Expanding universe and energy question

[fys iks!]

Hey so I've started learning some cosmology and i have a question about the expanding universe.

So i was told to picture a 3D graph with time on the vertical axis and space making a plane perpendicular to the vertical. I am using the metric where the diagonals are (1,-a,-a,-a) where a is a function of time. Now when the graph is drawn it looks like a grid which just gets bigger a time increases. Now i was told that dX which is the space between two points on the grid is always measured to be 1 unit. So for example as the grid expands the distance between points is always taken to be 1 unit, but your measuring stick would have also grown too.

Now my question is to say i were to travel between two points in the expanding space but at two different times. Technically the earlier time i would travel a farther distance then the later time. But i would still always be traveling the distance of 1 unit. Would the later journey require more energy compared to the earlier journey, and doesn't this mean that energy would be increasing?

I thought of it being some sort of Lorentz transformation but i don't think that would work because the two frames are different since one is stretched.

thanks for your help

 

[Chalnoth]

Well, there are different ways of talking about distance. The grid itself is expanding, and if you could freeze the expansion at anyone point, then bounce some photons around to see how far away the points are, you'd get very different answers at different times. In that sense, the distance between different points most definitely is increasing with time.

If, by contrast, you just use the grid points themselves as a measure of distance, then there is no change in distances as the universe expands.

Or, you could talk about the actual light travel time between objects, which not only depends upon the grid distance but also upon how fast the universe is expanding at any given time. This sort of distance will sometimes increase, sometimes decrease, and sometimes diverge past infinity (indicating that light can never travel between two points, no matter how long you wait). This sort of distance is useful in understanding real observations.

 

[Passionflower]

The grid itself is expanding, and if you could freeze the expansion at anyone point, then bounce some photons around to see how far away the points are, you'd get very different answers at different times. In that sense, the distance between different points most definitely is increasing with time.

There is no such thing as "the grid". Equating spacetime coordinate charts with physical properties in general relativity is very often going to mislead rather than help people understand.

 

[Chalnoth]

There is no such thing as "the grid". Equating spacetime coordinate charts with physical properties in general relativity is very often going to mislead rather than help people understand.

Perhaps. I was a little short in my explanation. Obviously the numbers we place on reality are not reality, and in some cases lead to effects such as singularities that just aren't there.

In this case I don't really see what the problem is, however. The flat FRW metric, from which one can visualize space-time as a three-dimensional grid that is expanding or contracting with time, is quite well-behaved and also an accurate description of our universe.