How can galaxies exist with the expansion of space?

[ACG52]

http://en.wikipedia.org/wiki/Metric_expansion_of_space

 

 

 

The metric expansion of space is the increase of the distance between two distant parts of the universe with time. It is an intrinsic expansion whereby the scale of space itself is changed. That is, a metric expansion is defined by an increase in distance between parts of the universe even without those parts "moving" anywhere. This is not the same as any usual concept of motion, or any kind of expansion of objects "outward" into other "preexisting" space, or any kind of explosion of matter which is commonly experienced on earth.

Metric expansion is a key feature of Big Bang cosmology and is modeled mathematically with the FLRW metric. This model is valid in the present era only on large scales (roughly the scale of galaxy clusters and above). At smaller scales matter has become bound together under the influence of gravitational attraction and such bound objects clumps do not expand at the metric expansion rate as the universe ages, though they continue to recede from one another. The expansion is a generic property of the universe we inhabit, though the reason we are expanding is explained by most cosmologists as having its origin in the end of the early universe's inflationary period which set matter and energy in the universe on an inertial trajectory consistent with the equivalence principle and Einstein's theory of general relativity (that is, the matter in the universe is separating because it was separating in the past). Additionally, the expansion rate of the universe has been measured to be accelerating due to the repulsive force of dark energy which appears in the theoretical models as a cosmological constant. This acceleration of the universe, or "cosmic jerk", has only recently become measurable, and billions of years ago, the universe's expansion rate was actually decelerating due to the gravitational attraction of the matter content of the universe. According to the simplest extrapolation of the currently-favored cosmological model (known as "ΛCDM"), however, the dark energy acceleration will dominate on into the future.

 

[Iggy]

Yes, the metric expansion of space is one valid way of looking at it. Your link describes it well. Another valid set of coordinates and associated way of measuring and looking at the cosmos, is what Ned Wright calls, in his tutorial, special relativity coordinates in which galaxies move through space. Both are valid as the link I already gave says so clearly and goes on to say exactly what I said... "the only means by which expansion occurs is gravity and momentum".

 

Boo yeah

 

Boosh

 

Bomb goes the dynamite!

 

Do we have to start another thread on this too?

[ACG52]

 

"the only means by which expansion occurs is gravity and momentum".

 

The changing metric does not need momentum to drive the expansion. And given that the rate of change is increasing, there's another factor at work.

[elfmotat]

Thought I might add this:

 

You can modify Newton's Law with a Cosmological Constant term to approximate weak-field gravity:

 

[math]F=m\left (-\frac{GM}{r^2} + \frac{c^2 \Lambda}{3}r \right )[/math]

 

Since the CC term is proportional to distance while the mass term is inversely proportional to the square of distance, you can see that eventually the second term will overwhelm the first. This means that at some distance from a mass gravity actually becomes repulsive.

 

As a quick example, let's say that the Milky Way is the only galaxy in the universe. The MW has a mass on the order of 6×10⁴² kg. We know the cosmological constant is of the order of 10^-52 m^-2. Using these values, we can determine that at a distance of about 5.4 million light-years = 1.7 Mpc away from the MW gravity becomes repulsive.

[Iggy]

Thought I might add this:

 

You can modify Newton's Law with a Cosmological Constant term to approximate weak-field gravity:

 

[math]F=m\left (-\frac{GM}{r^2} + \frac{c^2 \Lambda}{3}r \right )[/math]

 

Since the CC term is proportional to distance while the mass term is inversely proportional to the square of distance, you can see that eventually the second term will overwhelm the first. This means that at some distance from a mass gravity actually becomes repulsive.

 

As a quick example, let's say that the Milky Way is the only galaxy in the universe. The MW has a mass on the order of 6×10⁴² kg. We know the cosmological constant is of the order of 10^-52 m^-2. Using these values, we can determine that at a distance of about 5.4 million light-years = 1.7 Mpc away from the MW gravity becomes repulsive.

 

Well said.

 

... And given that the rate of change is increasing, there's another factor at work.

 

I anticipated your objection, HA!

 

The only thing that affect's a galaxies motion (in any reference frame) is gravity and momentum (the cosmological constant is part of gravity for those who were about to object).

[Lazarus]

Now I understand. We modified gravity to match our assumptions.

An equation can be constructed to match almost any assumption.

