# Gravity - Integrating General Relativity with Gravitons

Gravity - Integrating General Relativity with "Gravitons"

Every time I read about the hunt for gravitons I never see an explanation of how they will actually produce their effect. Maybe "integrating" is not the best word, but how will gravitons, if proven to exist, lead to the warping of spacetime that is so elegantly explained by G.R., where mass and spacetime are intertwined in a little dance.

Thanks, Howard

## Answers and Replies

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pervect
Staff Emeritus
Science Advisor
There is an approach that appears (from certain consistency arguments) to arrive at full curved-space GR from hypothetical "gravitons" (which are just spin 2 particles) in a hypothetical flat Minkowski space-time. It has not to my knowledge, however, been "popularized".

[digression]
This is probably a good thing, too many people are eager to embrace QED-like field theories without the math to actually calculate with them. I could write a lot more on this point, but it's probably better if I stop, unless someone is interested. I'll just add that this viewpoint leads to certain characteristic mistakes.
[end digression]

Going back to the original point.

We are starting with a hypothetical flat "background" space-time. But we actually observe this space-time by means of rulers and clocks. These rulers and clocks are ultimately based on atoms - a point I will defend if needed, and not explain further, to avoid another digression.

When you factor in how rulers and clocks are affected by gravity, the hypothetical "flat" space-time we started out with becomes unobservable by means of actual rulers and clocks. What we can actually observe with actual rulers and clocks is the dynamical (changing) curved space-time of GR.

Basically, everything couples to gravity (any form of energy). A curved space-time is just a mahetmatically elegant way of handling this fact. It is needed because the gravitational interactions affect our clocks and rulers, changing how they tick and how long they are (relative to the hypothetical, unobservable flat background).

For more details, see the source (link below). I have to warn you that it can be a bit intimidating, but if you actually know Lagrangian field theory, a lot of that intimidation is not conceptual, it's just working through the details (there is a lot of math presented very quickly). If you don't already know Lagrangian physics and its generalization to distributed systems (i.e. Lagrangian field theory), you'll probably get lost quickly (anything past the abstract).

The source for this is:

http://xxx.lanl.gov/abs/astro-ph/0006423

and the abstract is:

A pedagogical description of a simple ungeometrical approach to General Relativity is given, which follows the pattern of well understood field theories, such as electrodynamics. This leads quickly to most of the important weak field predictions, as well as to the radiation damping of binary pulsars. Moreover, certain consistency arguments imply that the theory has to be generally invariant, and therefore one is bound to end up with Einstein's field equations. Although this field theoretic approach, which has been advocated repeatedly by a number of authors, starts with a spin-2 theory on Minkowski spacetime, it turns out in the end that the flat metric is actually unobservable, and that the physical metric is curved and dynamical.

Short sections are devoted to tensor-scalar generalizations, the mystery of the vacuum energy density, and quintessence.
I should add that this approach gives one an "effective field theory". It doesn't solve any of the deeper issues with quantum gravity, which is known to fail at short enough distances / high enough energies. The theory you get by this means will work at distances well above the "cutoff" distance, i.e. for most anything that we can currently measure (but it wouldn't work in the heart of a black hole).

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Are gravitons purely hypothetical "mathematical" quanta, pervect? Or are thought to be genuine phenomena? And if so does this put them in opposition to the geometrical underpinning of General Relativity?

pervect
Staff Emeritus
Science Advisor
Gravitons are hypothetical "spin 2" particles.

Real gravitons would represent gravitational radiation, just as real photons represent electromagnetic radiation.

We have observed that electromagnetic gravitation is quantized. We expect that gravitational radiation should be quantized, but currently we are not even able to directly detect gravitational radiation, though we infer its existence from certain binary pulsar measurements. (The binary pulsars are losing energy at exactly the rate we'd expect from theoretical caluclations of how my gravitational radiation they should be emitting. While we cannot yet directly observe this radiation, we can predict the amount that is missing, and confirm that that much energy is actually disappearing).

As we cannot even detect gravitational radiation, we are in no position to determine that it is quantized as we expect it to be.

Note that real gravitons do NOT represent gravitational force, just as photons do not represent the columb force.

Virtual gravitions would represent gravitational force, just as "virtual photons" represent the columb force.

The idea that force is represented by virtual particles is not wrong, but is commonly misunderstood. There are many different layers of misunderstanding to tackle here. The first layer of misunderstanding is to point out that force is not due to real particles, but is due to virtual particles. The second layer of misunderstanding is to point out that forces do not "aberrate" in the same manner as radiation does.

