The thread thread: Strangeness of the expanding space paradigm

[Zanket]

Let a floating thread span the distance between two galaxies fast receding from each other due to space expanding between them. Eventually the thread must break. Expanding space forces apart adjacent particles of the thread all along the thread. The thread breaks at an arbitrary spot. Then any thread on Earth may break due to expanding space. There's a lot of fabric on Earth. Perhaps a thread somewhere spontaneously broke while you were reading this.

 

[Garth]

Unless the thread itself expands with the universe.
(Not according to GR but SCC)
Garth

 

[matt.o]

the space the Earth inhabits does not expand with the Hubble flow, so the thread would not break on Earth. You never see galaxies stretching and breaking due to the expansion of the universe, do you?

 

[Garth]

If you treat gravitation as a force then as it is ~10^-40 the strength of the other forces we can safely conclude that the thread and physical rulers will not expand with the universe. The binding energies of the e-m and nuclear forces holding them together, and the local gravitational forces in the solar system and the galaxy holding the solar system and the galaxy together, are much stronger than those of the Hubble expansion. The Earth bound thread does not break, but the cosmological thread suspended between two galaxies does break.

If however we treat gravitation as space-time curvature, as indeed we do in GR, then the question arises as to whether this expansion applies to everything embedded in that space-time. So then, what expands with space-time?

As the Schwarzschild solution for gravitational orbits is embedded in that space-time should not its solutions co-expand? Also as the Bohr/Schrödinger/Dirac equations of atomic physics are also so embedded then should not their solutions, i.e. atoms, also expand? If so, as the thread is made of atoms it expands with the universe, so the Earth bound and now the cosmological threads do not break!

Furthermore, we might ponder that, if physical rulers expand with the universe, then there should be no expansion as measured by those rulers.

In such a case Hubble red shift would be interpreted as other than recession Doppler shift. (e.g. a variable mass effect).

If we ask whether there is any evidence for the solar system as a whole to so expand then such might be given by the intriguing Pioneer anomaly, which, interestingly, is of the same order as the Hubble acceleration cH.

So which is the more consistent approach in answering the ‘thread thread’ question, to treat gravitation as a force or as curvature?

Garth

 

[Zanket]

the space the Earth inhabits does not expand with the Hubble flow, so the thread would not break on Earth. You never see galaxies stretching and breaking due to the expansion of the universe, do you?

The Earth expands too, but gravity and other binding forces reel the pieces back in. The same with galaxies; they are not oases where expansion does not apply. A thread would break on Earth the same as in deep space.

 

[Zanket]

The Earth bound thread does not break, but the cosmological thread suspended between two galaxies does break.

The location at which the thread between the galaxies breaks is arbitrary. The Earth is subject to cosmic expansion to the same degree as is an Earth-sized region in deep space. Then the Earth bound thread can also break.

If however we treat gravitation as space-time curvature, as indeed we do in GR, then the question arises as to whether this expansion applies to everything embedded in that space-time. So then, what expands with space-time?

Cosmic expansion is independent of gravity. Gravity and other binding forces work to counteract expansion (by reeling back in the pieces). In the expanding space paradigm, all space expands. Even you are expanding, but the binding forces counteract it.

 

[Zanket]

There is a paradox of the expanding space paradigm here: If gravity and other binding forces work to counteract expansion of you or the Earth or a galaxy, then how can the thread spanning the galaxies break and the resulting ends fly apart as must happen? As far as I know, there is no answer.

 

[Garth]

You have misunderstood what I was saying.
If we define atomic (rest) masses to be constant, as indeed is required by the conservation of energy-momentum, which is also consistent with the equivalence prinicple. Consequentially an atom, and the Earth, does not expand with the universe. That expansion is then interpreted as a real expansion and Hubble red shift is recessional Doppler shift in nature. A thread between two distant galaxies would break, but one strung between two poles on Earth would not.

Furthermore cosmological expansion is a prediction of Einsteins GR field equation, which is a gravitational theory. The standard version of the theory (without Dark Energy) predicts that the expansion should be decelerating 'because of the gravitational attraction between matter within it'. (BTW the fact that its not decelerating may be a more radical discovery than simply that of DE).

I was agreeing with you in proposing that such expansion might affect everything within the universe, but that is not the normal understanding of the cosmological solution of GR.

In that normal understanding the expanding universe is not modeled by an blown up balloon with dots painted on it, as such dots themselves would expand too. Rather it is normally modeled by a balloon with coins glued onto it. The balloon expands but the coins, galaxies, do not.

As I have said I question this understanding.


Garth

 

[Zanket]

A thread between two distant galaxies would break, but one strung between two poles on Earth would not.

That is what books say. What I’m saying is that it’s inconsistent. Books say, to paraphrase one for example, “A galaxy is held together by its own gravity and is not free to expand with the universe. Similarly, the Solar System, Earth, an atom, or almost anything is held together by various forces in some sort of equilibrium and cannot partake in cosmic expansion.” This does not imply that these things are in expansion-free zones. The space in which things exist does expand. But the binding forces of the things reel the separating pieces back in. In your sentence the only differences between the two threads is the length and the presence of the Earth. Neither is relevant. The thread between the galaxies breaks at an arbitrary location, so one meter of thread is as good as a megaparsec. (I string it between galaxies only to make it obvious that the thread will break. Nothing about the length of the thread makes it break.) And nothing about the Earth prevents the thread from breaking, because the Earth itself is not prevented from breaking. The paradigm just implies that the pieces of the Earth will be reeled back in by gravity and other binding forces. Since the Earth expands only something like a millimeter per century, this reeling back in, which happens continuously, is imperceptible.

