Gravity: real force or artefact of acceleration?

[Brinx]

After some forum searching, I concluded that the question I'm confused about was too hard to find (or not yet posted at all), so I'll be so bold as to post it myself. Apologies if this has already been treated exhaustively! I'm not sure where to post this exactly, as it ties in with both classical physics and relativity - at least, I think it does...

The main question is really: can you consider a reference frame at rest w.r.t. a non-rotating massive object to be an inertial frame? I'd say you can't, as you would experience an acceleration in that frame and, according to the equivalence principle, you hence might as well be in an accelerating frame, which would be non-inertial - and as such you would be equating an inertial frame to a non-inertial frame, which would seem nonsensical.

Others have said that you can very well treat the frame at rest w.r.t. a massive object as an inertial frame, when you just treat the gravitational force as a real force instead of an artefact of an accelerating reference frame.

This might not seem like a problem at all (but merely like two alternative interpretations), but I think there is a definitive difference once you start considering the problem of a charge in a gravitational field (which has been talked about on these forums already I believe), and whether or not it radiates - as opposed to a uniformly accelerating charge.

So, what do you people think? At rest w.r.t. a massive object, are you in an inertial reference frame? Why, or why not?

Thanks in advance for your thoughts.

 

[Micha]

It depends, how massive the massive object really is.

In the weak field limit you can use special relativity plus Newtonian gravity with good accuracy,
eg. for the gravitational field of the earth. So you can treat the surface of the Earth as an inertial
frame, the biggest error coming from the Earth rotating around the sun, not from the
small corrections of general relativity.

For a really strong field you have to use general relativity. As you know, the "inertial" frames of
general relavity (the ones with Minkowski metric) are the freely falling system. Of course,
in general relativity inertial frames exist only locally. Local means so small, that you can neglect
the inhomogenities of the gravitational field of your massive body.

 

[Bob Walance]

[snip]
The main question is really: can you consider a reference frame at rest w.r.t. a non-rotating massive object to be an inertial frame? I'd say you can't...
[snip]
This might not seem like a problem at all (but merely like two alternative interpretations)...
[snip]
So, what do you people think? At rest w.r.t. a massive object, are you in an inertial reference frame? Why, or why not?
Thanks in advance for your thoughts.

From what I've learned, it's easy to tell if you're in an inertial frame of reference or not.

If you can feel a net force on your body then you are NOT in an inertial frame of reference but rather are in an accelerated frame of reference.

When we're maintaining a fixed velocity with respect to the Earth then we feel a net force, right? Therefore, we are in an accelerated frame of reference. This agrees with the Principle of Equivalence.

This is a difficult concept to grasp and to believe. We are all accelerating? With respect to what? Well, my answer would be that we're accelerating with respect to the geometry of our curved spacetime.

This whole idea of forces and non forces and intertial frames of reference and accelerating frames of reference is what drove me to learn more about this subject and then create a website. Have a look at it. If the ideas are incorrect then I would really appreciate that feedback and I will be happy to update the information there.

www.gravityforthemasses.com

Regards,
Bob Walance

 

[Mentz114]

Bob Walance :

Well, my answer would be that we're accelerating with respect to the geometry of our curved spacetime.

Can you explain this ? Frames of reference must be defined by matter. Matter does determine the local space-time geometry, but space-time geometry is an abstract idea.

 

[Bob Walance]

Can you explain this ? Frames of reference must be defined by matter. Matter does determine the local space-time geometry, but space-time geometry is an abstract idea.

I don't know enough to argue against this concept of "frames of reference must be defined by matter". How would you pharse it?

Perhaps:

Matter that is in an inertial frame of reference, in our region of spacetime, is following its geodesic. We are not following a geodesic therefore we're in an accelerated frame of reference.

What is your view?

Thanks.

Bob

 

[cesiumfrog]

My take on this is that the "gravity" known by high-school students is merely an artefact of acceleration (and hence that stationary frames on Earth are not inertial). This seems the logical conclusion to draw from GR, however, I think many people do resist this interpretation. And as for whether a charge radiates, I've discussed that in another thread..

 

[pervect]

My $.02.

In Newtonian mechanics, gravity is a force.

In GR, it is not in general describable as a force. GR is a more accurate theory than Newtonian gravity, and the experimental differences (such as gravitational time dilation) are detectable by experiment.

In string theory, gravity may be described some other way. People need, I think, to get used to the idea that science doesn't offer unique answers to questions like "what is gravity".

So if you happen to be doing classical GR, you should probably think of gravity as curved space-time. It can be challenging to describe what this means in lay terms. (I describe it very briefly as drawing space-time diagrams on curved surfaces.)

As far as whether or not an falling charge radiates, there is some debate. Much of the debate turns out to be what one means by "radiates". See any of the old threads for more detail. One particular reference is http://www.springerlink.com/content/lhx7734t86163837/

Abstract We address the old question of whether or not a uniformly accelerated charged particle radiates, and consequently, if weak equivalence principle is violated by electrodynamics. We show that radiation has different meanings; some absolute, some relative. Detecting photons or electromagnetic waves is not absolute, it depends both on the electromagnetic field and on the state of motion of the antenna. An antenna used by a Rindler observer does not detect any radiation from a uniformly accelerated co-moving charged particle. Therefore, a Rindler observer cannot decide whether or not he is in an accelerated lab or in a gravitational field. We also discuss the general case.

 

[meopemuk]

What is your view?

I disagree with the idea that observers free falling in the field of gravity should be considered inertial. There are two reasons.

First. In physics we normally separate between the observer and the physical system. The assumption is that the physical system has no effect on the observer apart from the measurement process. For example, when we observe a system of charges (e.g., an atom) we do not take into account the fact that there is (though very weak) Coulomb interaction between the charges and the measuring device. Your approach is completely different. When you study a system with gravitational interaction (e.g., Earth + stone) you place the observer right in the middle of the Earth's gravitational field and let it fall in this field. In my opinion, this approach is questionable. I would prefer to call "inertial" those observers which are far away from the gravitational field and are not affected by it. Speaking about observers on the Earth surface, those of them who move with constant velocities (without acceleration) with respect to distant inertial observers have more rights to be called "inertial" as well.

