I Is Big G and Dark Energy Constant Over Time?

[WhatIsGravity]

TL;DR Summary

Wanting to research big G

I'm wondering if any of the physics Jedi out there might know of any credible papers that suggest big G and/or the cosmological (dark energy) aren't constant through time?

 

[Ibix]

Big G isn't a thing that can be constant or not in any meaningful way - it's basically a unit conversion factor. You would need to search for papers investigating change in one of the fundamental dimensionless quantities from which G is derived, most probably the gravitational coupling constant.

I don't think the term "cosmological constant" is used much any more. Dark energy, which has more or less the same effect, is so named at least partly because we're not certain that its density is constant. "Quintessence" is the name of one model that allows it to vary.

 

[Bandersnatch]

I don't think the term "cosmological constant" is used much any more. Dark energy, which has more or less the same effect, is so named at least partly because we're not certain that its density is constant. "Quintessence" is the name of one model that allows it to vary.

I believe the convention is to treat DE as a more general term, with CC and Quintessence being more specific subsets.
I'm not sure why you'd say CC is not used any more, though. That's the lambda in LCDM, after all.

 

[Vanadium 50]

Big G isn't a thing that can be constant or not in any meaningful way - it's basically a unit conversion factor.

I don't think I agree. Which units? kilograms, meters, and seconds are all defined non-gravitationally.

 

[PeterDonis]

Big G isn't a thing that can be constant or not in any meaningful way - it's basically a unit conversion factor.

While this is true in classical GR, it is not true in quantum gravity (which means it probably isn't really true--the classical GR choice of "geometric" units where $G = c = 1$ does not really reflect the underlying physics if our current understanding of quantum gravity is correct). In quantum gravity, the "natural" units of $G$ (if we are in units where $c = \hbar = 1$) are inverse mass squared.

One way of looking at this is that it is a reflection of the quantum field theory of a massless spin-2 field being non-renormalizable. Another way of looking at it is that quantum gravity has a natural length/mass scale, the Planck length/Planck mass. (The "natural" QFT value of $G$ is basically the inverse Planck mass squared.)

 

[Ibix]

Three "<someone knowledgeable> has quoted your post" alerts is never a good sign...

I believe the convention is to treat DE as a more general term, with CC and Quintessence bein

Fair enough - I was under the impression that dark energy was the preferred term rather than an umbrella term. Apparently I misunderstood.

I don't think I agree. Which units? kilograms, meters, and seconds are all defined non-gravitationally.

At least in GR, $c$ is the ratio between [L] and [T] units and is typically set to 1. Then you can fix $G$ as 1 too by picking appropriate units, so it's a conversion factor between [M] and whichever of [L] and [T] you kept when you fixed $c$. @PeterDonis explains why that's not generally correct above (although I think I'm going to need to get around to learning QFT and QG to actually understand him). I do recall that someone I've read (I thought it was Carroll, but can't find it if it was) did observe that they didn't approve of setting $G$ to 1, although they were happy to set $c$ to 1. It struck me as inconsistent at the time, but maybe this was the reason.

On the subject of unit definitions, though, even if my argument were correct, I'd be surprised if the mass unit were defined gravitationally. Our measurement of $G$ is much less precise than other fundamental constants, so a definition based on it would mean a large uncertainty in the definition of the unit of mass. I don't think it would be acceptable to metrologists.

 

[Haelfix]

Strictly speaking, one would need the notion of a dimensionless gravitational constant to really make sense of this question. Unfortunately this is actually quite subtle and gets into details of quantum gravity.

As mentioned before Newtons constant has natural units of inverse length squared. So you really want to have an invariant dimensionless constant or something like:

$$ g(k)=Gk^{2} $$
$$ g_{(k->\infty) } \rightarrow g_{*} $$

where $g_{*}$ is a fixed point of the theory. This then leads people to parametrize the running of G like so:
$$G(k) = \frac{G}{1+G\frac{k^{2}}{g_{*}}}$$
This is what Weinberg did in his original papers on the nonrenormalizability of gravity and asymptotic safety and what some modern practitioners use to try to get a handle on what various 'quantum' corrections look like in the appropriate classical limit for various processes.

