Couldn't you unify gravity & the cosmological constant?

[Vree]

...through inertial mass, namely to explain away the sameness of inertial and gravitational mass?
If you assume that only inertial mass is a "real" effect, then gravity would simply become a fictious force arising from inertial mass holding matter back from expanding alongside spacetime during the expansion of the universe.

I know this is already achieved for the most part in relativity but it seems to me that it is never explicitly stated that gravity within a universe expanding at an ACCELERATING rate could be viewed as identical to any other fictious force within a non inertial reference frame.

I don't know Big Bang cosmology even nearly well enough but it seems to me that the origin of the "motivating" force to cause & drive the expansion is largely unaccounted for. It does not seem very logical to imagine two opposing forces, one eventually running out allowing the other to drive the universe towards a "Big Crunch" when you can just imagine a single force, held back by a known phenomenon.

Please excuse my very basic understanding. I'm grateful for any pointers you can give me to satisfy my curiosity about this.

 

[mfb]

A cosmological constant is part of gravity. It is very easy to include it in General Relativity.
This has nothing to do with inertial or gravitational mass - and GR requires them to be the same anyway.

If you assume that only inertial mass is a "real" effect, then gravity would simply become a fictious force arising from inertial mass holding matter back from expanding alongside spacetime during the expansion of the universe.

No it would not.

but it seems to me that it is never explicitly stated that gravity within a universe expanding at an ACCELERATING rate could be viewed as identical to any other fictious force within a non inertial reference frame.

This is never mentioned because it is not true.

 

[Vree]

No it would not.

This observation could use some elaboration. :)
I appreciate the response, but you realize you are not helping me understand anything if you do not say why this is true? :)

(Clearly my goal here is not to demonstrate how I have overthrown Einstein with grade school logic, but to better understand where the flaws in my own assumptions are.)

 

[mfb]

The idea is too far away from science for a clear response, I think. It just does not make sense.

 

[marcus]

First thing on the agenda, I think, is try to be clear about what we mean by universe expanding at accelerating rate.

"Universe expanding" does not mean ordinary motion we're familiar with. It means percentage growth of distances between objects at rest with respect to the ancient matter, or rather the ancient light we are receiving from the most ancient matter we can see.

In GR (our basic geometry) you have no right to expect the distance between two stationary objects to remain the same. Geometry is dynamic. Geometry changes from one location or moment to the next.

So the first thing is not to imagine expansion as ordinary motion. Nobody gets anywhere by it---no destination is approached---relative positions are unchanged---everybody just becomes farther apart. (I'm neglecting the small individual motions objects have in the space around them---they are pretty much random and too small to matter on large scale).

"Accelerating" was an unfortunate choice of word. It makes people think of an object like a car accelerating, in ordinary motion. As if there were some force.
The percentage growth rate of distance is actually DECLINING. But it is declining so slowly that it can be thought of as nearly constant. Percentage growth obviously has a kind of "acceleration" in the sense that your savings account at the bank grows by an increasing dollar amount each year as the principal grows. It will grow by an increasing dollar amount even if the bank is gradually lowering the interest rate it pays, as long as the percentage rate is not lowered too rapidly.

 

[marcus]

Vree, your idea is not useful because you started out with the mental image of accelerated motion. My advice is to get used to the expanding balloon picture where none of the objects move but all become farther apart at a roughly constant percentage distance growth rate. (All existence concentrated on the 2D surface of the balloon.)
Get used to geometry itself changing. then come back to what you were wondering about---the cosmological constant.

the current distance growth rate is 1/144 of a percent per million years. For a long time it was declining quite rapidly (it is governed by a differential equation called Friedmann equation, derived from GR). But recently the decline has leveled out enough that we are beginning to see almost-exponential growth. The rate is tending towards 1/173 % per million years. It is that 1/173% that embodies/reveals the cosmological constant.

 

[Vree]

"Universe expanding" does not mean ordinary motion we're familiar with. It means percentage growth of distances between objects at rest with respect to the ancient matter, or rather the ancient light we are receiving from the most ancient matter we can see.

In GR (our basic geometry) you have no right to expect the distance between two stationary objects to remain the same. Geometry is dynamic. Geometry changes from one location or moment to the next.

Right. This is exactly my understanding.
No, I did not start out with an idea about "motion". (In fact, I feel a little insulted becaue I said no such thing. :D ) That would have been a very basic mistake. We can skip the rubber sheet stuff.

But when you say
"growth of distances between objects at rest"
that also accurately describes -as far as I can say - the way gravity works (just replace "growth" with "decrease").
In fact the Big Bang model seems to suggest that both of these effects can be expressed as two effecs working in opposite directions.
So I want to know - why.

Just from a very basic Newtonian viewpont, gravitational acceleration would be regular motion. In GR gravity itself is the result of space changing relative to matter. This does not seem to me fundametally different from how the expansion of space works.

