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captain
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i am confused what a lorentz transformation really is or is it just a transformation described by the boost transformation.
Lorentz Transformation Explained: What Is It?
- Thread starter captain
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In summary, a Lorentz transformation establishes a relationship between the space-time coordinates of the same event detected from two inertial reference frames in relative motion. This transformation is an element of the Lorentz group and includes not only boost transformations, but also spatial rotations and possibly reflections. It is necessary for the relative motion to be along the x-axes with the origins coinciding at t = t' = 0 for the transformations to be valid. This scenario leads to the simplest shaped Lorentz transformations.
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bernhard.rothenstein
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A Lorentz transformation establishes a relationship between the space-time coordinates of the sameevent detected from two inertial reference frames in relative motion and in the standard arrangement and with well defined initial conditions. The two events (E(x,y,z,t) and E'(x',y',z',t') take place at the same point in space when the synchronized clocks (a la Einstein) of the two inertial frames, located at that point, read t and t'.captain said:
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neutrino
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[emphasis(underlined) mine]bernhard.rothenstein said:
Is that a necessary condition? (By "standard arrangement" I assume you are referring to the standard configuration of inertial coordinate systems.)
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bernhard.rothenstein
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neutrino said:
I assume the same thing as you do. Parallel axes, overlapped OX(O'X') axes, motion of I' relative to I in the positive direction of the overlapped axes, coincidence of the origins at the origin of time. I am not very familiar with the standard English terms.
Thanks for your question and help
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neutrino
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bernhard.rothenstein said:
But you still haven't answered my question.
Is it necessary for the relative motion be along the x-axes (y- and z-axes parallel) and the origins to coincide at t = t' =0 for the transformations to be valid?
I ask this because the OP didn't specifically mention
[tex]x' = \gamma\left(x - \beta ct)[/tex]
[tex]ct' = \gamma\left(ct - \beta x)[/tex]
(or its inverse).
- #6
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bernhard.rothenstein said:
A Lorentz transformation is simply an element of the Lorentz group, the group of the linear, homogenous and orthogonal transformations of the Minkowski space ([itex] \mathbb{M}_{4}=\left(\mathbb{R}^{4},\eta\right) [/itex]), group shown to be isomorphic to [itex]O(1,3,\mathbb{R}) [/itex]. That's the mathematical definition.
The physical one is contained in your post: <<A Lorentz transformation establishes a relationship between the space-time coordinates of the same event detected from two inertial reference frames in relative motion>>.
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The Lorentz Transformations include more than the boost transformations... spatial rotations [and possibly reflections] are included.
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bernhard.rothenstein
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The way in which you present the LT, they hold in the case when the I' frame where the event involved in the transformation is E'(x',y',t') moves with speed v in the positive direction of the overlapped OX(O'X') axes relative to the I frame where the same event is E(x,y,t) in a two space dimensions approach. You can easy test the condition x'=0 for t=0 and x=0. You can add y=y'=0. That is the scenario that leads to the simplest shaped LT. Further questions?neutrino said:But you still haven't answered my question.
Is it necessary for the relative motion be along the x-axes (y- and z-axes parallel) and the origins to coincide at t = t' =0 for the transformations to be valid?
I ask this because the OP didn't specifically mention
[tex]x' = \gamma\left(x - \beta ct)[/tex]
[tex]ct' = \gamma\left(ct - \beta x)[/tex]
(or its inverse).
FAQ: Lorentz Transformation Explained: What Is It?
What is Lorentz Transformation?
Lorentz Transformation is a mathematical concept that describes how space and time coordinates change between two reference frames that are moving relative to each other at constant velocity. It was first introduced by Hendrik Lorentz in the late 19th century and later refined by Albert Einstein in his theory of special relativity.
Why is Lorentz Transformation important?
Lorentz Transformation is important because it helps us understand the effects of motion on space and time. It is a fundamental concept in the theory of special relativity and has many practical applications in modern physics, such as in the study of particle accelerators and the behavior of objects at high speeds.
How does Lorentz Transformation relate to time dilation and length contraction?
Lorentz Transformation is the mathematical framework that explains time dilation and length contraction, which are two of the key principles of special relativity. Time dilation refers to the phenomenon where time appears to pass slower for an observer moving at high speeds, while length contraction describes how objects appear shorter in the direction of motion for an observer in a different reference frame.
Can Lorentz Transformation be visualized?
Yes, Lorentz Transformation can be visualized using spacetime diagrams or graphs. These diagrams help to illustrate the relationships between space and time coordinates for two reference frames and how they change as their relative velocity changes.
Are there any limitations to Lorentz Transformation?
Lorentz Transformation is based on the assumption of constant velocity and therefore does not apply to non-inertial reference frames, such as those undergoing acceleration. It also does not account for the effects of gravity, which are described by the theory of general relativity.