Second. Your definition of free-falling inertial observers relies heavily on the principle of equivalence. However, this principle is just a heuristic assumption. What if this principle will be found inaccurate by future experiments?

Eugene.

 

[pervect]

I disagree with the idea that observers free falling in the field of gravity should be considered inertial. There are two reasons.

First. In physics we normally separate between the observer and the physical system. The assumption is that the physical system has no effect on the observer apart from the measurement process. For example, when we observe a system of charges (e.g., an atom) we do not take into account the fact that there is (though very weak) Coulomb interaction between the charges and the measuring device. Your approach is completely different. When you study a system with gravitational interaction (e.g., Earth + stone) you place the observer right in the middle of the Earth's gravitational field and let it fall in this field. In my opinion, this approach is questionable. I would prefer to call "inertial" those observers which are far away from the gravitational field and are not affected by it. Speaking about observers on the Earth surface, those of them who move with constant velocities (without acceleration) with respect to distant inertial observers have more rights to be called "inertial" as well.

Second. Your definition of free-falling inertial observers relies heavily on the principle of equivalence. However, this principle is just a heuristic assumption. What if this principle will be found inaccurate by future experiments?

Eugene.

I'd agree that free-falling observers in GR are not quite inertial, but not for the reasons you state.

The issue is that a free-falling observer will still experience a tidal force. The true inertial observer, such as the observer at infinity that you mention, will not experience any tidal force.

If one considers a small enough region of space-time, though, the tidal force won't matter. This can be made more exact (as to when tidal forces can be neglected and when they can't) - MTW goes through this, IIRC.

Worrying about what happens if the equivalence principle is violated isn't very fruitful, IMO. One can only answer the question as to what gravity is in the context of some particular theory. In the context of what gravity is according to GR, it doesn't make sense to worry about what happens if GR is falsified.

 

[pmb_phy]

The main question is really: can you consider a reference frame at rest w.r.t. a non-rotating massive object to be an inertial frame?

The first question that I want to ask you is this: What exactly do you mean when you use the term "real"? This term, while widely used in physics for certain things, is not not belong to the philosophy of physics. Consider the following letter from Einstein to Eduard Study (Sept. 25, 1918)

"The physical world is real." This is supposed to be the basic hypothesis. What does "hypothesis" mean here? For me, a hypothesis is a statement whose truth is temporarily assumed, whose meaning, however, is beyond all doubt. The above statement seems intrinsically senseless though, like someone saying "The physical world is a cock-a-doodle-do." It appears to me that "real" is an empty, meaningless category (draw) whose immense importance lies only in that I place certain things inside it and not certain others. It is true that this classification is not a random one ... now I see you grinning and expecting me to fall into pragmatism so that you can bury me alive. However, I prefer to do as Mark Twain, by suggesting that you end the horror story yourself.
<Real and unreal seem to me like right and left.> I admit that science deals with the "real" and am nonetheless a "realist." -

Your answer may depend on your response to this question. However I will not need to consider it in what follows. Now back to your question...


With respect to general relativity the answer to your question above is No. An inertial frame near a body like Earth is one which is in free-fall. Thus a frame of rest is accelerating with respect to such a free-fall inertial frame. Thus an inertial frame at rest relative to the surface of the Earth is not an inertial frame of reference.

I'd say you can't, as you would experience an acceleration in that frame and, according to the equivalence principle, you hence might as well be in an accelerating frame, which would be non-inertial - and as such you would be equating an inertial frame to a non-inertial frame, which would seem nonsensical.

That is correct.

Others have said that you can very well treat the frame at rest w.r.t. a massive object as an inertial frame, ...

For Newtonian mechanics that'd be true. For general relativity that is not true.

...when you just treat the gravitational force as a real force instead of an artefact of an accelerating reference frame.

Consider the situation in Newtonian mechanics; if you're in an inertial frame and there are particles which have no force acting on then and are at rest of in uniform motion then they are said to be free particles. Now change frames of reference to a non-inertial frame, i.e. one that is rotating or accelerating relative to the inertial frame. The particles no move as if there are forces on them. Many physicists, not all, consider those forces to be fictional or apparent or whatever because, as you mentioned, the acceleration is entirely due to viewing nature from a non-inertial frame.

Then came Einstein. Einstein layed out the following picture for us. Suppose you are at rest in a uniformly accelerating frame of reference. Bodies which were moving force free in the original inertial frame are now accelerating with respect to this frame. Now consider yourself to be at rest in a uniform gravitational field. Particles in free-fall (i.e. subject only to the gravitational force) will behave just as the ones observered in the accelerating frame. Einstein's equivalence principle states that there is no way to tell the difference and therefore they are considered equivalent. Thus, Einstein concluded, what was a a "fictitional" force in Newtonian mechanics is now considered to be subject to a "real" force. There are thus two classes of force. One is a force which can be represented by a 4-vector and the other are called inertial forces which can be transformed away. I did a lot of research in the literature about this topic and while the majority of the cases call the gravitational force a "fictitious" force the ones I found which consider these forces to be "real" include those from Einstein, A.P. French, Cornelius Lanczos and John A. Peacock. I listed them here
http://www.geocities.com/physics_world/gr/inertial_force.htm

As an example, consider what Cornelius Lanczos has to say on this topic. From his book, a very popular one which is highly respected in the physics community, The Variational Principles of Mechanics - 4th Ed., Dover Pub., page 98;

Whenever the motion of the reference system generates a force which has to be added to the relative force of inertia I’, measured in that system, we call that force an “apparent force.” The name is well chosen, inasmuch as that force does not exist in the absolute system. The name is misleading, however, if it is interpreted as a force which is not as “real” as any given physical force. In the moving reference system the apparent force is a perfectly real force which is not distinguishable in its nature from any other impressed force. Let us suppose that the observer is not aware of the fact that his reference system is in accelerated motion. Then purely mechanical observations cannot reveal to him that fact.

