OK, I understand the distinction you are making here. Two non-inertial frames could be obtained from one another with an inertial boost. They would both be accelerating, but they would both be moving with constant velocity wrt each other. However, I was not intending to compare two frames. I was talking strictly about the behavior of inertially moving objects as analyzed from a single reference frame. Wether or not the object is moving inertially can be determined completely independently of the frame by wether or not any forces are acting on it. Once that is determined then you only need to determine if the equation of motion for that object in a specific reference frame is a straight line, without reference to any other frame. I think we agreed to begin with, but I now understand the subtle distinction you are making between accelerating and non-inertial. -Dale
I admit freely that my understanding of GR and QM is very weak; I could easily be mistaken. However, my understanding is that GR still has inertial and non-inertial reference frames. For example, the rest frame of a satellite orbiting the earth is considered an inertial frame while the rest frame of a person standing on the surface of the earth is an accelerating reference frame. The laws of motion look different in the two frames because in the accelerated frame there is a "frame force", gravity, which appears to accelerate inertially moving projectiles. -Dale
Again, I could easily be mistaken, but as PM said earlier "It is the general theory of relativity, not the theory of general relativity". I am pretty certain that in GR the laws of physics are variant in, e.g. rotating reference frames where the speed of light is definitely not constant. I certianly may be wrong. -Dale
I agree. I don't know what the hold up is. I thought the people involved in such an expensive project would have known how they were going to analyze the data before they even launched the thing. -Dale
Not trying to argue, but wouldn't the distinction be whether or not applying the brakes changed the velocity of the car? If I am sitting in my car while it is at rest in my carport, applying the brakes has no effects, other than foot/brake pedal forces felt. Myself and the car are in an accelerated frame because of the acceleration due to Earth's gravity. However, if the car has accelerated gaining a relative velocity wrt the Earth's surface, then applying the brakes results in a change in relative velocity. If no forces are acting on the Earth's surface to cause it to accelerate, I can assume I am also in a non-inertial frame when, by applying the brakes, I change the relative velocity between the Earth's surface and my car. Is this wrong?
My point is that it does make sense to talk about accelerating to rest. When you apply the brakes you undergo an acceleration and you can end up with 0 velocity after that acceleration in a very reasonable reference frame that most everyone would agree on. So the mere fact that something accelerated does not imply that it ends with a non-zero velocity. -Dale
Dalespam, You can for example select a frame in a body you know is not affected by any force (an inertial frame) and study the behaviour of the object and can determine the kind of movement it has, inertial or not. I agree but this can only be done if you know at first, before the movement, all the forces that will act on the object. But I don't agree the laws could look different in different frames, even inertial from non-inertial. I have the first book of Einstein here and it says (is a spanish version so forgive me a bad traduction) : "We will understand as the principle of General Theory of Relativity the following assertion: All the bodies of reference K, K', etc, whatever could be its state of movement, are equivalent to the description of nature ( formulation of the general laws of nature)." After he states that this formulation must be done in another way since there are no rigid bodies in nature and finally state that the principle of GR must be formulated as: "All the gaussian coordinate systems are essentially equivalent for the formulation of the general laws of nature" Then in GR any law looks the same whatever the referential choosed! May be you are in front of a non-invariant formula... If so let me know! I have special interest in non invariant relations in Physics, do you know some?
A couple of very minor points. First, I don't think you need to know the future to do this kind of experiment. If it begins with inertial movement and then at some point a force does act on the object then you simply suspend the analysis during the application of the force. You must be able to determine wether or not forces are acting on it at any given moment, but not have some kind of pre-knowledge of it's future state. Second, if an object is not experiencing any force then it has inertial movement by definition, and its motion does not need to be studied to determine that. By analyzing its motion you can determine if the frame of analysis is inertial, but the object's motion is inertial by definition. -Dale
To everybody: I would like to know about recognized non-invariant laws in Physics. Please tell me if you know some.
Sorry, I was assuming that the language of the Twin Paradox was known to all. The "travelling twin" is a traveller with respect to the Earth-bound twin. And you are quite right to point out that the travelling twin doesn't go anywhere in his own frame. But you are not correct when you suggest that the Earth-based frame is given preferential treatment. In any analysis of the twin paradox, neither frame is treated as the "correct" frame. No, for two reasons. First, and most obviously, because the spaceship twin observes the Earth frame moving away at an increasing rate. Just on kinematic grounds he concludes that the Earth is accelerating away. And second, how would the twin on the rocket know he is accelerating? Mightn't he do some experiment to show that he is non-inertial? But if he did that, it would only show that he is non-inertial. It wouldn't show that he is accelerating in some absolute sense. This is also made clear by the mathematical analysis that I presented. A 4-vector (such as velocity) doesn't become a Lorentz scalar just by differentiating with resepect to a scalar.