As far as gravitons being in conflict with GR, the entire point of the post I made and the paper I quoted was to point out how there is no real conflict - that one can start with a theory of "gravitions" in a hypothetical flat space-time, and wind up with the fact that this hypothetical flat space-time cannot be obseved via means of actual, physical, clocks and rulers. The space-time that clocks and rulers would observe is curved in the manner that GR predicts. The only difference is philosophical. The actual predictions of the thoery are identical.

You might think about Einsteins example of measurements made with rulers on a disk of varying temperature. The rulers are assumed to expand and contract with temperature, so measurements made via the rulers of the geometry of the disk would not be euclidean.

The same thing is happening with gravity. Gravity is making the "rulers" expand and contract, and the clocks slow down, thus the geometry of space as measured by our rulers is not Euclidean, just as the geometry of the disk of varying temperature was not Euclidean.

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pervect said:
As far as gravitons being in conflict with GR, the entire point of the post I made and the paper I quoted was to point out how there is no real conflict - that one can start with a theory of "gravitions" in a hypothetical flat space-time, and wind up with the fact that this hypothetical flat space-time cannot be obseved via means of actual, physical, clocks and rulers. The space-time that clocks and rulers would observe is curved in the manner that GR predicts. The only difference is philosophical. The actual predictions of the thoery are identical.
Gr8!
What's so special about gravitons in a flat spacetime--one could even take material objects in a flat spacetime &. argue the same way--is that right?

The same thing is happening with gravity. Gravity is making the "rulers" expand and contract, and the clocks slow down, thus the geometry of space as measured by our rulers is not Euclidean, just as the geometry of the disk of varying temperature was not Euclidean.
In that case,could we say that the cosmol. expansion is an 'apparent' expansion caused by changing rulers and clocks?

pervect
Staff Emeritus
Science Advisor
gptejms said:
Gr8!
In that case,could we say that the cosmol. expansion is an 'apparent' expansion caused by changing rulers and clocks?
There is no way to distinguish an expanding universe from shrinking rulers - its a purely philosphical issue. It's basically an issue of how one assigns coordinates to specific points in space-time. If one assigns coordinates in one manner, the universe stays constant and rulers shrink. In a different coordinate system rulers stay constant, and the universe shrinks.

Note, though, that this does not mean one can always use "standard" physical equations to describe our universe in the coordinate system of "shrinking rulers".

Schrodinger's equations, for instance, predict a constant size of the atom. Other well-known equations also need to be modified. For some details, see section 2.4 of the paper I quoted, where the process is done in reverse - the equations are presented in arbitrary coordinates first, then they are converted to standard coordinates.

Non-standard coordinate systems should generally be approached with caution. There is a possibility for significant confusion here, as many assumptions that are true in standard coordinates are not necessarily ture in arbitrary coordinates.

The technical way of describing the situation is that GR is "diffeomorhpism invariant". Other laws of physics are not formulated in a diffeomorphism invariant manner. If they were, they would need the same mathematical machinery that GR uses. This machinery is usually popularized as "curved space-times", but it could just as well be called "being able to use arbitrary coordinate systems".

I shoud probably add that the coordiante systems are actually not totally arbitary, there must exist a smooth transformation, i.e. a diffeomorphism, between any "valid" coordinate systems.

Garth
Science Advisor
Gold Member
To endorse and expand on what pervect said, the question is more than simply a matter of mathematically assigning a coordinate system to the universe, it is also a matter of physics.

The physical question is: "How do we make a measurement?"

Physical measurements are comparisons of 'objects', such as atoms, or 'entities', such as photons, with some defined standard. They are measurements of ratios.

But the further physical question for astophysics and cosmology is: "How do you make such a comparison of distant objects across the vast expanse of space and time and compare distant objects with standards in the laboratory back on Earth?"

gptejms said:
In that case,could we say that the cosmol. expansion is an 'apparent' expansion caused by changing rulers and clocks?
If rulers are to shrink and clocks speed up as suggested, then what is remaining constant, what doesn't change, so that measurement comparisons can be made?

You need a Conservation Principle, that is something that doesn't change, in order to make any comparisons at all.

In GR the Conservation Principle is the Conservation of energy-momentum, or 'rest mass' , which means that, together with the constancy of h, e and c, atoms are defined not to change size and atomic clocks not to change rate. The universe thus expands from a Big Bang around 'fixed' rulers and 'regular' clocks.