Furthermore cosmological expansion is a prediction of Einsteins GR field equation, which is a gravitational theory. The standard version of the theory (without Dark Energy) predicts that the expansion should be decelerating 'because of the gravitational attraction between matter within it'.

The expanding space paradigm (that space itself expands) arose circa 1930, after GR. GR's expansion is just a free-rise between pairs of objects, like throwing a ball up in the air.

A book of mine says, "Slowly [circa 1930] emerged the idea that the universe consists of expanding space! The lesson we must learn from general relativity is that space can be dynamic as well as curved." Seeing as how GR came about in 1915, expanding space is presumably not predicted by GR. I'd like to know more about why books attribute the exanding space paradigm, newly emerged in circa 1930, with a theory of 1915.

I was agreeing with you in proposing that such expansion might affect everything within the universe, but that is not the normal understanding of the cosmological solution of GR.

I say that the expansion does affect everything within the universe, and then binding forces reel the pieces back in so that, for example, the galaxies do not expand.

In that normal understanding the expanding universe is not modeled by an blown up balloon with dots painted on it, as such dots themselves would expand too. Rather it is normally modeled by a balloon with coins glued onto it. The balloon expands but the coins, galaxies, do not.

A more accurate model would have the coins continuously expanding and then immediately contracting. When I drop an apple from a meter above ground, its fall to the ground is delayed by cosmic expansion, but negligibly so. Gravity overwhelms the cosmic expansion. The higher the height I drop it from, the more significant the delay, until, at some height, cosmic expansion overwhelms gravity and the apple recedes from the Earth instead of falling toward it.

As I have said I question this understanding.

Can you elaborate? What is SCC?

 

[Mike2]

The paradigm just implies that the pieces of the Earth will be reeled back in by gravity and other binding forces. Since the Earth expands only something like a millimeter per century, this reeling back in, which happens continuously, is imperceptible.

So here's an idea: Expansion and being reeled back in sounds like some sort of uncertainty principle. If objects cannot be located with absolute certainty, then maybe there some sort of minimum spacetime "energy".

 

[Zanket]

Good thought, but the paradigm doesn't suggest that. The apple example above shows that the "reeling in" is just gravity overwhelming the expansion. Maybe a better example is when you throw an apple up. Cosmic expansion keeps the apple in the air a bit longer (that is, longer than expected when gravity alone is considered), but isn't significant enough to keep the apple from coming back down. Likewise, as cosmic expansion continuously expands every part of your body, even at the subatomic level, the binding forces continuously pull the parts of you back to where they were. You expand only at a rate of something less than a nanometer per century, so the binding forces have easy work to keep you in shape.

 

[pervect]

Let a floating thread span the distance between two galaxies fast receding from each other due to space expanding between them. Eventually the thread must break. Expanding space forces apart adjacent particles of the thread all along the thread. The thread breaks at an arbitrary spot. Then any thread on Earth may break due to expanding space. There's a lot of fabric on Earth. Perhaps a thread somewhere spontaneously broke while you were reading this.

Calculate the actual force (acceleration) on a kilometer long thread due to the expansion of the universe

For standard Friedman-Walker cosmologies, the acceleration / unit distance turns out to be -q H^2, where H is hubble's constant, and q is the "deceleration parameter", another (rather hard to measure) constant.

For the details see

https://www.physicsforums.com/showthread.php?t=63805&page=2&highlight=expansion+universe

To put it in perspective, this number is

3.12 × 10-33 m / s-2 per kilometer (also worked out in this thread) with soem reasonable assumptions for q and H.

There's another thread where this got brought up, I pointed out that the tidal forces due to the gravity of the Earth (or the moon) are MUCH stronger than this *extremely* weak tidal force.

So if you aren't worried about the moon breaking threads here on Earth (the moon pulls more strongly on threads closer to it than it does on threads further away, stretching them), you should be even less worried about the expansion of the universe breaking them - at least with the current values of the various constants involved. The force/ unit distance can evolve with time, in some sceneraios with a non-zero cosmological constant it can eventually become significant.

 

[chronon]

Calculate the actual force (acceleration) on a kilometer long thread due to the expansion of the universe

Zero - the so called expansion of space has no physical effect. (Of course a non-zero cosmological constant is a different matter)

For standard Friedman-Walker cosmologies, the acceleration / unit distance turns out to be -q H^2, where H is hubble's constant, and q is the "deceleration parameter", another (rather hard to measure) constant.

-q H^2 is negative, so the thread would contract. This is simply the effect of gravity due to the other matter in the universe.

See http://www.chronon.org/Articles/stretchyspace.html

 

[Zanket]

So if you aren't worried about the moon breaking threads here on Earth (the moon pulls more strongly on threads closer to it than it does on threads further away, stretching them), you should be even less worried about the expansion of the universe breaking them - at least with the current values of the various constants involved.

I read the other thread you gave, thanks. Regardless of the smallness of the force on the thread spanning the galaxies, it must break eventually. It cannot stretch forever. Right? And when it breaks, it breaks at an arbitrary spot and the new ends must fly apart. Right? And then there is a paradox, as to how gravity can keep a galaxy together against cosmic expansion when the much stronger forces besides gravity that holds the thread together are not enough to keep it together.