In Newtonian Mechanics, A.P. French, The M.I.T. Introductory Physics Series,W.W. Norton Pub. , (1971) , French states on page 499

From the standpoint of an observer in the accelerating frame, the inertial force is actually present. If one took steps to keep an object "at rest" in S', by tying it down with springs, these springs would be observed to elongate or contract in such a way as to provide a counteracting force to balance the inertial force. To describe such force as "fictitious" is therefore somewhat misleading. One would like to have some convenient label that distinguishes inertial forces from forces that arise from true physical interactions, and the term "psuedo-force" is often used. Even this, however, does not do justice to such forces experienced by someone who is actually in the accelerating frame of reference. Probably the original, strictly technical name, "inertial force," which is free of any questionable overtones, remains the best description.

The term Gravitational Force is a well defined term in General Relativity. I created a web page that derives the expression for it while motivating the espression. It is at
http://www.geocities.com/physics_world/gr/grav_force.htm if you care to review it.

This might not seem like a problem at all (but merely like two alternative interpretations), but I think there is a definitive difference once you start considering the problem of a charge in a gravitational field (which has been talked about on these forums already I believe), and whether or not it radiates - as opposed to a uniformly accelerating charge.

This notion has been studied by several relativists and the conclusion is that there is no problem at all. You can read exerpts from these articles at
http://www.geocities.com/physics_world/ref/falling_charge.htm

I can very easily give you access to any of those files, or all of them if you wish, by e-mail. If you'd rather not give out your e-mail address then I can try to find another way. I usually upload such files to one of my websites. However most of them are full. But where there is a will there is a way. But it would be much easier to send them in e-mail. I'm very trustworthy and state that I will not give out or abuse access to your e-mail. Of course that's just my word you have. But you can ask others about trusting me if you'd really like those papers. In the mean time I will either delete files from some of the my other websites or find another way.

So, what do you people think? At rest w.r.t. a massive object, are you in an inertial reference frame? Why, or why not? Thanks in advance for your thoughts.

If you are at rest in the presence of a body such as the Earth there are tidal forces which cannot be transformed away. Tidal forces are defined and described on another of my web pages here
http://www.geocities.com/physics_world/mech/tidal_force_tensor.htm

The Tidal Force Tensor is defined in Eq. (5). In fields where tidal gradients exist (Or in General Relativity lingo, in curved spacetime, the equivalence is a local effect, where the term local means that you've restricted your attention to a region of spacetime so small as to be unable to detect these tidal forces using the equipment your using. But in principle the gravitational field can only be transformed away at least at one single point in spacetime. Venture too far outside the region of this region then you can actually determine if you're in an gravitational field or not.

Best wishes

Pete

 

[Mentz114]

I don't know enough to argue against this concept of "frames of reference must be defined by matter". How would you pharse it?

Perhaps:

Matter that is in an inertial frame of reference, in our region of spacetime, is following its geodesic. We are not following a geodesic therefore we're in an accelerated frame of reference.

What is your view?

Thanks.

Bob

Bob, I think we've been told ... lots of good stuff above. I can recommend pmb's website.

 

[Dale]

In Newtonian mechanics, gravity is a force.

In GR, it is not in general describable as a force. ...

People need, I think, to get used to the idea that science doesn't offer unique answers to questions like "what is gravity".

Excellent point and well worded.

To the OP: if you are trying to describe a situation that is within the scope of Newtonian mechanics then treat gravity as a real force with free-falling frames considered non-inertial, but if you are trying to describe a situation where Newtonian mechanics breaks down then treat gravity as a ficticious force with free-falling frames considered inertial. If you are just trying to understand gravity then both ways are good descriptions within their respective limits and you shouldn't neglect either.

 

[pmb_phy]

Bob, I think we've been told ... lots of good stuff above. I can recommend pmb's website.

Thank you Mentz114. That is very kind of you to say!


I was at a library today and looking at the October 2007 issue of Scientific American. On page 114 David Politzer (Nobel Laureate) wrote an article in response to the question "What is a fictitious force?" Toward the end of the article the author writes

With general relativity, Albert Einstein managed to blur forever the distinction between real and fictitious forces. General relativity is his theory of gravity - certainly the paradigmatic example of a "real" force. The cornerstone of Einstein's theory, however, is the propsition that gravity itself is a fictitious force (or rather that it is indistinguishable from a fictitious force).

From reading Einstein's papers I get the impression that because he considered the gravitational field to be a "real" force then since inertial forces are of the same class of forces that inertial forces are also "real." Other people read/interpret it differently of course. I recommend that you read what Einstein himself wrote in his 1916 GR review article and see what you think he's saying. Do you have access to that paper? If not the search the Internet for it. The title of the paper is The Foundation of the General Theory of Relativity. Also note an Einstein quote from my website at
http://www.geocities.com/physics_world/gr/inertial_force.htm

In the February 17, 1921 issue of Nature Einstein wrote

Can gravitation and inertia be identical? This question leads directly to the General Theory of Relativity. Is it not possible for me to regard the Earth as free from rotation, if I conceive of the centrifugal force, which acts on all bodies at rest relatively to the earth, as being a "real" gravitational field of gravitation, or part of such a field? If this idea can be carried out, then we shall have proved in very truth the identity of gravitation and inertia. For the same property which is regarded as inertia from the point of view of a system not taking part of the rotation can be interpreted as gravitation when considered with respect to a system that shares this rotation. According to Newton, this interpretation is impossible, because in Newton's theory there is no "real" field of the "Coriolis-field" type. But perhaps Newton's law of field could be replaced by another that fits in with the field which holds with respect to a "rotating" system of co-ordinates? My conviction of the identity of inertial and gravitational mass aroused within me the feeling of absolute confidence in the correctness of this interpretation.

In your opinion what is Einstein trying to say here?

Best regards

Pete

 

[Mentz114]

Extracted from pmb's post above "February 17, 1921 issue of Nature Einstein wrote"

if I conceive of the centrifugal force, which acts on all bodies at rest relatively to the earth, as being a "real" gravitational field of gravitation, or part of such a field? If this idea can be carried out, then we shall have proved in very truth the identity of gravitation and inertia.

Does the Kerr metric achieve this - i.e. include the centripetal force ? I'm going off to find the Riemann tensor of the Kerr metric ...

 

[pervect]

Bob, I think we've been told ... lots of good stuff above. I can recommend pmb's website.

