Relativist effects

Содержание и основные понятия

The time is measured by the clock moving with the process, and the length is measured in the object's rest system. In another system, the intervals are linked by Lorenz's factor.
GEF · 11 grade
PIF · Baseline
Interactive model
Your own time
own length
World Line
Twin paradox
01
The physical picture
What happens and what boundaries the model has.
Main message
The time is measured by the clock moving with the process, and the length is measured in the object's rest system. In another system, the intervals are linked by Lorenz's factor.
The moving clock is slower in relation to the reference time.
The longitudinal size of the moving object is decreasing.
The effects are mutual, but the comparison after acceleration requires an analysis of world lines.
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.
Δ
t
=
γ
Δ
t
0
\Delta t=\gamma\Delta t_0
Δ
t
=
γ
Δ
t
0
​
time deceleration
l
=
l
0
γ
l=\frac{l_0}{\gamma}
l
=
γ
l
0
​
​
length reduction
Review of the situation
Space muons reach the Earth's surface because of the relativist increase in life time in the Earth system.
04
Links and application
In the real world
Space muons reach the Earth's surface because of the relativist increase in life time in the Earth system.
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 "Relative effects" through the model, not just through the formula.
Outcome 2
To distinguish and correctly use terms: own time, own length, world line.
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.
Your own time
Time between events, measured by the hours that lie in relation to the process under way.
own length
The length of the object measured in the counting system where the object is resting.
World Line
A line in space-time representing the sequence of events of the object's motion.
Twin paradox
The effect of the FTA is to distinguish time between twins moving along different world lines.
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.
Δ
t
=
γ
Δ
t
0
\Delta t=\gamma\Delta t_0
Δ
t
=
γ
Δ
t
0
​
model effect
Slow down time.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
Δ
t
=
γ
(
Δ
t
′
+
v
Δ
x
′
c
2
)
\Delta t=\gamma\left(\Delta t'+\frac{v\Delta x'}{c^2}\right)
Δ
t
=
γ
(
Δ
t
′
+
c
2
v
Δ
x
′
​
)
Lorenz's reverse conversion links the time interval of the laboratory system to the time of the moving clock system.
Δ
x
′
=
0
,
Δ
t
′
=
Δ
t
0
\Delta x'=0,\qquad\Delta t'=\Delta t_0
Δ
x
′
=
0
,
Δ
t
′
=
Δ
t
0
​
Time itself is measured by the clocks around which both events occur at the same point.
Δ
t
=
γ
Δ
t
0
\Delta t=\gamma\Delta t_0
Δ
t
=
γ
Δ
t
0
​
After the setup, Δx.x = 0, the laboratory interval is equal to once more than its own.
Conditions:
Two events occur at one point of the moving clock system; systems are inertial and are moving evenly at v speed.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
l
=
l
0
γ
l=\frac{l_0}{\gamma}
l
=
γ
l
0
​
​
model effect
Shortening.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
l
0
=
Δ
x
′
l_0=\Delta x'
l
0
​
=
Δ
x
′
Its own length is measured in the rest system of the rod.
Δ
t
=
0
\Delta t=0
Δ
t
=
0
In a moving system, the coordinates of both ends need to be measured simultaneously.
Δ
x
′
=
γ
(
Δ
x
−
v
Δ
t
)
=
γ
l
⇒
l
=
l
0
γ
\Delta x'=\gamma(\Delta x-v\Delta t)=\gamma l\quad\Rightarrow\quad l=\frac{l_0}{\gamma}
Δ
x
′
=
γ
(
Δ
x
−
v
Δ
t
)
=
γ
l
⇒
l
=
γ
l
0
​
​
Lorenz's conversion at the same time reduces the longitudinal length.
Conditions:
The length is parallel to the relative speed of inertial systems; l0 is the length of the body rest system, 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 change the formula to any situation just because the letters match. The key condition of this topic is that the moving clocks go slower relative to the coordinate time.
How to Check the Mind
The longitudinal size of the moving object is reduced. Then check the units, vector direction, and the behaviour of the result at zero or very large parameter.
Σ
Conclusion on the topic
Relativist effects
The time is measured by the clock moving with the process, and the length is measured in the object's rest system. In another system, the intervals are linked by Lorenz's factor.
The moving clock is slower in relation to the reference time.
The longitudinal size of the moving object is decreasing.
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.