General Relativity: Curved Spacetime vs. A Gravitational Field

http://metaresearch.org/cosmology/speed_of_gravity.asp

Thanks for your response!

Since I haven't made sense of my original question yet (even after skimming / reading the article you pointed me to), I'm going to make an effort to post a sort of status update on my thinking after each (or most) response(s) in this thread.

So, I'm not yet satisfied with an answer.

With respect to the article you pointed me to:

* I was hoping I was trying to learn something on which there was general (or even better, universal) agreement. At least based on this article, that is not the case, and that makes my quest that much harder.

* (part of) the problem is that I don't have enough knowledge in the subject to try to judge whether the article expresses some better truth or not--that won't keep me from trying (to judge) at some point, but that will not be my first priority--my first priority will be trying to understand the general consensus "truth"

* therefore, I will try to seek out the answers on which there is fairly general agreement, while not really ignoring this article (and the other articles on that site)--I've read / skimmed it once, and expect to do so again...

I'll probably amplify some points of this in my response to the next response.

I guess what I want to say (and didn't quite yet) is that I'll start to use this thread as a sort of thinking out loud (on paper) exercise to, maybe among other things, show the state of my thinking--hopefully (I know), as people recognize errors in my thought, they will point them out to me, and, again, hopefully, that will lead me to understanding... ;-)

This is a tough one to explain, but there is a specific reason for the terminology. I am sure someone with a better grasp of Physics will probably correct me, but here it goes.

A field is typically used to describe a force related to a point source. The electromagnetic field is probably the most common example. The effect of the electromagnetic force is mathematically related to the distance from the point source of the electromagnetic field and is a direct effect. The current Quantum Physics theories ascribe this force to the interaction of virtual photons.

On the other hand, gravity is not a directly interacting force like electromagnetism. It is a side effect of mass and momentum curving spacetime. The typical imagery is of a heavy ball bearing on a rubber sheet. Now just take that stretched rubber concept and expand it to 4 dimensions, 3 spacial and one time-like. The forces are real, but they are the side effect of the curve in space time. Gravity is the name for all the mass trying to reach a stable low energy state within curved space time. Richard Feynman described gravity as a Pseudo Force because of this difference. It makes my head spin to be honest.

Hopefully a physics genius will helpfully come along and correct my errors and explain it more accurately. Until then I hope my explanation helps a bit.

Doug

Thanks for your response!

As noted in comment #4, a satisfactory answer has not yet penetrated my thick skull, so, again as noted in #4, I'm going to start responding to most of the responses in this thread in sort of a thinking out loud (on paper) exercise, in hopes that by exposing the state of my thinking, someone will point out where I'm wrong or missing a key point and that will lead to understanding. ;-)

What I didn't say there, but will state now, some of my responses will be quite "nit-picky"--not for the sake (I hope) of nit-picking, but (I hope) for the reasons that I think are stated above--among others to expose the state of my thinking.

So, I might start that right now--maybe this is partly an example, and maybe not entirely necessary at this point, because I've re-read Jorrie's page on the speed of gravity, and notice some things there that I didn't notice the first time through--notably that he quite often describes it as a gravitational field, seemingly interchangeable with his description of it as curved spacetime. But, I'll nit pick that page next... (I'll also make little notes to myself, maybe often about things I should dig into...)

So, you (drobertson) wrote (and I'm (as stated) going to nit pick): "A field is typically used to describe a force related to a point source. The electromagnetic field is probably the most common example. The effect of the electromagnetic force is mathematically related to the distance from the point source of the electromagnetic field and is a direct effect. The current Quantum Physics theories ascribe this force to the interaction of virtual photons."

* re: "A field is typically used to describe a force related to a point source.": (nit) we often discussed (and solved problems, drew sketches) of the fields around things other than points--like wires with moving currents, coils with moving currents, etc.--maybe because I studied electrical engineering (?)