And the Earth is not an expansion-free zone, so a thread on Earth can spontaneously break due to cosmic expansion and its ends can fly apart.

 

[Zanket]

Zero - the so called expansion of space has no physical effect.

How can that be? It does stretch things, right? Do you mean almost zero?

See http://www.chronon.org/Articles/stretchyspace.html

I read this, thanks. (I had also previously read Ned Wright’s stuff and other books on this.) It seems to me that the main reason you want to think in terms of stretching space is because things in stretching space break eventually, whereas things moving apart do not. That’s a big difference. The way I see it, the expanding space paradigm implies that the galaxies (and all other material things) are continuously stretching or breaking apart due to cosmic expansion, and continuously being kept together or put back together by gravity and other binding forces. That is, these two sets of forces are in equilibrium. And that leads to the paradox mentioned above.

 

[Zanket]

Also, is it true to say that the expanding space paradigm (created circa 1930) was shoehorned into GR (1915)? My understanding is that expanding space in GR was originally just a cosmos mostly filled with objects free-rising from each other. The inclusion of the expanding space paradigm to GR adds stretching space, so that objects that look to be free-rising from each other either are, due to peculiar velocity, or are stationary with space stretching between them. Can someone give the history on this?

 

[Mike2]

Good thought, but the paradigm doesn't suggest that. The apple example above shows that the "reeling in" is just gravity overwhelming the expansion. Maybe a better example is when you throw an apple up. Cosmic expansion keeps the apple in the air a bit longer (that is, longer than expected when gravity alone is considered), but isn't significant enough to keep the apple from coming back down. Likewise, as cosmic expansion continuously expands every part of your body, even at the subatomic level, the binding forces continuously pull the parts of you back to where they were. You expand only at a rate of something less than a nanometer per century, so the binding forces have easy work to keep you in shape.

How much would the plank length have stretched in 13.7Gyrs? Yet if particles were strings and the expansion of space does not make particles any larger so that the physics would have changed in that time, then doesn't this prove that particles are not extended objects but are singularities instead? Thanks.

 

[Zanket]

If I understand your question, I think the paradigm would say that a smallest-length-object would not stretch. It would slip on the expanding space to always maintain its length. In other words, this object is infinitely rigid hence non-stretchable.

 

[Janus]

Let a floating thread span the distance between two galaxies fast receding from each other due to space expanding between them. Eventually the thread must break. Expanding space forces apart adjacent particles of the thread all along the thread. The thread breaks at an arbitrary spot.

Does it? Assumimg that the string is of uniform strength along its entire length, then it will break at its midpoint. The molecular bonds of the string try to hold it together, thus the expansion force felt at the ends is transmitted down the thread by these bonds, as will be the force acting at any point of the string. Each point will be subject not only to its own force due to expansion, but also that transmitted to it by the points 'outward' from itself, which it in turn transmits down the line to the next point. The midpoint will feel the result of all the expansion force working along the entire length of the thread, and being the point where the greatest amount of force is felt, will be the point at which the thread would break.
Imagine a thread hanging from an anchor point. each point of the string not only has to support its own weight, but the weight of all the thread below it. the anchor point has to support the whole weight of the string, and if the string gets long enough, this is th point where it will break. In your example, the 'anchor point' is the middle of the thread.

Then any thread on Earth may break due to expanding space. There's a lot of fabric on Earth. Perhaps a thread somewhere spontaneously broke while you were reading this.

But any thread won't break due to expanding space, only one long enough where the cumulative expansion force acting along the whole length exceeds the strength of the molecular bonds at the midpoint of the string.

 

[Mike2]

If I understand your question, I think the paradigm would say that a smallest-length-object would not stretch. It would slip on the expanding space to always maintain its length. In other words, this object is infinitely rigid hence non-stretchable.

I have trouble with strings because it is not clear whether strings are spacetime itself of lower dimension embedded in the background of higher dimension or if they are something else. If they are embeddings, then they would stretch with the background, right, with all the physics changing with it. But if the physics does not change (e.g the tension, etc), then strings are not embeddings but are themselves different than lower dimensions embedded in higher dimensions.

My personl view is that everything that exist must ultimately be describible in geometric terms, manifolds within manifolds. Otherwise we are dealing with something that cannot be explained as having an origin describible in terms of mathematics. Yet it seems intuitive that if everything arises smoothly from a singularity, it must be explainable in terms of smooth geometry. It would not be possible to impose some arbitrary function on this geometry from the outside. All would have to result from the growth of the singularity in some smooth predictable way.

 

[Hurkyl]

Also, is it true to say that the expanding space paradigm (created circa 1930) was shoehorned into GR (1915)?

No. That space would globally expand or contract fell naturally out of the math. Einstein introduced the Cosmological Constant precisely so that he could have an adjustable parameter that would eliminate that effect (when set to the right thing).

And even that wasn't "shoehorned". IIRC, it's essentially a constant of integration.



Also, you seem to have a fairly fundamental misconception about the effects of tension. If you grab the ends of a string and tug on them without breaking its elastic limit, you can tug for all of eternity with a constant force, and the string will never break. It will stretch once so that its intermolecular forces balance your tension force, and then it will stay in equilibrium until the applied tension is changed.

 

[chronon]

How can that be? It does stretch things, right? Do you mean almost zero?.

