From Newsgroup: sci.physics.relativity

Den 06.01.2026 23:27, skrev Thomas 'PointedEars' Lahn:

Paul.B.Andersen wrote:

The mass of an objects is invariant,

It is _Lorentz_-invariant, NOT invariant /per se/.

and so is the energy content of the object.

No.

The E in the equation E = mc² is invariant,

This pop-cultural equation is *wrong*, as I have pointed out /ad nauseam/.>

which means that it is independent of the speed of the object.

/Ex falso quodlibet./

It makes no sense to call E = mc² "the *rest* energy of
_an object_ whose mass is m."

It *does*. That is what it *is*. "Rest energy" is the agreed physical/scientific term for that form of energy.

You are right, E₀ = mc² is called the "Rest energy" of
a body with mass m.
It is also called "the invariant energy" of a body with mass m.

Because the energy E₀ = mc² is invariant, the same in all
frames of reference, independent of the speed of the object.

That's why find the name "rest energy" rather misleading.


Above I was quoted to have said:
"The E in the equation E = mc² is invariant, which means
that it is independent of the speed of the object."

Your response was:
"This pop-cultural equation is *wrong*, as I have pointed out
/ad nauseam/.

Can you explain your response?

-----------------------------------
To give the context of discussion below:

One possible fission process is:

1n + U-235 → Ba-141 + Kr-92 + 3n

The atomic weight of these are:

Left side:
1n 1.008664 u
U-235 235.0439299 u
-------------------
236.0525939 u = 3.919748214E-25 kg

Right side:
Ba-141 140.914412 u
Kr-92 91.926156 u
3n 3.025992 u
---------------------
235.866560 u = 3.916659047E-25 kg

Lost mass: m = 0.1860339 u = 3.089167695E-28 kg

E = mc² ≈ 2.776404839E-11 J ≈ 174 MeV

Energy before fission:
Energy content of mass m₁: E = m₁c² = 3.522894007E-8 J

Energy after fission:
Energy content of mass m₂: E = m₁c²= 3.520117602E-8 J

The difference is ΔE = m₁c² - m₁c² = Δm⋅c² = 2.776404839E-11 J

The binding energy holding the nucleons together is
part of the energy content of the mass of the U-235 nucleus.
When the nucleus is split, the binding energy in the Ba-141
and Kr-92 nuclei will be ΔE less. The sum of the kinetic energy
of the two nuclei and 3 neutrons will be ΔE = 2.776404839E-11 J

You keep missing the point.

Which point am I missing?

I say that the mass Δm lost from the U-235 nucleus is converted
to kinetic energy of the two nuclei and 3 neutrons.

Which is simply the wrong idea.

What actually happens here is that rest energy is (partially) converted to other forms of energy. This is equivalent to a reduction in mass;

How is this different from what I said?

The "rest energy" of the U-238 nucleus is
E = m₁c² = 3.522894007E-8 J

The part of this energy ΔE = 3.089167695E-28 J
is converted to kinetic energy.

This is equivalent to a reduction in mass Δm = 3.089167695E-28 kg

The energy equivalent of the reduction of the mass
is Δm⋅c² = 2.776404839E-11 J
This energy is converted to kinetic energy.
--
Paul

https://paulba.no/
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From Newsgroup: sci.physics.relativity

On 1/6/2026 1:57 PM, Paul.B.Andersen wrote:

Den 06.01.2026 09:15, skrev Thomas Heger:

Am Sonntag000004, 04.01.2026 um 20:51 schrieb Paul.B.Andersen:

E = mc² is the energy content, or the energy equivalent of
the mass m. Mass is invariant, so this equation is valid for
all speeds of the mass.

You contradicted yourself!!

Here your claim is, that mass is invariant, while a little below you
claim, that energy is conserved, while mass has vanished from a
radioactive sample.

But you can't keep both claims, because they contradict each other.

Invariant means "the same in all frames of reference"
or "independent of speed".

It does _not_ mean "constant".

Mass is invariant.
The mass of an object is the same in all frames of reference.
The mass of an object does not depend on the speed of the object.

But mass can change. Heat the object, and its mass will increase,

I have told you before, but I know you will not learn.
You never do.

Its odd to think of a cup of water as the water evaporates. The cup is
an object with its own mass. But, now its holding water. So, the cup
"weighs" more in a sense... But, as the water evaporates, that weight
will go back to the weight of the original cup...

Think of two equal mass cups on a scale. They balance. Add water to one,
its not balanced. However, the water will evaporate and the scale shall
go back to balanced over time?
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From Newsgroup: sci.physics.relativity

On 1/7/2026 1:20 PM, Chris M. Thomasson wrote:

On 1/6/2026 1:57 PM, Paul.B.Andersen wrote:

Den 06.01.2026 09:15, skrev Thomas Heger:

Am Sonntag000004, 04.01.2026 um 20:51 schrieb Paul.B.Andersen:

E = mc² is the energy content, or the energy equivalent of
the mass m. Mass is invariant, so this equation is valid for
all speeds of the mass.

You contradicted yourself!!

Here your claim is, that mass is invariant, while a little below you
claim, that energy is conserved, while mass has vanished from a
radioactive sample.

But you can't keep both claims, because they contradict each other.

Invariant means "the same in all frames of reference"
or "independent of speed".

It does _not_ mean "constant".

Mass is invariant.
The mass of an object is the same in all frames of reference.
The mass of an object does not depend on the speed of the object.

But mass can change. Heat the object, and its mass will increase,

I have told you before, but I know you will not learn.
You never do.

Its odd to think of a cup of water as the water evaporates. The cup is
an object with its own mass. But, now its holding water. So, the cup "weighs" more in a sense... But, as the water evaporates, that weight
will go back to the weight of the original cup...

Think of two equal mass cups on a scale. They balance. Add water to one,
its not balanced. However, the water will evaporate and the scale shall
go back to balanced over time?

LOL! Think if the cups were made of paper. The water itself might break
down the cup and parts of the cup would wash away...
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From Newsgroup: sci.physics.relativity

Chris M. Thomasson wrote to sci.physics.relativity and sci.physics:

Its odd to think of a cup of water as the water evaporates. The cup is
an object with its own mass. But, now its holding water. So, the cup "weighs" more in a sense...

The mass of the cup only has increased because when we say "cup" now we mean the substance of the cup *and* the water.

But, as the water evaporates, that weight will go back to the weight of
the original cup...

That is only true if the water actually leaves the cup. Put a lid on the
cup so that the water cannot escape, and the mass of the water-filled cup
will not decrease.

But, more relevant to this discussion, by increasing the rest energy of the water(-filled cup) by increasing the kinetic energy of the water molecules
(and to some extent the substance of the cup, too) by heating the
water(-filled cup), the mass of the water(-filled cup) increases slightly (probably unmeasurably, given m = E_0/c^2).

See also the videos that I referred to in <mid:10j721n$1i2q$1@gwaiyur.mb-net.net>.

Think of two equal mass cups on a scale. They balance. Add water to one,
its not balanced. However, the water will evaporate and the scale shall
go back to balanced over time?

If the water *leaves* the cup, yes.

Notice also that what you are measuring there is weight, not mass. That is, this is only an indirect determination of mass that depends on gravitation, therefore the assumption of a uniform gravitational field (which we know is
not so, but just a relatively good approximation near the surface).

F'up2 sci.physics.relativity
--
PointedEars

Twitter: @PointedEars2
Please do not cc me. / Bitte keine Kopien per E-Mail.
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