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Reference frames

  1. Apr 14, 2003 #1
    Just a little question.

    I'm a little curious. In the classical sense, a reference frame in freefall would, of course, be said to accelerate. However, no forces are felt within a freefalling reference frame. Am I correct, then, in assuming a freefalling reference frame to be an inertial reference frame? Am I also correct in stating that a reference frame on the surface of Earth is an accelerating reference frame, since a force of gravity is felt toward the ground? (Even though in the classical sense, this reference frame is "at rest.")

    Don't limit this thread to an answer to my question. I would like a continuous discussion. Please? LOL.

    Good day everybody.
     
  2. jcsd
  3. Apr 14, 2003 #2
    Umm, really intersting point !
    Well i can't say lot, but i have an idea.
    When you are on earth, the frame of refference is said to be 'inertial' because the frame itself is not under any force (other than centrifugal, which we (somehow) omit).
    Now the gravitional force on objects inside this frame are not acting on the frame itself, but on the objects inside it, therefore you (as a person inside this frame) feel gravitional force.
    Since you feel gravitional force, you can also know that (for example) as you get higher the gravitional force will become smaller.
    But, if you are in frame of refference that is falling in the gravitional field of the earth, the frame itself has the force acting on it (meaning that if the origin point of the frame is moving under gravitional force), now here you will face a problem (and i think this is why it is not taken to be inertial).

    In this frame you do not feel any force acting on you (omit air resistance), now suppose there is a ball 1 KM above you, it is supposed to stay at this distance from you (since there is not force acting on it as you see it).
    But since the gravitional force acting on the ball will be smaller than this acting on you, then the ball will start to get farther and farther from you.
    So the 1st law of Newton doesn't hold righ here, therefore the frame of refference is NOT inertial :smile:.
     
  4. Apr 14, 2003 #3
    Just assume for a second gravity is not a force that acts between two bodies of mass,but only spacetime.since gravity curves spacetime,then also assume spacetime has energy that gravity attracts.so what if when a body of mass attracts this energy from spacetime,and pulls it towards it at light speed or more.then on a planet like the earth,what sends you into acceleration is your attraction to the spacetime energy that is in motion towards the earth.this could be why you feel no forces in freefall.so as the earth spins,the spacetime energy is being pulled in,while being forced into a spiral motion at the same time.looks like a galaxy in motion.since your in the planets gravitational field your body has the combined field of the entire planet in the field,as matter adds each others field to each other as a mass grows.this is why objects fall at the same rate,they attract spacetimes energy with the entire planets field by itself.so in freefall no force is felt because your in acceleration by spacetimes motion,so of course how would you be able to feel space moving!
     
    Last edited: Apr 14, 2003
  5. Apr 14, 2003 #4
    In the strictest sense of the definition, a frame in free-fall, that is if you know it is in free-fall, is not an inertial frame of refrense, also the earth is not an inertial frame of refrence, even though it is usually refered as one.
     
  6. Apr 14, 2003 #5
    MrCan,
    I'm curious as to what, exactly, they are then. If niether is inertial, are they both accelerating reference frames? If so, why?

    Technically, of course, no body anywhere in the universe is free of a gravitational force, so from that standpoint, if a freefalling object and a standing object are both accelerating reference frames, there is no such thing as an inertial reference frame.

    So I guess it's all more about approximation. Which is more inertial? Does that make sense? I'm just wondering in which case you apply SR, and in which you use GR. It seems to me that from the standing reference point, spacetime is curved. Yet spacetime must also be curved in freefall. So what is the difference? There has to be one, right?
     
  7. Apr 14, 2003 #6
    matter has no interaction with matter itself only spacetime.so matter is just a big energy magnet sucking energy toward it.spacetime curves from this pull on the energy.then the energy is converted into magnetism for TIME.and gravity between to suns or masses is the motion of spacetime moving around,though,and between both masses,the attraction between both masses and the motion of spacetime energy forces a object into motion.so the bigger the current of spacetime energy,times the gravitational attraction to spacetime give a mass a better chance of being forced into motion
     
  8. Apr 14, 2003 #7
    Any frame of reference with massive bodies affecting it is not truly an inertial frame of reference. There are tidal effects that tend to attenuate the observer frame, and radial effects causing differential increase of acceleration, nearest the mass (unless that frame is a singularity or no masses exist at all). Think of squaring the section in circular coordinates between r and r+dr, between [the] and [the]+d[the], where the mass is at the origin.
     