No, I mean zero. If you ignore any cosmological constant/dark energy (i.e. the situation up until the 1990's) then there is nothing driving the galaxies apart. They are moving apart because they started out that way. The only force between them is gravitational, which causes deceleration.

It seems to me that the main reason you want to think in terms of stretching space is because things in stretching space break eventually, whereas things moving apart do not. That’s a big difference. The way I see it, the expanding space paradigm implies that the galaxies (and all other material things) are continuously stretching or breaking apart due to cosmic expansion, and continuously being kept together or put back together by gravity and other binding forces. That is, these two sets of forces are in equilibrium. And that leads to the paradox mentioned above..

No the reason for the expanding space paradigm was because the natural time coordinate chosen by cosmologists is the proper time, which is not compatible with special relativity. Expanding space was invented so that objects wouldn't seem to be moving apart faster than light. (My impression was that this paradigm started when it became common to detect objects beyond the Hubble sphere, that is in the last 30 years).

What GR introduced was the idea of spacetime as something real, which could be curved. However, it can't be said to expand, as that is a time based notion.

 

[Zanket]

Does it? Assumimg that the string is of uniform strength along its entire length, then it will break at its midpoint. The molecular bonds of the string try to hold it together, thus the expansion force felt at the ends is transmitted down the thread by these bonds, as will be the force acting at any point of the string. Each point will be subject not only to its own force due to expansion, but also that transmitted to it by the points 'outward' from itself, which it in turn transmits down the line to the next point. The midpoint will feel the result of all the expansion force working along the entire length of the thread, and being the point where the greatest amount of force is felt, will be the point at which the thread would break.

Space expands everywhere in the paradigm, so the stretch force is equalized everywhere. There’s no excess anywhere to be transmitted. The thread is not being stretched from any particular direction. It is being stretched throughout from within. Tell me, where would an infinitely long thread break? It has no midpoint. If it breaks, it breaks at an arbitrary point. And if it doesn’t break, then you must explain how it can stretch forever. That seems to address the rest of your post.

 

[Zanket]

I have trouble with strings because it is not clear whether strings are spacetime itself of lower dimension embedded in the background of higher dimension or if they are something else.

String theory seems outside the scope of this topic. The expanding space paradigm says nothing about strings. By "thread," I mean a thread like your clothes are made of. Can you start a new thread(!) about this?

 

[pervect]

Zero - the so called expansion of space has no physical effect. (Of course a non-zero cosmological constant is a different matter)
-q H^2 is negative, so the thread would contract. This is simply the effect of gravity due to the other matter in the universe.

See http://www.chronon.org/Articles/stretchyspace.html

I went through the math not that long ago in that thread with Hellfire - there is in theory a physical effect due to the expansion of the universe. However, the effect is so small that it is not experimentally detectable as you can see by the numbers that I quoted.

The reason there is a physical effect is that the components of the Riemann tensor are not zero. Consider for instance the "flat" FRW metric

ds^2 = a^2(t)*(dx^2+dy^2+dz^2) - dt^2

The first clue that this space-time isn't flat is in the Christoffel symbols. They are a bit numerous to list, but consider for instance one example:

\Gamma_{txx} = -a(t) \frac{\partial a}{\partial t} = - a \dot{a}

This is easy to compute directly because we are in a coordinate basis:
(see MTW pg 210, for instance)

\Gamma_{abc} = \frac{1}{2}(g_{ab},c+g_{ac},b - g_{bc},a)

The comma notation is convenient, a comma means an ordinary partial derivative, hence the meaning of g_{ab},c is \frac{\partial g_{ab}}{\partial c}

So to work our our example

G_txx = .5*(g_tx,x + g_xt,x - g_xx,t)

But g_tx = g_xt = 0, so the only non-zero component is g_xx,t, which is 2 a \dot{a}. Thus \Gamma_{txx} = -a \dot{a} as stated.

The fact that the Christoffel symbols are not identically zero should be enough for you to realize that the (t,x,y,z) coordiante system is NOT an inertial one! This means that pseudo-forces exist.

The detailed computation of the Riemann confirms that space-time isn't flat and gives the magnitude of the stretching components of the Riemann tensor. The thread also explains why \Gamma^x{}_{txt} represents the tidal force.

As this has previously been done on the other thread, and is rather long, I won't repeat it here. You also might find it convenient to look up the Riemann for the FRW metric in a textbook, MTW gives the Einstein tensor on pg 728 for starters (you can figure out the Riemann from the Einstien, but it takes more work).

Note that q is a negative number for the numbers quoted, as far as sign issues go.

 

[pervect]

To address this issue without the math, it's already been argued that a very long string must break in an expanding universe, when it passes the Hubble horizon.

Therfore it should not be a terrible surprise that there are tidal forces on a small string. The math just confirms this and gives us a formula for the magnitude of said forces.

These tidal forces are not any more mysterious than the tidal forces that the moon exerts on the Earth - but are MUCH smaller in magnitude.

 

[Zanket]

No. That space would globally expand or contract fell naturally out of the math. Einstein introduced the Cosmological Constant precisely so that he could have an adjustable parameter that would eliminate that effect (when set to the right thing).

But the Hubble constant is not the cosmological constant. The Hubble constant can imply that space is expanding even when the cosmological constant is zero. And the Hubble constant is not part of GR. Right?

If you grab the ends of a string and tug on them without breaking its elastic limit, you can tug for all of eternity with a constant force, and the string will never break. It will stretch once so that its intermolecular forces balance your tension force, and then it will stay in equilibrium until the applied tension is changed.

