# Thread: Accelerating Expansion vs Increasing Curvature

1. I've been hung-up on this idea for years & need closure. Can the redshift of a distant object be simulated via stretching its light geodesic along an increasing arc? To illustrate: picture an elastic band anchored to two posts, grab its center, & gradually pull in one direction. If the elastic band were light following curving space, wouldn't the resulting phenomenon be a redshift?

If plausible, I'd like to accelerate the expansion of this topic until it collapses.

2.

3. Can the redshift of a distant object be simulated via stretching its light geodesic along an increasing arc?
Can you explain this a little further - changing the geometry of a null geodesic does not necessarily equal redshift. Consider, for example, this image of a gravitational lens :

The light here is gravitationally deflected in the manner you describe ( I think - rubber band ), but there is no net red/blueshift involved. Do you have any maths to describe what your idea is - what would the global curvature in your universe be like ? I can't really picture it, because for redshift to be present in an otherwise static space-time the receiver and emitter need to be in differing gravitational potentials relative to one another.

4. Originally Posted by 6nqpnw
I've been hung-up on this idea for years & need closure. Can the redshift of a distant object be simulated via stretching its light geodesic along an increasing arc? To illustrate: picture an elastic band anchored to two posts, grab its center, & gradually pull in one direction. If the elastic band were light following curving space, wouldn't the resulting phenomenon be a redshift?
Red shift is dependent on the relative motion of the emitter, not upon the distance traveled.

5. Suppose an emitter emits two pulses of light, 1 second apart as measured at the emitter. These two pulses of light follow two different paths in four-dimensional spacetime, each path reaching the observer at a different time as measured at the observer. If the interval between the two pulses as seen by the observer is greater than 1 second, then we would say that there has been a redshift. Simply bending the paths wouldn't change the time between them.

6. Originally Posted by KJW
Simply bending the paths wouldn't change the time between them.
However, if the path were continuously getting longer ...

7. Originally Posted by Strange
Originally Posted by KJW
Simply bending the paths wouldn't change the time between them.
However, if the path were continuously getting longer ...
Yes. But not a simple bending of the paths.

8. Originally Posted by KJW
Originally Posted by Strange
Originally Posted by KJW
Simply bending the paths wouldn't change the time between them.
However, if the path were continuously getting longer ...
Yes. But not a simple bending of the paths.
That's precisely why I said "curving space" rather than "curved space". If the light were traveling along an increasing curvature, would the end result be a redshift? No different than accelerating expansion, only that it's exaggeratedly non-linear.

9. Originally Posted by 6nqpnw
No different than accelerating expansion
It is different because the shape of the three-dimensional space is independent of its expansion.

10. It should be remarked that expanding a curved space tends to decrease the magnitude of that curvature.

11. Originally Posted by Markus Hanke
Can the redshift of a distant object be simulated via stretching its light geodesic along an increasing arc?
[...] for redshift to be present in an otherwise static space-time the receiver and emitter need to be in differing gravitational potentials relative to one another.
Mr. Markus, that's what I was building up to. But not static space-time, rather static distant objects relative to each other (the two posts in my aforementioned analogy); space-time is the stretching rubber band (expanding space-time, curvature increasing over time, . Thank you for not talking down to me, but I fear my ignorance is preventing a clearer explanation ('cause I had to chew on what you said for a while before I could start to respond) ::: I cannot provide descriptive math, only bad analogies. When you say, "differing gravitational potentials", it somewhat eludes my understanding, though I am most certainly implying a strong gravitational influence on the space-time between two distant objects.

I need to confirm this initial concept (behavior of light / redshift) before I can elaborate any further. For if it is impossible, then I have built a house on the sand as high tide approacheth.

12. Originally Posted by KJW
It should be remarked that expanding a curved space tends to decrease the magnitude of that curvature.
Does that mean blueshift would be observed?

13. As far as I'm aware, though I'm not an astrophysicist to be able to offer confirmation, the measurements we make of the cosmos are sufficient to distinguish between the qualitatively different geometries of spacetime.

14. Originally Posted by 6nqpnw
Originally Posted by KJW
It should be remarked that expanding a curved space tends to decrease the magnitude of that curvature.
Does that mean blueshift would be observed?
I think so, though it's hard to say without doing the mathematics.

