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bernhard.rothenstein
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Please let me know when do we say that a physical quantity is observable. Is the answer related to clock synchronization?. If possible do not involve quantum physics.
Makep said:What quantity are you thinking about? An event or energy or mass or what?
HallsofIvy said:The only place I have ever seen "observable" used is in Quantum Physics!
On further thought I would be reluctant to describe as "observable" or "measurable" something that you calculate from more than one quantity you have measured. I think I'd reserve that name for raw measurements.bernhard.rothenstein said:Could we say that following Reichenbach’s relativity theory and deriving relativistic formulas which do not contain his anisotropy factor, they relate measurable physical quantities? Is that the situation in the case of (3) which has the same shape in all “theories” that correspond to different values of the anisotropy factor?
Practically speaking yes.bernhard.rothenstein said:Consider the "radar echo" experiment in which a stationary source emits at a time t(e) a light signal toward a moving mirror which reflects it back being received at the location of the source at a time t(r). If the mirror moves with speed V and the time intervals dt(e) and dt(r) are measured using the same clock then
dt(r)=dt(e)[(1+V/c)/(1-V/c) (1)
The derivation of (1) is clock synchronization free.
There are other effects which relate the same physical quantities via the square root of [(1+V/c)/(1-V/c)] (Doppler shift, Radar detection of moving rods). Is it correct to say that they are synchronization free (measurable).
Thanks for your answer.
dte and dtr are "measurable" but V is not. V is coordinate velocity, i.e. coordinate distance divided by coordinate time. Coordinate time certainly does depend on synchronisation, so any formula involving V is synchronisation-dependent.bernhard.rothenstein said:Consider the "radar echo" experiment in which a stationary source emits at a time t(e) a light signal toward a moving mirror which reflects it back being received at the location of the source at a time t(r). If the mirror moves with speed V and the time intervals dt(e) and dt(r) are measured using the same clock then
dt(r)=dt(e)[(1+V/c)/(1-V/c) (1)
The derivation of (1) is clock synchronization free.
There are other effects which relate the same physical quantities via the square root of [(1+V/c)/(1-V/c)] (Doppler shift, Radar detection of moving rods). Is it correct to say that they are synchronization free (measurable).
Thanks for your answer.
DrGreg said:On further thought I would be reluctant to describe as "observable" or "measurable" something that you calculate from more than one quantity you have measured. I think I'd reserve that name for raw measurements.
In your case, quantities that are independent of Reichenbach's [itex]\epsilon[/itex] factor could be described as "independent of synchronisation" or "sychronisation-free" or something like that. Ultimately, whatever terminology you use, you need to explain it clearly to your reader.
1. I'm not aware of any official name. I'd just say "synchronisation-dependent" or maybe even "convention-dependent". I think maybe some authors might say "conventional" but I think that's a confusing word to use in this context.bernhard.rothenstein said:Thank you.
1. Please tell me which is the best name for epsilon dependent transformation equations.
2. All theories that result from different values of the synchrony parameter epsilon lead to the same transformation equation for the space coordinates
x'=g(x-Vt)
which is epsilon independent. Is there an explanation for that. Is that the result of the fact that it is derived considering length contraction and time dilation two relativistic effects that compensate each other??
If we use the formula that accounts for the radar echo (police radar) in order to reckoned the speed V we speek about a calulated physical quantity? Does special relativity trust in calculated ohysical quantities?DrGreg said:dte and dtr are "measurable" but V is not. V is coordinate velocity, i.e. coordinate distance divided by coordinate time. Coordinate time certainly does depend on synchronisation, so any formula involving V is synchronisation-dependent.
Note however that the term
[tex]\sqrt{\frac{1 + V/c}{1 - V/c}}[/tex]
is the doppler factor which is synchronisation-independent and can be easily calculated from two "measurable" frequencies. So if you use the symbol k (e.g.) for this quantity and derive the relevant equations without reference to V, then you have a synchronisation-independent argument.
If you want to completely avoid synchronisation, instead of saying A moves relative to B "with velocity V" you can instead say "...with doppler shift k".
Note also that "rapidity" is just logek (or c loge k if you prefer it in units of velocity) and therefore also a synchronisation-independent quantity, so you could also say "...with rapidity [itex]\phi[/itex]".
Coordinate velocity V = dx/dt is synchronisation-dependent because coordinate time t is synchronisation-dependent. (If you like, V is a one-way speed, not a two-way speed; you already know that the one-way speed of light can differ from the two-way speed in non-standard coordinates.)bernhard.rothenstein said:If we use the formula that accounts for the radar echo (police radar) in order to reckoned the speed V we speek about a calulated physical quantity? Does special relativity trust in calculated ohysical quantities?
An observable physical quantity in relativity refers to a physical quantity that can be measured or observed in a given system or frame of reference. In relativity, these quantities can change depending on the observer's frame of reference and are described using mathematical equations.
In relativity, observable physical quantities can appear different in different frames of reference due to the effects of time dilation and length contraction. These effects are a result of the theory of special relativity, which states that the laws of physics are the same for all inertial observers.
Some examples of observable physical quantities in relativity include time, distance, mass, and energy. These quantities can be measured and observed in different frames of reference and can be affected by the relative motion between the observer and the system being observed.
The theory of general relativity states that gravity is a result of the curvature of spacetime. This means that the measurement of observable physical quantities, such as time and distance, can be affected by the presence of massive objects, as they can cause changes in the curvature of spacetime.
Understanding observable physical quantities in relativity is crucial in accurately describing and predicting the behavior of objects and systems at high speeds or in the presence of strong gravitational fields. It also allows for the development of technologies, such as GPS, that rely on precise measurements of time and distance in different frames of reference.