That's not what I was saying. I was saying that an inertial frame O could be correctly said to be accelerating by some frame O', as long as the displacement of O with respect to O' has a nonzero second derivative with respect to time. In short: Accelerating is not the same as non-inertial, and not-accelerating is not the same as inertial. It all depends on the observer making the judgment.
Of course I know the language of the twin paradox. I didn't state the Earth-bound twin's frame was the 'correct' frame, I said that the wording of the twin paradox gave preferential treatment to the Earth frame of reference. Why would it be incorrect to assume the observer was located on the spaceship? In that case, the travelling twin would be the Earth-based twin. Can you work the paradox from the spaceship twin's reference frame in which the Earth accelerates away from spaceship frame, then the Earth reverses its acceleration to join the spaceship twin in his frame of reference? Of course you can, but the Earth-based twin will be the younger of the two if it is worked from the spaceship twin's perspective. I abmit it seems like an impossible task to determine which frame has actually accelerated by mathematical analysis. But if the frame observers are allowed to look out a window to view the other frame, it is easy to determine which frame is accelerating away due to mechanical acceleration. Simply place a hourglass full of sand in each frame. If the spaceship is accelerating away from the Earth, the sand will fall toward the Earth in both frames. If the Earth were accelerating away from the spaceship, the sand in the hourglass on Earth would cease to flow assuming a 1g acceleration, or fall toward the spaceship if the acceleration were more than 1g. By looking at hourglasses in both frames, it is easy to determine which has had a change in acceleration.
OK, the inverse (converse?) of what I was saying. Both are correct. In your example O is inertial yet it is accelerating wrt O', in my example O was not inertial yet it was not accelerating wrt O'. Inertial is a description of the physics and accelerating is a description of the coordinates. In any case, since inertial is a description of the physics you cannot determine the inertial-ness of a reference frame without some physics experiment. In other words, if you just have two frames that are not accelerating wrt each other you cannot know if they are inertial or not. If you have some physics, like the earth accelerating without a corresponding force, then you do not need a second reference frame in order to determine if a frame is inertial. -Dale
While I have become accustomed to members here either ignoring me or attacking my post, I just want to point out that you have invoked my arguement that the frame which will be affected is the one which experiences F = ma. The other frame based on nothing but relative velocities and observation that does not experience F = ma is not affected. That is what emperical data supports, not the reciprocity predicted by SR.
You're missing the point. It IS known that the traveling twin IS accelerating away from the Earth. The point is that the traveling twin cannot know that by simply observing the Earth moving away. It is the same with the Earth bound twin, he knows the traveling twin is accelerating away but cannot tell from simply observing the rocket moving away.
I know that you weren't saying that there was one correct frame. I understood that you were saying that my wording gave that impression. I was merely stating that despite the wording, SR doesn't give preferential treatment to either observer. So for definiteness: Yes, either twin could be said to be travelling. It all depends on the point of view. More than "seems like", it is impossible. Acceleration is kinematic, and the kinematics of the situation are perfectly reciprocal. This is exactly what Dale and I were talking about, and it is exactly the subject of the other discussion I liked him to. When you look at the sand in the hourglass you are effectively doing an experiment to see if the laws of physics hold good in your frame. If you were on the ship you would see that they don't hold good. From this you could infer that you are noninertial. You could not infer that you are accelerating. If you are on board the ship, then your coordinate acceleration in your frame is zero.
This is gibberish. The expression "frame which will be affected" has no meaning at all, and the second paragraph opens with an ambiguous run-on sentence. As for empirical tests, twin paradox experiments have been done and unequivocally support SR. http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html#5. Twin paradox
Only for those blinded by rhetoric. Absolutely false. Emperical data has only supported a one way gamma function, never relative velocity including reciprocity.
This post is more in line with the thread's topic than with the last few posts, but I think this argument may be relevant... If there's an absolute reference frame, and the earth is moving at a speed comparable to c relative to that frame, wouldn't the light from torches and lightbulbs stream in a particular direction? If there is an absolute reference frame, what are the chances that the earth isn't moving relative to that frame? My first reaction would be 'very low', but if a frame not close to the absolute frame weren't conducive to life, then of course the anthropomorphic principle kicks in, i.e. we could only evolve because earth is close to this absolute reference frame...