15. Originally Posted by 6nqpnw
That's precisely why I said "curving space" rather than "curved space". If the light were traveling along an increasing curvature, would the end result be a redshift? No different than accelerating expansion, only that it's exaggeratedly non-linear.
The thing is, we have an existing theory derived from some pretty basic principles that explains gravity and other effects in terms of the curvature of space-time. One solution to these equations ends up showing that the distances between objects are increasing, which matches what we observe.

Now it might be possible that there is another solution to these equations that describes the path between two objects getting increasingly curved, but I have never heard of such a thing and have no idea if it is possible.

One problem is that we measure the distance between things by measuring the path. You seem to be suggesting that the path gets more curved, and so gets longer, but without them getting further apart. That seems to be a contradiction. Unless you are suggesting that this somehow only affects light ... or something.

16. Originally Posted by Strange
You seem to be suggesting that the path gets more curved, and so gets longer, but without them getting further apart. That seems to be a contradiction.
YES! You got it. And not only without getting further apart, but possibly moving closer. So long as the rate of increasing curvature is greater than the rate of decreasing distance between two objects. Undoubtedly, I have not sufficiently explained & probably further confused everyone, myself included.

I'm not asking whether it's been observed or hypothesized, but whether this phenomenon could occur (given all our modern-day understandings). If not, then what law is being violated?

17. Originally Posted by 6nqpnw
If not, then what law is being violated?
Geometry?

If the path is more curved, then it is longer. That is what "further apart" means. Isn't it?

18. Originally Posted by KJW
It should be remarked that expanding a curved space tends to decrease the magnitude of that curvature.
Could you elaborate? If a geodesic is longer from one moment to the next, whether it be straight, curved, curly-cue, squiggly, or what have you, it would result in a redshift ::: as I understand it anyway. And like you, I am by no means a cosmetologist or astrological physicist but do value your feedback (as well as most others here).

19. Originally Posted by Strange
Geometry?

If the path is more curved, then it is longer. That is what "further apart" means. Isn't it?
Yes sir, the path is longer but the points of origin are a fixed distance from one another; so they're not further apart... I think I just clued-in to what u were saying about affecting only light and nothing else. Lemme try another bad analogy:

Two boats failing to escape a whirlpool are tethered together by a loosely hanging, nylon tube. Tension on the tube increases as it approaches the whirlpool, causing it to stretch. Since this is occurring in the pitch black of night, the only way for the boats to be aware of one another is by looking through the tube & measuring the red blue shift, which they determine to be red / moving further apart; whereas another observer (with night vision) would see the boats about to collide.

20. Originally Posted by 6nqpnw
Yes sir, the path is longer but the points of origin are a fixed distance from one another; so they're not further apart...
The thing is, the path is what defines the distance. My turn to try a bad analogy.

Imagine two cities on Earth. They are some distance apart, along the curved surface. Now, if a ridge of mountains starts rising between them, the path gets longer. Looking at it from outside, you might say that the cities are no further apart. But if the residents want to travel from one city to another, they have to travel that path and they will tell you the cities are much further apart.

There is a reason "geodesic" (the equivalent of a straight line in a curved space) comes from geodesy, the science of measuring the size and shape of Earth!

21. Originally Posted by 6nqpnw
Originally Posted by KJW
It should be remarked that expanding a curved space tends to decrease the magnitude of that curvature.
Could you elaborate?
A larger sphere has a lower surface curvature than a smaller sphere.

Originally Posted by 6nqpnw
If a geodesic is longer from one moment to the next, whether it be straight, curved, curly-cue, squiggly, or what have you, it would result in a redshift
Correct. But redshift isn't the only information available. One could examine the size of objects at a given distance from us, comparing their angular size in the sky to their physical size. Everything is encapsulated in the Friedmann-Lemaître-Robertson-Walker metric.

22. Originally Posted by Strange
The thing is, we have an existing theory derived from some pretty basic principles that explains gravity and other effects in terms of the curvature of space-time. One solution to these equations ends up showing that the distances between objects are increasing, which matches what we observe.

23. And if it's as complicated as FLRW metric, don't bother ::: too many technical references.

24. Originally Posted by 6nqpnw
And if it's as complicated as FLRW metric, don't bother ::: too many technical references.

I'm sure there are some good non-technical descriptions ... but I'm not familiar with them, I'm afraid.

25. Originally Posted by 6nqpnw