Preferred Frame Theory indistinguishable from SR
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From: Daryl McCullough on 25 Jun 2010 09:14 There is a variety of anti-relativity dissident that consists of people who accept length contraction and time dilation, but don't accept the relativity principle. They assume something along the lines of: There is a preferred frame, F, and there is an associated coordinate system such that 1. Light travels in straight lines at speed c, as measured in F's coordinate system. 2. An ideal clocks in motion relative to F has an elapsed time given by dT/dt = square-root(1-(v/c)^2), where t is the time coordinate of F's coordinate system, and v is the velocity of the clock, as measured in F's coordinate system, and T is the elapsed time on the clock. 3. An ideal meterstick in motion, with the stick aligned in the direction of its motion, will have a length given by L = square-root(1-(v/c)^2). I would think that anybody could see that rules 1-3 are consistent. You cannot deduce a contradiction from these rules. Note that the contradiction that so many anti-relativists think that they have found in SR, namely, mutual time dilation, is not present in these rules, because these rules only mention time dilation with respect to a specific, preferred frame. So there is no possibility of deriving a "twin paradox" that is a logical contradiction. Right? Well, all the weirdness of SR, including mutual time dilation and the relativity of simultaneity *follows* logically from principles 1-3! You can prove that if 1-3 are true in the preferred coordinate system, then they are *also* true as measured in any coordinate system that is related to the preferred coordinate system through the Lorentz transforms. There are two ways to go about seeing this. The first way is to start with 1-3, perform a Lorentz transform to get a new coordinate system, and then show that 1-3 still hold in this new coordinate system. The other way is to assume 1-3 and then show that for observers moving relative to the preferred frame, the natural way to go about setting up a coordinate system in their frame will result in a system related to the first through the Lorentz transforms, or rotations, or translations (or some combination of the three). Full SR (well, the part that is relevant for thought experiments involving trains, light signals, pole vaulters, twins in rockets, moving clocks, etc.) is *derivable* from 1-3. If 1-3 is consistent, then so is SR. If the theory of the preferred frame is consistent, then so is SR, since they are empirically indistinguishable theories. If you don't see any paradox from the theory of the preferred frame (which you don't, since there is none), then there is no paradox from Special Relativity. Note: 1-3 only captures the aspects of relativity that involve length, time and motion. Those things are called "kinematics". That's not all of relativity, because it doesn't have any *dynamics*. It doesn't say anything about forces, or about how electromagnetism affects charged particles, or vice-verse. However, for most thought experiments exploring SR, 1-3 is completely adequate. -- Daryl McCullough Ithaca, NY
From: kenseto on 25 Jun 2010 10:23 On Jun 25, 9:14 am, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: > There is a variety of anti-relativity dissident that consists of > people who accept length contraction and time dilation, but don't > accept the relativity principle. They assume something along the > lines of: > > There is a preferred frame, F, and there is an associated > coordinate system such that > > 1. Light travels in straight lines at speed c, as measured in F's > coordinate system. Yes as measured by the F clock and F meter stick. > 2. An ideal clocks in motion relative to F has an elapsed time > given by dT/dt = square-root(1-(v/c)^2), where t is the time > coordinate of F's coordinate system, and v is the velocity of > the clock, as measured in F's coordinate system, and T is the > elapsed time on the clock. Yes but this is true only in the F frame. In any inertial frame an observed clcok can run fast by a factor of gamma or it can run slow by a factor of 1/gamma. This means that SR is incomplete because it only incldues the possibility that all observed clocks are running slow. > 3. An ideal meterstick in motion, with the stick aligned in the > direction of its motion, will have a length given by > L = square-root(1-(v/c)^2). No...length contraction is not physical or material. However, the F frame predicts that a moving meter stick will have a light-path length of L = sqrt(1-v^2/c^2). An inertial observer must also include the possibility that a moving meter stickcan have light-path length of L = 1/sqrt(1-v^2/c^2) Ken Seto > > I would think that anybody could see that rules 1-3 are consistent. > You