How do you envision a gravitational field?

[jnorman]

For many years, i have struggled with the concept of a "field", and i basically simply have no idea what a field is or how it operates, whether it is a magnetic field, gravitational field or other.

when you think of a gravitational field, as per GR, you think of "curved spacetime", but what exactly is spacetime and how does it impart its curvature to objects moving within it? what exactly is curved? gravitons seem to be a particularly awkward mechanism, as, to my understanding, each particle in the universe would have to be emitting endless number of gravitons continuously. but how else does a field "communicate" with bodies?

of course, a magnetic field is equally mysterious - how does a magnet move iron particles into a field pattern? are photons being emitted by the magnet which impart momentum to the iron particles to make them move into place? what are magnetic field lines?

anyway, you can probably recognize my confusion, and i would appreciate any helpful comments or thoughts, or layperson level readings which might assist in my understanding of fields. thanks.

 

[pervect]

GR doesn't use gravitons. Nor does it use fields. Though I doubt you'll find the GR replacement for fields that much easier to grasp, unfortunately.

If you've seen a space-time graph from special relativity, you can think of curved-space time as drawing those same graphs, on a curved piece of paper. As far as "why" you need to do this, you do it because it works.

 

[bcrowell]

GR doesn't use gravitons.

Agreed, the quantum stuff is not the key issue here.

Nor does it use fields.

I disagree. It's true that the Newtonian gravitational field g is not particularly useful in GR, but that doesn't mean GR doesn't use fields. It's a classical field theory.

 

[pervect]

I assume you regard the metric tensor as the field? (Or perhaps the Riemann tensor)? How would you go about explaining either of them to a popular audience, in a few paragraphs (refering them to your book isn't fair :-) ).

 

[atyy]

How about:

Electric field: 3 numbers at every point in space

Metric field: 10 numbers at every point in spacetime (well, or at least on the underlying manifold, since usually the manifold plus the metric field is considered spacetime)

?

 

[PAllen]

Alternatively, what more directly affects the path of light test particle is the connection (cristoffel symbol), rather than the metric.

In any case, there are several major relativists who reject a geometric interpretation of GR and view it as a field theory. Personally, I don't see the point, but I don't know any reason it is invalid. For example:

http://arxiv.org/abs/gr-qc/9912051

 

[bcrowell]

I assume you regard the metric tensor as the field? (Or perhaps the Riemann tensor)?

I would probably say the Riemann tensor, but I would hasten to say, before the OP's eyes glaze over, that that is a technical detail, and not really relevant to his/her question. If you try to make an analogy between the EM field and the gravitational field, the analogy doesn't really work in detail. For example, the observable electric field falls off like 1/r², whereas the observable in GR would be the Riemann tensor, which falls off like 1/r³; the difference in exponents is because in some sense GR forces you to take one more derivative then EM when you go from the sources to the directly observable quantity.

How would you go about explaining either of them to a popular audience, in a few paragraphs (refering them to your book isn't fair :-) ).

I would tell them to read Relativity Simply Explained, by Gardner, which is much better than my book :-)

But seriously, I think the OP's feelings of discomfort are very reasonable, but I don't think they have much to do with GR as opposed to other field theories.

Back in the 19th century, many of the greatest physicists felt uncomfortable with the idea that they didn't have a mechanical explanation of electromagnetism. Some of them tried to make elaborate systems of springs and masses that would model the polarization properties of an EM wave propagating through the aether. They failed. I think their discomfort is the same discomfort as that expressed by the OP. My basic answer to this discomfort, which admittedly is not very helpful, is --- well, get over it. God just didn't choose to make the universe operate according to mechanical principles, he chose to make it operate according to the principles of fields of force.

I hesitate to take the chance on exposing impressionable young minds to this, but:

A. Einstein, "Über den Äther" ("On the aether"), Schweizerische naturforschende Gesellschaft 105 (1924) 85, English translation at http://www.oe.eclipse.co.uk/nom/aether.htm

To avoid turning into a raving crank after reading this paper, please follow up by reading this commentary: http://web.archive.org/web/20070204022629/http://math.ucr.edu/home/baez/RelWWW/wrong.html

My point here is that experiments really do show that empty space has observable, dynamical properties. Some of those are electromagnetic, and some are gravitational. It's counterintuitive and nonmechanical.

 

[TrickyDicky]

I assume you regard the metric tensor as the field? (Or perhaps the Riemann tensor)?

Alternatively, what more directly affects the path of light test particle is the connection (cristoffel symbol), rather than the metric.

As PAllen says , the gravitational field is generally compared to the Christoffel symbols when this kind of analogies are made, leaving the metric tensor as the analogy of the potential.

In any case, there are several major relativists who reject a geometric interpretation of GR and view it as a field theory. Personally, I don't see the point, but I don't know any reason it is invalid.

I don't see the point of confronting the two approaches either. They are not mutually excluding. Geometry is just the most practical way to relate physical properties. IMO, it should be taken as the best description model since it is the best mathematical way suited to the task of relating spacetime events. But let's not forget it is an operational tool. Tensors are the best tools to deal with this properties, but tensors and the geometry are not the physical underlying reality, they are the tool to operate in a physical reality with certain physical properties.

My point here is that experiments really do show that empty space has observable, dynamical properties. Some of those are electromagnetic, and some are gravitational. It's counterintuitive and nonmechanical.

I agree. Here is where the concept of field can give us some clue about the nature of physical matter and "empty" space. Perhaps it would help the OP to think of "empty" space as something with some "quasimaterial dynamical properties" in consonance with the properties QFT assigns to the vaccum. This properties would express for instance as magnetic lines of force perceived as the disposition of iron filings or in the case of GR as test particle geodesic trajectories converging or diverging.

 

[jnorman]

bcrowell - yes, i have read einstein's "on the aether", which i found quite interesting, since his original premise behind relativity was to get rid of the concept of an aether.

tricky - inre empty space having dynamical properties, how do you think this concept fits into the standard model? or is the SM simply not yet advanced enough to cover this topic? at some point, there will need to be a way to incorporate GR into the standard model, right? or some way that "fields" fit into a standard model - it has always been my understanding that particles were actually just manifestations of fields or interacting fields, and i have suffered some small confusion over the whole idea of building a standard model on particles rather than fields. perhaps one of you could address that for me? thanks.