  9. Apr 14, 2003 #8
    Welcome Loren.

    I understand that now. However, there is no object in the universe that is truly free of gravitational pull or tidal forces. Earth orbits the sun, the sun orbits the center of the galaxy, the galaxy is being pulled on by other galaxies. So, in effect, a completely inertial reference frame doesn't actually exist. It is an idealization, an estimation of reality.

    Anyway, what I'm curious about, is what a gravitational field "looks like" from the perspectives of the two reference frames I gave. How is the standing frame's perception of spacetime different from the falling frame's perceptions? In both, it seems, spacetime must be curved. But something is different, because one frame feels the pull of gravity, and the other only feels a slight tidal pull stronger at the "bottom" of the frame than at the "top". (Reference frames don't have bottoms and tops but work with me.)

    Another question, what about a reference frame that is viewing Earth as it passes by it? What is the perception of spacetime there? (The spacetime surrounding Earth.)
     
  10. Apr 15, 2003 #9
    Anybody have an answer?
     
  11. Apr 16, 2003 #10

    pmb

    User Avatar

    re - "Just a little question. I'm a little curious. In the classical sense, a reference frame in freefall would, of course, be said to accelerate. However, no forces are felt within a freefalling reference frame. Am I correct, then, in assuming a freefalling reference frame to be an inertial reference frame?"


    Yes.


    re - "Am I also correct in stating that a reference frame on the surface of Earth is an accelerating reference frame, since a force of gravity is felt toward the ground? (Even though in the classical sense, this reference frame is "at rest.")"


    It is a non-inertial frame. However when saying whether a frame is accelerating you have to say accelerating with respect to what? With respect to Earth? No. With respect to an inertial frame which is located where you are? Yes. With respect to an inertial frame whis is at rest 10 light years from you? No.

    Pete

    Don't limit this thread to an answer to my question. I would like a continuous discussion. Please? LOL.

    Good day everybody.


    __________________
     
  12. Apr 16, 2003 #11

    drag

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    Science Advisor

    Greetings !

    Elementary dear CJames !
    You can not possibly discuss your reference frame
    as an observer standing on the Earth as that of
    a body that is not affected by any forces (an
    isolated system all by itself) IF you then
    intend to consider something that IS affected by
    the space-time curvature due to the presense of the
    Earth. You simply can't consider something in
    one reference frame in relation to another while
    the contents of each system is different. The
    trick is to define all the bodies and forces
    in ONE system that you need and THEN pick reference
    frames (easier not to make mistakes this way).

    Live long and prosper.
     
  13. Apr 16, 2003 #12
    Welcome drag,

    Actually, I don't think that is the case, since the measurements of the bodies and forces are different from the point of view of each reference frame. I don't believe, by relativity, you are allowed to define anything without first choosing a reference frame.

    I'm not entirely sure what you meant by this. I'm just trying to discuss the effects of spacetime within each reference frame, not necessarily use one reference frame to figure out what happens in another.

    Take care and have a great day.
     
  14. Apr 16, 2003 #13
    Thanks for your response pmb. Does anybody have anything to add to this? Is he right? (I rarely take one unknown source alone as a definite answer, nothing against you pmb.)
     
  15. Apr 16, 2003 #14
    pmb points out that acceleration is relative (as the elevator equivalence model was supposed to resolve). Free fall is accelerative relative to an outside gravitating body such as Earth. Such an "inertial" frame is not even approximately so classically for the vast majority of geodesics.

    Inertial frames, I believe, should be defined in terms of approaching the zero mass case. Whether one can determine this preferred inertial frame in spacetime is moot. (CMB?)

    Also, think of the Earth represented by an equivalent black hole gravitating mass, with enough charge to maintain avoidance of collapse of your Earth-bound frame. The nature of a massive body insures an eventually singular frame with the inertial approaching the noninertial (or vice versa).
     