 

That seems reminiscent of the equation called the Roulette. It quite accurately predicted the motion of
the sun and planets about the earth. Probably doesn't prove the sun rotates around the earth.

 

It seems more logical that the source of the Red Shift was moving at a high
velocity many years ago when the light started its journey.

 

The Red Shift itself could be caused by the difference in energy that it takes to
change an electron's energy level in the direction of motion of the atom than
in the opposite direction. That might even mean the Red Shift is not completely linear.

 

It's a good thing that you can't through things through the internet or I would have
to wear my hard hat.

[Iggy]

Now I understand. We modified gravity to match our assumptions.

An equation can be constructed to match almost any assumption.

 

I'm sure that's fun to say, but the cosmological constant first appeared 81 years before it's value was known in 1998. It was a part of the first three models ever to be made of the universe with general relativity. Einstein said specifically that the constant arrived naturally from the derivation and it would be the measurements of the motion of the cosmos that will tell us if its value is zero or not. Anyone who thought the term had to be added after '98 must first have been under the false impression that the term had ever been prematurely removed. That would have been against the counsel of quantum mechanics and Einstein.

[elfmotat]

I'm sure that's fun to say, but the cosmological constant first appeared 81 years before it's value was known in 1998. It was a part of the first three models ever to be made of the universe with general relativity. Einstein said specifically that the constant arrived naturally from the derivation and it would be the measurements of the motion of the cosmos that will tell us if its value is zero or not. Anyone who thought the term had to be added after '98 must first have been under the false impression that the term had ever been prematurely removed. That would have been against the counsel of quantum mechanics and Einstein.

 

As you say, introducing the Cosmological Constant is a natural generalization of the Field Equations. Essentially the simplest, most general metric theory of gravity has the Lagrangian [math]\mathcal{L}=k(R+C)\sqrt{-g}[/math]. This yields the Field Equations with [math]\Lambda =C/2[/math]. Arbitrarily setting [math]C=0[/math] results in a less general theory, because it is a tunable parameter which we should fit with observation.

 

From the Field Equations with non-zero Cosmological Constant, plus some simplifying approximations (everything is moving slowly compared to light, the gravitational field is weak, etc.) we can derive a modified form of the Newtonian Poisson equation for gravity:

 

[math]\nabla^2 \phi =4\pi G\rho -c^2\Lambda[/math]

 

Apply Gauss' Law to that and you obtain the modified force law in my previous post.

 

 

Also, interestingly, Newton himself realized that the shell theorem only applied to gravity forces which varied either linearly or inversely as the square of distance, so a logical next-step would be a superposition of the two:

 

[math]F=ar+\frac{b}{r^2}[/math]

 

The following article is rather interesting: http://www.homepages.ucl.ac.uk/~ucapola/CLrev.pdf

Edited February 12, 2013 by elfmotat

[Iggy]

 

As you say, introducing the Cosmological Constant is a natural generalization of the Field Equations. Essentially the simplest, most general metric theory of gravity has the Lagrangian [math]\mathcal{L}=k(R+C)\sqrt{-g}[/math]. This yields the Field Equations with [math]\Lambda =C/2[/math]. Arbitrarily setting [math]C=0[/math] results in a less general theory, because it is a tunable parameter which we should fit with observation.

 

From the Field Equations with non-zero Cosmological Constant, plus some simplifying approximations (everything is moving slowly compared to light, the gravitational field is weak, etc.) we can derive a modified form of the Newtonian Poisson equation for gravity:

 

[math]\nabla^2 \phi =4\pi G\rho -c^2\Lambda[/math]

 

Apply Gauss' Law to that and you obtain the modified force law in my previous post.

 

 

Also, interestingly, Newton himself realized that the shell theorem only applied to gravity forces which varied either linearly or inversely as the square of distance, so a logical next-step would be a superposition of the two:

 

[math]F=ar+\frac{b}{r^2}[/math]

 

The following article is rather interesting: http://www.homepages.ucl.ac.uk/~ucapola/CLrev.pdf

Extremely well said

[Lazarus]

OK guys,

 

By modifying gravity we can now account for the motion

of all the stars and galaxies in a straight forward manner.

(With the possible exception of the newly discovered

giant galactic cluster.)

 

Does that mean that we did away with the expansion of

space?

 

If not the extra effect should mess up our calculations,

 

If so what accounts for the stretched photons of the

background radiation?

 

I hope you can excuse my dumb questions because

this is an enlightening thread with all the sharp and

knowledgeable people posting to it. I trust there are

people besides myself benefiting from it.