Agreed. To tug with constant force while keeping your grip on the string, you must hold still. But expanding space does not hold still; it keeps stretching. If the string can slip against the stretch, the opposing forces can maintain equilibrium so the string won’t break. This is like continuously moving pinched fingers along the string, applying a constant tug. In the expanding space paradigm, such slippage explains how the galaxies do not expand. But the explanation is lacking. The tug I apply to the string has a direction, giving the string an opposite direction to slip to. The tug on the floating intergalactic thread has no direction, giving the thread no direction to slip to. That let's me create a paradox, where the intergalactic thread must obviously eventually break (it cannot stretch forever) and the new ends must fly apart, and it breaks in an arbitrary spot, hence there is no explanation as to why a galaxy held together only by weaker gravity cannot break and the pieces fly apart. I wish I could explain the paradox better.

 

[Mike2]

String theory seems outside the scope of this topic. The expanding space paradigm says nothing about strings. By "thread," I mean a thread like your clothes are made of. Can you start a new thread(!) about this?

"outside the scope of this topic", you say. "start a new thread", you say. As I understand it, the entire question is on how a thread (and all it inter-molecular parts) would respond to expanding space. But if those molecular parts are extended objects, then this is exactly equivalent to asking how those extended objects, strings, respond to expanding space. If they stretch along with space, then the thread will not break. In fact we would never observe expansion because as things got farther away, they would also grow so that the difference would not be noticeable. But if they don't respond to expansion, then what does this prove?

 

[Hurkyl]

But the Hubble constant is not the cosmological constant. The Hubble constant can imply that space is expanding even when the cosmological constant is zero. And the Hubble constant is not part of GR. Right?

The Hubble constant is an observed quantity. It's value is determined using General Relativity... I can't really make sense of just what you're trying to suggest in this paragraph.




I assume by "slipping" you mean something like:

If we put a colored dot on the string, and place a dust particle next to the string so that it is initially comoving with the dot, then as time goes on, the dot and dust particle separate.

It seems pretty obvious to me what "slipping" would occur -- each particle would respond to the intermolecular forces acting on it.


Maybe it would do you better to consider individual particles. Consider a two-particle system, and then a three-particle system, and so on, to get an idea what's going on.

 

[Zanket]

No, I mean zero. If you ignore any cosmological constant/dark energy (i.e. the situation up until the 1990's) then there is nothing driving the galaxies apart. They are moving apart because they started out that way. The only force between them is gravitational, which causes deceleration.

OK, and I assume the Hubble constant just quantifies their movement apart. But you said, “the so called expansion of space has no physical effect”. That implies to me that a floating intergalactic thread (between galaxies fast-receding due to the expansion of space) will not physically stretch. Is that what you meant?

No the reason for the expanding space paradigm was because the natural time coordinate chosen by cosmologists is the proper time, which is not compatible with special relativity. Expanding space was invented so that objects wouldn't seem to be moving apart faster than light.

That makes sense. But the paradigm also introduced the idea of things physically stretching, didn’t it?

What GR introduced was the idea of spacetime as something real, which could be curved. However, it can't be said to expand, as that is a time based notion.

That again implies to me that a floating intergalactic thread will not physically stretch. But if not, then a paradox arises in determining in which direction relative to one or both galaxies (on either end of the thread) will move, given that no force pushes the thread in a particular direction.

 

[Hurkyl]

Also, I get the feeling the basis of your argument is based on something like:

"I can't figure out how to answer this qualitative question with pure logic, therefore there must be a problem."

But physical theories are strongly quantitative. If you put numbers to everything in the problem, you could (in principle) turn the numerical crank to get the answer.

 

[Zanket]

To address this issue without the math, it's already been argued that a very long string must break in an expanding universe, when it passes the Hubble horizon.

The Hubble horizon is everywhere. The spot you are at is on the Hubble horizon for some hypothetical observer. Saying it must break there is saying it must break everywhere.

 

[Zanket]

"outside the scope of this topic", you say. "start a new thread", you say. As I understand it, the entire question is on how a thread (and all it inter-molecular parts) would respond to expanding space. But if those molecular parts are extended objects, then this is exactly equivalent to asking how those extended objects, strings, respond to expanding space.

The questions I pose here are as to whether the expanding space paradigm is consistent, i.e. free of self-contradiction. That should be determinable without including string theory in the discussion.

 

[Zanket]

The Hubble constant is an observed quantity. It's value is determined using General Relativity... I can't really make sense of just what you're trying to suggest in this paragraph.

Chronon cleared it up some. What still doesn’t make sense is, why is the expanding space paradigm attributed to general relativity (as in the quote from the book, above), which pre-dated the paradigm’s creation by 15 years? My understanding is that the paradigm implies that a floating intergalactic thread will break due to expanding space. Was that really predicted by GR, and if so, why was there a need to create a paradigm 15 years later?

Maybe it would do you better to consider individual particles. Consider a two-particle system, and then a three-particle system, and so on, to get an idea what's going on.

I had done that. Take particles A and B next to each other as AB. The space between them expands to try to make them become A__B, but the binding force between them makes the particles slip past the expanding space so that the system becomes _AB_. Likewise, expanding space tries to make ABC become A__B__C, but the binding force keeps it __ABC__. And so on. But for a very long system, that obviously doesn’t work. It seems that an intergalactic thread must break. The problem with the paradigm seems to be related to the fact that the slippage must occur toward some direction, but the direction is arbitrary, hence nonsensical, allowing a paradox to be created. I think I gave a better example of that above.