However this remains controversial, b/c its unclear exactly what G(k) measures at any given scale. It need not represent the same sort of thing that we are used to in identical cases with say the finestructure constant which runs logarithmically with a scale (indeed the power law running is quite unfamiliar).

So in short, while setting G = 1 is simply a choice that facilitates notation, what happens to the real physical quantity that measures gravitational coupling strength and how it's rescaled for a given process is going to be quite a bit more complicated and need not be expressible in a simple mathematical form..

 

[PeterDonis]

I'd be surprised if the mass unit were defined gravitationally.

In SI units, it isn't. The latest definition of the kilogram is based on setting Planck's constant to a fixed value.

 

[Ibix]

In SI units, it isn't. The latest definition of the kilogram is based on setting Planck's constant to a fixed value.

I'm aware. Vanadium50 seemed to be implying that this was evidence that $G$ could not be a unit conversion factor like $c$. My point was that even if it were reasonable to base a unit system on $G$ (and you and Haelfix have explained why it isn't), I would not expect metrologists to accept a number so imprecisely known as part of such a unit system. I was questioning his inference process, not his start or end point.

 

[PeterDonis]

Vanadium50 seemed to be implying that this was evidence that $G$ could not be a unit conversion factor like cc.

More precisely, it is evidence that the thing we usually call $G$ can't be purely a unit conversion factor like $c$. It mixes together a unit conversion factor and a physical coupling that is not dimensionless. Picking "natural" QFT units in which $\hbar = 1$ separates out these two aspects, so what is left of $G$ is now just the physical coupling, with no unit conversion factor involved.

 

[WhatIsGravity]

Holy smokes, humbly and thanks for the responses.

On the subject of unit definitions, though, even if my argument were correct, I'd be surprised if the mass unit were defined gravitationally. Our measurement of $G$ is much less precise than other fundamental constants, so a definition based on it would mean a large uncertainty in the definition of the unit of mass. I don't think it would be acceptable to metrologists.

With our understanding of G, I can't imagine mass being defined by gravity. I was working with a company probably a decade ago who proposed a gravity (not mass) standard to BIPM (free fall gravimeter with laser length and atomic clock, both length and time standards); understandably- nothing doing.

Really, the basis for my question was thinking about a QFT's gravitational gradient, and the lattice, or LQG or whatever that might suggest such a (constant?) gravitational gradient. In GR at least, units for a gravitational gradient are 1/s^2. CC or dark energy or 'whatever', times G... is related to the gravity gradient? Probably I'm misunderstanding the physics, but I just don't see G, or the gravitational gradient, as being a dimensionless constant, or simply a units conversion factor.

I don't think I agree. Which units? kilograms, meters, and seconds are all defined non-gravitationally.

I guess, this is really the basis for my question. Any papers, suggestions or references; appreciated.

 

[PeterDonis]

In GR at least, units for a gravitational gradient are 1/s^2.

What do you mean by "gravitational gradient"?

 

[WhatIsGravity]

What do you mean by "gravitational gradient"?

The change in gravity/acceleration in regards to a change in distance. m/s^2, per m.

 

[hutchphd]

Getting back to the original question may I direct the OP historically to Dirac and his immediate progenitors:

https://en.wikipedia.org/wiki/Dirac_large_numbers_hypothesis

Any analysis of changes in time will have to compare the value of G to that of other parameters ("constants") and therefore cannot be dispositive about G.
For instance to measure a "force" one must compare it somehow to another different "force" and examine the ratio.

 

[PeterDonis]

The change in gravity/acceleration in regards to a change in distance.

The proper name for this is "tidal gravity" or "spacetime curvature". Its units are more usually given as inverse meters squared instead of inverse seconds squared.

The units of $G$ in QFT do happen to be the same as the units of spacetime curvature (in QFT units, inverse length squared is the same as mass squared), but that's not because they're the same thing. It's because $G$ is the coupling constant in the Lagrangian for the QFT of a massless spin-2 field, and the field itself appears in the Lagrangian as the Ricci curvature. Each term in the Lagrangian density has units of $\text{mass}^4$, since the Lagrangian density gets integrated over all of spacetime to get the action and the action is dimensionless. So since the Ricci curvature has units of mass squared (inverse length squared), the coupling constant that multiplies it also has to have units of mass squared to get a term with overall units of $\text{mass}^4$.

