Subject: |
Re: Ballistic Theory and the Sagnac Experiment |
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From: |
"Paul B. Andersen" |

Date: |
Wed, 22 Mar 2006 16:42:29 +0100 |

Newsgroups: |
sci.astro, sci.physics.relativity, sci.physics |

Henri Wilson wrote: On Mon, 20 Mar 2006 16:37:19 +0100, "Paul B. Andersen" <[email protected]> wrote:Henri Wilson wrote:On Fri, 17 Mar 2006 14:50:00 -0000, "George Dishman" <[email protected]> wrote:I have pointed out your mistake. I am a little reluctant to answer this posting. I am tempted to repeat that it is too stupid to respond to because you are quibbling about elementary mechanics. But I always end up with doing it anyway, so OK. What is YOUR definition of centrifugal force, Paul? I think your 'coriolis force' is my centrifugal force, and my 'coriolis force' is something you appear to know nothing about. Maybe you live to close to the N pole. There is but one definition of the centrifugal and Coriolis pseudo forces in _mechanics_. You can look it up in any text book. Or you can read my posting. But OK, let me repeat it. In a frame rotating with the angular velocity w (a vector) we have the following pseudo forces acting on a body with mass m which is moving with the velocity u (a vector) in the rotating frame: The centrifugal force: F = m* (w X (w X r)) where r is the radius vector. The magnitude of this force will be m*w^2*|r|, and its direction will always be radially outwards. Expressed with the speed v = |w|*|r| : F = m*v^2/|r| Note that the centrifugal force does NOT depend on the velocity u in the rotating frame. The Coriolis force: F = 2*m*(w X u) Note that the direction of this force always is in the plane of rotation, and is perpendicular to the velocity u. When u is tangential as in our case, the direction will be radial. This NG is a sci group. When you discuss in this group, you better use the normal accepted definitions of centrifugal and Coriolis, don't invent your own. Much of your confusion is probably due to the fact that you are not aware of which frame of reference you are using. You seem to operate with three different rotating frames: #1; the frame fixed to the carousel #2: the rotating frame where you are stationary when you are running in one direction #3: the rotating frame where you are stationary when you are running in the opposite direction. In this case it should be obvious that the "rotating frame" is the frame fixed to the carousel, and nothing else. Twirl an object around by hand, on a string. In the non-rotating frame, both the object and your hand rotate around the barycentre. A centripetal force is required to accelerate both your hand and the object towards the barycentre. These two CENTRIPETAL forces are opposite in direction and show up as a tension in the string = mv^2/r or MV^2/R. Centrifugal force does not stricty exist in this frame, although in most cases R is so small that even the best scientists and engineers (including myself) tend to call the object's 'pull' on the string a 'centrifugal force'. This is also convetient in the case of a balanced wheel where the barycentre is also the centre of rotation. The force the 'pull' is exerting on the object is acting towards the centre. It is a centripetal force. No other forces are acting on the object. In the rotating frame, The object does not move but the same tension remains in the string. How can this happen? It is due to the imaginary 'centrifugal forces', of course. But the centripetal force is the same. The centripetal force that is a real measureable force _which is independent of frames of references_. But this is trivial, Henri. The point you seem to miss completely is that when you are running around in your carousel, you are not stationary in the "rotating frame" which is fixed to the carousel. Your velocity in the rotating frame is tangential c. Coriolis force goes like this. In the above example, if the string is shortened, the object's rotation rate Right. The Coriolis force is always perpendicular to the velocity. So if the velocity of the object is radial, then the Coriolis force is tangential. But when you run around the carousel your velocity is tangential, so the Coriolis force is radial! I hope the students of Norway will benefit from your 'lesson'. Students in Norway learn this the first year. You obviously didn't. Or have you forgotten what you once knew? Read my analysis again, carefully. Remember that there is but one rotating frame, namly the one fixed to the carousel. And before you do, be sure to learn the correct definitions for the centrifugal and Coriolis forces. or: " 'centrifugal' often confused with 'centripetal'.... and they have the same values anyway." (In the example below the centripetal force is ten million times greater than the centrifugal force.) To be a valid analogy, you will have to run at a vastly higher speed than the peripheral velocity of the carousel. A 1 m radius I-FOG can detect the rotation of the Earth, that's a peripheral speed of 2.3*10^-13 c. But let us be generous, let the peripheral speed of the carousel be as high as a 10^-4 part of your speed. Let the radius of the carousel be r = 10m. Let the speed with which you run be c = 10 m/s. Let the peripheral velocity of the carousel be v = 0.001 m/s.Let your mass be m = 100kg. The centripetal forces the carousel exerts on your feet are now: Running with the rotation: The centripetal acceleration is (c+v)^2/r The force is Ff = m*(c+v)^2/r = 1000.20001 N Running in opposite direction: The centripetal acceleration is (c-v)^2/r The force is Fb = m*(c-v)^2/r = 999.80001 N Note that these are the actual centripetal forces acting on your feet. These forces could be measured and are obviously independent of which frame you use to calculate them in. Note that this suffice to address your problem. The centripetal forces are: Ff = m*(c+v)^2/r = 1000.20001 N Fb = m*(c-v)^2/r = 999.80001 N These forces do NOT depend on which frame of reference you use to calculate them in. The rest is only to demonstrate this fact: calculated in the rotating frame fixed to the carousel, the centripetal forces MUST remain the same. So what about the 'centrifugal' force? Let us calculate the forces in the rotating frame. The centripetal acceleration is c^2/r and the component of the centripetal force causing it is thus Fca = m*c^2/r = 1000 N The centrifugal force is m*v^2/r = 0.00001N, Since it proves you wrong, it is reasonable that you don't like it. :-) But I note with interest that you do not even try to refute neither my method nor my math. You should burn all the books in Norway, they are obviously wrong.In an I-FOG with a much smaller v/c ratio it would be even worse. The very idea is idiotic beyond belief.The fact is, I have proved my point. There are two separate effects. 1. The beam's 'energy centre' is thrown slightly off the 'fibre centre', thus The fact is, I have proven why this point of yours is idiotic beyond belief. I have shown that to be wrong.You have shown nothing whatsoever. Post the results of your experiment. If you do manage to prove it wrong then you have shown ballistic theory to be wrong.The light beams DO NOT experience the same 'centrifugal' forces in both directions. Right or wrong, George?Wrong. The centrifugal forces do not depend on velocity (neither speed nor direction), and it is tiny. It is however correct that the centripetal forces are very slightly different.That proves my point and I win the argument. I never claimed that htis was the major cause of the sagnac effect. The main reason it occurs is basically due to the fact that photons have AXES that don't like turning corners. The interfere strangely with photons whose axes point in different directions. When you realize that one of your "explanations" doesn't work, you always come up with an even more idiotic "explanation". :-) To explain the Sagnac, the light would have to slow down to a fraction of it original speed in an I-FOG. It doesn't. Face it, Henri. The Sagnac falsifies the ballistic theory. No way out.I suppose it proves LET too, eh Paul?...because that's what YOU use to explain the effect. Sagnac proves no theory, of course. But it is in accordance with ether theories as well as SR. The only theory it falsifies, is the ballsitic theory. Paul |

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