 

[Zanket]

If you put numbers to everything in the problem, you could (in principle) turn the numerical crank to get the answer.

A theory can be self-contradictory and still give an answer. Then to determine self-contradiction, you cannot rely on the math. I'm trying to determine whether the paradigm is self-contradictory. So far, it seems to be. So far as has been determined (I haven't got a reasonable answer as to why not), the floating intergalactic thread breaks at an arbitrary spot and the new ends fly apart, and the length of the thread is irrelevant to that conclusion. Then there is no explanation as to why a galaxy, held together only by the weaker force of gravity, does not break apart and the pieces fly apart.

 

[Hurkyl]

Take particles A and B next to each other as AB.

But they aren't next to each other -- remember that intermolecular forces are also repulsive when they're too close.

Their natural equilibrium state might be A...B. When placed in a region of expanding space, they would settle into A...B. (Actually, the difference wouldn't even be that large, but the separation would settle to something slightly larger than "normal")

But for a very long system, that obviously doesn’t work.

Why is it obvious?

It seems that an intergalactic thread must break.

If you mean a thread whose ends are anchored to galaxies, you would be correct. (I'm assuming that the string won't be strong enough to actually keep the galaxies from being carried along with expansion -- I have no idea just how much tension would be generated)

The problem with the paradigm seems to be related to the fact that the slippage must occur toward some direction, but the direction is arbitrary, hence nonsensical,

This is what I meant by my comment in post #31. If you precisely set down the scenario, then you could simply work through the kinematics and determine what happens.

The fact is, the problem you've specified is very vague, and there are any number of things that could happen depending on the precise details of the problem. That is not nonsensical, nor paradoxical.

A theory can be self-contradictory and still give an answer. Then to determine self-contradiction, you cannot rely on the math.

That is 100% wrong. Being self-contradictory means precisely that if you work through the math of one problem in two different ways, you get answers that are not compatable. You can't talk about self-contradiction of a mathematical theory without doing math.

 

[pervect]

The Hubble horizon is everywhere. The spot you are at is on the Hubble horizon for some hypothetical observer. Saying it must break there is saying it must break everywhere.

You are missing the point. If you can't get a light beam from point A to point B, because there is a horizon in between A and B, you can't have a string connecting A and B. The exact form or location of the horizon doesn't matter to the argument - whether it is the Hubble horizon, a black hole horizon, or a Rindler horizon is irrelevant.

To assume that there could be a string connecting A to B yields a contradiction. A string has the following characteristic - when you pull on either end of the string, the other end of the string moves (not instantly, but delayed by the speed of sound in the string).

Now, if light cannot go from A to B because there is a horizon in the way, they are causally disconected.

Therefore there cannot be an intact string connecting them either - when you pull on the string at A, the signal cannot reach B. What happens phyiscally is that the string breaks. (It didn't break from the pull - it broke when you tried to first stretch it from A to B).

Another way of thinking about this is that a light beam is the strongest possible string - it's a string that's so strong that the speed of sound in the string is the maximum velocity possible in the universe, the speed of light. If you can break a light beam, any weaker string must necessarily fail.

 

[pervect]

There is something I should probably point out.

To summarize, it's true that there are no tidal forces when an expanding universe is totally empty (i.e. it contains no energy or matter). But there isn't really any universe in this case. It's only when the universe actually contains matter that one finds that there are tidal forces due to it's expansion.

The details:

The metric for the flat-FRW space-time is

ds^2 = a(t)^2 (dx^2+dy^2+dz^2) - dt^2

The tidal force in terms of the above parameters as I mentioned in another thread is

-\frac{\ddot{a}}{a}

This is computed directly from the Riemann from the metric above.

This tidal force isotropic, the same in all directions (it's actually an acceleration per unit length, so it has units of 1/sec^2).

Now let's look at the the solution for a(t).

First, let's look at a totally empty universe.

When there is no matter in the universe, we have the boring solution a(t) = k*t, and \ddot a is zero, therefore there are no tidal forces. But there is no universe, either, really - it's just empty space-time.

Things get a lot more interesting when our universe has matter in it. To make it easy, let's assume there is basically no pressure, i.e. the expansion is matter dominated, and there is no radiation pressure.

The pressure term must be zero, which leads to the equation

\dot{a}^2+2a\ddot{a} = 0

(take my word on this, or if you really want to, look up or compute the Einstein tensor for the metric above, and remember that G_ab = 8*pi*T_ab, and we are assuming that T_ab has no pressure terms)

This has the solution

a(t) = t^(2/3)

The matter density is now non-zero, and equal to

3 (\frac{\dot{a}}{a})^2

And, we now have tidal forces, because -\frac{\ddot{a}}{a} is nonzero as well.


So the tidal forces are not appearing out nowhere or in any way "mysterious" - from one point of view, they are due to the gravitational interaction of the "string" with the rest of the universe.

 

[Garth]

Can you elaborate? What is SCC?

Self Creation Cosmology

One error in a previous post of mine was that in the static Jordan conformal frame of SCC, in which particle masses increase exponentially (exp(Ht)) and atomic diameters shrink exponentially (exp(-Ht)), the cosmic thread does not increase in length, but as its atoms shrink it will still break. The cosmic string breaks in both the Einstein and the Jordan conformal frames of measurement.