Most of it (Pete's website) is OK, but Pete has a few funny ideas that aren't quite mainstream.

 

[pervect]

The term Gravitational Force is a well defined term in General Relativity.

I created a web page that derives the expression for it while motivating the espression. It is at
http://www.geocities.com/physics_world/gr/grav_force.htm if you care to review it.

This webpage is not a standard textbook defintion of gravitational force. See for instance pmb's arguments with Steve Carlip

in this old usenet thread..

 

[pmb_phy]

There is also sort of a definition of gravitational force in Weinberg's GR text. The section called Gravitational Force (within the theory of relativity) which begins on page 70. There is also another mention of it on page 123 between equations Eq. (5.1.11) and Eq. (5.1.12). He defines it differently then the other texts so I guess I'll have to retract my claim that what I posted was the standard definition found in GR texts. I guess I should have looked beyond two references before I made that assertion.

Note: The definition I used is the one that makes the most sense to me and the reasons for it are in the web page. It corresponds to the definition given in Basic Relativity, by Richard A. Mould, Springer-Verlag, (1994). Mould used Moller as a source so I assume that Moller also used this definition but upon looking at Moller's text I'm not sure that his definition of G-force is the same as Moller.

Pete

 

[pervect]

https://www.physicsforums.com/showpost.php?p=272277&postcount=15

is a related thread on this argument, with a nice quote from Wald on the issue. (Wald basically says there are some circumstances in which gravity can be regarded as a force, but in general it should be regarded as an aspect of space-time structure).

 

[pmb_phy]

https://www.physicsforums.com/showpost.php?p=272277&postcount=15

is a related thread on this argument, with a nice quote from Wald on the issue. (Wald basically says there are some circumstances in which gravity can be regarded as a force, but in general it should be regarded as an aspect of space-time structure).

I recall that quote, but I don't believe his interpretation of it. Steven Weinberg is very clear on the subject of gravitational forces in curved spacetimes and explains the very simple situation that if the observer is located at the origin of an inertial frame (aka a free-fall frame) then while there is not gravitational field, and hence if an object is placed there the gravitational force on it will be zero, at points off the origin have a non-zero gravitational field and thus a particle placed there will experience a gravitational force. Thus in a curved spacetime the gravitational field/force cannot be fully transformed away. I'll say this. If I was forced to choose either Wald or Weinberg because perhaps I was simply unable to comprehend a topic and had to take someones word, then I'd choose Weinberg over Wald any day of the week.

Tell me pervect, have you ever read any part of Weinberg's GR text? Do you have a copy? Would you like to read his section Gravitational Force? If not then I ask why?

Wald says

The basic framework of the theory of general relativity arises from considering the opposite possibility: that we cannot in principle--even by complicated procedures-- construct inertial observers in the sense of special relativity and measure the gravitational force.

Well that comment is not all that useful since the gravitational force is an inertial force and thus cannot be present in any inertial frame of reference. That's just the first thing a student would learn in a GR 101 course. However if one changed to a non-inertial frame then the a gravitational field would be present and thus inertial forces such as the gravitational force would then be present if an object was there for the gravitational force to act on.

Wald goes on to say

In this way, the "background observers" (geodesics of the space-time metric) automatically coincide with what was previously viewed as motion in a gravitational force field. As a result we have no meaningful way of describing gravity as a force field; rather, we are forced to view gravity as an aspect of spacetime structure.

That makes no sense. Wald definitely contrdicts Weinberg, who does make sense. Perfect sense in fact. Wald doesn't even attempt to prove this claim. He states it as if it is an obvious fact. Since this "fact" is wrong then I can see why there's no proof of it. Wald claims that background observers must be inertial observers since he states that such observers move on geodesics. But since he is speaking of a curved spacetime such observers will measure an inertial force (aka a gravitational force) on an object which is not on his world line. If course we know this even from Newtonian gravity and as Wald says its just tidal forces.

Shall I continue? I don't expect you to agree with me. But I do expect that you respect my opinion on the matter even if that opinion is opposite to yours and even when you don't consider the opinion to me contrary to what you believe to be facts. In those cases I request a counter example.

Until then, what is the purpose of you constantly making these objections when I post on the subject? Do you do this to everyone here? I.e. do you believe that you have to correct everyone's comments in all physics posts?? Seems like a lot of work to me. Good luck with that.

I personally believe that the correct way to handle these things is to direct your comments to the person who asked the question. You can easily state your opinion on the topic to that person such as disagreeing with a definition or quoting your favorite GR book (since it is that book which agrees with you) and avoid quoting others (like Weinberg's book since that agress with me). I had made the mistake of responding to your disagreement but later realized that was not the proper way to handle it. So I deleted that post as you probably know. I was using a bad habit, one that I'm trying to break. So many discussions about something the OP was never interested in.

Pete

 

[robphy]

Pete,
Is your "gravitational force" a 3-vector or a 4-vector quantity?
Is it a coordinate-dependent quantity?

 

[pmb_phy]

Pete,
Is your "gravitational force" a 3-vector or a 4-vector quantity?
Is it a coordinate-dependent quantity?

The gravitational force, like all other inertial forces, are not 4-vectors. They are 3-vectors.

Pete

 

[pmb_phy]

Most of it (Pete's website) is OK, ...

Thanks.

Pete

 

[robphy]

The gravitational force, like all other inertial forces, are not 4-vectors. They are 3-vectors.

Pete

In response to your declaration: (my boldfacing)

But there is another reason, apart from just organizing complication, that the tensor calculus plays such a fundamental role in Einstein’s theory. This goes back to the foundational principle of equivalence which started Einstein’s whole line of thinking. Gravitation is not to be regarded as a force; for, to an observer who is falling freely (such as our astronaut A), there is no gravitational force to be felt. Instead, gravitation manifests itself in the form of spacetime curvature. Now it is important, if this idea is to work, that there be no ‘preferred coordinates’ in the theory. For, if a certain limited class of coordinate systems were taken to be Nature’s referred choices, then these would define ‘natural observer systems’ with respect to which the notion of a ‘gravitational force’ could be reintroduced, and the central role of the principle of equivalence would be lost. The point is, in fact, a rather delicate one, and many physicists have, from time to time and in one way or another, departed from it. To my way of thinking, it is essential for the spirit of Einstein’s theory that this notion of coordinate independence be maintained. This is what is referred to as the principle of general covariance.
...For the moment, the importance of the principle of general covariance to us is that it forces us into a coordinate-free description of gravitational physics. It is for this reason, most particularly, that the tensor formalism is central to Einstein’s theory.

