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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?
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 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.
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)).
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
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?
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.
That is EXACTLY what the CADO reference frame does.
Please be aware that the views in this website are not accepted as valid by most relativity experts.
I dont 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.
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.
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.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).I concur with PAllen.
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.