cannot deduce a contradiction from these rules. Note that the > contradiction that so many anti-relativists think that they have > found in SR, namely, mutual time dilation, is not present in these > rules, because these rules only mention time dilation with respect > to a specific, preferred frame. So there is no possibility of deriving > a "twin paradox" that is a logical contradiction. Right? > > Well, all the weirdness of SR, including mutual time dilation and > the relativity of simultaneity *follows* logically from principles > 1-3! You can prove that if 1-3 are true in the preferred coordinate > system, then they are *also* true as measured in any coordinate system > that is related to the preferred coordinate system through the > Lorentz transforms. > > There are two ways to go about seeing this. The first way is > to start with 1-3, perform a Lorentz transform to get a new > coordinate system, and then show that 1-3 still hold in this > new coordinate system. The other way is to assume 1-3 and > then show that for observers moving relative to the > preferred frame, the natural way to go about setting up > a coordinate system in their frame will result in a system > related to the first through the Lorentz transforms, or > rotations, or translations (or some combination of the three). > > Full SR (well, the part that is relevant for thought experiments > involving trains, light signals, pole vaulters, twins in rockets, > moving clocks, etc.) is *derivable* from 1-3. If 1-3 is consistent, > then so is SR. If the theory of the preferred frame is consistent, > then so is SR, since they are empirically indistinguishable theories. > If you don't see any paradox from the theory of the preferred frame > (which you don't, since there is none), then there is no paradox from > Special Relativity. > > Note: 1-3 only captures the aspects of relativity that involve > length, time and motion. Those things are called "kinematics". > That's not all of relativity, because it doesn't have > any *dynamics*. It doesn't say anything about forces, or about > how electromagnetism affects charged particles, or vice-verse. > However, for most thought experiments exploring SR, 1-3 is > completely adequate. > > -- > Daryl McCullough > Ithaca, NY
From: rotchm on 25 Jun 2010 10:36 <SNIP> > I would think that anybody could see that rules 1-3 are consistent. > You cannot deduce a contradiction from these rules. Note that the > contradiction that so many anti-relativists think that they have > found in SR, namely, mutual time dilation, is not present in these > rules, <SNIP> All that is well know; LET, as a preferred frame and SR have the same predictions for standard experiments. Most relativist, etherist and dissidents are oblivious to that fact.
From: Surfer on 25 Jun 2010 15:05 On 25 Jun 2010 06:14:55 -0700, stevendaryl3016(a)yahoo.com (Daryl McCullough) wrote: >There is a variety of anti-relativity dissident that consists of >people who accept length contraction and time dilation, but don't >accept the relativity principle. They assume something along the >lines of: > >There is a preferred frame, F, and there is an associated >coordinate system such that > >1. Light travels in straight lines at speed c, as measured in F's >coordinate system. >2. An ideal clocks in motion relative to F has an elapsed time >given by dT/dt = square-root(1-(v/c)^2), where t is the time >coordinate of F's coordinate system, and v is the velocity of >the clock, as measured in F's coordinate system, and T is the >elapsed time on the clock. >3. An ideal meterstick in motion, with the stick aligned in the >direction of its motion, will have a length given by >L = square-root(1-(v/c)^2). > >I would think that anybody could see that rules 1-3 are consistent. >You cannot deduce a contradiction from these rules. Note that the >contradiction that so many anti-relativists think that they have >found in SR, namely, mutual time dilation, is not present in these >rules, because these rules only mention time dilation with respect >to a specific, preferred frame. So there is no possibility of deriving >a "twin paradox" that is a logical contradiction. Right? > >Well, all the weirdness of SR, including mutual time dilation and >the relativity of simultaneity *follows* logically from principles >1-3! You can prove that if 1-3 are true in the preferred coordinate >system, then they are *also* true as measured in any coordinate system >that is related to the preferred coordinate system through the >Lorentz transforms. > >There are two ways to go about seeing this. The first way is >to start with 1-3, perform a Lorentz transform to get a new >coordinate system, and then show that 1-3 still hold in this >new coordinate system. The other way is to assume 1-3 and >then show that for observers moving relative to the >preferred