Now you could tell me for example that gravitational acceleration and how it defines distance over time is in no way comparable to how universal expansion works, because the ratio is is different, or the way it is calculated is different. Or there is an extra angle or component in the equation which puts the two on completely different footing. And I would accept that.

 

[Vree]

For example, here is an example of the kind of disproof that I am looking for.

Fundamental forces can propagate at the speed of light, which the expansion of the universe is not bound by. Since we have clear proof that gravitational waves exist and they also propagate at the speed of light, as evidenced by the time delay it takes for a gravitational effect from the Sun to be felt on Earth, or an object in space to be affected by Earth's gravity, which matches the speed of light exactly, this clearly proves that gravity is a fundamental force completely unrelated to the expansion of the universe. QED.

Now I have no idea if this is true, but it is a good example of a simple and clear counter-argument.

Or you could disprove it mathematically like I said above. That is even better since it allows me to learn something useful. Formula to express cosmological constant in GR is this and this, gravity relative to that is this and this, and as you (I) can see, the way this is exchanged into this clearly shows that this category X is not this category of Y. Equally good, or better.

 

[marcus]

Good! so you DIDN'T start with the bad mental image of distance growth as like ordinary motion of objects through space. I was mistaken about how you were thinking.

quite possibly I cannot help you. but I will say a few things and you can see if they help. If not, I apologize.

Anyway I take your reply to indicate that you are already thinking along the lines of dynamic geometry i.e. spatial curvature (triangles not adding to exactly 180) and distances able to expand and contract.

And you realize that this changing geometry has a kind of "momentum". Once it gets started expanding it tends to continue. But the effect of ordinary and dark matter can gradually whittle away at the rate. Geometry has momentum of change but matter effects it.

And the changing geometry is governed by the GR equation ( the simpler Friedmann derived from it is all we really need here) which allows to calculate how rates evolve and both GR and Friedmann have a place in the equation for the long term target rate that distance growth will evolve towards, a target or asymptotic rate which does not have to be zero. that is just a feature or characteristic of the GR equation in the most general form allowed by the symmetry of the theory (general covariance) . (That essentially is what the cosmo constant Lambda IS.)

now I think the core of your question is HOW DID THE EXPANSION GET STARTED and you're kind of teasing and speculating around with that question.

So I will give you a link to a paper to read which gives the clearest explanation I have seen so far of one of the ways people conjecture that the expansion got started. We don't know, after all. so far there are just diverse models of how it might have. the standard consensus model only takes over once it HAS started. So the field is open for people to propose models for how it actually got started. Here is what Yi-Fu Cai and Edward Wilson-Ewing (two young researchers) have proposed.
Google "LambdaCDM bounce" to get their December paper.
http://arxiv.org/abs/1412.2914
Google "wilson-ewing pirsa" to get the January talk (at Perimeter Institute Recorded Seminars Archive)
http://pirsa.org/15010074/
Ed W-E is fantastic, this is a video of him explaining their idea in a seminar talk at Perimeter Institute. I can't get the video to play so I downloaded the slides PDF and listen to the MP3 audio.

 

[marcus]

==quote==
But when you say
"growth of distances between objects at rest"
that also accurately describes -as far as I can say - the way gravity works (just replace "growth" with "decrease").
==endquote==
Falling objects are typically not at rest with respect to the background of ancient light. Where possible we can calculate their speeds relative to background.
So falling is best understood as actual motion thru space (along the geodesics determined by the geometry).

Growth or decrease of distances between objects at CMB rest is measurably different from ordinary free-fall or orbital motion (ie. along geodesics). One can actually measure the doppler changes as the Earth orbits the sun because it is moving in accordance with gravity. It is not at CMB rest. And one can measure the motion of the solar system relative to the CMB (cosmic microwave background) the same way.

When we state Hubble law of expansion we are talking about growth of distances between objects at CMB rest disregarding whatever individual motion they may have through their local surroundings.

 

[Vree]

Great!
thank you so much for humoring me and sacrificing some of your time to give a proper answer :D

Yes, I agree, my problem seems to boil down to trying to interpret the expansion and the cosmological at least partially as something else (ie. an illusionary difference between forces) and the solution would be to learn more about where the gaps and absolutes that give credibility to the Big Bang version are, so that's what I'll have to read & learn more about.

(And also filling the gaps in my GR understanding to see why Einstein couldn't have interpreted the cosmological constant in a similar manner. I suspect it shouldn't be too hard to find out which of the above data was avaliable in Einstein's time.)

I'll start with following those links you gave me, thank you so much again for helping me.

(I realize I could just do things the long and boring way, try to learn aaall I can about GR and any new alternative theories and then try to find some experimental results that would disprove my findings and then maybe in a few years I'd get my answers (xD), but since there is this great forum I check all the time (and this kind of thing is what it seems to be for) I though it'd be more fun to ask these things and maybe learn a new thing or two. xD
Also, when I read general relativity or any related arguments I sometimes get angry, I can't follow the logic of the creator of the theory and where it came from. For example, why did Einstein choose to resolve the equivalence principle in this particular manner? etc)