Energy and Pulse

Содержание и основные понятия

The power of the rest is connected to the mass, and the full energy includes movement. For a massless photon, the energy and impulse remain non-zero.
GEF · 11 grade
PIF · Baseline
Interactive model
The Energy of Peace
Relativist Pulse
Photon
Annuation
01
The physical picture
What happens and what boundaries the model has.
Main message
The power of the rest is connected to the mass, and the full energy includes movement. For a massless photon, the energy and impulse remain non-zero.
The mass of peace is the invariant of the particle.
Neither a massive body can be dispersed to the end power.
Reactions preserve the full energy and momentum of the system.
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.
E
0
=
m
c
2
E_0=mc^2
E
0
​
=
m
c
2
The Energy of Peace
E
2
=
p
2
c
2
+
m
2
c
4
E^2=p^2c^2+m^2c^4
E
2
=
p
2
c
2
+
m
2
c
4
energy and pulse
Review of the situation
When the electron and positron are annexed, the energy of the rest becomes that of the photons with the momentum being maintained.
04
Links and application
In the real world
When the electron and positron are annexed, the energy of the rest becomes that of the photons with the momentum being maintained.
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 "energy and impulse" through the model, not just the formula.
Outcome 2
Clear and correctly use terms: rest energy, relativist impulse, photon.
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.
The Energy of Peace
Body energy or particles in the rest system equal to mc2.
Relativist Pulse
Particle pulse p = .mv aligned with the laws of preservation in special relativity theory.
Photon
Quantity of electromagnetic field with energy h and pulse h/.
Annuation
Conversion of particles and antiparticles into other particles with energy, impulse and charge.
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.
E
0
=
m
c
2
E_0=mc^2
E
0
​
=
m
c
2
model effect
The power of peace.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
E
2
=
p
2
c
2
+
m
2
c
4
E^2=p^2c^2+m^2c^4
E
2
=
p
2
c
2
+
m
2
c
4
Relativist dynamics bind full energy, impulse, and invariant mass.
p
=
0
p=0
p
=
0
In the particle rest system, its pulse is zero.
E
0
2
=
m
2
c
4
⇒
E
0
=
m
c
2
E_0^2=m^2c^4\quad\Rightarrow\quad E_0=mc^2
E
0
2
​
=
m
2
c
4
⇒
E
0
​
=
m
c
2
The positive root gives its own energy to the particle.
Conditions:
Free body or particle with an invariant mass m in its own counting system; E0 includes the internal energy of the system.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
E
2
=
p
2
c
2
+
m
2
c
4
E^2=p^2c^2+m^2c^4
E
2
=
p
2
c
2
+
m
2
c
4
model effect
Power and impulse.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
E
=
γ
m
c
2
,
p
=
γ
m
v
E=\gamma mc^2,\qquad p=\gamma mv
E
=
γm
c
2
,
p
=
γm
v
The relativist energy and impulse of the moving mass particle contain one Lorenz factor.
E
2
−
p
2
c
2
=
γ
2
m
2
c
4
(
1
−
v
2
c
2
)
E^2-p^2c^2=\gamma^2m^2c^4\left(1-\frac{v^2}{c^2}\right)
E
2
−
p
2
c
2
=
γ
2
m
2
c
4
(
1
−
c
2
v
2
​
)
The impulse square multiplied by c2 is deducted from the energy square.
γ
2
(
1
−
v
2
/
c
2
)
=
1
⇒
E
2
=
p
2
c
2
+
m
2
c
4
\gamma^2(1-v^2/c^2)=1\quad\Rightarrow\quad E^2=p^2c^2+m^2c^4
γ
2
(
1
−
v
2
/
c
2
)
=
1
⇒
E
2
=
p
2
c
2
+
m
2
c
4
It's the same thing as the "C" that eliminates speed and gives you an invariant ratio.
Conditions:
Free particle with invariant mass m and pulse p in special relativity theory; positive branch of energy.
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
The key condition of this subject is that the mass of rest is the invariant of the particle.
How to Check the Mind
Neither the mass body can be dispersed to the final energy. Then check the units, vector direction, and behaviour of the result at zero or very large parameter.
Σ
Conclusion on the topic
Energy and Pulse
The power of the rest is connected to the mass, and the full energy includes movement. For a massless photon, the energy and impulse remain non-zero.
The mass of peace is the invariant of the particle.
Neither a massive body can be dispersed to the end power.
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.