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giants86
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Are Lorentz transformations only work between inertial frames? if so, is there a simple counter-example e.g. for them not to work?
giants86 said:Are Lorentz transformations only work between inertial frames? if so, is there a simple counter-example e.g. for them not to work?
PAllen said:If you propose that you can use the Lorentz transform of a momentarily comoving inertial frame at each event of a non-inertial observer, you run into the problem that you assign two sets of coordinates to points of a region. Specifically, if you assume an observer moving in the +x direction, accelerating in the -x direction, then in a region on +x side of the point where direction of motion changes, you assign conflicting coordinates to the same event.
Demystifier said:Lorentz transformations can be generalized to coordinate transformations inherent to local observers in arbitrary motion:
http://arxiv.org/abs/gr-qc/9904078
Therefore, for a
small range of values of t′ , the transformations (6)-(7) can be approximated by the ordinary
Lorentz boosts (see (19)).
GrammawSally said:That's not a problem at all. The CADO reference frame specifies the current local time at, and the current distance to, any event in (assumed flat) spacetime, from the perspective of an arbitrarily accelerating observer at any instant in her life. That's ALL that is required of the CADO reference frame: the CADO frame is NOT a GR chart, and has no need to BE a GR chart. See, in particular, Section 9 of this webpage:
https://sites.google.com/site/cadoequation/cado-reference-frame
giants86 said:Let me clarify my question. I have two frames that are moving with the accelerations against an inertial frame, therefore one frame moves with a constant speed against another. Can I use Lorentz transformations between these two frames?
PAllen said:A non-inertial frame would be expected to represent world lines of various objects in the non-inertial frame. CADO does not attempt this at all, so it is not an answer to the OP question.
GrammawSally said:That is EXACTLY what the CADO reference frame does.
PAllen said:Please be aware that the views in this website are not accepted as valid by most relativity experts.
Underwood said:I don't think your right about no experts believing it. I saw a NOVA show not too long ago where the guy told about someone riding a bike around in a circle at a far away place, and how he says time here is moving lots of centuries back and forth. That sounds like the same thing CADO says.
PAllen said:No, it does not. A frame as defined by everyone except this author, must assign one label to one event, not 2 or more labels to the same event.
giants86 said:Are Lorentz transformations only work between inertial frames? if so, is there a simple counter-example e.g. for them not to work?
Nowadays the Fermi normal coordinates are usually - although improperly - called Fermi coordinates. In exper-
imental gravitation, Fermi normal coordinates are a powerful tool used to describe various experiments: since the
Fermi normal coordinates are Minkowskian to first order, the equations of physics in a Fermi normal frame are the
ones of special relativity, plus corrections of higher order in the Fermi normal coordinates, therefore accounting for
the gravitational field and its coupling to the inertial effects. Additionally, for small velocities v compared to light
velocity c, the Fermi normal coordinates can be assimilated to the zeroth order in (v/c) to classical Galilean coordi-
nates. They can be used to describe an apparatus in a “Newtonian” way (e.g. [1, 3, 8, 10]), or to interpret the outcome
of an experiment (e.g. [11] and comment [21], [5, 6, 15, 17]).
You cannot, but let me be more precise. Let S1 and S2 be the proper coordinates of two non-inertial observers, such that they move with a constant non-zero velocity with respect to each other, as seen either* by an inertial or an accelerated observer. Then the coordinate transformation from S1 to S2 is not a Lorentz transformation.giants86 said:Let me clarify my question. I have two frames that are moving with the accelerations against an inertial frame, therefore one frame moves with a constant speed against another. Can I use Lorentz transformations between these two frames?
Me too (or three).pervect said:I concur with PAllen.
bcrowell said:Getting back to non-crackpot science, I agree with PAllen's analysis in #16.
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Are Lorentz transformations only work between inertial frames? if so, is there a simple counter-example e.g. for them not to work?
If you take the result that MTW calcluates for "the frame of reference of an accelerated observer"... you'll find that Lorentz transforms do not work globally in this "frame".
/QUOTE]
phew! I was worried before I read your post since the first thing my simple mind thought about the OP was...[a counter example is] curved spacetime.
Lorentz transformations in non-inertial frames are mathematical equations that describe how the space and time coordinates of an event change when observed from different reference frames that are accelerating or rotating. They are a fundamental concept in Einstein's theory of special relativity.
Lorentz transformations are important because they allow us to understand how the laws of physics, particularly the laws of electromagnetism, behave in different reference frames. They also help us reconcile the differences between Newtonian mechanics and special relativity.
Lorentz transformations differ from Galilean transformations in that they take into account the effects of relativity, specifically the fact that the speed of light is constant for all observers. Galilean transformations only apply to non-accelerating frames of reference and do not take into account the effects of special relativity.
Lorentz transformations in non-inertial frames have applications in a wide range of fields, including particle physics, astrophysics, and engineering. They are used to understand and predict the behavior of particles moving at high speeds, as well as the effects of gravity and acceleration on light and other electromagnetic waves.
Yes, Lorentz transformations are reversible. This means that if you apply a Lorentz transformation to a set of coordinates to move from one reference frame to another, you can also use the inverse transformation to move back to the original reference frame. This property is important in maintaining the consistency of physical laws across different reference frames.