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Mass and Energy

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  Mass and Energy ram@zedat.fu-berlin.de (Stefan Ram) - 2026-01-01 16:19 +0000
    Re: Mass and Energy nospam@de-ster.demon.nl (J. J. Lodder) - 2026-01-01 22:38 +0100
    Re: Mass and Energy x <x@x.net> - 2026-01-02 10:03 -0800
    Re: Mass and Energy x <x@x.net> - 2026-01-02 10:06 -0800
      Re: Mass and Energy Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-02 21:07 +0100
        Re: Mass and Energy x <x@x.net> - 2026-01-02 15:40 -0800
        Re: Mass and Energy x <x@x.net> - 2026-01-02 16:05 -0800
          Re: Mass and Energy Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-03 14:30 +0100
        Re: Mass and Energy Thomas Heger <ttt_heg@web.de> - 2026-01-04 09:06 +0100
          Re: Mass and Energy nospam@de-ster.demon.nl (J. J. Lodder) - 2026-01-04 12:28 +0100
            Re: Mass and Energy Thomas Heger <ttt_heg@web.de> - 2026-01-06 09:03 +0100
              Re: Mass and Energy nospam@de-ster.demon.nl (J. J. Lodder) - 2026-01-06 10:56 +0100
                Re: Mass and Energy Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-06 06:52 -0800
                  Re: Mass and Energy nospam@de-ster.demon.nl (J. J. Lodder) - 2026-01-06 16:12 +0100
    Re: Mass and Energy "Paul.B.Andersen" <relativity@paulba.no> - 2026-01-04 20:51 +0100
      Re: Mass and Energy Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-06 03:04 +0100
        Re: Mass and Energy "Paul.B.Andersen" <relativity@paulba.no> - 2026-01-06 22:12 +0100
          Re: Mass and Energy "Paul.B.Andersen" <relativity@paulba.no> - 2026-01-06 22:27 +0100
          Re: Mass and Energy Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-06 13:43 -0800
            Re: Mass and Energy Python <python@cccp.invalid> - 2026-01-06 21:46 +0000
              Re: Mass and Energy Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-07 04:32 -0800
          Re: Mass and Energy Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-06 23:27 +0100
            Re: Mass and Energy Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-01-07 04:14 -0800
            Re: Mass and Energy "Paul B. Andersen" <relativity@paulba.no> - 2026-01-07 22:18 +0100
      Re: Mass and Energy Thomas Heger <ttt_heg@web.de> - 2026-01-06 09:15 +0100
        Re: Mass and Energy "Paul.B.Andersen" <relativity@paulba.no> - 2026-01-06 22:57 +0100
          Re: Mass and Energy Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-06 23:51 +0100
            Re: Mass and Energy Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-07 05:12 +0100
              Re: Mass and Energy Maciej Woźniak <mlwozniak@wp.pl> - 2026-01-07 08:16 +0100
          Re: Mass and Energy "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-07 13:20 -0800
            Re: Mass and Energy "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-07 13:29 -0800
            Re: Mass and Energy Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-01-07 22:53 +0100

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#668098

On 01/06/2026 01:46 PM, Python wrote:
> Le 06/01/2026 à 22:43, Ross Finlayson a écrit :
>> [snip non sense] Einstein's mass/energy equivalency
>> formula, a truncation of an expression.
>
> You are the result of the truncation of sanity, Ross.
>
>

Honi soit qui mal y pense?


Before Einstein, like two or three decades before,
already mass/energy equivalency in a form about the
same as Einstein's first example, which is a truncation
of a Taylor series, it was Karl somebody, Neumann I
think it was,

https://en.wikipedia.org/wiki/Carl_Neumann

where I'm not exactly sure about that, yet the
idea of mass/energy equivalency was already around.


So, the "severe abstraction" of the "mechanical reduction",
or as after Lagrange what arrived at Kelvin and these days
is most usually about thermo 2'nd law the statistical ensemble,
is an example of, "restriction of comprehension", which is a
term from logic, opposite "expansion of comprehension".


Anyway ideas about mass/energy equivalency like "impetus"
and "vis viva" have been around a long time.

Then, space-contraction-linear and space-contraction-rotational
have also been around a long time, for example about the
gyroscopic effects. (Here "heft".)


The most usual ideas of the laws of motion as
rest/rest motion/motion and equal/opposite are
ideals, as they are, with classical mathematical setups,
yet, practically never so. Thinkers like DesCartes
and Kelvin attribute more to mechanics than that.


Wow, Einstein's haircut is a lot like that Carl Neumann's.

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#668090

Paul.B.Andersen wrote:
^^^^^^^^^^^^^^^
I just noticed that since 2025-12-14, when the "Organization" header field
of your postings changed, you also do not have a space in there anymore.
Not including a space there may exclude your postings from being read,
through real-name filters.

> Den 06.01.2026 03:04, skrev Thomas 'PointedEars' Lahn:
>>> E = mc² is the energy content, or the energy equivalent of
>>> the mass m.
>>
>> The first wording is simply wrong.  E (better: E₀) is the *rest* energy of
>> _an object_ whose mass is m.  One can also call that the energy content _of
>> that object_ at relative rest (as Einstein did, but this wording is
>> obsolete), but NOT "of the mass".  Mass is a quantity, not a object; a
>> quantity has no content.
> 
> You are nit-picking again!