 

[WhatIsGravity]

Getting back to the original question may I direct the OP historically to Dirac and his immediate progenitors:
https://en.wikipedia.org/wiki/Dirac_large_numbers_hypothesis

I'm feeling quite uneducated and humble in this forum; much thanks hutchphd for the reference, but that seems kinda... numerological?

The proper name for this is "tidal gravity" or "spacetime curvature". Its units are more usually given as inverse meters squared instead of inverse seconds squared.

Can't yet wrap my brain around how 1/m^2 in regards to a gravity (position) gradient is also (equally?) expressed as 1/s^2, but will read and think about it. Any papers or especially experiments on a massless spin-2 field you might suggest, but please consider I'm not too knowledgeable on the subject?

 

[PeterDonis]

Can't yet wrap my brain around how 1/m^2 in regards to a gravity (position) gradient is also (equally?) expressed as 1/s^2

Because the natural units of relativity are units where $c = 1$, so inverse length squared and inverse time squared are the same units.

If you insist on using "conventional" units like SI units, where $c$ is not $1$, then of course you will need to apply a conversion factor between inverse square meters and inverse square seconds. But that is an artifact of your choice of units and has nothing to do with the physics.

 

[PeterDonis]

Any papers or especially experiments on a massless spin-2 field you might suggest

The Wikipedia article on the graviton does a fair job:

https://en.wikipedia.org/wiki/Graviton

Experimentally, as the article notes, we can't observe any actual massless spin-2 field properties for individual gravitons, because gravity is so weak as an interaction. We can barely observe classical gravitational waves, and we need huge devices like LIGO to do it. Gravitational wave observations confirm the massless spin-2 field properties of those waves as far as is possible for such observations.

 

[WhatIsGravity]

To bring up an older thread which I don't have too much time (or experience, education or knowledge) to think about...

The units of $G$ in QFT do happen to be the same as the units of spacetime curvature (in QFT units, inverse length squared is the same as mass squared), but that's not because they're the same thing. It's because $G$ is the coupling constant in the Lagrangian for the QFT of a massless spin-2 field, and the field itself appears in the Lagrangian as the Ricci curvature. Each term in the Lagrangian density has units of $\text{mass}^4$, since the Lagrangian density gets integrated over all of spacetime to get the action and the action is dimensionless.

I guess now I'm wondering how a gravitational field, unlike the Higgs, might be defined without a gradient (spacetime) dependent field?

 

[PeterDonis]

I guess now I'm wondering how a gravitational field, unlike the Higgs, might be defined without a gradient (spacetime) dependent field?

I'm afraid I don't understand what you're asking.

 

[WhatIsGravity]

I'm afraid I don't understand what you're asking.

Yeah, sorry about that, I'm not exactly sure what I'm asking either?! I guess I was wondering how gravity might be defined, simplistically speaking, without the 1/r^2 term. Basically tidal gravity. I think I can maybe understand how the EM fields work out in QED, but I can't yet wrap my brain around how gravity doesn't necessarily need a gradient in spacetime as a reference.

 

[PeterDonis]

I guess I was wondering how gravity might be defined, simplistically speaking, without the 1/r^2 term. Basically tidal gravity.

You just answered your own question.

Note that, in GR, you can make the 1/r^2 term vanish by an appropriate choice of coordinates. Tidal gravity is what is left over--what you can't make vanish by any choice of coordinates. That's why GR focuses on tidal gravity, aka spacetime curvature.

I can't yet wrap my brain around how gravity doesn't necessarily need a gradient in spacetime as a reference.

In Newtonian terms, the 1/r^2 force is not a "gradient in spacetime". It's a gradient of gravitational potential. Big difference.

However, the concept of "gravitational potential" isn't even well-defined in all spacetimes, which means the concept of "gradient of gravitational potential" isn't either. That's another reason why GR focuses on tidal gravity, aka spacetime curvature: that concept is well-defined in all spacetimes.

 

[spacejunkie]

Summary:: Wanting to research big G

I'm wondering if any of the physics Jedi out there might know of any credible papers that suggest big G and/or the cosmological (dark energy) aren't constant through time?