  16. Apr 17, 2003 #15

    drag

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    Science Advisor

    Greetings !
    When you define ANY physical system you must
    consider ALL the bodies that are in it and
    ALL the qualities of these bodies. The values
    of the forces will of course be different.
    What could I POSSIBLY talk about ?!
    Of course that the space-time curvature due to
    the presense of the Earth is "felt" by bodies
    in both reference frames equally. But, you
    CAN'T just consider that the Earth exits in
    the falling reference frame - creating the
    space-time curvature and not existing in the
    standing reference frame in terms of supporing -
    pushing back on your standing body on its surface
    (Not considering the Earth that you're standing on !).

    If you consider the falling reference frame to be
    at rest then you will see the standing frame
    accelerating towards you. An object on the surface
    of the Earth is at rest relative to the Earth.

    Live long and prosper.
     
  17. Apr 18, 2003 #16
    Thanks for your contributions.

    LBooda:
    Thanks, I can understand that. I'm just trying to get a general idea of what's going on in GR. Like, from what reference frame is the general idea of a bowling ball curving a trampoline employed? (Yeah, I know, it's way more complicated than that.) Is that what spacetime looks like from the reference frame of Earth, the reference frame of an inertial reference frame stationary w/ respect to Earth, or the reference frame of anything within Earth's gravitational field regardless of motion?

    Hi drag,
    Oops! Sorry, I think we have some confusion here. I missed it in your first post. I didn't realize you were under the impression that I was saying Earth doesn't exist from a certain reference frame. Yes, of course Earth exists in both. My point was that in freefall, an accelerometer will yield no measurement, while on the surface of Earth it will find an acceleration of 1g.

    But now I can understand that if an elecator suddenly falls, it isn't exactly equivalent to if Earth's gravitational field had disappeared. There would be a measureable difference in force from the top to the bottom of the elevator. So it's not exactly equivalent unless you consider the elecator to be a point. My question now is what does this imply?
     
  18. Apr 18, 2003 #17

    pmb

    User Avatar

    CJames - Its easy to see the true meaning of gravity in General Relativity if you keep three things in mind

    (1) tidal forces and spacetime curvature are exactly the same things. The former in the language of Newtonian Physics and the later in the language of differential geometry.

    (2) The gravitational field can always be transformed away at least at one point in spacetime - physically that means that there always exists a frame of referance in which a point partilce (with no internal structure) is at rest at the origin.

    (3) Mass-energy is the source of gravity where "source of gravity" is to be interpreted in the same way one would interpret the statement "charge is the source of a EM field"


    re - "I was saying Earth doesn't exist from a certain reference frame. Yes, of course Earth exists in both. My point was that in freefall, an accelerometer will yield no measurement, while on the surface of Earth it will find an acceleration of 1g."


    This isn't quite correct. There is a distinction between gravity and spacetime curvature. The former can be measured with a gravity gradiometer and the later with an accelerometer. So using an accelerometer you can easily see that the gravitational field can be transformed away - just change to a frame of referance in free-fall. However the tidal forces can't be transformed away.


    If that seems confusing then think in terms of a two equal charges. At the point in space midway between the two charges the electric field is zero - but only at that one point. However that does not mean that the field is uniform anywhere and if you place charged body with a non-zero spatial extent then there will be stresses imposed in the body due to the electric field gradient.


    re - "So it's not exactly equivalent unless you consider the elecator to be a point. My question now is what does this imply?"

    The equivalence principle states that a *uniform* gravitational field is equivalent to a uniformly accelerating frame of referance. It does say that you can't tell the difference between gravity and an accelerating frame of referance. In fact Einstein was very clear on this point and stated this explicity.

    But what your example means is that spacetime curvature cannot be transformed away but that the gravitational field can. I.e. the gravitational force can always be transformed away but not gravitational tidal forces.

    Pete
     
  19. Apr 18, 2003 #18
    Thank you very much for your response pmb.

    So, for example, an elevator in freefall and one at "rest" will measure the exact same tidal force? Is that correct? Another question (and I appologize for asking so many). What if freefall is approaching c, will special relativity effects alter this measurement, thus altering the measurement of spacetime curvature?

