, is going to end up seeming rather longer to a photon.

Well, that's fine, but it doesn't seem to answer my question of why you believe time expansion is "necessary" to maintain the speed of light, and it doesn't address my other questions about the details of your particular description.

Grant Hutchison

The "necessary" part is in not separating space from time and recognizing that changes in space are also changes in time. Also "empty" space is an abstract idea and adding more space to space is one abstraction on top of another. We only know of space-time by the matter it contains and how objects interact so looking at how the dynamics of space-time effects material objects and their interactions via light beams, detectors, and clocks is a more down to Earth point of view than speculating about adding distance to distance.

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