Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Gravity: real force or artefact of acceleration?

  1. Oct 10, 2007 #1
    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.
  2. jcsd
  3. Oct 10, 2007 #2
    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.
    Last edited: Oct 10, 2007
  4. Oct 10, 2007 #3

    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 [Broken]

    Bob Walance
    Last edited by a moderator: May 3, 2017
  5. Oct 10, 2007 #4


    User Avatar
    Gold Member

    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.
  6. Oct 10, 2007 #5
    I don't know enough to argue against this concept of "frames of reference must be defined by matter". How would you pharse it?


    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?


  7. Oct 10, 2007 #6
    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..
  8. Oct 10, 2007 #7


    User Avatar
    Staff Emeritus
    Science Advisor

    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/

  9. Oct 10, 2007 #8
    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?

  10. Oct 10, 2007 #9


    User Avatar
    Staff Emeritus
    Science Advisor

    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.
  11. Oct 10, 2007 #10
    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)
    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.
    That is correct.
    For Newtonian mechanics that'd be true. For general relativity that is not true.
    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

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

    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.
    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

    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

    Last edited: Oct 10, 2007
  12. Oct 11, 2007 #11


    User Avatar
    Gold Member

    Bob, I think we've been told ... lots of good stuff above. I can recommend pmb's website.
  13. Oct 11, 2007 #12


    Staff: Mentor

    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.
  14. Oct 11, 2007 #13
    Thank you Mentz114. That is very kind of you to say! :approve:

    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
    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

    In the February 17, 1921 issue of Nature Einstein wrote
    In your opinion what is Einstein trying to say here?

    Best regards

  15. Oct 11, 2007 #14


    User Avatar
    Gold Member

    Extracted from pmb's post above "February 17, 1921 issue of Nature Einstein wrote"
    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 ...
    Last edited: Oct 11, 2007
  16. Oct 12, 2007 #15


    User Avatar
    Staff Emeritus
    Science Advisor

    Most of it (Pete's website) is OK, but Pete has a few funny ideas that aren't quite mainstream.
  17. Oct 12, 2007 #16


    User Avatar
    Staff Emeritus
    Science Advisor

    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..
  18. Oct 12, 2007 #17
    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.

    Last edited: Oct 12, 2007
  19. Oct 13, 2007 #18


    User Avatar
    Staff Emeritus
    Science Advisor


    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).
  20. Oct 13, 2007 #19
    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
    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
    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. :biggrin:

    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.

    Last edited: Oct 13, 2007
  21. Oct 13, 2007 #20


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Is your "gravitational force" a 3-vector or a 4-vector quantity?
    Is it a coordinate-dependent quantity?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook