The prevalent theory of Gravity is Einstein's Theory of General Relativity, in which gravity is not considered as force. So we explore few examples, others are welcome to add to the list. 1. Millikan oil drop experiment Without considering the drag aspect, in its simple form the electrostatic force is equated with the gravitational force qE = mg to get the e/m ratio. The point is Gravity is taken as force here ? 2. Archimedes' principle Well the upward thrust, Buoyancy force, is equated with the weight of the body, another suggestion that gravity is a force ? 3. Keplarian Orbits We all know that Centripetal Force = Gravitational attraction Force 4. The Simple Pendulum When we apply an electrostatic force on the bob the equation accordingly changes as mg-qE or mg+qE....Suggesting that gravity is a force ? 5. Work done = Force * Displacement (Scalar product) We do work against gravity, suggesting gravity is a force ? 6. An object dropped from height gains momentum, change in momentum means force, so gravity is a force ? 7. The gravity is the curvature of the spacetime, spacetime bends or warps..whatever. But a curved space will not cause any motion if some other action is not present. 8. Many more PS : All these are under Newtonian Mechanism, non relativistic approximation, suggesting that even in GR gravity is force ?
The God: It was my longstanding impression that in QM the gravitational action is treated as just another force/strain value to measure and calculate in the QM mathematical treatments. Just because the abstract GR maths also treats the gravitational action as a 'background state' action which is unidentified as force, it does not necessarily follow that gravitational action is not fundamentally a force in and of that 'background' which GR is abstractly overlaid on and left unexamined as to nature and mechanisms which couple to the test particle/energy feature affected and accelerated as if by some force or imbalance in forces. That is my understanding and impression for long time. I am open to anyone who can unambiguously explain the real space nature and mechanisms involved which make it 'not a force' in practice, however it may be currently interpreted and treated in the GR theory and QM maths. Thanks.
In GR it is unequivocally treated as no-force ? To the extent that the definition of straightline gets linked to it, infact the definition of straightline in 4D spacetime, thanks to GR, becomes non intuitive.
Origin; You do not understand the basis behind what you pluck and quote. Look at your above statement in the "straightline- Helix" thread. This is not a correct statement in totality. Everything or anything can move through space in a straightline even when acted upon by a force...is also equally good or equally bad. The above statement of yours is taken from Newtonian Concept of Inertia, which emphasises the state of motion unless acted upon by a force, you have plucked it out of context to give definition to straightline, which is bad. Straightline definition is well established and unambigious in Euclidean Geometry and it requires no reference to force. PS : If you intend to troll the thread like you did with that Helix thread (along with your pal Exchemists), then please stay away. If you wish to contribute positively, then most welcome.
Likewise, TheGod, you can't switch back and forth from GR and some other physical theory and make any sense. What Newton calls acceleration is deviation from the equation of a straight line in Euclidean space + time and that he defines as proportional to force. Here straight lines are trajectories through space and time. We have different definitions in different physical theories. But these theories made assumptions about geometry being very simple. In GR we have a different situation: So since the definition of straight line changes, so must the definition of force. Gravity is not a force in the language of General Relativity. I think it is very intuitive. Coordinates are unintuitive -- they are mathematical conveniences (fictions) used because we need to label events in space-time systematically and metrically. If space-time were Euclidean or Minkowski, we would still have choices of Cartesian, Cylindrical, Spherical, Oblate, etc, coordinate systems to describe the same universe. In such coordinate systems, how one describes vectors and derivatives necessarily changes. But no one thinks that just because we switch from Cartesian coordinates to Spherical coordinates that particles which move in parallel straight lines should now move in circles, because straight lines in space-time, trajectories of constant velocity, have a geometrical meaning invariant over which choice of coordinates one uses to represent them. But if the geometry of space-time is not Euclidean or Minkowski, then we need a new type of definition of straight line that makes sense. Like the meridians and the equator on a globe, we need the concept that straight lines have tangent vectors that are preserved by sliding in the direction they point. That intuitive logic lets us describe triangles on a globe with three right angles. And in purely geometric language we have \(\mathbf{\nabla_u u} = 0\) which is a very compact and non-scary definition of a straight line. Then coordinates come in to terrorize everyone because someone thinks physics should be about precisely predicting the details of phenomena observed in our universe.
If you look on the Einstein digital papers, you can find plenty of instances where Einstein refers to "gravitational force". So IMHO it isn't quite satisfactory to say gravity is not considered to be a force in GR, and a better statement might be in GR the force of gravity is not a force in the Newtonian sense. When you push a brick in space, you exert a force on it for some distance, you do work on it, and you add energy to it. In similar vein when you're standing on the surface of the Earth and you lift that brick, you exert a force on it for some distance, you do work on it, and you add energy to it. However when you drop that brick, the "force" of gravity doesn't do any work on the brick. It merely converts potential energy into kinetic energy - conservation of energy applies. When you dissipate the kinetic energy you're then left with a mass deficit, see the Wikipedia binding energy article. Then when you lift the brick back up, you exert a force on it for some distance, you do work on it, you add energy to it, so its mass increases. Interestingly, the same principle applies for electromagnetic force, in that the mass of the hydrogen atom is less than that of the free proton and the free electron. However geometry does not currently feature much in non-gravitational theories, so these similar phenomena are treated very differently at present.
I do not wish to be in cross with the definition of straightline in GR. My only assertion is that concepts of point, line, plane (without further qualifiers like curved line or curved plane) are well entrenched in people's mind as geometrical aspects. There was absolutly no need to call the Geodesics as Straightline when in principle in 3D space they are not as what we perceive. Havng different defintions of well established concept like straightline is bound to cause issues. I disagree with your above assertion in Newtonian Mechanics. I am sure in Newtonian Mechanics a particle can traverse straightline path even in presence of force. All high school kids do straightline motion physics involving acceleration etc. The second equation of motion x = ut+1/2at^2...certainly represent a straightline motion even with nonzero 'a'. Where is the issue ?
