Why the pythagoras theorem is used in the second equation?

  • Thread starter Thread starter Atran
  • Start date Start date
Atran
Messages
93
Reaction score
1
Hi,

I know that,

E1 = E0 + EK, and
E2 = (mc2)2 + (pc)2 = E02 + EK2, but
E0 + EK ≠ (E02 + EK2)1/2

Is one of them wrong?
Why the pythagoras theorem is used in the second equation?

Thanks.
 
Physics news on Phys.org
Atran said:
Hi,

I know that,

E = E0 + EK, and
E2 = (mc2)2 + (pc)2
Correct

Atran said:
... = E02 + EK2
Incorrect

E2 = E02 + 2 E0EK + EK2
 

Thread 'Describing the Big Bang'

I started reading a National Geographic article related to the Big Bang. It starts these statements: Gazing up at the stars at night, it’s easy to imagine that space goes on forever. But cosmologists know that the universe actually has limits. First, their best models indicate that space and time had a beginning, a subatomic point called a singularity. This point of intense heat and density rapidly ballooned outward. My first reaction was that this is a layman's approximation to...
View full post »
Thread 'Dirac's integral for the energy-momentum of the gravitational field'

Thread 'Dirac's integral for the energy-momentum of the gravitational field'

See Dirac's brief treatment of the energy-momentum pseudo-tensor in the attached picture. Dirac is presumably integrating eq. (31.2) over the 4D "hypercylinder" defined by ##T_1 \le x^0 \le T_2## and ##\mathbf{|x|} \le R##, where ##R## is sufficiently large to include all the matter-energy fields in the system. Then \begin{align} 0 &= \int_V \left[ ({t_\mu}^\nu + T_\mu^\nu)\sqrt{-g}\, \right]_{,\nu} d^4 x = \int_{\partial V} ({t_\mu}^\nu + T_\mu^\nu)\sqrt{-g} \, dS_\nu \nonumber\\ &= \left(...
View full post »

Thread 'A sufficient condition for integrability of equation ##\nabla g=0##'

In Philippe G. Ciarlet's book 'An introduction to differential geometry', He gives the integrability conditions of the differential equations like this: $$ \partial_{i} F_{lj}=L^p_{ij} F_{lp},\,\,\,F_{ij}(x_0)=F^0_{ij}. $$ The integrability conditions for the existence of a global solution ##F_{lj}## is: $$ R^i_{jkl}\equiv\partial_k L^i_{jl}-\partial_l L^i_{jk}+L^h_{jl} L^i_{hk}-L^h_{jk} L^i_{hl}=0 $$ Then from the equation: $$\nabla_b e_a= \Gamma^c_{ab} e_c$$ Using cartesian basis ## e_I...
View full post »

Similar threads

I What is Einstein's equation used for?
Replies
7
Views
2K
Find the change in the Kinetic energy of an Ideal Gas
Replies
39
Views
4K
I Noether's second theorem: two questions
Replies
7
Views
3K
Flux of Electric field through sphere
Replies
2
Views
2K
B Question about Morin's time dilation explanation
2
Replies
73
Views
5K
Calculating of currents in a circuit
Replies
2
Views
720
Length contraction and the speed of light
2
Replies
54
Views
6K
Muzzle Velocity by Analyzing Ballistic Pendulum
Replies
2
Views
2K
Calculating Work to Put Spacecraft in Orbit
Replies
17
Views
4K
Electric field vector equation: Finding the neutral point for two charges
Replies
35
Views
2K

Hot Threads

Recent Insights

Back
Top