* re: "The effect of the electromagnetic force is mathematically related to the distance from the point source of the electromagnetic field": well, whether we want to call it curved spacetime or a gravitational field, there seems to be a force (as something affects motion) that is "related to the distance from the point source" of, in that case, gravity. Hmm, massive objects are not really point sources--is that part of the reason for the difference in terminology? (I don't really think that is an important difference--in the scale of the universe, they should be treatable as point sources, I think.)

* re: "and is a direct effect.": well, I was about to make a note to myself to do some reading up on exactly what a virtual photon is (I've encountered the term before, maybe also for other virtual particles?), but it's interesting to talk about a direct effect from a virtual particle--it sounds almost like a contradiction (assuming a virtual photon is the definition I'd expect--one which doesn't really exist)

* Note to me: read up on "virtual photons"

* Note to me: (based on your reference to Feynman's description of gravity as a Pseudo Force)--read up on that--I'll try online, even though somewhere here at home I think I still have a copy of at least one volume of his lectures.

I was going to continue this kind of nit-picking (maybe a nicer or kinder term might be deconstruction) for Jorrie's page on the speed of gravity (http://www.einsteins-theory-of-relativity-4engineers.com/speed-of-gravity.html), but I think I'll do that in a future post (on this thread). I might do some other things first.

You seem to be struggling with the same issues I have been wrestling with (intellectually) for years, and I am enyjoying following your thread (although I have little of substance to contribute).

In this sort of study, I come up against three brick walls. One is that there really is a very poor understanding, from a physics standpoint, of just exactly what mass and gravity are. The hunt for the Higgs boson (if successful) will take us in the direction of greater understanding (I hope), or it may result in a major rewrite of the Standard Model (if it is unsuccessful, or if the Higgs appears at a significantly different energy level than theory predicts). The only thing we can do is "wait and see". Meanwhile, there are other approaches to gravity that are being explored. My personal opinion, which is NOT based on any true scientific study or theoretical underpinning, but rather intuition rooted in years of amateur study, is that the attempt to combine gravity with other forces into a Grand Unified Theory is misdirected- I suspect we may ultimately find that gravity is fundamentally different than the other "forces" of nature.

Next, we come up against Heisenberg's Uncertainty Principle- we can not know both momentum and position simultaneously. The more accurately we know the momentum of a particle, the more ambiguous our information about its position, and vice versa. This suggests to me that we have a fundamental conflict at the root of how we define and measure our universe. It is interesting that we now define both distance and time in terms of the fundamental constant "c"- which is usually defined in terms of a ration between distance and time...Does this not sound circuitous to you? It seems that the Powers that Be are beginning to re-evaluate the definition of Mass in terms of fundamental constants as well- it will be interesting to see what comes of that...

And finally, we have the concept of variable mass/time dilation (both, it seems, modeled by the Lorentz contraction) when approaching the speed of light. I have played around a bit with incorporating the Lorentz contraction (square root of 1 minus the ration of the square of the object velocity to the square of "c") in Einstein's famous formula, mostly because I am bothered by the aspect of variable mass. Some intriguing algebraic manipulations are possible...But I have never seen this approach studied in the literature, and I suspect most professional physicists may find this a rather trivial or amateurish approach...

I am fairly confident that gravity is a very real effect, although I don't think anyone really understands it. I have trouble trying to define it as a "virtual" field, although some of the mathematical attempts to define gravity as a virtual field do seem to offer some potential insights. I think the concept of "curved space-time" is more of an artifact of the current Standard Model and our establishing "c" as the fundamental defining ratio on which we base all of out measurements. Either light travels in a straight line, or it doesn't. What manipulations physicists and mathematicians must make to their models to explain observations really won't alter that basic idea...

And I suspect I may have left you just as confused, if not more so, as when I started writing this...

Yeah, this is a complex one, and as I said before I am not sure I understand it well enough or even accurately enough to explain it well.

