Talk:Objectivity (frame invariance)

Older comments
In this set up the time t is independent of x. And so should be the definition of position vector x (one point in 3-d space. When we write x(t) we mean multitude - not one point) independent of time. That means that Q(t) can not depend on t because since x and x* are connected by Q(t) then one or the other: or x* is not definite; or x is not definite. All this is before we consieder a multitude of points like x(t). For instance a Galilean transformations is not allowed in this setup.

134.129.9.141 (talk) 18:06, 9 December 2008 (UTC)

Objectivity vs Isotropy
The main drawback of this arcticle is that it essentially just recites the only source - "Nonlinear solid mechanics" by Holzapfel. Like in the book, it is not clear from the article, what is the difference between the conditions of objectivity and isotropy. It looks like objectivity $$Q \sigma Q^T= g(QF)$$ implies isotropy by simply introducing $$h(b)=h(FF^T)=g(F)$$, and hence $$Q \sigma Q^T= g(QF)=h(QFF^TQ^T)=h(QbQ^T)$$. However, it is clear that the objectivity (frame-indifference) and the isotropy (the intrinsic material property) are the different conditions. Thus, I suppose (not sure) that the assumption that the Cauchy stress is a function of the left Cauchy-Green (aka Finger) tensor, i.e. $$\sigma=h(b)$$, is the assumption of material isotropy its self. I suggest that a better qualified mathematician clarifies this in the article. — Preceding unsigned comment added by 163.1.81.118 (talk) 11:51, 3 September 2012 (UTC)
 * Indeed this article seems to expound a very subjective view of the subject of objectivity. (Sorry I could not resist 8-) Seriously, it is not clear why displacement is "objective" while velocity is not. If the original and displaced points are recorded at different times t1 and t2 (the same two times by two different observers) then obviously each may get a different value for the distance.  This is a seems to be a real concern, for example when describing the motion of satellites and spaceships ("what was the total distance covered by Apollo 11?").  Conversely, if one observer knows the movement of the other, then he can properly translate the other guy's measurements of velocity and they will agree with his own.  So, is the "objectivity" as defined in this article really relevant to reality?
 * To quote Truesdell and Noll, "Physically, a frame of reference is a set of objects whose mutual distances change comparatively little in time ...". For satellites and spaceships  such a frame can be provided by distant stars. Bbanerje (talk) 04:04, 27 June 2013 (UTC)

Principle of Relativity
It appears to me that what is defined as "objectivity" here is just the principle of relativity, i.e. fundamental laws of physics should be coordinate independent. So the article is redundant. Also temperature is not a good example of a scalar field, because it is different for observers moving at different velocities. This is because temperature depends on the mean velocity of the particles in the medium (usually air). --5.61.187.205 (talk) 10:57, 17 January 2015 (UTC)

Conflicting interpretations
Bertram (2012, p. 156) disagrees with Holzapfel (2000, p. 191) about the objectivity of $$F$$ and $$P$$. It seems he considers their "two-pointness" irrelevant in this case: even if they transform like vectors, they are still tensors of order 2. I'll try to survey more authors to get a sense of what is conventional, but most likely some consideration should be made about each interpretation. Bad geometer (talk) 02:59, 15 January 2017 (UTC)

Multiple issues
Hello! I just added a "multiple issues" template to this page. Here's what I think needs to be addressed, and I'd like your help addressing it:

Rename page
So I was going to initially just move this page to Frame invariance or Frame indifference, because that seems to be what the article is actually about. However, as I was reading the article, it seems that the term "objective" in this context is actually the name of the mathematical property. Therefore, I propose that the article be moved to Objectivity (mathematical property), or one of the ones I put above..

Fix lead
Next, the lead says: "The concept of objectivity in science means that qualitative and quantitative descriptions of physical phenomena remain unchanged when the phenomena are observed under a variety of conditions.'" As per Objectivity (science), this does not seem to be true, hence why the lead currently has a citation needed tag. Therefore, I added a "seems to contradict..." tag. I think this should be able to be fixed just by cleaning up the lead of this article. The new lead also needs to do a better job of contextualizing the article. I propose something like "In mathematics and physics, a quantity is said to be objective, frame invariant, or frame indifferent if it does not change under an observer transformation. These quantities can be scalars, vectors, or tensors."