[Iggy]

OK guys,

 

By modifying gravity we can now account for the motion

of all the stars and galaxies in a straight forward manner.

(With the possible exception of the newly discovered

giant galactic cluster.)

 

Does that mean that we did away with the expansion of

space?

 

No. The expansion of space is a description of the metric on which the gravity-inclusive model of the universe is the most simply described. The FLRW metric expands by way of a scale factor in a Friedmann universe which is an exact solution of general relativity which is a theory that takes gravity well into account. Neither gravity, nor your inaccurately phrased notion of "modifying gravity" necessitates that one stop speaking in terms of expanding space. The two are 100% non-mutually exclusive.

 

 

IIf not the extra effect should mess up our calculations,

 

The expansion of space is not an "extra effect". It just means the expansion (ie getting larger) of space (ie distance). It isn't a force. It is a description of a metric.

[Lazarus]

I see how to make the two calculations match.

 

Just "modify gravity" again and then space can

slip by with the distance between things looking

like the calculations from the other method.

So as you say, the two methods are consistent.

 

Case closed.

 

I do prefer a more intuitive theory but nobody else does.

This thread gives an excellent and simple answer
to my original question.

Thank you all.

[elfmotat]

I see how to make the two calculations match.

 

Just "modify gravity" again and then space can

slip by with the distance between things looking

like the calculations from the other method.

 

So as you say, the two methods are consistent.

 

Case closed.

 

I do prefer a more intuitive theory but nobody else does.

 

This thread gives an excellent and simple answer

to my original question.

 

Thank you all.

 

You might find my post here to be informative. Essentially the answer to your question is that the "correct" way of thinking about it is with the metric expansion of space. Metric expansion is a result derived from General Relativity, whose predictions about the way gravity behaves are much more accurate than the predictions of Newtonian gravity (especially with strong gravitational fields and when things are moving close to the speed of light). When you make some very simplifying approximations (everything is moving slow, all gravitational fields are weak) you can recover Newtonian gravity from Einstein's equations. In Newtonian gravity, the Cosmological Constant isn't a term which contributes to metric expansion (indeed the metric is not dynamical), but it turns up as a repulsive term which is linear with distance that is added to Newton's Law of Gravitation. This viewpoint is approximately correct ( it is correct up to first order). But still, what's "really" happening is that space is expanding. The two viewpoints aren't completely consistent because one of them is just a simplifying approximation of the other.

[Iggy]

You might find my post here to be informative. Essentially the answer to your question is that the "correct" way of thinking about it is with the metric expansion of space. Metric expansion is a result derived from General Relativity, whose predictions about the way gravity behaves are much more accurate than the predictions of Newtonian gravity (especially with strong gravitational fields and when things are moving close to the speed of light). When you make some very simplifying approximations (everything is moving slow, all gravitational fields are weak) you can recover Newtonian gravity from Einstein's equations. In Newtonian gravity, the Cosmological Constant isn't a term which contributes to metric expansion (indeed the metric is not dynamical), but it turns up as a repulsive term which is linear with distance that is added to Newton's Law of Gravitation. This viewpoint is approximately correct ( it is correct up to first order). But still, what's "really" happening is that space is expanding. The two viewpoints aren't completely consistent because one of them is just a simplifying approximation of the other.

 

The dichotomy isn't between Newtonian and Relativistic. A de Sitter universe in static coordinates vs. a de Sitter universe in comoving coordinates are neither Newtonian. Yet, in one the receding galaxies move through space and in the other you have metric expansion. Neither is a Newtonian expectation. "What is really happening is that space is expanding" can't be right because in other valid coordinate systems space could well be static. Galaxies move through space, and GR is perfectly able to solve that too.

 

Coordinate choice. Neither is "really" correct. Relative to the perspective they both are.

