Allusion does not constitute discussion. Merely the major point not brought up in the link or response here. As has been alluded to many times in this and many other threads. Research does involve funding without which we'd have nothing to talk about except your philosophical complaints.
The precise formula, or metric, we use for calculating the distance between points with specified coordinates depends on the number of spatial dimensions.
In 2D space we describe points using coordinates (x, y) and use the formula below to calculate the distance between them.
In 3D space we have (x, y, z) coordinates and so must include a (z1 - z2)^2 factor.
In spacetime, instead of describing points using coordinates (x, y, z), spacetime events are described using coordinates (x, y, z, ct), where c is the speed of light. (Note that c has units of length/time and t has units of time, so ct has units of length, just like x, y, and z.)
This conveys to me that the spacetime metric contains a fourth 'spatial' term which is time dependent.
Now, and this is way too simplistic, I deduce that a change in the time dependent term will result in a change in distance between spacetime events even though the x, y and z coordinates remain the same. So, to some extent, I can imagine how space is somehow 'growing' in between galactic clusters without the clusters themselves actually moving!
However, like you indra1, the required mathematical knowledge of metric transformations, metric tensors (or whatever) remains way above my head!
You see this in your mind's eye? I can see how coordinates don't change but with expansion, objects would have to move to maintain their respective positions? The only way this can happen is if objects' size reduces accordingly which draws the question whether space is expanding. Just thinking out loud.
It's not that I can visualise the way space expands any more than the next person, but I can accept that mathematics can describe the process.
Take the simple example of measuring the distance between two cities on the Globe.
If I use a straight line cut through the Earth's crust, I would find the distance between Los Angeles and New York to be 2,428 miles.
If I now measure along the spherical surface of the Globe, I would find that the distance between the two cities has increased to 2,468 miles - even though their positions on the Globe have not changed.
Spacetime is a bit like that. The distances between spacetime events can change depending on the metric with which they are measured (and that metric is changing with time).
The unavoidable fact is that spacetime geometry is unintuitive and extremely difficult to visualise. If it were otherwise, I would have found a convincing visualisation through the use of my legendary Google powers by now! 😉
Try changing your perspective from "objects would have to move" to "distances between spacetime events can change".
This analogy of differing metrics is in fact intuitive, needing no explanation. The difficulty I'm having is that for coordinates to stay the same, objects can't not have to move in order to accommodate the changes in distance. Forget about the Earth surface analogy. If you use the rising dough with raisins analogy(raisins throughout the lump, not just on the surface), as the dough expands maintaining the raisins' coordinates, rest assured those raisins are moving. How can they not when you start with a lump 4" across and end up with a lump 8" across, coordinates unchanged? This is also intuitive.
The raisin bread model provides an analogy of how all points in an expanding spacetime become more distant from one and other and do not simply move away from a common centre of origin.
In all other aspects the model breaks down and we must accept its limitations. Let's face it, spacetime is not a material substance like dough!
P.S. Before I headed for bed, I heard that Dart had scored a bullseye! I shall look at the video evidence later.
In all other aspects the model breaks down and we must accept its limitations. Let's face it, spacetime is not a material substance like dough!
P.S. Before I headed for bed, I heard that Dart had scored a bullseye! I shall look at the video evidence later.
Okay, but the point I was making is they must "move" simultaneously from each other otherwise coordinates cannot stay unchanged. Math cannot help but confirm this, no?
So I'm not sure how spacetime equates to our physical universe.
Or are you telling me cosmology does not consider what I’m suggesting as “movement” within the confines of the cosmos? That only from the perspective of an external observation could this be true?
It makes perfect sense to me. The time between objects is increasing because of the passage of time - which is exactly what we see when we look at distant celestial objects i.e. an expanding universe. no need for dark energy od special particles. This is just a consequence of GR.
Locally, gravitation overcomes this effect, so for example we see the Milky Way and Andromeda being attracted to each other.
Locally, gravitation overcomes this effect, so for example we see the Milky Way and Andromeda being attracted to each other.
I submit that there is "real movement" and "apparent movement".
"Real movement" corresponds to the fact that the Milky Way and Andromeda galaxies are on a collision course due to their mutual gravitational attraction.
"Apparent movement" corresponds to the fact that the distances between distant points in the Universe are increasing.
"Real movement" corresponds to the fact that the Milky Way and Andromeda galaxies are on a collision course due to their mutual gravitational attraction.
"Apparent movement" corresponds to the fact that the distances between distant points in the Universe are increasing.
Another way to visualise the Universe is as a lattice.
In this analogy, each cube is a cluster of galaxies, and the connecting rods represent the space between these clusters. When the Universe expands, imagine that every rod connecting the cubes grows longer at an even pace. Every single cube gets further and further away from every other cube, but the size of the cubes themselves stays the same. The cubes are not moving along the latticework but are being carried by the expansion of the lattice itself.
https://www.universeadventure.org/big_bang/expand-galaxy.htm#:~:text=The Apparent Movement of Galaxies The expansion of,appear to be moving apart from each other.
In this analogy, each cube is a cluster of galaxies, and the connecting rods represent the space between these clusters. When the Universe expands, imagine that every rod connecting the cubes grows longer at an even pace. Every single cube gets further and further away from every other cube, but the size of the cubes themselves stays the same. The cubes are not moving along the latticework but are being carried by the expansion of the lattice itself.
https://www.universeadventure.org/big_bang/expand-galaxy.htm#:~:text=The Apparent Movement of Galaxies The expansion of,appear to be moving apart from each other.
Attachments
Last edited:
- Status
- Not open for further replies.