
#1
Jun2508, 04:34 PM

P: 531

Please excuse me for what is possibly a meaningless or misinformed question about the motivations behind GR.
John Wheeler famously said: "matter tells Spacetime how to curve, and Spacetime tells matter how to move." I interpret this school of thought to reflect a conjecture that Spacetime is not simply a mathematically convenient tool for calculating and graphing the effects of relativity; it also is the actual physical mechanism by which gravity operates. That is, gravity actually changes the physical geometry of local space and time. I understand that this school of thought originally was motivated to provide an explanation for aspects of the Equivalence Principle which in the absence of that definition were considered to be coincidental or mysterious. For example this definition of the Strong Equivalence Principle: "The gravitational motion of a small test body depends only on its initial position in spacetime and velocity, and not on its constitution." My question is, why should we be at all puzzled that gravitational motion is independent of the constitution of the test body? If gravity is thought of as a plainvanilla force, rather than as a creator of "spacetime curvature", the SEP is not only intuitively obvious, but any behavior other than the SEP would be inexplicable. Any massive test body is comprised of atoms, and the vast majority of the mass of atoms is comprised of hadrons (protons and neutrons). So to simplify this discussion I'll just ignore the mass of electrons and assume that all hadrons have the same mass. When a "force" such as gravity acts on a hadron, Newton tells us that F=Ma, so any given force potential causes a single hadron of mass=1 (in a hadronbased mass scale) to accelerate toward the source at a specified acceleration rate (let's say a=1 in our scale). The hadron's inertia is what resists the force of gravity and it is what that force must overcome in order to accelerate an M=1 hadron at a=1. If our test mast contains 1M hadrons, then the same force of gravity as before will separately and equally pull on each hadron, causing each hadron to accelerate at a=1 and, indirectly, causing the test particle as a whole to accelerate at a=1. Gravity is an inexhaustible source of force, in the sense that it can pull on an unlimited number of hadrons at once (subject to physical space limitations) without diminishing the force it applies to each individual hadron. By this elementary reasoning it would defy common sense to expect a more massive object to accelerate faster than a less massive object. Linking individual hadrons together (chemically) does not cause any (significant) change in their individual inertias. It would be bizarre indeed if linking hadrons together caused them to each become more (or less) susceptible to gravitational force than the same number of hadrons that are unlinked. As I said, all of this seems entirely obvious and elementary. So I don't understand why so many great minds have spent so much time marveling about it. I am missing something. Of course GR makes slightly different predictions about the effects of gravitational force than Newton does. Plotting gravity on a 4axis spacetime diagram makes these differences seem easily explainable as geodesics through a physically curved local spacetime. But why can't an oldfashioned "force" have complexities in its effects, without mandating that we adopt spacetime curvature as the physical mechanism? Jon 



#2
Jun2508, 06:35 PM

PF Gold
P: 4,081

I don't think many people are amazed that all matter appears to fall with the same acceleration. It has been experimentally established for a long time.
Given that this is the case, it seems that gravity is not a force field but an acceleration field. And this acceleration acts equally on all bodies, and so may be thought of not as a property of the body but the spacetime. Spacetime was first geometrised some years before GR in order to formalise the rules of special relativity as Minkowski spacetime, and this leads naturally to GR when the field is coded into the curvature of the spacetime. Metric theories automatically include the SEP, other types of gravity theories have to state the relationship between inertial and gravitational mass. I think you've said this in your long question. M 



#3
Jun2508, 06:48 PM

P: 1,545

Your description of GR as accounting for gravity using no force or “gravitons” by using warping across an extra dimension we cannot see directly is reasonable. Consider it as requiring at least 4 or 5 dimensions to effect the warping with no force action reactions required. Contrast that with the QM – Standard Model expectation; gravitons emitted from all elements of mass cause mass to react in attraction to account for gravity. And yes I expect that for force based on gravitons to be built into a successful explanation of gravity (Let alone being detected some day) will require some “complexities in its effects”. Not sure if calling that “old fashioned” would fit; if someone were to crack that nut and show GR wrong I’m sure it would be a new big deal. 



#4
Jun2508, 06:58 PM

P: 531

Matter tells matter how to move
Hi M, thanks for answering.
Is the concept of a "force field" you are referring to one in which there is a total amount of force available, which divides itself among the hadrons located in the field, such that a test particle of 1M hadrons in a "force field" will accelerate less than an individual hadron? That strikes me as a nonconventional definition of a "force field." Are you aware of any "force" which acts in that manner? Or conversely, is there any example of a force field which accelerates a structure made of multiple identical particles at a higher acceleration rate than an individual such particle? Jon 



#5
Jun2508, 07:10 PM

P: 531

Hi Randall,
Jon 



#6
Jun2508, 07:12 PM

P: 2,043

He actually said: "Matter tells space how to warp. And warped space tells matter how to move". 



#7
Jun2508, 07:22 PM

P: 531

Hi Jennifer,
In any case, the words "warp" and "curve" seem to me to have essentially the same meaning in this context. So do you mean that it makes more sense for "space" to tell matter what to do than for "spacetime" to do so? Jon 



#8
Jun2508, 07:37 PM

P: 2,955

Weak Equivalence Principle: A uniformly accelerating frame of reference is equivalent to a uniformly accelerating frame of reference. Strong Equivalence Principle: Any physical law which can be expressed in tensor notation in SR has exactly the same form in a locally inertial frame of a curved spacetime (also known as the 'commagoestocolon' rule). I.e. One can discover how all the forces of nature behave in a gravitational field by postulating that their laws in a freely falling frame are identical to their laws in SR, i.e. when there are no gravitational fields. Pete 



#9
Jun2508, 07:38 PM

P: 2,955

Pete 



#10
Jun2508, 08:26 PM

P: 531

Hi Pete,
Jon 



#11
Jun2508, 08:48 PM

P: 531

Hi Pete, one more thought:
Jon 



#12
Jun2508, 08:50 PM

PF Gold
P: 4,081

I doubt if anyone knows what 'actually' causes motion of any kind. M 



#13
Jun2508, 09:31 PM

P: 2,955

Have you ever wondered what Kip Thorne meant in Black Holes & Time Warps on page 111 where he wrote Pete 



#14
Jun2508, 09:53 PM

P: 531

Hi Pete,
Obviously saying that you can "observe the effect of X" is different from saying you can "observe X itself." We can all agree that certain gravitational effects we observe are physically real and are the result of ... uh, some particular mechanism which is physical ... but that realization in itself provides nothing to help us decide whether any particular postulated physical mechanism is physically real or is the correct choice. Unfortunately this kind of justification is circular. Edit: Tidal gradients depend on certain configuration features of the gravitational source: finite size, specific shape (e.g. spherical), inversesquare distance law. None of those features helps us distinguish whether gravity is a force field or a curvature of spacetime. Jon 



#15
Jun2508, 11:07 PM

Mentor
P: 11,255





#16
Jun2608, 12:10 AM

P: 2,955

Pete 



#17
Jun2608, 12:37 AM

P: 2,043





#18
Jun2608, 08:20 AM

PF Gold
P: 4,081

Pete,
I stick to my assertion that spacetime curvature may not have a physical correlate. Observing something and then stating it is caused by this or that is not the same as a direct measurement. I see that jonmtkisco makes this point. It's not important, surely, whether curvature is real or not, is it ? So long as we can use it to calculate effects properly. M 


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