[elfmotat]

I've been putting this off because I'm not sure how useful you'll find it. The purpose of showing you Newton's law with nonzero CC was to intuitively demonstrate how gravity is attractive when things are close together, but repulsive when the are very far away. In General Relativity, gravity is the geometry of spacetime. The solution to Einstein's equations with nonzero CC which describes a spherical mass [math]M[/math] is called the de Sitter-Schwarzschild metric:

 

[math]ds^2=-\left (1-\frac{2GM}{c^2r}+\frac{\Lambda r^2}{3} \right )dt^2+\frac{dr^2}{1-\frac{2GM}{c^2r}+\frac{\Lambda r^2}{3}}+r^2d\theta^2+r^2sin^2\theta d\phi^2[/math]

 

This solution isn't particularly useful because the effect that a nonzero CC has is very very small. Since the field equations are highly nonlinear the superpostion principle does not apply either, so you can't simply "add" the metric of another spherical mass to get a solution describing the spacetime around two masses. Nonetheless, this solution might be the key to putting your mind at ease:

 

The metric tells you how things move in spacetime. If you restrict movement to be along the radial coordinate and calculate the equations of motion (called the geodesic equations) for particles moving near the mass [math]M[/math], you'll get some complicated-looking equations. But if you take the Newtonian limit where the field is weak and everything moves slow compared to light, you get the following equation:

 

[math]\frac{d^2r}{dt^2}=-\frac{GM}{r^2}+\frac{c^2\Lambda r}{3}[/math]

 

So with our approximation we can see that the CC term still acts as a "repulsive" term while the mass acts as an attractive term.

 

 

 

The dichotomy isn't between Newtonian and Relativistic.

 

One is a linear approximation of the other. So yes, there is a "dichotomy." They don't have equivalent predictions.

 

 

 

A de Sitter universe in static coordinates vs. a de Sitter universe in comoving coordinates are neither Newtonian. Yet, in one the receding galaxies move through space and in the other you have metric expansion.

 

 

Co-moving with what? I'm not sure whether or not you can perform a coordinate transformation on the FLRW metric so that the spacial components are independent of the scale factor. Regardless of if you can, I don't think it would be particularly useful or meaningful.

 

 

Neither is a Newtonian expectation.

 

 

I thought I pretty clearly demonstrated that adding a constant term to the Einstein Field Equations is just as valid as adding a constant term to the Newtonian Poisson Equation. So "galaxies receding due to gravity" is indeed predicted by Newtonian gravity.

 

 

"What is really happening is that space is expanding" can't be right because in other valid coordinate systems space could well be static. Galaxies move through space, and GR is perfectly able to solve that too.

 

 

Maybe. But then that wasn't really my point, was it? My point was that GR provides the correct description of the expansion of the universe, while Newtonian gravity only supplies us with an approximation.

Edited February 13, 2013 by elfmotat

[Iggy]

My point was that GR provides the correct description of the expansion of the universe, while Newtonian gravity only supplies us with an approximation.

 

That is non controversial. We're talking about two different things.

[elfmotat]

That is non controversial. We're talking about two different things.

 

Then you're arguing with a point that I wasn't making.

[Iggy]

Then you're arguing with a point that I wasn't making.

 

The point you made is "But still, what's "really" happening is that space is expanding." You're treating a coordinate choice as an aspect of reality and you aught to know better. I gave the source already to refute it. "Is space expanding or are galaxies moving through space?" is a question that can only be answered "it is a coordinate choice" between different relativistic models.

 

Please don't start talking Newtonian approximations again.

[elfmotat]

 

The point you made is "But still, what's "really" happening is that space is expanding." You're treating a coordinate choice as an aspect of reality and you aught to know better. I gave the source already to refute it. "Is space expanding or are galaxies moving through space?" is a question that can only be answered "it is a coordinate choice" between different relativistic models.

 

Please don't start talking Newtonian approximations again.

*sigh* you're still arguing a strawman. The hint that that wasn't meant to be taken literally was the quotes around the word "really." My only point was that GR is more accurate than Newton, which OP didn't seem to be aware of.

[Iggy]

that wasn't meant to be taken literally

 

Fantastic to hear. Perhaps I was being too pedantic in my criticism. That's been going around I hear.

[pantheory]

 

How can galaxies exist with the expansion of space?

 

The standard model answer to this question is simply that gravity is stronger than the force(s) that supposedly causes space to expand. Of course if space does not expand, then there's no problem

 

Some have even proposed that such forces only operate within a collective of vacant distance intervals, or in the lowest densities of matter per large volume.

[Lazarus]

From the discussion on this thread it appears that there are

two distinct sources of the acceleration of stars and galaxies.

One is the expansion of space and the other is gravity.

The equation for gravity has to produce the force necessary

to offset the expansion of space.

The equation that works today will be wrong tomorrow

because the rate of expansion changes.

It would be difficult to modify the gravity equation to account

for the changing rate because we really don't know how fast

it is gong to change or even why it is changing.

