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When a train is moving with respect to a stationary observer, he will measure an object on the train as shorter than an observer on the train would measure it.
However if he later climb onto the train and measure the object again he will find it longer than he measured it previously
a contradiction for a global observer (Gods eye view)
One can't say the object was really shorter.
What is a global observer?
An observer observing both observers from outside of time.
When a train is moving with respect to a stationary observer, he will measure an object on the train as shorter than an observer on the train would measure it. However if he later climb onto the train and measure the object again he will find it longer than he measured it previously: a contradiction for a global observer (Gods eye view). One can't say the object was really shorter.
a contradiction for a global observer (Gods eye view).
Length isn't a property of an object. Length is a property of the object AND the environment in which it is measured. Change the environment and the value of the length can change.
A rigid object has a proper length,
"Rigid bodies" are not a thing you can have in special relativity.
"Rigid bodies" are not a thing you can have in special relativity. A Rigid body is an idealisation used in Classical Mechanics but the concept of it is not consistent with special relativity.
The speed of sound in a rigid body would be infinite.
E.g. Simultaneity cannot be maintained in all frames of reference where there is some spatial seperation between the events. So, if a rod was "rigid" in one frame then all particles in it must have the same acceleration at the same time.
Switch to another frame and that acceleration loses its simultaneity and the body isn't "rigid" anymore.
You're absolutley right, talanum.
You can't say the object was really shorter because it assumes that length is a property that the object can have all on its own.
Again my point is not about idealized Born rigid objects, but rather about ordinary real objects where the two endpoints are effectively stationary relative to each other. Such objects have a proper length, which is a property of the object, not a frame dependent relation.
If you you don't think that is accurate then you don't think Special Relativity is accurate which, considering all of the rigorous testing SR has undergone, seems like you are on the wrong side of science.
You can choose exactly how you want to try and define a rigid body. That's what I was trying to say. You don't have to imagine it as a body where all parts accelerate together simultaneously - but you can. That is what a classical rigid body would do.
If you try to keep this characteristic then you sacrifice the constancy of length in the reference frame where the rod is stationary (exactly as you said).
Alternatively, you can consider it more in terms of a rigid motion, in this case the length of the rod is constant in the reference frame of the rod BUT you sacrifice the uniformity of acceleration of its parts (exactly as you said).
(I'm not going to add all the details about in which frame and where, the sentences are already too long). You seem to favour a definition based on the idea of a rigid motion.
Quote from: Halc on 11/05/2021 20:19:32Again my point is not about idealized Born rigid objects, but rather about ordinary real objects where the two endpoints are effectively stationary relative to each other. Such objects have a proper length, which is a property of the object, not a frame dependent relation. I'm not following this, which is probably my fault. "The two endpoints are stationary relative to each other" - so there is a frame of reference involved
it seems that Talanum thinks objects should just have a length. I was suggesting they don't have a unique length until we know something about the reference frames and motion.
By classic, you mean non-relativistic?
so discussing Newtonian rigid motion is off topic, no?
My example was simply the proper length of a train
I think I need a citation somewhere that this is a valid form of rigid motion
You use the word ‘sacrifice’
Not necessarily... (is a reference frame involved)
The unique proper length is a frame independent quantity and thus serves as the length property of the object. This is the length that Talanum probably means
Pauli wrote "the concept of a rigid body has no place in relativistic mechanics,”
while Panofsky and Phillips state that special relativity “precludes the existence of the ‘ideal rigid body’ .”
The idea of a rigid body is easily defined in Newton Mechanics.
However, the concept is not easily defined in SR and some of the properties that a rigid body has in Newton Mech. cannot be maintained.
If you do define a rigid body in SR as something where length between particles = constant
in a frame where the object is at rest
THEN acceleration of the object causes problems. As you mentioned previously, to allow for length contraction, there will be some inertial frames of reference where the back end has to accelerate more than the front end.
In such a frame of reference the object has clearly lost something that a rigid body in Newtonian mechanics would have had (the object looks like it is being compressed as time evolves, which wouldn't be allowed in Newtonian mechanics)
If you want to ensure that there is never an inertial reference frame where the object seems to be deformed
Another problem with such an object is that if you assume the body is rigid in this way then external forces applied to the front end must be instantly transmitted through the body to the back end in every reference frame.
(If it wasn't then the front and back end won't retain the same acceleration and the object should deform as time evolves). I believe this is where the common reference to "the speed of sound" comes in.
We aren't really interested in sound, it's just that in a real world object the forces between particles would be produced only by a small movement of one particle toward or away from another
This lead people like Pauli to believe that there wasn't any place for anything like a rigid body in SR.
Quote from: HalcMy example was simply the proper length of a train But someone mentioned rigid objects, not sure who and it was days ago.
Quote from: HalcI think I need a citation somewhere that this is a valid form of rigid motionSome citations were given in an earlier post.
Is Talanum willing to consider "proper length" as a property of the object? I'm only guessing but most people just want to consider length as something they can measure with a ruler.
I may have got this wrong but when people are questioning if length contraction can happen, then it seems unlikely they are considering length as "proper length".