In this geometric viewpoint, the use of 3-vectors cannot be considered fundamental unless the 4-dimensional spacetime provides a distinguished geometrical structure with which 3-dimensional quantities can be constructed. (This does not mean that such 3-vectors aren't useful in certain situations...since they maybe associated with a particular observer with his set of measurement devices, which could be considered a choice of coordinates. For beginners, they might be useful to connect with Newtonian thinking... but, in my opinion, one must wean oneself from that kind of thinking to get a better understanding of relativity.)

Here's are some passages from Synge, who is probably the most vocal advocate for the geometric viewpoint.

preface, p. VIII:
If we accept the idea that space-time is a Riemannian four-space (and if we are relativists we must), then surely our first task is to get the feel of it just as early navigators had to get the feel of a spherical ocean. And the first thing we have to get the feel of is the Riemann tensor, for it is the gravitational field - if it vanishes, and only then,
there is no field.
...I know now that if I break my neck by falling off a cliff, my death is not to be blamed on the force of gravity (what does not exist is necessarily guiltless), but on the fact that I did not maintain the first curvature of my world-line, exchanging its security for a dangerous geodesic.

p. 109:
In relativity there is no such thing as the force of gravity, for gravity is built into the structure of space-time, and exhibits itself in the curvature of space-time, i.e. in the non-vanishing of the Riemann tensor.

Certainly, the modern geometric viewpoint [which probably started with Synge] is not the only viewpoint. However, it proves itself to be very effective in clarifying the physics and settling confusions [often caused by trying to extract the underlying physics from coordinate-dependent results]. (For example, Synge is credited with clarifying the coordinate singularity found at the horizon of the Schwarzschild black hole: http://arxiv.org/abs/gr-qc/0408017v1 (which apparently tripped up Einstein). In addition, the strength of the Penrose-Hawking singularity theorems relies on its use of [non-coordinate based] geometrical methods.)

 

[pmb_phy]

You didn't need to post all that. pervect already did something similar, i.e. he posted a link to one of your old posts where you quoted Wald. I know that a lot of people believe that. Someone would have to have a lack of knowledge not to know that there are misgivings about the gravitational force. I'm just not one of those people


I've had these discussions the past. If I continued posting on this subject then, as I see it, the only possible outcome is to repeat what I've already said before. The OP doesn't show any interest in my views on this (God Bless him!) so I find that it would be unwise for me to discuss this in open forum. However I'll e-mail you because I have some questions/comments on the material you've posted from Wald and the books you quoted above. Thanks Rob!

Best wishes

Pete

ps - See Weinberg's text on this subject

 

[pmb_phy]

I ran across a few interesting comment. From The Feynman Lectures on Physics - Volume I, page 12-12

Einstein found that gravity could be considered a pseudo force only at one point at a time.

From Introducing Einstein's Relativity, by Ray D'Inverno, Oxord/Clarendon Press, (1992) page 122

Notice that all inertial forces forces have the mass as a constant of proportionality in them. The status of inertial forces is again a controversional one. One school of thought describes them as apparent or fictitious which arise in non-inertial frames of reference (and whichcan be eliminated mathematically by putting the terms back on the right hand side). We shall adopt the attitude that if you judge them by their effects then they are very real forces. [author gives examples]

My attitude is the same as that of the author's of this book, i.e. inertial forces are "real". Since some people disagree with me I believe that it is this subject (reality of inertial forces) that cause others to refer to the idea as one of my funny ideas when in actuallity it is not all that unfounded given the references I've given from French, Einstein, Lanczos, Peacock and now D'Inverno. I didn't invent this idea, I just live by it. :)

So what is so funny about that? Please tell me. I'd love to know?

Pete

 

[pmb_phy]

I'd agree that free-falling observers in GR are not quite inertial, but not for the reasons you state.

The issue is that a free-falling observer will still experience a tidal force. The true inertial observer, such as the observer at infinity that you mention, will not experience any tidal force.

The term "observer" is defined as a system of clocks and rods. In a curved spacetime it is considered an infinitesimally small region of spacetime with a particular "observer" (small system of clocks and rods) defined as a timelike velocity vector of such as small system of clocks and rods. It does not refer to a real person. That is the fundamental reason that you won't find the term "observer" as person used in texts like Introducing Einstein's Theory of Relativity, by Ray D'Inverno or in spacetime Physics Second Version[/b], by Taylor and Wheeler, or in Exploring Black Holes, by Taylor and Wheeler. If you have the last of these texts then look in the glossary on page GL which states

observer: Collection of rods and recording clocks associated with a given frame of reference.

While you have the book open look at page GL-2 at the title of the glossary and see who wrote it. Want to take a guess as to whom that might be?

We use terms in relativity which have a well defined meaning which, at times, are different from what the layman would use. This is a good example. Otherwise everytime I used a term like "observer", which is quite often in fact, I'd have to quote this over and over again. So let's get this straight: For theoretical purposes an observer is pointlike and represented by a timelike vector.

Pete

 

[robphy]

I ran across a few interesting comment. From The Feynman Lectures on Physics - Volume I, page 12-12

From Introducing Einstein's Relativity, by Ray D'Inverno, Oxord/Clarendon Press, (1992) page 122

My attitude is the same as that of the author's of this book, i.e. inertial forces are "real". Since some people disagree with me I believe that it is this subject (reality of inertial forces) that cause others to refer to the idea as one of my funny ideas when in actuallity it is not all that unfounded given the references I've given from French, Einstein, Lanczos, Peacock and now D'Inverno. I didn't invent this idea, I just live by it. :)

So what is so funny about that? Please tell me. I'd love to know?

Pete

So, it seems you demonstrate one of two schools of thought:
"Einstein, Lanczos, Peacock and now D'Inverno"
and, from example quotes I have posted,
Wald, Penrose, Synge.
Folks are certainly free to choose which way, if any, they wish to think.
I follow my academic upbringing and my personal research interests, which of course may change.