Both gravity and electromagnetism exhibit themselves as a force. I think the nuance is what the root cause of the force is. In the case of electromagnetism the root cause is the communication of the force directly between two particle via the virtual photons. With gravity the force is actually a side effect of the curvature of spacetime therefor the physicists refer to curved spacetime instead of gravitational force.

Another example of a pseudo force is centrifugal force. As you swing a ball on a string in a circular motion you feel a force pulling your hand towards the ball. What is actually happening is you are feeling the effects of inertia resisting your effort to change the path of the ball. The ball wants to move in a straight line, but you and the string are exerting a force to change that. The ball isn't creating the force, you are. It is a bit of a stretch, but gravity is similar in concept.

Pseudo forces are real forces and the term pseudo is probably bad, but they have used the concept to specify a force that is a secondary effect to something else. I think the term is actually out of favor at this point, but that just shows how out of the loop I am. :-)

Electromagnetism as you know it from engineering is actually just the sum of all the point sources of electromagnetism in the system you are working with. Electromagnetism is a hugely powerful force, a great many orders of magnitude more powerful than Gravity, but it is all very neatly balanced out with positives and negatives (North and South poles). Magnetism that we see from wires, coils and such is just the side effect of those point sources (electrons) moving and relativity having its effect on the balance of super powerful forces.

I am getting a headache thinking about this. Hopefully it helps a bit.

Doug

Years ago when I was in Nuke School we had an amazing Physics Instructor. We got off topic while discussing sub-atomic particles one day and wandered into a discussion of how can space be bent. He gave us a description that created a picture that sticks in my head 33 years later.

Picture space as a large thick foam matress. All the distances between points on the surface are straight. Now place several bowling balls on the matress. To travel along the surface from mass to mass the path while you are traveling will appear straight but is really curved because of the effect of mass on all the things we can measure. Or perhaps it is really straight but appears curved because of the measurements.

Thanks for your response!

You should probably look at my comments in #4 and/or #5 about my intent to think out loud (on paper) here, and quite possibly, engage in nit picking while doing it...

I almost didn't respond, as, as helpful as the mattress example is, it seems to be exactly the same as the rubber sheet example already mentioned.

But, I will say that thinking about that reinforced my understanding of what a geodesic is--it is those apparently straight but really curved (because they follow the curved surface) lines on the mattress or rubber sheet.

Still, I've not heard anyone say that the path would be any different if "it" were described as a gravitational field instead of curved spacetime (well, with the exception of the link provided by "Guest" in #1.

I'm off to try to read up on Feynman's "pseudo force" and/or quantum theories' "virtual photons".

When we refer to Space Time think about what we are referring to and how we percieve it. We know where a body (mass) is in space because we can "see" waves either originating from it (a sun) or reflected off it. These waves are a combination of waves from visible light all the way down the frequency range to the invisible to the eye (X-Ray, Radio, etc). Each of these waves takes a finite amount of time to reach us and must pass many bodies (each one is a mass). Some of these masses are charged, some are not. Each wave is affected by the mass as it passes proportional to the size of the mass and any charges involved. We see the location when the wave gets to us (by sight, or radio telescope). If the wave took a curved path and we followed it back to the body it came from we would be following a curved path back but percieved it as straight.

The problem I've always had with the "bowling ball on a rubber sheet" image is that it depends upon an outside source of gravity pulling the ball down into the sheet to form the depression. The foam mattress idea conjures up the same problem.

corelite-

GA from me...too many of the "explanations" tend to substitute one obfuscation for another, without actually explaining anything...

I'll start by saying I'm by no means an expert, but I have had some great professors. I've been following this and the prior forum and am finding I'm still learning. (Oh and a big "HI" and glad to see you to another fellow X-Nuke)

I do have 2 cents for this analogy though and maybe it'll help a bit. This is how it was explained to me....