For an alternative view of a static eternal universe with shrinking rulers and accelerating clocks you need another conservation principle. Such as the Conservation of energy as proposed in the Jordan conformal frame of http://en.wikipedia.org/wiki/Self_creation_cosmology [Broken].

As the matter is a question of physics these theories may be distinguished by experiment as is happening at this moment with the analysis of the GP-B data.

Garth

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pervect
Staff Emeritus
Science Advisor
Just to add a quick note to what Garth said - if you read the paper (section 2.4), you'll see that the "effective mass" of atoms does not stay constant in the "shrinking rulers" coordinate system. This is roughly similar to what happens to mass in Garth's theory in his Jordan frame.

Of course the link I quoted is just a presentation of GR in different clothing, the physics is actually identical because the predictions are identical after one takes into account the different coordinates.

Garth's theory is actually different physics - it makes different predictions than GR.

Thanks for getting back to me pervect. I read the paper, but couldn't keep up with the mathematics. I'll read it again and follow up on google for the things I'm not clear on.

Garth
Science Advisor
Gold Member
pervect said:
You might think about Einsteins example of measurements made with rulers on a disk of varying temperature. The rulers are assumed to expand and contract with temperature, so measurements made via the rulers of the geometry of the disk would not be euclidean.

The same thing is happening with gravity. Gravity is making the "rulers" expand and contract, and the clocks slow down, thus the geometry of space as measured by our rulers is not Euclidean, just as the geometry of the disk of varying temperature was not Euclidean.
May I may a point of clarification about this statement?

There are two different ways of interpreting the same phenomenon.

In the standard GR interpretation, atomic rest masses remain constant so that rulers do not 'expand or contract' nor clocks 'slow down'. (In any case you have to define very carefully how such changes in measuring devices would be detected.)

Consequently red shift is interpreted as the combined effect of both the expansion and the curvature of space. This is described by the Friedmann (GR) Robertson-Walker space-time metric.

You can, however, conformally transform the standard GR R-W metric into a flat space metric, which changes the expansion rate and affects rulers and clocks.

In such a conformal transformation, if there is no alternative conservation principle to that of energy-momentum in GR, then this would be only a rewriting of GR is some inconvenient coordinate system. It is true, the system might describe some cosmological effect more simply, but only at the expense of making laboratory experiments more complicated.

As atomic clocks and rulers would 'vary' in these coordinate systems then something would also be happening to the physical constants ma, h, c, or e in those systems. Try reworking BB nucleosynthesis in these units; you would have to rewrite all the nuclear physics books of the last century!

Without a clear principle to guide you, it might be better, or at least easier(!), to work in the simple GR system with constant atomic masses, so rulers do not 'shrink' and clocks do not 'accelerate'.

However, the fact that the standard cosmological model thus obtained, the $\Lambda$CDM model, has a cosmological constant, or lambda, problem, that it requires Inflation, DM and DE - all as yet undiscovered in laboratory physics - and that it has not yet yielded to a quantum gravity generalisation, may of course indicate that the more complicated conformal gravity coordinate system, or some alternative theory, is actually required!

Garth

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HallsofIvy
Science Advisor
Homework Helper
pervect said:
We have observed that electromagnetic gravitation is quantized.
Surely you meant "electromagnetic radiation" here!

Nice to see that my post has generated so many replies.Garth,can you make a summary of the main points of your SCC?Pl. also include the logical sequence that led you to---a theory is never discovered in the way it is presented.

Garth
Science Advisor
Gold Member
gptejms said:
Nice to see that my post has generated so many replies.Garth,can you make a summary of the main points of your SCC?Pl.
I have done so already on a separate thread, I try not to 'hog' other threads with the subject. Try Self Creation Cosmology or the Wikipedia http://en.wikipedia.org/wiki/Self_creation_cosmology [Broken].
also include the logical sequence that led you to---a theory is never discovered in the way it is presented.
I have transferred my reply to that Self Creation Cosmology thread, post #78, so as not to 'hog' this one.

Garth

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ok,moved my reply--find me there (SCC thread).

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Garth
Science Advisor
Gold Member
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pervect
Staff Emeritus
Science Advisor
HallsofIvy said:
Surely you meant "electromagnetic radiation" here!
Definitely. Somedays my proofreading isn't very good :-(.