Concerning the ` inertial forces are "real" `comment, I find that in conflict with
the way I have been teaching students to think about forces that he/she might draw on a free-body diagram... namely that they should be able to identify the "source" of the force [the agent that applies the force] on the free-body. In an inertial frame, one student would draw in what I would call 'real' forces, applied by agents I can name [rope, surface, etc] ... but in a non-inertial frame, what is the agent for the 'inertial force' that would be drawn?

Certainly, if I am in that non-inertial frame, things that happen might seem 'real' to me and I and my attached instruments might react in some way to them... but objectively [to other observers], is it really there? Or is it an effect because I actively choose to be different and actively travel in a non-inertial way? That is to say, is the 'inertial force' [objectively] real? or is it just a figment of my 4-acceleration?

 

[pmb_phy]

So, it seems you,...

Me? I thought this was fairly well known?? Oh well. I guess I guessed wrong!

... demonstrate one of two schools of thought:
"Einstein, Lanczos, Peacock and now D'Inverno"
and, from example quotes I have posted,
Wald, Penrose, Synge.
Folks are certainly free to choose which way, if any, they wish to think.

Thanks.

I follow my academic upbringing and my personal research interests, which of course may change.

Same here.

Concerning the ` inertial forces are "real" `comment, ...

I'd like to retract that statement. I don't like the terms "real" or "fictitous". I was really saying that I dislike any term which gives the impression that something is "fictitious" which would imply that its real. But all I'm saying is that I prefer the term "inertial force" rather then fictitious/apparent/pseudo etc. since it is devoid of all conotations of "real/unreal". I think Einstein got it right when he said

"The physical world is real." This is supposed to be the basic hypothesis. What does "hypothesis" mean here? For me, a hypothesis is a statement whose truth is temporarily assumed, whose meaning, however, is beyond all doubt. The above statement seems intrinsically senseless though, like someone saying "The physical world is a cock-a-doodle-do." It appears to me that "real" is an empty, meaningless category (draw) whose immense importance lies only in that I place certain things inside it and not certain others. It is true that this classification is not a random one ... now I see you grinning and expecting me to fall into pragmatism so that you can bury me alive. However, I prefer to do as Mark Twain, by suggesting that you end the horror story yourself.
<Real and unreal seem to me like right and left.> I admit that science deals with the "real" and am nonetheless a "realist." - Letter from Albert Einstein to Eduard Study (Sept. 25, 1918)

I find that in conflict with
the way I have been teaching students to think about forces that he/she might draw on a free-body diagram... namely that they should be able to identify the "source" of the force [the agent that applies the force] on the free-body. In an inertial frame, one student would draw in what I would call 'real' forces, applied by agents I can name [rope, surface, etc] ... but in a non-inertial frame, what is the agent for the 'inertial force' that would be drawn?

So you're saying that a charged particle moving in a circle in an EM field should have an identifiable source, such as a large magnetic, right? And you're saying that inertial forces have no such source? If so I'd like to direct your attention to Mach's priciple. For example: consider the gravitomagnetic field inside a uniformly rotating very think shell. Inside the shell there is Minkowski space which is rotating about the axis of rotation. In this case if you remained in the initial frame (in which the shell was not rotating at first, then you'd be in an inertial frame in flat spacetime. As the shell started rotating and you remained in your original coordinate system then you'd detect centrifugal forces and coriolis forces. The source in this case is the shell of matter. That is to say that the inertial reference frame is with respect to the rest frame of the rotating matter.

This is derived in a SR/GR text by Rindler. Would you like me to scan it in and e-maail it to you?

Now suppose that you're interested in a uniformly accelerating frame of reference. Very difficults stuff. But it is mentioned in Peacock. In fact that part is online athttp://assets.cambridge.org/052142/2701/sample/0521422701WS.pdf

See pages 5-6 in the section called Inertial Frames and Mach's Principle

Certainly, if I am in that non-inertial frame, things that happen might seem 'real' to me and I and my attached instruments might react in some way to them... but objectively [to other observers], is it really there?

Please define the term "real" as you are using it.

Thanks

Pete

 

[pmb_phy]

Hi Rob

Another quote I thought you might find interesting. From Gravitation, by Misner, Thorne and Wheeler, Box 6.1, page 164

Can a physicist by local effects convince him that this "gravity" is bogus? Never, says Einstein's principle of the local equivalence of gravity and accelerations. But then the physicist will make no errors if he deludes himself treating true gravity as a local illusion caused by acceleration.

I agree with this box. How about you?

Pete

ps - I tried PMing you once or twice with no response. Is there something wrong with your PM or do you prefer that I don't contact you through PM or anyother means except open forum?

 

[robphy]

Hi Rob

Another quote I thought you might find interesting. From Gravitation, by Misner, Thorne and Wheeler, Box 6.1, page 164

Can a physicist by local effects convince him that this "gravity" is bogus? Never, says Einstein's principle of the local equivalence of gravity and accelerations. But then the physicist will make no errors if he deludes himself treating true gravity as a local illusion caused by acceleration.

I agree with this box. How about you?

Pete

It sounds agreeable. Note the restrictions implied by "local". (See below the related discussion of "real".)

ps - I tried PMing you once or twice with no response. Is there something wrong with your PM or do you prefer that I don't contact you through PM or anyother means except open forum?

Yes, I got them... but didn't think they needed a response of receipt... unless it was to be something more substantial from me. I'll look them over again later.To address an earlier post of yours...

Please define the term "real" as you are using it.

I take the point of view in this discussion that "real" implies something objective, independent of a particular observer, and independent of the choice of coordinates. In this sense, the electromagnetic field tensor is "real"... it's F_{ab}... "the electric field" is not real but observer-dependent E_{a}=F_{ab}v^b... just as "the x-component of a vector" (that is, "the" as in "the unique coordinate-independent") isn't real... a vector has an an x-component-[whose-properties-depend-on-the-choice-of-axes].