Let's build a universe... Forget about fields for a moment. Imagine a section of space void of mass, gravity, EM fields, etc... this is the rubber sheet/mattress. It is for our purpose 2D. In this space, objects are confined to traveling on it surface. If we throw 2D baseballs, they must stay on the surface. A light ray traveling must stay on its surface and this is how we will define a straight line... by its path. In fact, feel free to draw a nice square grid so it's easy to see.

Now, let's place a ball on the sheet. From the 3D perspective its easy to see the warp, but imagine yourself back on the sheet... the light is still travelling along those straight lines (i.e. nothing has changed). Now on the sheet we could start taking measurements perhaps measure the lengths of our squares on the grid and figure out that our 2D world is, in fact not flat. Somethings up!

So the only thing left here is the warping. In the example, gravity pulls the ball and deforms our 2D sheet, but in our 3D world it is the simple presence of mass that warps space-time. The field equations are our attempt to describe mathematically how it is warped. It isn't that mass generates some mysterious field, by simply existing it actually changes the local arrangement of space-time.

As a minor end note, there was a recent paper that claims that all the effects from gravity can be derived from thermodynamics and electromagnetism... which implies that gravity itself isn't a fundamental force, but arises from others.

The change from force to curved space was because of Einstein's theory of gravity. The problem, as I see it, is that it doesn't explain the attraction of two bodies that are not in motion (as measured by C.V. Boys, Cavendish, and others).

Again, I'm not an expert, but as I understand it Relativity most certainly explains the attraction of 2 bodies (whether they are accelerating or moving at a constant velocity (including 0) relative to each other.

Although the math is a degree of order more difficult than classical mechanics, Newton's Law of Gravity can be derived from Einstein's Field Equations.

It was Einstine who introduced M1 M2 into Physics. This was the attraction of two masses was proportional to their mass. There was maybe a distance component involved also. Basically the attraction of Earth on the Moon is greater than the attraction of the Moon on Earth, but each is attracted to the other. Please excuse the language. The course work was in the late 70's and I remember the concepts better than the math and the formulas.

In regards to the OP...

(1)... the shape of a path in a gravitational field vs curved space-time.

I understand that the answer lies in interpreting the question. The field and curved space-time are the same thing... so their shape would be the same. I think you have it correct in that the only reason for calling it a field or calling it curved space-time is for situational clarity.

(2)... the speed of gravity

Hopefully, clarifying that the field and curved space-time are two names for the same thing cleared this up.

* re: "A field is typically used to describe a force related to a point source.": (nit) we often discussed (and solved problems, drew sketches) of the fields around things other than points--like wires with moving currents, coils with moving currents, etc.--maybe because I studied electrical engineering (?)

The solutions you used for wires are derived by integrating point sources.

* re: "The effect of the electromagnetic force is mathematically related to the distance from the point source of the electromagnetic field": well, whether we want to call it curved spacetime or a gravitational field, there seems to be a force (as something affects motion) that is "related to the distance from the point source" of, in that case, gravity. Hmm, massive objects are not really point sources--is that part of the reason for the difference in terminology? (I don't really think that is an important difference--in the scale of the universe, they should be treatable as point sources, I think.)

You are correct in that on a celestial scale / at large distances, even planets and stars can be considered point sources for most situations. I try to think of these topics like newsprint or a computer screen. When viewed from very close, it is obvious that the print or screen is made from individual pixels. While there is nothing wrong with looking at each individual pixel, you loose nothing by considering it as a whole and in fact, gain clarity of the situation (you can read the paper!).

Thanks to those who replied to my post 13. I have always believed that we needed Newtons force (F= G*m1*m2/r^2) which is oversimplified, as well a Einsteins curved space. You seem to be agreeing with that. However, there are plenty of places where they say force is removed from curved space. Here is a quote from the link in this post:

"Einstein: It is not necessary to "solve" for the

motion. All motion is along "straight lines"

(geodesics) in a curved spacetime! The notion of

gravitational "force" then has essentially been

eliminated."

