Mass of Space (B but approaching I)

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Discussion Overview

The discussion revolves around the concept of the mass or energy associated with expanding space, particularly in the context of cosmology and general relativity. Participants explore the implications of space expansion on energy density, the nature of gravity, and the conceptual understanding of vacuum energy and dark energy.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • Some participants propose that if space is expanding, it must be moving objects by providing energy, raising questions about the energy or mass of a volume of space devoid of matter.
  • Others argue that the expansion of space does not imply that objects are being moved by a force; rather, they are moving apart due to the geometry of spacetime.
  • A participant mentions an estimate of vacuum energy density, suggesting a connection to the energy present in empty space.
  • Concerns are raised about the apparent contradiction between different explanations of energy in expanding space, particularly regarding the conservation of energy in an expanding universe.
  • Some participants challenge the idea that energy can be created from the expansion of space, asserting that dark energy density remains constant and does not arise from the expansion itself.
  • Questions are posed regarding the concept of Planck units and whether there is a smallest unit of space, with some participants clarifying that current models do not support this notion.
  • There is a discussion about the visualization of space expansion, with some participants arguing against the idea of new space being created between objects as they move apart.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the nature of space expansion, energy conservation, and the implications of dark energy. The discussion remains unresolved, with no consensus reached on these complex topics.

Contextual Notes

Limitations include varying interpretations of energy conservation in an expanding universe, the conceptualization of space expansion, and the role of dark energy, which are not universally agreed upon among participants.

  • #31
timmdeeg said:
Is it correct that the wordlines of these particles are representing a "congruence of wordlines"
Yes.

timmdeeg said:
and that the rate at which the volume of this ball shrinks or grows is given by the expansion scalar?
I don't know off the top of my head if it's numerically equal, but it's related. However...

timmdeeg said:
would it be correct to describe the "expansion" of the universe as corresponding to an increasing volume of comoving galaxies?
No, because there's a big difference between Baez's scenario and the universe: in Baez's scenario, you are working in the rest frame of the ball (more precisely, the rest frame of its center of mass) and the ball is very small. For the universe, there is no single "rest frame" for comoving objects and the comoving objects are not restricted to a small ball--they are spread throughout the entire universe, which is spatially infinite.
 
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  • #32
PeterDonis said:
this is a coordinate dependent concept
I hear this over and over, but here's my confusion. If you have two galaxies, each X units of distance in diameter and separated by a distance of 10X, then after some amount of time they will each still be X units of distance in diameter but the distance between them will be 12X units of distance. How is this coordinate dependent? Is it somehow that their diameter is not coordinate dependent but the distance between them is?
 
  • #33
phinds said:
If you have two galaxies, each X units of distance in diameter and separated by a distance of 10X, then after some amount of time they will each still be X units of distance in diameter but the distance between them will be 12X units of distance. How is this coordinate dependent?
"After some amount of time" depends on the time coordinate you choose. "Separated by a distance of..." depends on the space coordinates you choose.
 
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  • #34
PeterDonis said:
"Separated by a distance of..." depends on the space coordinates you choose.
OK, but how can you choose a different space coordinate for the distance across the galaxies vs the distance between the galaxies?
 
  • #35
PeterDonis said:
No, because there's a big difference between Baez's scenario and the universe: in Baez's scenario, you are working in the rest frame of the ball (more precisely, the rest frame of its center of mass) and the ball is very small. For the universe, there is no single "rest frame" for comoving objects and the comoving objects are not restricted to a small ball--they are spread throughout the entire universe, which is spatially infinite.
Ah ok, so there seems no possibilty to extend Baez's ball somehow to the universe.
 
  • #36
phinds said:
how can you choose a different space coordinate for the distance across the galaxies vs the distance between the galaxies?
I didn't say you had to. I just said "separated by a distance of...". The point is simply that "distance" is coordinate-dependent.
 
  • #37
PeterDonis said:
The point is simply that "distance" is coordinate-dependent.
While if we say "increasing distances" (standing for increasing redshifts) that's invariant, right?
 
