# What is Lorentz transform: Definition and 57 Discussions

In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation is then parameterized by the negative of this velocity. The transformations are named after the Dutch physicist Hendrik Lorentz.
The most common form of the transformation, parametrized by the real constant

v
,

{\displaystyle v,}
representing a velocity confined to the x-direction, is expressed as

t

=
γ

(

t

v
x

c

2

)

x

=
γ

(

x

v
t

)

y

=
y

z

=
z

{\displaystyle {\begin{aligned}t'&=\gamma \left(t-{\frac {vx}{c^{2}}}\right)\\x'&=\gamma \left(x-vt\right)\\y'&=y\\z'&=z\end{aligned}}}
where (t, x, y, z) and (t′, x′, y′, z′) are the coordinates of an event in two frames, where the primed frame is seen from the unprimed frame as moving with speed v along the x-axis, c is the speed of light, and

γ
=

(

1

v

2

c

2

)

1

{\displaystyle \gamma =\textstyle \left({\sqrt {1-{\frac {v^{2}}{c^{2}}}}}\right)^{-1}}
is the Lorentz factor. When speed v is much smaller than c, the Lorentz factor is negligibly different from 1, but as v approaches c,

γ

{\displaystyle \gamma }
grows without bound. The value of v must be smaller than c for the transformation to make sense.
Expressing the speed as

β
=

v
c

,

{\displaystyle \beta ={\frac {v}{c}},}
an equivalent form of the transformation is

c

t

=
γ

(

c
t

β
x

)

x

=
γ

(

x

β
c
t

)

y

=
y

z

=
z
.

{\displaystyle {\begin{aligned}ct'&=\gamma \left(ct-\beta x\right)\\x'&=\gamma \left(x-\beta ct\right)\\y'&=y\\z'&=z.\end{aligned}}}
Frames of reference can be divided into two groups: inertial (relative motion with constant velocity) and non-inertial (accelerating, moving in curved paths, rotational motion with constant angular velocity, etc.). The term "Lorentz transformations" only refers to transformations between inertial frames, usually in the context of special relativity.
In each reference frame, an observer can use a local coordinate system (usually Cartesian coordinates in this context) to measure lengths, and a clock to measure time intervals. An event is something that happens at a point in space at an instant of time, or more formally a point in spacetime. The transformations connect the space and time coordinates of an event as measured by an observer in each frame.They supersede the Galilean transformation of Newtonian physics, which assumes an absolute space and time (see Galilean relativity). The Galilean transformation is a good approximation only at relative speeds much less than the speed of light. Lorentz transformations have a number of unintuitive features that do not appear in Galilean transformations. For example, they reflect the fact that observers moving at different velocities may measure different distances, elapsed times, and even different orderings of events, but always such that the speed of light is the same in all inertial reference frames. The invariance of light speed is one of the postulates of special relativity.
Historically, the transformations were the result of attempts by Lorentz and others to explain how the speed of light was observed to be independent of the reference frame, and to understand the symmetries of the laws of electromagnetism. The Lorentz transformation is in accordance with Albert Einstein's special relativity, but was derived first.
The Lorentz transformation is a linear transformation. It may include a rotation of space; a rotation-free Lorentz transformation is called a Lorentz boost. In Minkowski space—the mathematical model of spacetime in special relativity—the Lorentz transformations preserve the spacetime interval between any two events. This property is the defining property of a Lorentz transformation. They describe only the transformations in which the spacetime event at the origin is left fixed. They can be considered as a hyperbolic rotation of Minkowski space. The more general set of transformations that also includes translations is known as the Poincaré group.

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1. ### I Why Do Some Events in My Lorentz Transformation Appear Incorrect?

Here is the space-time diagram of an observer: Here is the diagram as seen by an observer travelling from left to right: I have attempted to represent the axis system of the moving observer on the axis system of the stationary observer in the following diagram: Event D seems to lie in...
2. ### Galilean transform and Lorentz transform questions

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3. ### Lorentz transformation of multiple events into one frame of observation

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4. ### Question about the Lorentz transform

Image below. Is the Lorentz transform just switching between a stationary frame and a moving frame? I forgot to write Alice's frame but I assume that is obvious.

13. ### B Using Lorentz Transformations vs Time Dilation/Length Contraction

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14. ### Imaginary Transverse Space of Superluminal Lorentz Transform

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15. ### Assuming Lorentz transform is affine

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16. ### Can you use the Lorentz transform for a function of time?

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17. ### Lorentz scalars - transformation of a scalar field

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18. ### Consequences of space-/time-/light-like separations

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19. ### Relative Velocity in Lorentz Transform: Agree or Disagree?

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20. ### How To Understand This Lorentz Transform?

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22. ### Lorentz Transform on Covariant Vector (Lahiri QFT 1.5)

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23. ### Solving Lorentz Transform problem using only length contraction

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24. ### Determination of Lorentz transform from euclid geometry

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25. ### Lorentz Transform of Radial & Longitudinal Dependent Magnetic Field

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26. ### Detailed working out Lorentz contraction from the Lorentz transform

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27. ### Infinitesimal Lorentz transform and its inverse, tensors

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28. ### Wave equation invariance under Lorentz transform

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29. ### Lorentz transform low velocity limit

Why do we say that t'=t for Galilean transformation, when the low velocity limit of the Lorentz transformation is t'=t+vx/c2? If x is really big, then doesn't time cease to be absolute, no matter how small v/c is?
30. ### Confusion about Lorentz Transform

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39. ### Easy Lorentz Transform Problem

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44. ### S,S' in the Lorentz transform.

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45. ### Lorentz transform for momentum

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48. ### Lorentz Transform in Non-Minkowski Spaces

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