Thats the point of this thread. All th examples I gave in OP, need obfuscation free explanations with gravity as no-force.
Sure I do. I also understand this is another trolling thread. You are mixing Newtonian physics and general relativity to say physicist are confused and don't know what they are talking about. This is just showing your ignorance however. Take some classes, learn some physics.
I'll deal with this minor point so rpenner doesn't have to. What rpenner should have said is that Newtonian physics define a straight line with constant velocity as the path followed by a particle absent any force. A net force can certainly cause a particle to speed up or slow down without changing its direction of motion. But by definition, a particle moving at constant velocity (i.e. constant speed and direction) has no net force on it; that is the contrapositive form of Newton's second law of motion.
To quote Doc Brown: "You're not thinking four-dimensionally." I'm not talking about motion in a one direction of space, but space+time trajectories in one direction of space + time. Newton's First Law of motion has a fork in it if you use three-dimensional descriptions: at rest stays at rest and in motion stays in motion with constant velocity. That's like saying a thermos keeps hot things hot and cold things cold, as if it had two different jobs and somehow distinguished between them. Ha ha. But in the language of Newton's own calculus, there is a unification in 3-D Cartesian coordinates: \( \frac{d^2x}{dt^2} = \frac{d^2y}{dt^2} = \frac{d^2z}{dt^2} = 0\) which handles both cases. Or in 3-D vector language: \( \frac{d^2 \vec{x}}{dt^2} = 0\). Meanwhile time, in Newton's view, was absolute, so \(\frac{dt}{dt} = 1, \frac{d^2t}{dt^2} = 0\) seemed too trivial to contemplate. Likewise in 4-D Euclidean space + time, this is a straight line, because, if k is any quantity with units of speed, we can write \(ds = \sqrt{(k dt)^2 + (dx)^2 + (dy)^2 + (dz)^2}\) as an element of arc-length and show \( \frac{d^2 \vec{x}}{dt^2} = 0 \Rightarrow ds \propto dt\) so we have \(\frac{d^2x}{ds^2} = \frac{d^2y}{ds^2} = \frac{d^2z}{ds^2} = k \frac{d^2t}{ds^2}= 0\). Now arc-length in Euclidean space + time isn't used in physics because k is arbitrary, and nothing physical seems to depend on it and it isn't preserved by Galilean transforms. But it's just a hop-skip-and-jump to the Minkowski generalization of arc-length where \((ds)^2 = - (c dt)^2 + (dx)^2 + (dy)^2 + (dz)^2\) and \(\frac{d^2x}{d\lambda^2} = \frac{d^2y}{d\lambda^2} = \frac{d^2z}{d\lambda^2} = c \frac{d^2t}{d\lambda^2}= 0 \Rightarrow \frac{d^2s}{d\lambda^2} = 0\). So I was talking about straight lines in 4-D Euclidean space + time specifically because I wanted to compare and contrast trajectories with no forces in Newtonian mechanics, SR and GR in coordinate and geometric languages.
What principle? Simply put and as everyone is telling you, everything will tend to stay travelling in a straight line unless acted on by a force, [Newtonian] or affected by curved spacetime [GR] All straight lines are simply geodesics, but not all geodesics will be straight lines. Again, a geodesic simply relates to or denotes the shortest possible path between two points in curved spacetime.
This seems to be the objective of many god botherers and other anti science frauds. Simply put, but by whatever fabricated means they can imagine at their disposal, they will go out to try and deride science and the scientific method, particularly cosmology and GR: In doing this they can then pretend that the sciences in general are incapable of describing or explaining the Universe around us, and then use whatever spaghetti monsters, magical Unicorns or whatever deity they favour, to try and explain illogically and mythically what in their own minds, science can't. 'Tis a dream some have. Please Register or Log in to view the hidden image!
Muddled at best. Twin paradox demonstrates this is wrong. A geodesic is an extremal path through space-time.
Rpenner, I had already stated that I am talking about motion in space, while you are talking about 4D spacetime mapping. I am not in dispute with you on this. Please permit me to re state what you are saying, in simple language and simple maths..... 1. In GR we represent spacetime events, that is a mapping between spatial position and time. 2. In dressed down version let us convert 4D spacetime [3D space + time] as 2D (x,t). 3. Now if the acceleration term (second derivative of x wrt t), that is d2x/dt2 is a non zero constant, then simple maths results into a quadratic relationship between x and t. If this second derivative is time dependent then this relationship becomes a polynomial of degree 3 or more. 4. Thus for non zero acceleration (External force not being zero), the spacetime mapping of x and t, will be non linear, otherwise it is linear. The same can be extended to 3D Euclidean space + time, if acceleration is present the x and t mapping is non linear. So in presence of acceleleration if you talk about 3D Euclidean + t spacetime mapping, it is non-straightline but if you talk of motion through space then it is straightline. Two different perspectives, both correct. PS: What you are talking about is a plot between x and t, a particle even if it appears stationary in space, will be moving in a straightline in spacetime mapping as t is unstoppable. You are talking about maths, I am talking about reality, perception. Thanks anyway, that distinction is clear.
Reality? Please Register or Log in to view the hidden image! The reality of the situation is that everything will try and travel in a straight line unless acted on by a force [Newtonian] or unless influenced by curved/warped spacetime in GR. Gravity in Newtonian thinking is a force between two or more masses. Gravity in GR, is simply what is exhibited when spacetime is warped/curved/ twisted or waved in the presence of mass as shown by many experiments.