Dynamics of the cosmological and Newton’s constant
Lee Smolin
https://arxiv.org/abs/1507.01229

Abstract
A modification of general relativity is presented in which Newton’s constant, G and the cosmological constant, Λ, become a conjugate pair of dynamical variables.Smolin did a talk on this paper at Perimeter:-
http://pirsa.org/18110064/

 

[spacejunkie]

Dynamics of the cosmological and Newton’s constant
Lee Smolin
https://arxiv.org/abs/1507.01229

Abstract
A modification of general relativity is presented in which Newton’s constant, G and the cosmological constant, Λ, become a conjugate pair of dynamical variables.Smolin did a talk on this paper at Perimeter:-
http://pirsa.org/18110064/

Actually the correct talk is
http://pirsa.org/15060033/The previous link was about a different paper with a varying cosmological constant.

 

[PAllen]

So what’s wrong with using one of the standard forms of dimensionless gravitational coupling constants to discuss possible variation?

 

[PeterDonis]

one of the standard forms of dimensionless gravitational coupling constants

Which standard forms are these?

 

[PAllen]

Which standard forms are these?

https://en.wikipedia.org/wiki/Gravitational_coupling_constant

Lists several, with references. Structurally, they are very similar to the fine structure constant. The most common uses the mass of the electron, similar to using the charge for the fine structure constant.

 

[PeterDonis]

Structurally, they are very similar to the fine structure constant. The most common uses the mass of the electron, similar to using the charge for the fine structure constant.

There's a key difference, though. The article puts it this way: "there is an arbitrariness in the choice of which particle's mass to use", whereas only one charge can be used to define the fine structure constant. What this really is is a manifestation of the fact that the fine structure constant is genuinely dimensionless, whereas there is no genuinely dimensionless coupling constant for gravity, at least not as we currently understand gravity. In QFT terms, we should not expect the coupling constant for gravity to be dimensionless since the QFT of a massless spin-2 field is not renormalizable; whereas we should expect the fine structure constant to be dimensionless since QED is renormalizable.

In terms of looking for variation, if we found evidence of variation of, say, the dimensionless gravitational coupling constant defined using the electron mass, we wouldn't know whether that was evidence of gravity itself varying or of the electron mass varying, since, as the article notes, the electron mass is due to the Higgs mechanism (according to our best current understanding), which is independent of gravity. There is no such ambiguity with regard to the fine structure constant: it is a "pure" coupling constant for electromagnetism, with no other mechanism involved, so if we found evidence of it varying over time, there would be only one possible interpretation.

 

[PAllen]

There's a key difference, though. The article puts it this way: "there is an arbitrariness in the choice of which particle's mass to use", whereas only one charge can be used to define the fine structure constant. What this really is is a manifestation of the fact that the fine structure constant is genuinely dimensionless, whereas there is no genuinely dimensionless coupling constant for gravity, at least not as we currently understand gravity. In QFT terms, we should not expect the coupling constant for gravity to be dimensionless since the QFT of a massless spin-2 field is not renormalizable; whereas we should expect the fine structure constant to be dimensionless since QED is renormalizable.

In terms of looking for variation, if we found evidence of variation of, say, the dimensionless gravitational coupling constant defined using the electron mass, we wouldn't know whether that was evidence of gravity itself varying or of the electron mass varying, since, as the article notes, the electron mass is due to the Higgs mechanism (according to our best current understanding), which is independent of gravity. There is no such ambiguity with regard to the fine structure constant: it is a "pure" coupling constant for electromagnetism, with no other mechanism involved, so if we found evidence of it varying over time, there would be only one possible interpretation.

You could define a coupling constant using the Planck mass instead of the electron mass. Further, even if you don't have clean separation, you know that something fundamental is varying, even when using the electron mass. Any variation of G itself is far more problematic to untangle, or even define without arbitrary unit choices.

 

[PAllen]

You could define a coupling constant using the Planck mass instead of the electron mass. Further, even if you don't have clean separation, you know that something fundamental is varying, even when using the electron mass. Any variation of G itself is far more problematic to untangle, or even define without arbitrary unit choices.

Oops, you can't use Planck mass, because it is defined in terms of G, and if I work it all out, I get a coupling constant of identically 1 (ha ha).