-S

Or as Newton famously responded when asked "what is gravity?" he lightened the load on scientific progress when he replied, "I feign no hypothesis." -- here was insight from the greatest thinker of his time that you could go forward without getting bogged down in first needing to know what the prime mover is.

Perhaps all we can ever hope is to detect is it's action, and quantify it mathematically and that's all we need. Just as in the case of a ball on a rubber sheet, the 2d residents of the sheet can never hope to see the ball, but only as a 2D line, a barrier which they cannot overcome.

Sorry I haven't responded to many of the most recent comments on this thread. Many have been helpful, but I got sidetracked with my reading / research and with the "real world".

I actually started to summarize where I stand in my quest here, but wrote about 4 pages and quit.

I may make "random" comments to some of the posts.

The next (new to my quest) thing I want to dig into is gravitons--I guess I could do it quickly, but, without doing any digging, my understanding is that gravitons (the predicted "force carrier" for gravity) have not been found, yet force carriers have been discovered for the other elementary forces (that is, for the electromagnetic, weak, and strong forces).

So, maybe scientists are giving up hope of discovering a force carrier for gravity and seeking to explain gravity based on geometry instead, thus favoring the curved space-time explanation over the gravimetric force field explanation. (And, also, maybe that makes gravity a pseudo force, like the centrifugal, Coriolis, and the two other normally recognized pseudo forces.)

Oh, I should have mentioned, thanks to the comments made on this list and sources they pointed me to (and others I found), I'm pretty much convinced that the curved space-time and the gravimetric force field approaches to explaining gravity both result in the same predictions, matching real observations (as far as we can observe so far). (For example, to my specific question, if the predicted path of motion is a geodesic in the curved space-time explanation, the path would have the same shape (but maybe not be called a geodesic) in the gravimetric force explanation.)

Thus there is no reason to favor one explanation over the other in terms of their results / predictions.

I also inferred from something I read that Einstein didn't have a good reason to choose the curved space-time explanation over the gravitational force explanation--the article I read said that he eventually recognized that the curved space-time explanation was an alternate that he recognized would work, and then he seemed to adopt it. Maybe I have to try to read some of Einstein's paper's in German to get more understanding of why he chose the curved space-time explanation. ;-)

I've also read that the curved-space time explanation does make further explanations of some things easier, but I haven't found a list of what those things are, nor have I thought about it enough to infer any of those on my own.

I should provide sources for all the things I mention, but for the moment, I won't. I'm getting overwhelmed with my notes on the subject. If someone wants a reference on a particular point, let me know, I'll try to dig it out.

So, this 2nd attempt provides a summary of where I'm at, and is much shorter than the first attempt, so I'll post this...

There were a few errors in what I wrote above (at least, I think there were), so let me try to clarify them (they might require some research to confirm, and I won't do that immediately):

IIUC, at the time Einstein developed his theory of general relativity:

• There was no knowledge or expectation of gravitons--thus, I don't think his basis for preferring the curved space-time explanation could have been that gravitons had not been discovered (which they haven't, even to this day) (all requires confirmation). --wait, maybe I'm wrong about that-- Was it known at that time that photons were the force carrier for the electromagnetic force? So then he knew of a force carrier for the electromagnetic force (the photon), but not of a force carrier for the gravitational force. If so, he might have preferred the curved space-time explanation on that basis. (BTW, although that force carrier does not seem to exist, it has since been named the "graviton". (again, requires confirmation--I'm almost sure the photon was known at that time (at least as the "packet" (quantum) of light, and maybe Maxwell's equations pointed to the photon as being the carrier of the electromagnetic force)
• I don't think the weak and strong forces had been discovered yet (requires confirmation), thus his attempt at a unified theory only attempted to unify the electromagnetic and gravitational forces (requires confirmation)