What is the Lorentz transform formula about the Lorentz transform?

From the principle of invariance of the speed of light: DL=CDT, substitution: L 2=x 2+y 2+z 2 (icdt) 2=-(cdt) 2

That is, DX 2+DY 2+DZ 2+(ICDT) 2=0 is true in any inertial frame.

Define DS as a four-dimensional interval, DS 2=DX 2+DY2+DZ 2+(ICDT) 2 (1).

Then for the optical signal DS is always equal to 0, the principle of relativity requires that the form of equation (1) is unchanged under the coordinate transformation, so there is an invariant independent of the coordinate transformation in equation (1), and the principle of invariance of the speed of light requires that the optical signal DS is invariant under the coordinate transformation. Therefore, under the common constraints of the two principles, an important conclusion can be drawn: DS is an invariant under coordinate transformation.

The mathematical formula for the rotation transformation is: (keep the y, z axes still, rotate the x and ict axes).

x=xcosφ+(ict)sinφ

ict=-xsinφ+(ict)cosφ

y=y z=z

The above is what I found on the Internet, and it can be seen from your schematic diagram that the use of mathematical rotation transformation formula to convert x and ict can ensure that x 2 + (icdt) 2 does not change, that is, dx 2 + d (icdt) 2 = 0, so take the parameter to complete this change.

Which symbols, are they in the formula?

This involves a change in the coordinate system, x'is the next coordinate system, the angle should be the rotation angle of the coordinate system, v is the speed, c is the speed of light, and t is the time.

It's just that the coordinate system changes, x'is the next coordinate system, the angle should be the rotation angle of the coordinate system, v is the speed, c is the speed of light, t is the time, since x=x'y=y' indicates that the distance between them or the equivalent unit is certain, according to this idea to look at this question is OK!le?

Lorentz transform(Lorentz Transformation) isSpecial theory of relativityabout the differenceInertial framesThe basic relationship between the spatio-temporal coordinate transformations of physical events.

Let the two inertial frames be the s and the s frames, and their corresponding Cartesians.

The coordinate axes are parallel to each other, and the S system moves in the x direction with respect to the S system, and the velocity is v, and when t t 0, the coordinate origin of the s system and the s system coincide, then the Lorentz transformation of the event between the spatio-temporal coordinates of these two inertial frames is x x vt), y y, z z, t t vx c2), where (1 v2 c2) 1 2;c is the speed of light in a vacuum.

The laws of physics in different frames of inertia must remain unchanged in form under the Lorentz transformation.

The Lorentz transformation is a coordinate transformation between two inertial reference frames (s and swift splits) that move at a relatively uniform speed in special relativity, and is a physical quantity between different inertial reference frames by an observer.

The transformation relationship that is taken when the measurement is made is mathematically represented as a set of equations.

The Lorentz transform is named after its founder, the Dutch physicist H. Lorenz. The Lorentz transform was originally used to reconcile classical electrodynamics and Newtonian mechanics, which were established in the 19th century.

later became the basic system of equations in the special theory of relativity.

Lorentz transformBe the observer in the differentInertial frame of referenceThe transformation relationship between the physical quantities is mathematically represented as a set of equations. The Lorentz transform is due to its founder, the Dutch physicist Hendrik Lorenz.

And the name. The Lorentz transform was originally used to reconcile the contradictions between classical electrodynamics and Newtonian mechanics, which were established in the 19th century, and later became the special theory of relativity.

The basic system of equations. Positive slag.

Overview of the Lorentz Transform Formula:

Before the theory of relativity, Hendrik Lorentz started from the idea of the existence of an absolutely stationary aether and derived the Lorentz transform from the material process of contraction in the motion of objects. In Lorentz's theory, the quantities introduced by the transformation are only regarded as mathematical aids, and do not include a relativistic view of space-time.

Einstein. Unlike Lorenz, it is based on observed facts and is based on two basic principles: the principle of relativity and the principle of invariance of the speed of light.

Focusing on modifying the basic concepts of motion, time, space, etc., the Lorentz transform is re-derived and given a new physical content to the Lorentz transform.

In the special theory of relativity, the Lorentz transform is the most basic relation, and the kinematic conclusions and spatiotemporal properties of the special theory of relativity, such as the relativity of simultaneity, length contraction, time delay, velocity transformation formula, relativity theory, and Doppler effect.

and so on can be derived directly from the Lorentz transform.

Lorentz transformThe formula is a=dv dt, v=v0+ adt.

by Maxwell's equations.

Electromagnetic waves can be obtained.

The speed of light in a vacuum is a constant from the wave equation. According to the space-time view of classical mechanics, this conclusion should only be held in a specific inertial comic reference frame, which is the ether.

The measured speed of light in other frames of reference is the vector superposition of the speed of light in the ether and the speed of the observer in the frame of reference.

However, the 1887 Michelson-Morey experiment could not measure the speed of the Earth's motion relative to the aetheric frame of reference. In 1904, Lorenz proposed the Lorentz transform to explain the results of the Michaelson-Morey experiment.

According to his hypothesis, when the observer moves at a certain speed relative to the ether, the length of the length shrinks and impulses in the direction of motion, canceling out the difference in the speed of light in different directions, thus explaining the zero result of the Michelson-Morey experiment.

Origin of the Lorentz transform formula

Lorentz proposed that the Lorentz transform was based on the premise of the existence of the aether, which proved to be non-existent, and that the speed of light has the same value relative to any inertial frame of reference according to the principle of invariance of the speed of light.

Einstein. Based on this, the special theory of relativity is proposed.

In the special theory of relativity, space and time are not independent of each other, but a unified four-dimensional space-time whole, and the transformation relationship between different inertial frames of reference is consistent with the Lorentz transform in mathematical expression.

where x, y, z, and t are inertial coordinate systems, respectively.

coordinates and time, x'、y'、z'、t'They are inertial coordinate systems'coordinates and time. v is'The velocity of the coordinate system relative to the coordinate system, in the direction along the x-axis.

According to the principle of special relativity, it is only necessary to change v to -v,x in the Lorentz transform described above'、y'、z'、t'Swapping with x, y, z, and t respectively gives the inverse transformation of the Lorentz transform.

x=(x +ut) 1-u 2 c 2) t=(t +ux c 2) 1-u 2 c 2) or x = (x-ut) 1-u 2 c 2) t = (t-ux c 2) 1-u 2 c 2).

where u is the velocity of the s system relative to the s system.

Principle 1 The laws of physics are the same for any inertial frame, and the observer in the inertial frame cannot perceive the velocity of his own inertial frame.

Principle 2 The value of the speed of light in any inertial frame is always c

From the above principle, the Lorentz transform formula can be derived. Two important inferences can be derived from the Lorentz transform formula:

1 Slow Effect t=t0 (1-v 2 c 2)2 Shrinkage Effect Douye l=l0 (1-v 2 c 2) where v is the velocity of the object relative to the inertial observer.