Garth

 

[Mike2]

There is something I should probably point out.

To summarize, it's true that there are no tidal forces when an expanding universe is totally empty (i.e. it contains no energy or matter). But there isn't really any universe in this case. It's only when the universe actually contains matter that one finds that there are tidal forces due to it's expansion.

Thanks for the calculations. I'm wondering what happens as galaxies leave the cosmological event horizon? If the galaxies left can no longer feel the gravitation force of those galaxies that have disappeared behind the cosmological event horizon, then is the FRW model affected by this loss of matter? Does this loss of matter further accelerated the expansion? Thanks.

 

[pervect]

Thanks for the calculations. I'm wondering what happens as galaxies leave the cosmological event horizon? If the galaxies left can no longer feel the gravitation force of those galaxies that have disappeared behind the cosmological event horizon, then is the FRW model affected by this loss of matter? Does this loss of matter further accelerated the expansion? Thanks.

I'm not sure what sort of experiment would exactly answer this question.

However, if you accept the case of a black hole forming as an example (an example of matter going out of sight behind a horizon), you can see that the gravity before the object collapsed into the black hole is the same as the gravity after the collapse.

The sci.physics.faq "how does the gravity get out of a black hole" goes into this a little more - people who are overly attached to the "graviton" point of view get confused by this question a lot, people with either a field-oriented view or a geometrical view don't have any problem with the gravity existing after the object has passed beyond the event horizon. The philosophical explanations vary somewhat, but everyone agrees that information can't get out of a black hole, while gravity (and the electrostatic field) can.

 

[chronon]

You are missing the point. If you can't get a light beam from point A to point B, because there is a horizon in between A and B, you can't have a string connecting A and B. The exact form or location of the horizon doesn't matter to the argument - whether it is the Hubble horizon, a black hole horizon, or a Rindler horizon is irrelevant.

No, no, no. The Hubble sphere is not a horizon. See http://www.chronon.org/Articles/cosmichorzns.html, or if you don't believe me then read the Lineweaver & Davis article http://xxx.arxiv.cornell.edu/abs/astro-ph/0310808 .

 

[chronon]

That again implies to me that a floating intergalactic thread will not physically stretch. But if not, then a paradox arises in determining in which direction relative to one or both galaxies (on either end of the thread) will move, given that no force pushes the thread in a particular direction.

Where do you find a dog with no legs?
My assumption is that the thread is initially put into place to be stationary with respect to some galaxy, and the question is then 'Does it stretch because of the expansion of the universe'. My assertion is that it does not (Rather it begins to contract).

I recommend that you read the relevant part of Ned Wright's FAQ
http://www.astro.ucla.edu/~wright/cosmology_faq.html#MX , in particular the second paragraph

In the absence of the cosmological constant, an object released at rest with respect to us does not then fly away from us to join the Hubble flow. Instead, it falls toward us

Of course if you try to pull the ends of the thread apart, or attach it to two objects which are moving apart then it is likely to break, but this is nothing to do with cosmology.

 

[Zanket]

But they aren't next to each other -- remember that intermolecular forces are also repulsive when they're too close.

I think the question as to whether the paradigm is consistent can be answered without going into that level of detail.

Why is it obvious?

Because, for example, if the galaxies near either end of a floating thread are receding from each other due to expanding space between them, the ends of the thread presumably stay at rest with respect to either galaxy (no force exists to move the ends of the thread in any particular direction), and presumably the thread cannot expand to any length without breaking.

If you mean a thread whose ends are anchored to galaxies, you would be correct. (I'm assuming that the string won't be strong enough to actually keep the galaxies from being carried along with expansion -- I have no idea just how much tension would be generated)

Or not anchored, as above.

This is what I meant by my comment in post #31. If you precisely set down the scenario, then you could simply work through the kinematics and determine what happens.

The fact is, the problem you've specified is very vague, and there are any number of things that could happen depending on the precise details of the problem. That is not nonsensical, nor paradoxical.

I may not be putting the query in the best way (discussion help me improve that), but it’s not vague to me. It should not take any math to figure out the basic result for the intergalactic thread (like “it breaks” or “it moves relative to one or both galaxies” or “it stretches forever”). Presumably others cranked out such answers long ago (if that was even necessary, since the paradigm was created to match observation) and wrote about it. Lots of what I’ve read suggests that the thread will break, which seemingly leads to a paradox, as I noted. And the other two possibilities have problems.

That is 100% wrong. Being self-contradictory means precisely that if you work through the math of one problem in two different ways, you get answers that are not compatable. You can't talk about self-contradiction of a mathematical theory without doing math.

That’s a good point. I was talking about one answer. I don’t need to do the math myself, though, if someone else already wrote about it (like “it breaks” or “it moves relative to one or both galaxies” or “it stretches forever”).

 

[Zanket]

You are missing the point. If you can't get a light beam from point A to point B, because there is a horizon in between A and B, you can't have a string connecting A and B. The exact form or location of the horizon doesn't matter to the argument - whether it is the Hubble horizon, a black hole horizon, or a Rindler horizon is irrelevant.

I don’t see how that can be true in the case of a Hubble horizon. I’m on some hypothetical observer’s Hubble horizon as I write this. Am I not?

Now, if light cannot go from A to B because there is a horizon in the way, they are causally disconected.