  • #38
timmdeeg said:
While if we say "increasing distances" (standing for increasing redshifts) that's invariant, right?
Increasing with respect to what?
 
  • #39
PeterDonis said:
Increasing with respect to what?
increasing with respect to an arbitrary observer who measures the redshift of far away galaxies.
 
  • #40
timmdeeg said:
increasing with respect to an arbitrary observer
This is too vague. With respect to what property of the observer?
 
  • #41
PeterDonis said:
This is too vague. With respect to what property of the observer?
With respect to a co-moving observer.
 
  • #42
timmdeeg said:
With respect to a co-moving observer.
With respect to what property of a co-moving observer? You are talking about a rate of change--"increasing". A rate of change relative to what? To put it another way, you are taking a derivative of something; with respect to what are you taking the derivative?
 
  • #43
PeterDonis said:
With respect to what property of a co-moving observer? You are talking about a rate of change--"increasing". A rate of change relative to what? To put it another way, you are taking a derivative of something; with respect to what are you taking the derivative?
Hm, a rate of change relative to the proper time of the observer?
 
  • #44
timmdeeg said:
a rate of change relative to the proper time of the observer?
Yes. But this will only be an invariant if it's the rate of change of an invariant. So the rate of change of the observed redshift with respect to proper time will be an invariant; but the rate of change of "distance" with respect to proper time won't be, because "distance" is not an invariant, it's coordinate-dependent.
 
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  • #45
Thanks, that has been a helpful course!
 
  • #46
PeterDonis said:
... but the rate of change of "distance" with respect to proper time won't be, because "distance" is not an invariant, it's coordinate-dependent.
If one talkes about the expansion of the universe without further details wouldn't then the sign of the rate of change of "distance" with respect to proper time be invariant?
 
  • #47
timmdeeg said:
If one talkes about the expansion of the universe without further details wouldn't then the sign of the rate of change of "distance" with respect to proper time be invariant?
It can't be an invariant if "distance" isn't an invariant.
 
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  • #48
PeterDonis said:
It can't be an invariant if "distance" isn't an invariant.
So the sign of the observed rate of change of the redshift doesn't correspond to a certain sign of the rate of change of distance, that sign could still be positive or negative depending on the chosen coordinates if I understand you correctly.
 
  • #49
timmdeeg said:
the sign of the observed rate of change of the redshift doesn't correspond to a certain sign of the rate of change of distance
No.

timmdeeg said:
that sign could still be positive or negative depending on the chosen coordinates if I understand you correctly.
Not only due to choice of coordinates. The observed rate of change of the redshift depends on whether the expansion is accelerating or decelerating--or more precisely whether it was doing so when the light we are seeing now from a particular distant galaxy was emitted.

The observed redshift itself can be related to a "rate of change of distance", but the relationship is model dependent as well as coordinate dependent. The best way to interpret the redshift is not as telling you a speed of recession, but as telling you by what factor the universe has expanded since the light you are seeing now was emitted. But that, of course, involves the scale factor, which assumes that you have made a particular choice of coordinates (it isn't even meaningful in other coordinates).
 
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  • #50
PeterDonis said:
No.
Got it.
PeterDonis said:
Not only due to choice of coordinates. The observed rate of change of the redshift depends on whether the expansion is accelerating or decelerating--or more precisely whether it was doing so when the light we are seeing now from a particular distant galaxy was emitted.
Ok, that I've been missing.
Thanks for your great explanation!

Quite often here in PF it comes to a point where someone explains expansion of the universe doesn't mean that space expands, it means increasing distances. This seems quite vague and with no reference to coordinate dependence. But it at least points to right direction. Would you agree to that?

 
  • #51
timmdeeg said:
Quite often here in PF it comes to a point where someone explains expansion of the universe doesn't mean that space expands, it means increasing distances. This seems quite vague and with no reference to coordinate dependence. But it at least points to right direction. Would you agree to that?
Sort of. When you fill in the missing information about what "increasing distances" means, the coordinate dependence appears. So whether it "points in the right direction" depends on what your goal is.
 
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