Relativity postulates

Содержание и основные понятия

The laws of physics are the same in all inertial systems, and the speed of light in the vacuum is the same for all the inertial observers regardless of the movement of the source.
GEF · 11 grade
PIF · Baseline
Interactive model
inertial system
event
Sequence
space-time
01
The physical picture
What happens and what boundaries the model has.
Main message
The laws of physics are the same in all inertial systems, and the speed of light in the vacuum is the same for all the inertial observers regardless of the movement of the source.
The timing of remote events depends on the counting system.
Galileo's transformations are replaced by Lorenz's.
Causal events do not change order.
How to reason
First, name the system and the interaction, then select the values, and only then write down the law. The formula works within the model's assumptions.
02
Laws and values
Symbols should be read as a relationship of values, not as a recipe for substitution.
c
=
c
o
n
s
t
c=\mathrm{const}
c
=
const
Invariant of light speed
γ
=
1
1
−
v
2
/
c
2
\gamma=\frac{1}{\sqrt{1-v^2/c^2}}
γ
=
1
−
v
2
/
c
2
​
1
​
Lorenz factor
Review of the situation
Two synchronous events on the train may prove to be uneven for an observer on the platform.
04
Links and application
In the real world
Two synchronous events on the train may prove to be uneven for an observer on the platform.
Model verification
Compare the prediction with observation, evaluate the units, the order of magnitude and the influence of the factors not taken into account. Disparity does not always mean an error of law: often idealization is no longer sufficient.
C
What needs to be understood
Outcome 1
Explain the physical meaning of the topic "Postulats of Relativity" through the model, not just the formula.
Outcome 2
Distinguish and correctly use terms: inertial system, event, simultaneous.
Outcome 3
Indicate the conditions for the applicability of the law, verify units and limit cases.
T
Terms of the topic
The definition should indicate the physical meaning, not a substitute for a domestic synonym.
inertial system
The counting system in which the free body is resting or moving evenly and flatly.
event
A physical phenomenon that is localized in space and time.
Sequence
Convergence of the time coordinates of events in the selected countdown system; in the STO, the countdown depends on the system.
space-time
A single four-dimensional structure combining the spatial coordinates and time of the event.
F
Origin and conclusion of the formulas
The fundamental law cannot be "proven" by algebras: for each record, it is stated whether it is a definition, an experimental law, or a model effect.
c
=
c
o
n
s
t
c=\mathrm{const}
c
=
const
Postulate or Model
The speed of light.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
c
=
299
792
458
m
/
s
c=299\,792\,458\ \mathrm{m/s}
c
=
299
792
458
m/s
Experiments show the same speed of light in the vacuum, regardless of the movement of the source.
c
′
=
c
c'=c
c
′
=
c
Special relativity theory accepts: all inertial observers measure the same c.
x
2
+
y
2
+
z
2
−
c
2
t
2
=
i
n
v
a
r
i
a
n
t
x^2+y^2+z^2-c^2t^2=\mathrm{invariant}
x
2
+
y
2
+
z
2
−
c
2
t
2
=
invariant
This postulate is implemented by Lorenz's transformation, which preserves the light interval.
Conditions:
Light is distributed in a vacuum; measurements are made in inertial systems by local standard clocks and lines.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
γ
=
1
1
−
v
2
/
c
2
\gamma=\frac{1}{\sqrt{1-v^2/c^2}}
γ
=
1
−
v
2
/
c
2
​
1
​
model effect
Lorenza factor.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
x
2
−
c
2
t
2
=
x
′
2
−
c
2
t
′
2
x^2-c^2t^2=x'^2-c^2t'^2
x
2
−
c
2
t
2
=
x
′2
−
c
2
t
′2
The STO postulates require linear conversion of the coordinates, which preserves the space-time interval.
x
′
=
γ
(
x
−
v
t
)
,
t
′
=
γ
(
t
−
v
x
c
2
)
x'=\gamma(x-vt),\qquad t'=\gamma\left(t-\frac{vx}{c^2}\right)
x
′
=
γ
(
x
−
v
t
)
,
t
′
=
γ
(
t
−
c
2
vx
​
)
For systems with a relative v velocity, conversion takes the form of Lorenz.
γ
2
(
1
−
v
2
c
2
)
=
1
\gamma^2\left(1-\frac{v^2}{c^2}\right)=1
γ
2
(
1
−
c
2
v
2
​
)
=
1
The condition of the interval shall be determined by the factor Δ.
Conditions:
The relative speed of inertial systems satisfies 0 ≤ v < c.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
!
Model boundaries and typical errors
Error: Forget model condition
You can't move the formula to any situation just because the letters match. The key condition of this topic is that the timing of remote events depends on the counting system.
How to Check the Mind
Galileo's transformations are replaced by Lorenz's. Then check the unit, vector direction and result behavior at zero or very large parameter.
Σ
Conclusion on the topic
Relativity postulates
The laws of physics are the same in all inertial systems, and the speed of light in the vacuum is the same for all the inertial observers regardless of the movement of the source.
The timing of remote events depends on the counting system.
Galileo's transformations are replaced by Lorenz's.
Any numerical result shall be accompanied by a unit, a sign and an explanation of its physical meaning.
The content is consistent with the FRP on Physics of the OS/OSS 2025 and the subject matter of the current lines of the PNP: I. M. Peryškin and co-authors (7–9), G. J. Mäkishev and coauthors (10–11), and with the lines "Engineers of the Future" and V. A. Kasyanov. The original texts are not reproduced, the text of the textbooks is not reproduced.