But light can cross a Hubble horizon, by which I’m assuming you mean the surface of a Hubble sphere. My Hubble sphere is my observational limit. You have your own Hubble sphere. Whereas a black hole’s event horizon, say, is the same observational limit for everyone.

Another way of thinking about this is that a light beam is the strongest possible string - it's a string that's so strong that the speed of sound in the string is the maximum velocity possible in the universe, the speed of light. If you can break a light beam, any weaker string must necessarily fail.

That’s a good way of thinking in the case of a black hole’s event horizon, say (so long as you're careful; a thread can cross an event horizon intact so long as it's falling). But I don’t see it applying to a Hubble horizon. And why involve a Hubble horizon in this case at all, when galaxies fast-receding from each other due to expanding space exist within our Hubble sphere? We can put the thread in between those galaxies to answer our questions.

 

[Zanket]

My assumption is that the thread is initially put into place to be stationary with respect to some galaxy, and the question is then 'Does it stretch because of the expansion of the universe'. My assertion is that it does not (Rather it begins to contract).

I recommend that you read the relevant part of Ned Wright's FAQ
http://www.astro.ucla.edu/~wright/cosmology_faq.html#MX , in particular the second paragraph

Ned Wright’s FAQ, which I’ve spent a lot of time on, including this question, seems to dance around issues rather than get to the point, leading to confusion. For example, you took from the FAQ that the thread does not stretch. But consider… What happens to a thread released at rest with respect to both of two galaxies fast-receding due to space expanding between them? That is, either end of the thread is at rest with respect to a respective galaxy. That’s the intergalactic thread example I’ve used above. According to the FAQ, I presume that either end falls toward its respective galaxy, which means that the thread physically stretches, eventually to a breaking point. Then the paradox aforementioned arises.

 

[Zanket]

I think I can now better put the paradox that I gave above. I think no reasonable resolution has been given so far:

According to the expanding space paradigm of cosmology, the galaxies do not expand along with the intergalactic expanding space because gravity holds them together. Let a floating thread span the distance between two galaxies receding from each other due to space expanding between them. The ends of the thread are not anchored to their respective galaxies. According to Ned Wright's Cosmology FAQ here, either end falls toward its respective galaxy. Then the thread physically stretches. Presumably the thread cannot stretch forever, so eventually it must break. The thread breaks at an arbitrary spot (if you disagree, then tell me, at what spot does an infinitely long thread break?) and the pieces fly apart. Even the strongest binding force of the thread is not strong enough to keep the thread intact. The galaxies are not in expansion-free zones, and they exist in arbitrary spots. Then how can gravity, a binding force far weaker than the strongest binding force, keep the galaxies from breaking and the pieces flying apart?

 

[chronon]

OK, so let's ignore cosmology for a moment. The initial state of the thread is one of uniform expansion, and so the tension will be increasing, creating a force towards the centre of the thread, counteracting the expansion. Whether the thread breaks depends on whether the tension manages to stop the expansion before it reaches breaking point.

So what happens when we include cosmological effects. There will now be three forces.

1) Tension
2) Gravitational effects due to the matter in the universe. (Which is assumed to be evenly distributed)
3) A stretching effect due to dark energy/non-zero cosmological constant.

I'm ignoring (3). To start with (2) will be zero. However due to tension, each part the thread will begin to lag behind the surrounding matter (except for the centre). The important point to note is that each point will now be stationary with repect to some part of the universe nearer to the centre of the thread, and gravity will pull it towards that point, rather than causing it to catch up with the surrounding matter. Hence the thread will stretch less than in the non-cosmological case, and so is less likely to break.

 

[chronon]

Note that q is a negative number for the numbers quoted, as far as sign issues go.

q is a negative number (-0.6) according to recent measurements, but this needs a positive cosmological constant to explain it. If the cosmological constant is zero then q>=0. For instance, for the critical density model, where a=t^(2/3) you have q=1/2.

 

[pervect]

OK, so let's ignore cosmology for a moment. The initial state of the thread is one of uniform expansion, and so the tension will be increasing, creating a force towards the centre of the thread, counteracting the expansion. Whether the thread breaks depends on whether the tension manages to stop the expansion before it reaches breaking point.

So what happens when we include cosmological effects. There will now be three forces.

1) Tension
2) Gravitational effects due to the matter in the universe. (Which is assumed to be evenly distributed)
3) A stretching effect due to dark energy/non-zero cosmological constant.

I'm ignoring (3). To start with (2) will be zero. However due to tension, each part the thread will begin to lag behind the surrounding matter (except for the centre). The important point to note is that each point will now be stationary with repect to some part of the universe nearer to the centre of the thread, and gravity will pull it towards that point, rather than causing it to catch up with the surrounding matter. Hence the thread will stretch less than in the non-cosmological case, and so is less likely to break.

I'm not sure I follow your logic here, but I think I agree with the conclusion, which I take to be:

If (contrafactually) we had no cosmological constant, the deceleration parameter q would be positive, and our string would be in compression rather than tension.

[add]
In fact I get q=+.5 with no cosmological constant, though I haven't double checked my calculations.
[end]

As was pointed out in another thread by SpaceTiger

https://www.physicsforums.com/showthread.php?t=76405

in the same contrafactual case (no cosmological constant), there would be no event horizon - anyone would eventually be able to see the whole universe, if they waited long enough - so we don't have the impossibility of a string going through an event horizon.