Universe Expansion: Future of Dark Skies?

[touqra]

If our universe is expanding and light travels at a finite speed, then, will there be a time in future, where we won't see any light from stars and our whole sky will be black, since all the lights have not reach us?

 

[Wizardsblade]

We should always see the current and possibly new stars in the future. I'm not sure but I believe that near the beginning (when ever that was) there might have been no stars in the night sky. I think this because the universe has expanded faster then the speed of light. (Which I do not fully understand)

 

[S.P.P]

The way I understand it; Almost all galaxies are recceding from us (very nearby galaxies excluded). The galaxies themselves are not moving as such, the space between the galaxies is increasing, and appears to be so at an ever faster rate. So in theory, one day we won't be able to see any distant galaxies.

The stars in our own galaxy are gravitationally bound to the galaxy, and hence these stars are not receeding from us. So we will still be able to see the stars in our galaxy, at a time when we cannot see any other distant gallaxies.

 

[jhe1984]

If this were the case, wouldn't that mean that only "space" is expanding (as opposed to galactic regions)? If gravity can eventually overcome spacetime expansion, then doesn't that mean that the expansion is not a spacetime one but an addition of "outer space"?

Conversely, if the entirety of spacetime is expanding, wouldn't it be correct to say that, at some point in the future (provided a long enough period has elapsed) my big toe will have moved further away from my pinky toe?

 

[Garth]

Note: It is the space-like hyper-surface slice through space-time that expands as the cosmological parameter t increases. Space-time does not 'expand' as it is static, time having been already accounted for within the continuum.

The question is; "If space is expanding then what expands with it?"

It is generally accepted that gravitational attraction of the local gravitational fields, of the Earth, Sun, Milky Way galaxy, and possibly the Local Group, overwhelm the cosmological expansion and these bodies do not expand with the universe.

Einstein himself wrote a paper in the 1940's to prove that the solar system was not co-expanding with the universe. He did so by cutting out a spherical volume from the cosmological model and replacing it with a void with a spherical mass inserted in the middle; thus embedding a Schwarzschild solution inside a cosmological one. The question is how do you take the limit of the Schwarzschild metric as $r \rightarrow \infty$

It could be argued that the Pioneer Anomaly indicates that something might be wrong with this understanding.

Garth

 

[hellfire]

If our universe is expanding and light travels at a finite speed, then, will there be a time in future, where we won't see any light from stars and our whole sky will be black, since all the lights have not reach us?

Let’s consider we are located in a spatially infinite universe which contains a homogeneous distribution of light sources in space and let’s assume that no new light sources are created nor destroyed as time passes. Consider a spherical volume with a given radius. Due to expansion of space, it is true that this volume will contain a decreasing number of light sources as time increases and that it will be void sometime. However, the light we are receiving is not determined by the number of light sources contained in this volume as $t \rightarrow \infty$, but by the shape of our past lightcone as $t \rightarrow \infty$.

In my opinion the technical answer to your question is based on the fact that our past light cone will always intersect all past spatial hypersurfaces. This means that we are going to receive always light from every epoch in the universe (in our model). Consider a light source A from which we are receiving light emitted N years ago. As $t \rightarrow \infty$, we may not receive the light this source is currently emitting, if this source is located outside our current cosmological event horizon. However, we will receive light from some source located within our cosmological event horizon today (in the same spatial hypersurface than A). The problem is that, as $t \rightarrow \infty$, this source will be located very far in our past lightcone and therefore its light will be very redshifted.

Summary: some radiation will always reach us. However, this radiation will not be visible light, due to the increasing redshift of all sources.

 

[jhe1984]

So if I (being able to live forever without aging) were standing a meter away from a lamp (which also could go unchanging forever) - PRESUMING LOCAL GRAVITATION DID NOT INTERFERE WITH UNIVERSE EXPANSION - would the light from the lamp appear dimmer to me, say, a million or five hundred million years later?

If it does, is this because the lamp is further away from me or because the strength of the light "dims" (which I guess would mean redshifts) over the course of millions of years?

And would it thus be correct to say that light "dims" (in a non-relativistic or subjective sense) over time (again, observed time - not the actual light itself)?

More over, the universe can only expand if it also redshifts, because to expand without redshifting (or contract without blueshifting, I guess) would be a violation of the total conservation of a finite universe's energy?