Also, it is strange that gravity changes to match space expansion

without some cause and effect relationship.

The accuracy of the space expansion equations doesn't prove

space is really expanding any more than the Roulette equations

proved that the sun orbits the earth.

It would seem that it would take a lot less magic to formulate an

explanation based on the consideration that the Red Shift is

caused by the velocity of the source of the photons. That way

you don't need the two different causes of the Red Shift, velocity

and space expansion.

An example of a more straight forward approach is:

 

How Isaac Newton would explain the Red Shift of old light

The reason for the red shift of old light is that the source of the

light was moving away from where the Earth is now at a speed

that is related to the time of emission and the distance from the

center of the Big Bang. There is no real reason that the distance

from Earth is linearly proportional to the velocity of the source of

the light. So the apparent distance of la supernova deviating from

the linear formula of distance vs velocity is not a problem. The
following chart is a 2 dimensional slice of 4 dimensional Space/Time.

The units of the time axis are such that light would travel an equal

distance along the X axis to the Time value. This is what we see now.

Time

_______________________!__________________________

Now__________________e!__________________________

Stars_______________*___!_*________________________

1a Supernova_____1a_____!_____1a___Z=.4-.9, v=.32c-.56c

Oldest 1a SN ___0_______ !_________0__Z=1.7, v=.7c_____

\__Galaxies_@___________!___________@_Z=7,v=.97c_/_

__\_____/__Atoms form___!___Z=10, v=98.3 \_______/____

____/\__Farthest Visable __!_Z=infinity v=c ____\_/_______

__/_____\_______________!_______________/___\______

___________\____________!____________/________\____

______________\_________!_________/______________\_

_________________\______!______/___________________

____________________\___!___/______________________

Big Bang________________0_____________________X axis

The chart shows the velocity of objects at the time the light was emitted

that is arriving at the earth now. The Earth is a ways from the center of

the Big Bang. The chart shows: (1) the main la supernovas with Z=.4

to .9 V=.32c to.56c, (2) the oldest la supernova at Z=l .7 V=.7c,

(3) Galaxies at Z=7 V=.97c, (4) Atom formation at Z=l0V=.983c

and (5) the edge of the matter at Z=infinity, V=c.

The Red Shift due to the velocity of the light source can be accounted for

by the difference of energy required to change electron levels generating

photons in the direction of travel than in the opposite direction.

The slowing of clock in gravity can be accounted for by the change in the

path of an electron about the nucleus.

The confusion about photons being particles or waves can be resolved by

the assumption that all matter and radiation consists of minute entities that

can be represented as positive and negative vectors that always travel at

the speed of light. Electrostatic, electromagnetic and gravitational forces

are all that are needed to construct a universe.

 

 

 

[Lazarus]

I must appogize for my last post. Reading more of the Monitor's posts

I discovered that theories that were not in line with the Standard Model

were not allowed. It's your forum so it's your rules. I will move any

further thoughts to the Rational Science dot org board.

 

This thread has an excellent explanation of the compatabily of the

equations of space expansion and gravity.

 

I do not think it demonstrates "proof beyond a reasonable" doubt that

space itself really expands.

 

Einstein's posts would have been moved to the psuedoscience forum.

 

Thanks again.

[imatfaal]

That's a cheap trick - 4 pages of debate, everyone of your questions answered, zero warning points to your name, not a single staff member has even posted in this thread; yet you claim some form of censorship and act as if your questions have been unanswered due to our rules. Your points were all refuted by some excellent and well-written posts (and I am sure time-consuming for the authors); to flounce off in the pretence that somehow the forum rules have stopped you reaching the truth is shameful.

 

If you wish to discuss your speculative ideas then it would be best to do so in the Speculations Forum (by the way we do not have a pseudoscience forum). In the speculation forum the ideas will be tested by members and the promoter is expected to answer questions. Let me or any other member of staff know if you would like your post of 22 February 2013 - 03:36 PM split off to form a new thread in speculations.

[Lazarus]

Dear imatfall,

 

I did not intend to trick anyone.

 

I keep saying that I appreciate the effort and execellent

clarifications all the intricacies of the equations involved.

 

I should not have added anything about alternate theories.

 

My understanding of the interaction of gravity and space

expansion from this thread just is not in agreement with

the consensus.

 

I have nothing but respect for all who have posted to

this thread and the moderators.