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Can light photons be considered as a privileged inertial frame?
Ibix said:As far as I can tell, your last post simply restates your first post, but in Portuguese. The answer is the same. Please note that you are expected to post in English in this forum. While many of us speak more than one language, English is the one we have in common.
kent davidge said:Portuguese:
Suponha que você ficou sabendo, de algum jeito, que um referencial ##A## é inercial. Se outro referencial ##B## for inercial, então os dois referenciais podem ser conectados por uma transformada de Lorentz. Mas um raio de luz viaja sempre com a mesma velocidade (c) com respeito a um referencial inercial, desde que não haja matéria interagindo com ele. O fator de Lorentz, ##\gamma = 1 / \sqrt{1 - v^2 / c^2}##, tende para o infinito quando ##v \longrightarrow c##. Logo, não é possível fazer a transformação. Então um referencial viajando a velocidade da Luz não é inercial.
English:
Suppose we learned by whatever means that a reference frame ##A## is inertial. If another reference frame ##B## is inertial, then the two frames can be related through a Lorentz transformation. But a light ray travels at speed ##c## w.r.t. the frame ##A## as long as there's no matter interacting with it. The Lorentz Gamma factor assumes the behaviour ##\gamma \longrightarrow \infty## when ##v \longrightarrow c##. Therefore, it's not possible to connect frames ##A## and ##B## through a Lorentz transformation. We conclude that a frame attached to light is not inertial.
stevendaryl said:It's interesting (I'm not sure if there is any significance to it) that in Rindler coordinates (the coordinate system that would be used by people on board a rocket that was undergoing constant acceleration), there is a height-dependent apparent gravitational field. This gravitational field tells you the proper acceleration necessary to remain at "rest" at that height. This apparent gravitational field is singular (goes to infinity) at height 0. The path of an object that is at constant height of zero is the path of a photon. So in terms of Rindler coordinates, the path of a photon is not inertial, but is, on the contrary, a path with infinite proper acceleration.
stevendaryl said:in terms of Rindler coordinates, the path of a photon is not inertial, but is, on the contrary, a path with infinite proper acceleration.
PeterDonis said:This is not correct. First, since Rindler coordinates are singular at ##x = 0##, you can't draw any conclusions from Rindler coordinates about any "path of a photon" at ##x = 0##. Second, if we ignore the coordinate singularity and take limits as ##x \rightarrow 0## (and ignore another fact about the surfaces of constant ##t## in Rindler coordinates--see below), the locus ##x = 0## in Rindler coordinates is not a single lightlike curve: it's a "V" shape made of two of them (the future and past Rindler horizons), and the "infinite proper acceleration" is just an artifact of the "kink" in the V at the origin (meaning the point where the two horizons cross). Third, the surfaces of constant ##t## in Rindler coordinates all meet at the origin, so in fact the "locus" ##x = 0## is not actually the future and past horizons, but just the single point at the origin, so that locus doesn't even describe a curve at all, just a single point.
But fourth, and most importantly, there are lots of lightlike curves in Rindler coordinates that pass through positive ##x## values, and it's simple to show that they are geodesics, so the paths of photons in the non-singular region of Rindler coordinates are inertial.
An inertial reference frame is a frame of reference in which Newton's first law of motion holds true. This means that an object at rest will remain at rest and an object in motion will continue to move at a constant velocity unless acted upon by an external force.
No, light photons cannot be a privileged frame of reference. According to Einstein's theory of relativity, the speed of light is constant in all inertial reference frames, meaning that no frame of reference can be considered "privileged" over another.
The concept of inertial reference frame is important in understanding the behavior of light photons. Since the speed of light is constant in all inertial reference frames, this means that the laws of physics, including the behavior of light, must be the same in all inertial frames.
The concept of inertial reference frame is important in physics because it allows us to describe the motion of objects and understand the laws of physics in a consistent and universal way. It also helps us to make accurate predictions and measurements in experiments.
The theory of relativity, specifically the principle of relativity and the constancy of the speed of light, has a significant impact on our understanding of inertial reference frames. It shows that all inertial frames are equivalent and that there is no privileged frame of reference. It also explains the behavior of objects moving at high speeds and allows us to make precise measurements and calculations in these situations.