 

[Chronos]

I totally agree with hellfire. In a casually connected universe, all light cones, once connected, will forever remain connected [albeit they may redshift beyond detectability over time]. And all light cones too remote to make initial causal contact with our universe prior to inflation will forever remain disconnected.

 

[touqra]

So if I (being able to live forever without aging) were standing a meter away from a lamp (which also could go unchanging forever) - PRESUMING LOCAL GRAVITATION DID NOT INTERFERE WITH UNIVERSE EXPANSION - would the light from the lamp appear dimmer to me, say, a million or five hundred million years later?
If it does, is this because the lamp is further away from me or because the strength of the light "dims" (which I guess would mean redshifts) over the course of millions of years?

I don't know whether this have been implicitly answered anywhere, but I sure want to know the opinion to this.

 

[SpaceTiger]

So if I (being able to live forever without aging) were standing a meter away from a lamp (which also could go unchanging forever) - PRESUMING LOCAL GRAVITATION DID NOT INTERFERE WITH UNIVERSE EXPANSION - would the light from the lamp appear dimmer to me, say, a million or five hundred million years later?

That question can't really be answered because it depends primarily on the local distribution of matter instead of the Hubble flow. If you were instead to ask about a "lamp" one hundred million light years away, then yes, it would appear dimmer. If we only consider cosmology, its apparent brightness will depend on its redshift. The more redshifted its light is:

1) The less total energy it carries. This is just because red photons are less energetic than blue ones.
2) The slower the photons arrive at our telescope. This is a GR effect that leads to the lamp's clock ticking slower than ours.
3) The further it will have traveled after one hundred million years.

All of these things add up to a dimmer source. Remember, the faster the universe is expanding, the more the object is redshifted. Thus, the fact that the universe is accelerating means that the lamp will appear dimmer in a hundred million years.

More over, the universe can only expand if it also redshifts, because to expand without redshifting (or contract without blueshifting, I guess) would be a violation of the total conservation of a finite universe's energy?

Actually, energy is not always conserved in GR. The fact that light redshifts to begin with could be considered a violation of the energy conservation law, depending on your definition of "energy". See here for more details:

http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html"

 

[Chronos]

I feel compelled to vote in that quasi-poll, ST! I unwaveringly vote yes, energy is conserved when all is said and done . . . albeit with difficulty.

 

[bchui]

That question can't really be answered because it depends primarily on the local distribution of matter instead of the Hubble flow. If you were instead to ask about a "lamp" one hundred million light years away, then yes, it would appear dimmer. If we only consider cosmology, its apparent brightness will depend on its redshift.

Actually, energy is not always conserved in GR. The fact that light redshifts to begin with could be considered a violation of the energy conservation law, depending on your definition of "energy". See here for more details:

Is Energy Conserved in General Relativity?

According to SR, the [Energy,momentum] pair could be thought as another way to describe the physical world by the other pair
[displacement,velocity]

"Energy" should be regarded as an operator, which should be conserved, if we are describing the physical model correctly.
A physical model is "correct" because it has its own invariant, and the term "energy" could be defined as one of those invariants

 

[pervect]

The FAQ and Space Tiger are correct on the issue of energy conservation in GR being problematic.

Aside from the FAQ, there is a discussion of the history of energy conservation and Emily Noether's contribution in