However, "the electric field observed by observer A" is real since, once observer-A has been distinguished, (E_{\mbox{\small seen by A}})_{a}=F_{ab}(v_{\mbox{\small A}})^b is agreed by all observers. Similarly,
"the x-component of a vector with the usual axes parallel to the sides of this post" is real.

 

[pmb_phy]

I take the point of view in this discussion that "real" implies something objective, independent of a particular observer, and independent of the choice of coordinates.

That seems to imply that you believe that potential energy and kinetic enrgy are not real. That's fine but I don't think you'd have a problem defining them, right?

However, "the electric field observed by observer A" is real since, once observer-A has been distinguished, (E_{\mbox{\small seen by A}})_{a}=F_{ab}(v_{\mbox{\small A}})^b is agreed by all observers. Similarly,
"the x-component of a vector with the usual axes parallel to the sides of this post" is real.

It is always implied that inertial forces are observer dependant. That's something that should never be needed to say. So why would you assert that "the electric field observed by observer A" is okay but not "the gravitational field observed by observer A" not be? By the way. That definition you gave for the E field applies to only one point in spacetime whereas the gravitational field g_uv applies throughout spacetime as does the gravitational force.

I took a closer look at Wald. He says something weird. On page 67 he writes "...that we cannot in principle - even by complicated procedures - construct inertial observers in the sense of special relativity and measure a gravitational force."

That comment makes no sense since that is exactly how the gravitational force is seen to work. I.e. when you're in an inertial frame then you have transformed the gravitational force away! His further comments about geodesics is merely a description of what happens, not an explanation. He seems to want to geometerize the gravitational field like everybody else. That's fine. But that is his opinion and he, like most other GRists, are entitled to that. But I've have to go with Einstein and Weingberg when they say otherwise. That is part of the source of my opinion. And it is just that, an opinion, just as you and others have their opinion. This subject is juust as subjective as many otherones we've discussed.

Note: You don't have to respond to my last PMs. I was just uncertain if you were getting/reading them. Now that I know that you are then there's no need.

Pete

 

[robphy]

That seems to imply that you believe that potential energy and kinetic enrgy are not real. That's fine but I don't think you'd have a problem defining them, right?

I wouldn't say that the notions of "potential energy" and of "kinetic energy" aren't real.

For example:
"The [particular value of the] potential energy of a ball" has no objective reality.
"The [particular value of the] potential energy of a ball with respect to the ground" does.
As we often say, the value of the potential energy is not really physically meaningful... but the "difference in potential energy between two positions" is.

Similarly, as you know
"the [particular value of the] kinetic energy" depends on the frame of reference.
A ball on a jet has more kinetic energy with respect to the ground that with respect to the jet itself.

This is all classically speaking, of course.

So, this is consistent with my electric field example earlier... the notion of an electric field exists... but its value (i.e. magnitude and direction) is observer-dependent... so, it does not make sense to refer to it as "the electric field"... unless you say "the electric field observed by observer-A".

 

[pmb_phy]

For example:
"The [particular value of the] potential energy of a ball" has no objective reality.
"The [particular value of the] potential energy of a ball with respect to the ground" does.
As we often say, the value of the potential energy is not really physically meaningful... but the "difference in potential energy between two positions" is.

Similarly, as you know
"the [particular value of the] kinetic energy" depends on the frame of reference.
A ball on a jet has more kinetic energy with respect to the ground that with respect to the jet itself.

I assume you know that this is the reason I gave those examples? I.e. that there are quantities which by their very nature are observer dependant, just like inertial forces. Because I don't use the word "observer A" it should be understood that there is a particulate observer in mind since we already agree (I hope?) that there is an implied observer in mind.

This is all classically speaking, of course.

So, this is consistent with my electric field example earlier... the notion of an electric field exists... but its value (i.e. magnitude and direction) is observer-dependent... so, it does not make sense to refer to it as "the electric field"... unless you say "the electric field observed by observer-A".

Do you agree that a non-inertial observer would detect a particle, whose 4-velocity is zero (i.e. a "free-particle"), is, in general, accelerating moving with respect to the observer? Seems to me that one can apply the same reasoning to gravitational acceleration as you did above within the scope of relativity. Whether a 4-vector can be created from it is another story. I suspect that it's possible, but not easy. It would be defined by the deviation of the world lines, one of which is a geodesic (the free-particle) and the other is not. The observer would consist of the observers 4-velocity which is on a non-geodesic world line.

Edit:

It just occurred to me that my idea above would only work locally since a displacement 4-vetor only has meaning locally. I guess that's why define the gravity field/force according to the Christoffel symbols! In any case I want to make it clear that when I use the term "inertial force" then you should traslate it in your mind to mean "fictitious force." It seems to me that people might not understand what the term "inertial force" means, i.e. that it is a term which people use for "fictious forces" when they don't want people to get any idea of a negative conotation when the term "fictious " is used. Of course this was all explained in that web page I posted so anyone who actuall read the definition should already know this. Here is that link again for your convinience http://www.geocities.com/physics_world/gr/inertial_force.htm

Please note that this page is currently in flux since I've been trying to get it right without referencing gravity at the same time. I'm so used to the Equivalence Principle that its hard for me to not think of it when discussing only inertial forces.

Pete

 

[mendocino]

Gravity: real force or artefact of acceleration?

Following quote of California Institute of Technology theoretical physicist and 2004 Nobel laureate David Politzer

http://www.sciam.com/askexpert_question.cfm?articleID=ABE57453-E7F2-99DF-32538FF7C7B37F20

With general relativity, Einstein managed to blur forever the distinction between real and fictitious forces. General relativity is his theory of gravity, and gravity is certainly the paradigmatic example of a "real" force. The cornerstone of Einstein's theory, however, is the proposition that gravity is itself a fictitious force (or, rather, that it is indistinguishable from a fictitious force). Now, some 90 years later, we have innumerable and daily confirmations that his theory appears to be correct.

 

[Chris Hillman]

When is popsci too oversimplified?

Hi, mendocino,

I hope you noticed that Politzer was writing for a popular science organ (Scientific American). His statement is an oversimplified reference to the Equivalence Principle (c.f. "elevator experiment"), which is indeed one of the insights which guided AE on the path towards gtr, but gtr in fact treats gravitation rather differently from the impression which might be left by his statement read in isolation.

