Rookie Energy Query: Mass Outflow in Supernovas

[mooneyes]

I am a little unsure about something, take this example for instance:

In a supernova event, a star ejects X amount of mass at a relativistic speed, say 0.5c. What's the total energy of this outflow in the reference frame in which the star's at rest.

Now would I be correct to assume that the energy outflow would be the same in all inertial reference frames?

Thanks.

 

[JesseM]

I am a little unsure about something, take this example for instance:

In a supernova event, a star ejects X amount of mass at a relativistic speed, say 0.5c. What's the total energy of this outflow in the reference frame in which the star's at rest.

In relativity total energy can be determined from either $$E = \frac{m_0 c^2}{\sqrt{1 - v^2/c^2}}$$ or the equivalent equation $$E^2 = m_0^2 c^4 + p^2 c^2$$ where m₀ is the rest mass and p is the relativistic momentum $$\frac{mv}{\sqrt{1 - v^2/c^2}}$$. So using the first equation, if m₀ = X and v = 0.5c, then the total energy would be 1.1547*X*c².

Now would I be correct to assume that the energy outflow would be the same in all inertial reference frames?

No, conservation of energy just means that in any given frame the total energy doesn't change with time, but the total energy (like the total momentum) is different in different frames. This is true in classical physics as well as relativity.

 

[mooneyes]

No, conservation of energy just means that in any given frame the total energy doesn't change with time, but the total energy (like the total momentum) is different in different frames. This is true in classical physics as well as relativity.

Ah, I see, so

E² - (Pc)² = constant

for any inertial frame, but the energy and momentum can be different!

 

[Mentz114]

I have a supplementary question : Is the divergence Lorentz invariant ? That would be the total amount of matter crossing a spherical shell around the star, integrated over some time period ( I think ).

 

[mooneyes]

It is indeed!

 

[Mentz114]

It is indeed!

Thanks. I suppose (naively ?) with the amount of matter being a scalar, that the velocity and time transformations cancel. I'll look it up.

 

[bcrowell]

The answer is no, even in Newtonian mechanics. Suppose I use my two hands to throw two masses m with velocities +v and -v. The total energy is mv^2. In a different frame, the total energy is not mv^2.