http://arxiv.org/PS_cache/physics/pdf/9807/9807044.pdf

In general relativity, on the other hand, it has no meaning to speak of a definite
localization of energy. One may define a quantity which is divergence free analogous to the
energy-momentum density tensor of special relativity , but it is gauge dependent: i.e., it
is not covariant under general coordinate transformations. Consequently the fact that it is
divergence free does not yield a meaningful law of local energy conservation. Thus one has,
as Hilbert saw it, in such theories ‘improper energy theorems’.
A key feature for physics of Noether’s I.V. paper is the clarity her theorems brought
to our understanding of the principle of energy conservation. As Feza Gursey wrote [18]:
“Before Noether’s Theorem the principle of conservation of energy was shrouded in mystery,
leading to the obscure physical systems of Mach and Ostwald. Noether’s simple and
profound mathematical formulation did much to demystify physics.” Noether showed in her
theorem I that the principle of energy conservation follows from symmetry under time translations.
This applies to theories having a finite continuous symmetry group; theories that are
Galilean or Poincar`e invariant, for example. In general relativity, on the other hand, energy
conservation takes a different form as will be shown below. Noether’s theorem II applies in
the case of general relativity and one sees that she has proved Hilbert’s assertion that in
this case one has ‘improper energy theorems’, and that this is a characteristic feature of the
theory. It is owing to the fact that the theory is a gauge theory; i.e., that it has an infinite
continuous group of symmetries of which time translations are a subgroup. Indeed generally
she defines as “improper” divergence relationships, which vanish when the field equations are
satisfied, which correspond to a finite continuous subgroup of an infinite continuous group.
Generally they do not have the required invariance or covariance properties under the larger
group. For example, in general relativity a divergence free energy-momentum (pseudo) tensor
can be constructed but it is gauge dependent (see below). Because it is not covariant
under general coordinate transformations, it is more properly called a pseudotensor. Such
pseudotensors are covariant with respect to the linear transformations of the Poincar`e group
and may be used in asymptotic spacetime regions far from gravitating sources to derive a
principle of energy conservation.

The bottom line is that in GR we have theories of energy conservation that apply to static space-times, and theories of energy conservation that apply to asymptotically flat space-times, but there is no truly _general_ theorem of energy conservation in GR for arbitrary space-times.

The FRW metric is neither asymptotically flat nor is it static, as a consequence there is no conserved "energy of the universe".

This point is also made in most GR textbooks, including MTW's "Gravitation".

 

[Garth]

In general relativity, on the other hand, it has no meaning to speak of a definite localization of energy. One may define a quantity which is divergence free analogous to the energy-momentum density tensor of special relativity , but it is gauge dependent: i.e., it is not covariant under general coordinate transformations.

Therein lies the problem of a Quantum Gravity, may energy be represented by an operator or not? Does this not require a preferred foliation of space-time in contradiction to the principle of relativity?

In order to be able to define such a locally conserved energy one has to select out a preferred foliation, slice, of space-time.

SR is formulated for an empty, i.e. curvature free, universe, and there is nothing 'to hang' a selected frame on. However, once one has introduced curvature, i.e. proceeded from the SR limit into the more general GR situation, then matter or energy has been introduced into the system.

Such matter/energy may be used to define a specific frame of reference - the Centre of Mass/momentum of the system or the frame in which radiation is globally isotropic. Thus Mach's Principle ought to be important in the local conservation of energy.

This is the basis of http://en.wikipedia.org/wiki/Self_creation_cosmology .

Garth

 

[hejs]

Hi! Do scientists know why universe expands and even accelerates? Something is pushing or pulling?

 

[Garth]

hejs In the standard General Relativity (GR) cosmological theory the universe either has to expand or contract, it cannot 'stay still'.

The Hubble red shift indicates that distant galaxies are all isotropically moving away from us. Either we live in a very special position in space or the universe as a whole is expanding. It is generally accepted that it is the universe as a whole that is expanding and that agrees with the prediction of GR.

But what has it expanded from? If you follow GR all the way back you come to the singularity of the Big Bang in which the volume of the whole universe reduces to zero. Although before you reach that point quantum effects must come into play and they may well prevent the initial singularity from happening, instead the universe expanded from a very small and ultra dense volume, or 'bounced' from the collapse of a previous universe.

What made it expand in the first place? The energy of the Big Bang was such that it had to expand, even in the face of a fierce cosmological gravitational field. Interestingly, in GR the kind of energy you need is provided by a negative pressure.

This negative pressure shows up at two other places in the mainstream theory.

1. At an early stage of the Big Bang, 10^-35 sec after BB, it is thought the universe underwent a burst or very powerful expansion called Inflation.

2. At a later stage of its expansion (at z ~ 1) it is thought the universe underwent an extended period of accelerated expansion called cosmic acceleration.

Both would have been caused by two different kinds of negative pressure.

Garth

 

[heliocentricprose]

What do you mean by negative pressure? Could you give an analogy perhaps?

 

[kmarinas86]

What do you mean by negative pressure? Could you give an analogy perhaps?

Negative pressure is the result of sucking things into nothingness (High density to low density). Increase in momentum. Think of the opening of a vacuum cleaner.

positive pressure is the result of pushing things into entrapment (Low to high density). Cancellation of momentum. Think of the filter inside the vacuum cleaner.

See:
http://en.wikipedia.org/wiki/Negative_pressure