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.

 

[sardar]

I would respond to this question by first clarifying that the expanding universe is a complex and ongoing area of research in cosmology, and there is still much we do not fully understand about it. However, based on current theories and observations, here are some potential explanations for the questions raised:

1. The concept of distance in an expanding universe is a bit different from our everyday understanding of distance. In the context of the 3D graph described, the distance between two points is not measured by physical rulers or measuring sticks, but rather by the metric function (1,-a,-a,-a) which is a mathematical representation of the expansion of space over time. This means that the distance between two points may appear to increase as the universe expands, but it is not necessarily due to the actual physical distance between those points increasing.

2. In terms of energy, it is important to note that the expansion of the universe is not a process that requires or consumes energy in the traditional sense. It is a natural consequence of the Big Bang and the distribution of matter and energy in the universe. Therefore, the concept of energy increasing as the universe expands is not applicable in this context.

3. The concept of Lorentz transformations, which are used to describe the effects of relative motion in special relativity, may not be fully applicable in an expanding universe. This is because the expansion of space is not a motion in the traditional sense, and the reference frames used to measure distances and velocities may not be directly comparable.

Overall, it is important to keep in mind that our understanding of the expanding universe is constantly evolving and there is still much we do not know. While these questions are valid and thought-provoking, the answers may not be fully understood or agreed upon at this time.