frame, the natural way to go about setting up >a coordinate system in their frame will result in a system >related to the first through the Lorentz transforms, or >rotations, or translations (or some combination of the three). > >Full SR (well, the part that is relevant for thought experiments >involving trains, light signals, pole vaulters, twins in rockets, >moving clocks, etc.) is *derivable* from 1-3. If 1-3 is consistent, >then so is SR. If the theory of the preferred frame is consistent, >then so is SR, since they are empirically indistinguishable theories. >If you don't see any paradox from the theory of the preferred frame >(which you don't, since there is none), then there is no paradox from >Special Relativity. > I believe that is basically true, however a preferred frame theory allows derivation of a different formula for radar Doppler shift. The SR formula with c as the speed of light, V as the target velocity and Ft as the transmitted frequency, gives the shifted frequency Fr as: Fr = Ft (c+V)/(c-V) (1) However suppose a frame of reference is identified in which the one way speed of light is 'truely' isotropic, referred to below as the 'isotropic frame'. Suppose that relative to such a frame a radar system is moving with speed vi in the direction of a target, and that the target is moving towards the radar system with speed V relative to the radar system. (So vi, V and radar signals are collinear.) ------------ ------------ | Radar | ----------------c-vi------------>|Target | | System |<---------------c+vi------------ | | ------------- signal ----------- ---vi--> speeds <--V-- Radar system relative Target speed speed relative to radar relative to to isotropic system radar system frame To ensure consistent representation of distance and time, let time in the radar system frame be synchronized with time in the isotropic frame and let distance measurements be derived from the spatial coordinates of the isotropic frame. These conditions require the frames to be mapped to each other via Galilean transforms. Then in the frame of the radar system the transmitted signal will have a speed of c-vi and the reflected signal will have a speed of c+vi. Notes: 1) It would be usual to synchronize clocks in the frame of the radar system such that signal speeds in this frame APPEAR to be c in both directions. This would be consistent with mapping the frames to each other via Lorentz transforms. But doing so here would cause representation of signal propagation timing in the radar system frame to differ from that in the isotropic frame. That would prevent derivation of correct results. 2) The above speeds will give a calculated two way speed in the frame of the radar system of c (1 - vi^2/c^2) using the measures of length and time of the isotropic frame. This would convert to a value of c if converted to the measures of length and time that would apply in the radar system frame, if the mapping was via Lorentz transforms. So the way the Galilean transform is being used here does not conflict with observed constancy of the two way speed of light in inertial frames. In the radar system frame of reference, let the transmitted signal have frequency Ft, then the corresponding outgoing wavelength is, Lt = (c - vi)/Ft This signal will impinge on the target with period T = Lt/(c - vi + V) or frequency F = (c - vi +V )/Lt. The reflected signal has the same frequency, and so has wavelength Lr = (c + vi - V)/F, and is received by the radar system with frequency Fr = (c + vi)/Lr. Then overall we obtain, (c + vi) (c - vi + V) Fr = --------------- ---------------- Ft . (2) (c + vi - V) ( c - vi) This formula was derived using the measures of length and time of the isotropic frame, but since changing the measures at this point would change the denominators and numerators in equal proportion, such a change would not affect the ratio of Fr to Ft. So the formula can also be validly used with the measures that would normally apply in the radar system frame, that is, if the mapping between it and the isotropic frame had been performed with Lorentz transforms. When vi is zero the formula reduces to, Fr = (c+ V)/(c - V) Ft which is equivalent to the standard formula (1) above. But if the one way speed of light is truely isotropic only wrt to a preferred frame, then in general vi will not be zero and formulae (1) and (2) will give different results. This may be the case because use of (2) instead of (1) has been shown to allow resolution of the spacecraft earth flyby anomalies. Resolving Spacecraft Earth-Flyby Anomalies.... http://www.ptep-online.com/index_files/2008/PP-14-02.PDF
From: rotchm on 25 Jun 2010 16:56
> I believe that is basically true, however a preferred frame theory > allows derivation of a different formula for radar Doppler shift. Nope. It gives the formula as SR. |