See for example the popular book by Robert M. Wald, Space, time, and gravity : the theory of the big bang and black holes, University of Chicago Press, 1977. Wald is a specialist in gtr and IMO this little book paints a much more faithful picture for general audiences of how gtr treats gravitational phenomena and how its predictions differ from Newtonian gravitation.

You might also try various recent posts by myself in which I tried to clear up a common confusion concerning how "acceleration" is treated in gtr, as compared to how the effects of a "gravitational field" on the motion of small objects is treated. See [post=1494972]this[/post], [post=1498288]this[/post], and [post=1482542]this[/post], plus older posts collected in my current sig.

 

[robphy]

Indeed... It's best to learn modern general relativity from a modern expert in general relativity.
A Nobel or Fields Medal prize winner is not necessarily such an expert in modern GR.
A Caltech or Harvard professor is not necessarily such an expert in modern GR.
An early researcher in relativity is not necessarily such an expert in modern GR.

 

[pmb_phy]

The cornerstone of Einstein's theory, however, is the proposition that gravity is itself a fictitious force (or, rather, that it is indistinguishable from a fictitious force).

I disagree. What Einstein said was that the force of gravity cannot be distinguished from inertial forces (aka "fictitious" forces) and as such what used to be referred to as "fictitious" forces can just as easily be taken as "real".

I got into this much deeper in a new web page I created which is located at

http://www.geocities.com/physics_world/gr/inertial_force.htm

Notice Einstein's comments in the February 17, 1921 issue of Nature [28]

Can gravitation and inertia be identical? This question leads directly to the General Theory of Relativity. Is it not possible for me to regard the Earth as free from rotation, if I conceive of the centrifugal force, which acts on all bodies at rest relatively to the earth, as being a "real" gravitational field of gravitation, or part of such a field? If this idea can be carried out, then we shall have proved in very truth the identity of gravitation and inertia. For the same property which is regarded as inertia from the point of view of a system not taking part of the rotation can be interpreted as gravitation when considered with respect to a system that shares this rotation. According to Newton, this interpretation is impossible, because in Newton's theory there is no "real" field of the "Coriolis-field" type. But perhaps Newton's law of field could be replaced by another that fits in with the field which holds with respect to a "rotating" system of co-ordinates? My conviction of the identity of inertial and gravitational mass aroused within me the feeling of absolute confidence in the correctness of this interpretation.

Pete

 

[mendocino]

Hi, mendocino,

I hope you noticed that Politzer was writing for a popular science organ (Scientific American). His statement is an oversimplified reference to the Equivalence Principle (c.f. "elevator experiment"), which is indeed one of the insights which guided AE on the path towards gtr, but gtr in fact treats gravitation rather differently from the impression which might be left by his statement read in isolation.

See for example the popular book by Robert M. Wald, Space, time, and gravity : the theory of the big bang and black holes, University of Chicago Press, 1977. Wald is a specialist in gtr and IMO this little book paints a much more faithful picture for general audiences of how gtr treats gravitational phenomena and how its predictions differ from Newtonian gravitation.

You might also try various recent posts by myself in which I tried to clear up a common confusion concerning how "acceleration" is treated in gtr, as compared to how the effects of a "gravitational field" on the motion of small objects is treated. See [post=1494972]this[/post], [post=1498288]this[/post], and [post=1482542]this[/post], plus older posts collected in my current sig.

What's so different?
Could you elaborate the following statement?

>>> gtr in fact treats gravitation rather differently from the impression which might be left by his statement read in isolation.

 

[Chris Hillman]

Ftfl!

Could you elaborate the following statement?

I have done so in the past few days; please see the posts I cited.

 

[mendocino]

Can you tell me the following link is what you referred to?
https://www.physicsforums.com/showthread.php?t=196359
If not, where can I find it?
Thanks...

 

[Chris Hillman]

The links I mentioned were the links I mentioned.

 

[mendocino]

What's "modern General Relativity"?

Indeed... It's best to learn modern general relativity from a modern expert in general relativity.
A Nobel or Fields Medal prize winner is not necessarily such an expert in modern GR.
A Caltech or Harvard professor is not necessarily such an expert in modern GR.
An early researcher in relativity is not necessarily such an expert in modern GR.

Can you tell me what's this "modern general relativity"?
What's the difference between Einstein's GR and so called "modern GR"?

 

[robphy]

In my opinion,
I would describe "modern general relativity" as the geometrical formulations of relativity as found in modern textbooks like Wald and Hawking&Ellis. These texts [based on modern research in relativity, starting from, say, from 1956 (Synge's relativity text)] represent the attempt to capture physical ideas with precise mathematical structures that model them. With such precision, it becomes easier to discuss, analyze, and make predictions of the physics.

I'm not sure how Einstein would react to the formalism...
...but one might look to his initial reaction to Minkowski's reformulation
...then his eventual acceptance and extension of it.

 

[Chris Hillman]

I Hope You Aren't Just Playing Word Games...

What's the difference between Einstein's GR and so called "modern GR"?

For quite a few years after Einstein introduced gtr, physicists (including AE) had great difficulty disentangling geometric phenomena from artifacts of a particular coordinate chart. It took many decades before most physicists working on gravitation finally understood such a basic point as the fact that according to gtr, a gravitational wave consists of ripples in curvature. During these difficult years, mathematicians--- working in part to fill the need for simple computational tools--- introduced and popularized methods which focused attention on geometrical phenomena. During the Golden Age of Relativity, c. 1960-1970, many major advances where made due to adoption by the leading researchers of the new methods. A well known example is the kinematic decomposition of a timelike congruence in a Lorentzian manifold into acceleration and vorticity vectors and expansion tensor. One might also mention the optical scalars and various decompositions of the Riemann tensor.

These techniques were not discussed in the earliest textbooks on gtr because they were not yet available when those books were written. In 1973, two landmark books appeared: the monograph by Hawking and Ellis and the textbook by Misner, Thorne, and Wheeler. These finally made available the geometric viewpoint widely avaible to students and nonspecialists.

So roughly speaking, gtr textbooks published after 1973 are modern; those published before are premodern.