But the rest of my point stands. Variation of the gravitational coupling constant at least measures change in fundamental physics without dependence on any unit definitions.

 

[zoki85]

Summary:: Wanting to research big G

I'm wondering if any of the physics Jedi out there might know of any credible papers that suggest big G and/or the cosmological (dark energy) aren't constant through time?

Dirac had opinion that G wasn't really constant through time. He formed that idea based on his "Large number hypothesis". Quick search will point to lot of papers like this one

 

[hutchphd]

There is no such ambiguity with regard to the fine structure constant: it is a "pure" coupling constant for electromagnetism, with no other mechanism involved, so if we found evidence of it varying over time, there would be only one possible interpretation.

I do not wish to dispute this because I truly do not understand. The fine structure constant contains e²/ hc. How is this subject to a single interpretation if changing? Can e and c and h not change independently in principle? Does that not add impurity?

 

[PeterDonis]

The fine structure constant contains e²/ hc.

No, you have it backwards. The fine structure constant is the fundamental quantity, and $e$, $h$, and $c$ are derived from it in combination with other choices of units. For example, in the latest revision of SI units, $h$ and $c$ are set to fixed numbers, and that means the value of $e$ is also fixed because the fine structure constant's value is independent of your choice of units.

 

[PeterDonis]

Can e and c and h not change independently in principle?

No. Once you fix the value of any two, the third is fixed as well. My previous post gives an example.

 

[hutchphd]

Are you saying that alpha changes iff e² changes ?

 

[PeterDonis]

Are you saying that alpha changes iff e2 changes ?

No. I am saying that $\alpha$ doesn't change at all. You can "change" the value of $e$ or $h$ or $c$ by choosing different units. However, you can only pick two of those values by choosing units; once you've picked two, the third value is forced by the fact that $\alpha$ has to stay the same.

 

[hutchphd]

I thought the discussion here was changes to fundamental constants like G over time. I took this to mean changes instituted by the "hand of God". To my poor brain all you are saying is "by our definition of units if alpha changes then so must e²". I see that .
But if we entertain a "god" change in G over time why not then equally a change in e in the same spirit?

 

[PeterDonis]

I thought the discussion here was changes to fundamental constants like G over time.

As has been brought out in the discussion, calling $G$ a "fundamental constant" is problematic. What we call $G$ is a mixture of an inherent coupling constant of gravity, considered as an interaction (but we don't have a good underlying quantum theory of this interaction, so this is all speculative at this point) and a choice of units.

Also, even if we remove the choice of units and treat $G$ as a "fundamental constant" like $\alpha$, there is a key difference between them. Electromagnetism, as an interaction, is renormalizable; gravity is not. That is why $\alpha$ is a dimensionless constant but $G$ has units. (This was also discussed earlier in the thread.)

As far as actual evidence for $\alpha$ or the "fundamental constant" part of $G$ changing over time, we have none.

if we entertain a "god" change in G over time why not then equally a change in e in the same spirit?

Because the proper way to ask this question is not to ask if $e$ can change. It's to ask if $\alpha$ can change. (And, as I said just now, we have no evidence that it actually has. That is how to interpret my previous statement that $\alpha$ doesn't change at all.)

 

[Haelfix]

But the rest of my point stands. Variation of the gravitational coupling constant at least measures change in fundamental physics without dependence on any unit definitions.

You're guess about putting in the Planck Mass wasn't crazy, b/c that would be the naive yet natural scale to attempt to plug in for a reference system. And indeed the problem becomes manifest. Which is that
1) It is an intrinsically quantum regime, and so you have to make sense of that mess in order to really talk about the problem.
2) The value of 1 when you plug in the Planck mass^2 makes perturbation theory completely hopeless.. Which small parameter do you expand around?
3) Plugging in some arbitary reference value at scales that are order of magnitudes removed to get the dimensions to come out (like the mass of the electron and the mass of the proton) is very much a subjective choice that seems to have nothing to do with fundamental physics.

So then trying to get a hold on the problem using known methods of effective field theory it can be shown that the quantum mechanics of this putative dimensionless coupling constant is a great deal more involved than the analogous story with the QED version and the screening and running of the fine structure constant. So much so that there is doubt it even makes sense as a universal concept.