    Does "uniform gravitational field" imply a gravitational field with no tidal forces?

    Cool.

    So what differences are there in rotating reference frames and accelerating reference frames, in terms of spacetime curvature, compared to the curvature created by a large mass? For example, in a rotating reference frame, as you climb toward the center you will begin to feel a force in the direction opposite (I'm faily sure) of the frame's rotation, something that obviously doesn't occur via a mass-generated field. (This is due, in the classical sense, to your inertia.)
     
  20. Apr 18, 2003 #19

    pmb

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    Hi CJames

    re - "Thank you very much for your response pmb." - You're most welcome!

    re - "So, for example, an elevator in freefall and one at "rest" will measure the exact same tidal force? Is that correct?"

    Depends on the velocity. Tidal forces are velocity dependant - at least in General Relativity. The effect is probably too small to measure in practice.

    re - "Another question (and I appologize for asking so many)."

    Nah! Don't think twice about asking anything. If I didn't want to post then I wouldn't be here. Rememeber the most important thing about learning - When you can explain it to someone else such that they understand then you can rest assured that you yourself understand it. So the more I respond the better I get! At least that's the idea! :-)

    I tutored all through collge and it showed me the benefits of explaing things.

    re - "What if freefall is approaching c, will special relativity effects alter this measurement, thus altering the measurement of spacetime curvature?"


    Consider what happens when a body is in free-fall and is heading to a black hole. *As measured from a remote observer* - The speed will increase at first. After a certain period the body will slow down and the speed will keep decreasing and never even get to the event horizon! The tidal forces will change as measured by an observer falling with the body. But this is wicked complicated to calculate and I've never gotten around to it ... yet! So I don't know the exact functional relation between the tidal forces and the speed of the body.

    re - "Does "uniform gravitational field" imply a gravitational field with no tidal forces?"

    Yes!

    See journal referances to this effect in my web site

    http://www.geocities.com/physics_world/uniform_field.htm

    re - "Cool." - Yep! My sentiments exactly.

    I thought I was nuts when I started to learn GR. People are always saying that gravity is a curvature in spacetime. Then they say that spacetime curvature is the same thing as tidal forces. Sorry. There's something wrong there. Well it turned out that the world was wrong and I was right! :-)

    Well not the entire world. Einstein agrees with me, or to me exact - I agree with Einstein since it was he who came up with all of this. And then there is Dr. John Stachel, Boston University, GR expert, former editor of the Einstein papers project, and world renoun Einstein historian. I correspond with him and he confirmed this. I happend to have caught Kip Thorne (Black Hole Guru) at a lecture at Harvard and he too confirmed this.

    I wrote a paper on this. See

    http://arxiv.org/abs/physics/0204044

    re - "So what differences are there in rotating reference frames and accelerating reference frames, in terms of spacetime curvature, compared to the curvature created by a large mass?"

    If you're in an inertial frame of referance far from any gravitating body then there is no gravitational field. The spacetime is flat. There is no way to curve spacetime by changing your frame of referance. So now change to a frame rotating with respect to the first. No spacetime curvature - but gravitational field - where "gravitational field" is understood to mean "gravitaitonal field". At least according to Einstein.

    re - "For example, in a rotating reference frame, as you climb toward the center you will begin to feel a force in the direction opposite (I'm faily sure) of the frame's rotation, something that obviously doesn't occur via a mass-generated field. (This is due, in the classical sense, to your inertia.)"

    Well I don't know about that. Perhaps there is a configuration of matter which will do that. I don't know. But don't think exclusively a gravitational field as a point with a 1/r^2 force law.

    In fact here's an example of a gravitational field generated by mass and yet there is no spacetime curvature. In fact here are three such examples


    www.geocities.com/physics_world/grav_cavity.htm
    www.geocities.com/physics_world/domain_wall.htm
    www.geocities.com/physics_world/cosmic_string.htm

    Pete
     
  21. Apr 19, 2003 #20
    Thanks alot and I will read those but first...I think I'm going to lose my mind! If spacetime curvature isn't equivalent to gravity...how does GR explain gravity? Don't tell me it doesn't! That would just ruin my whole day. I thought that GR described gravity purely in terms of geometry!?
     
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