Discussion in 'Physics & Math' started by Prosoothus, Mar 27, 2006.
That is sure swell of you, Dale. You really are a good ol' boy.
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Anyway I believe an absolute frame is needed in Physics.
Consider the Foucault pendulum and the gyroscope behavior that is related to the conservation of the angular momentum of the bodies. If there is no special absolute referential then we may wonder: related to what referential are the directions determined by these apparatus fixed?
You are correct in the sense that a special kind of frame is needed for measuring angular behavior and have that behavior obey conservation of angular momentum. This is of course a non-rotating, non-accelerating reference frame, aka an inertial reference frame.
Given any one inertial reference frame one can construct <i>all</i> of the inertial reference frames by rotating the frame by some constant angle about some constant axis and by adding a constant velocity affine transformation. The laws of physics will be equally valid in each and every one of these frames. Which one of this myriad of choices is the absolute frame?
How would an absolute frame be needed to explain a gyroscope? I don't get the idea you are trying to get across here. D_H is correct, any inertial frame will do.
Yes, and the problem is to determine when a referential don't rotates and don't accelerates, gyroscopes and pendulus can determine that. But pay attention in what you are saying: "This is of course a non-rotating, non-accelerating reference frame". Now, they don't rotate and not accelerate relative to what referential? A basic referential of reference must be taken to decide if accelerates or not or if rotates or not! This is would be called the Absolute Frame.
I believe that the Absolute Frame is related to the entire Universe. The absolute frame is then an inertial frame located at the center of mass of the Universe and with its axis pointing to some special directions in the Universe that are special because of some properties of the Universe we could not know yet! For example symetries the Universe can have on some properties like the distribution of its mass, distribution of the galaxies, but could be some yet unknown property of the Universe.
Any object can determine that. If it is not acted on by any forces* and it moves in a straight line at a constant velocity then the frame is inertial.
*Classical physics and GR disagree on wether or not gravity is a force, so they disagree about which frames are inertial. But once you pick either GR or classical gravity then you can fairly easily determine if any given frame is inertial or not since every single law of physics looks different in non-inertial frames than in inertial ones.
There's a subtle distinction here that I was made aware of only recently. The "constant velocity" condition really has nothing to do with whether or not a frame is inertial. In the twin paradox setup you have the twin who accelerates away from Earth and the twin who stays home. Each twin is entitled to say he is at rest. In the traveling twin's frame it is the Earth that accelerates.
The difference between the two motions is that one is inertial and the other is not. The traveling twin can tell that he is not inertial by doing exeriments on board the ship and finding that the laws of physics don't take their "textbook form".
But it is the symmetries of the laws of physics that determine the very properties of mass and their distribution. The "unknown property" you refer would not follow with an absolute frame unless that symmetry was broken. Can you quantify that?
Dalespam and DH,
Please tell me if I'm right on the following:
It seems to me that the behaviour of gyroscopes are different for Classical Physics and RT. In Classic Physics one every gyroscope has no rotational movement relative to any othe gyroscope while in RT each gyroscope follows the specific time-space coordinates and different gyroscopes located at different places can rotate relative to others if the time-space is different on each one. For example a gyroscope located near the sun will follow the time-space attached to it and another near Earth will follow Earth's time-space.
This is why the Gravity Probe-B sattelite was launched isn't it?
I haven't heard anything about Gravity Probe-B experiment. Does anyone know if some conclusion have been reached?
So in the twin's frame the earth is not acted on by any forces that could explain the change in velocity and yet its velocity changes. Similarly for any other inertially moving object analyzed in the twin's rest frame. Therefore the twin knows that his frame is non-inertial. I don't understand the distinction you are trying to make; it sounds like a distinction with no difference.
This is exactly what I meant by "every single law of physics looks different in non-inertial frames than in inertial ones".
Even if all the laws have symmetries some physical properties can decide. For example Gravitation is a symmetric law but the center of mass of the Universe is a property of the Universe. The inertial frames located at the center of mass of the Universe are special frames different from all the others. What I believe is that some other property of the Universe could exist and could decide for one of these at the center. I believe we don't know enough about the entire Universe to be able to define such property.
Then you don't believe in General Relativity, isn't it? In GR every law looks the same in whatever considered frame, inertial or not.
That was the point I was making about the difference between classical gravity and GR gravity. They disagree on which frames are inertial. However, once you pick a gravity model (assuming that classical gravity is a reasonable approximation for your situation so you can make a choice), then it is easy to determine which frames are inertial, and the laws governing the behavior of the gyroscope are the same.
As far as I know the gravity probe B data is still being analyzed.
Don't forget: Newton's laws don't hold in the traveling twin's frame. Also don't forget that acceleration is purely kinematic. The travelling twin assigns a displacement s<sup>μ</sup> to the Earth. No problem there, right? From this he can calculate the 4-velocity as follows:
Most people would agree with that much because the Earth is clearly moving with respect to the ship. Notice that v<sup>μ</sup> is still a 4-vector because I differentiated with respect to a scalar (proper time).
Well, there's nothing stopping me from doing this again to obtain the acceleration.
Clearly the second derivative of the displacement is nonzero. The displacement of the Earth relative to the ship is increasing at an increasing rate. I know that the statement "velocity is relative, but acceleration is absolute" is commonly thrown about, but it is wrong. If acceleration is absolute then it must be a Lorentz scalar. But it is clearly the case that acceleration is not a Lorentz scalar, but rather a 4-vector.
Here is the discussion that pointed out to me the difference between "accelerating" and "non-inertial". Relativity Quiz
My point is that there is no connection between the definitions of "non inertial" and "accelerating". If you want to answer the question, "Is frame O inertial?" then in general you shouldn't try to answer the question, "Is frame O accelerating relative to some other frame O'?" instead. Those two questions only have the same answer if O' is inertial.
I don't understand something.
You are talking about inertial frames within General Relativity?
This has no sense. In GR any possible referential is valid for all the laws of Physics. I mean All the laws of Physics are invariant on any possible frame of reference even in two that are accelerated from the other.
That why it was called General Relativity isn't it?
This is strange...
The experiment was annonced with years of anticipation and I believe many labs around the world would have everything ready to put the data into a computer and have results in minutes!
It seems he sees what I see and that is that emperical data only supports the accelerated frame as having velocity. For only such F=ma accelerated frames accumulate less time. Never the recipocal frame. So the earth frame did not accelerate away from the twin, nor achieve any velocity.
No, this is Special Relativity. As you noted GR doesn't make a distinction between inertial and non-inertial frames.
This statement is ill-defined without specifying a reference frame. The Earth frame did not accelerate nor achieve any velocity according to whom?
If it is the Earth frame, then the statement is true.
If it is the travelling twin's frame, then the statement is false.
Being a little picky, this still seems ill-defined. The 'travelling twin's frame' is travelling according to whom? The Earth frame. In the spaceship twin's frame, he is not travelling according to the old STR, the Earth is. So, wouldn't the 'Earth frame' and the 'travelling twin's frame' BOTH give preferential treatment to an Earth-based observer's viewpoint?
Now, if the spaceship twin determines that there are no forces acting on the Earth to explain Earth's change in velocity, then it seems logical for the twin to assume he is accelerating and not the Earth, correct?
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