No, to distinguish between the concepts here is vital for a proper
understanding.

> Of course "mass" is the mass of an object.
> and E = mc² is the energy content of the mass of an object.

NOT E = m c², but E₀ = m c², is the _energy_ of an object with mass m at
relative rest, its *rest energy*.

> It is quite common to write things like:
>    "Let the speed of the mass m be v".

Maybe in colloquial or popular-scientific (con)texts; but this is a
scientific newsgroup, and it is not only good form but required to be
precise here and in this regard.

> Everybody will understand that m is the mass of an object.

Irrelevant.  The problem is that *you* do not understand it correctly
despite the many explanations and references that I gave (you) already.

> And so do you. So why the nit-picking ?

It is not nitpicking, but requiring a clarity of expression to arrive at a
proper understanding of a subject.

> This is a post in a Usenet group, not a scientific paper.

This is a _scientific_ newsgroup.

> 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.

If there is confusion: "rest" here is not meant as in "and all the rest",
but as in "at rest", i.e. "not moving".

See also: <https://en.wikipedia.org/wiki/Invariant_mass#Rest_energy>

> The energy of a moving object with mass m is:
>    E = γmc² = mc² + (γ-1)mc²

That is the *total energy* of *any* object with mass m, including one that
is moving in the chosen rest frame (then we have γ > 1).

[The total energy also includes the potential energy, but coordinates can be
chosen such that the latter is zero.]

> The term mc² is the invariant energy content of the object with mass m,

One can say that; but as I already pointed out, that wording is both
obsolete and imprecise.

> the term (γ-1)mc² is the kinetic energy of the object with mass m.

If the potential energy is zero.

> The energy content E = mc² of the object with mass m
> is a property of the object with mass m.

*No, it is the other way around*: The mass m of an object is a measure of
its rest energy or, as Einstein wrote in "Does the Inertia of a Body Depend
Upon Its Energy Content?" its "energy content" -- by which he meant "its
energy content _at relative rest_":

,-<https://web.archive.org/web/20240708111817/https://einsteinpapers.press.princeton.edu/vol2-trans/188>
|
| [...], we are led to the more general conclusion: The mass of a body is a
| measure of its energy content; if the energy changes by L, the mass
| changes in the same sense by L/9 * 10^20, if the energy is measured in
| ergs and the mass in grams.

[Unfortunately, since the commercialization of the Digital Einstein Papers
we are required to refer to archived versions or unofficial
translations/copies :-(]

> But a frame dependent entity

_quantity_, not entity

> like kinetic energy or relative speed is not a property of the moving object.

Self-contradictory.

> They are properties of the relationship between the object
> and a frame of reference.

/Non sequitur./

> The kinetic energy which can have any value depending on
> the arbitrary choice of frame of reference, is not part
> of the energy content of the object.

That depends on how one defines that.  "Energy content" is an obsolete term
to begin with.

However, if one simply substitutes "total energy" for "energy content", then
the total energy of an object depends on the choice of rest frame; and the
"energy content" that Einstein means is just that of an object/body (with
non-zero mass) *at relative rest* -- in modern terminology, the
object's/body's *rest* energy.

> So the mass isn't conserved, [...]

There is no and has never been a disagreement among the two of us about that.

>> Again: NOT the mass is partially converted to kinetic energy, but the rest
>> energy E_0 = m c^2 *equivalent to* the mass m.
> 
> 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 = 3.089167695E-28 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 = 3.089167695E-28 J

You keep missing the point.

> 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.

> You are free to choose your wording.

No, one is NOT free to choose one's wording if one wants to participate in a
fruitful scientific discussion.  That is a fundamental misconception.
Scientific terms have meaning, and the meaning of certain terms has been
agreed upon, like total energy, rest energy, mass, kinetic energy, and
potential energy.

What actually happens here is that rest energy is (partially) converted to
other forms of energy.  This is equivalent to a reduction in mass; precisely
what Einstein wrote in his paper, and in a sense precisely what he suggested
in that paper as an experimental test:

| Perhaps it will prove possible to test this theory using bodies whose
| energy content is variable to a high degree (e.g., salts of radium).

-- 
PointedEars

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

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#668097

On 01/06/2026 02:27 PM, Thomas 'PointedEars' Lahn wrote:
> Paul.B.Andersen wrote:
> ^^^^^^^^^^^^^^^
> I just noticed that since 2025-12-14, when the "Organization" header field
> of your postings changed, you also do not have a space in there anymore.
> Not including a space there may exclude your postings from being read,
> through real-name filters.
>
>> Den 06.01.2026 03:04, skrev Thomas 'PointedEars' Lahn:
>>>> E = mc² is the energy content, or the energy equivalent of
>>>> the mass m.
>>>
>>> The first wording is simply wrong.  E (better: E₀) is the *rest* energy of
>>> _an object_ whose mass is m.  One can also call that the energy content _of
>>> that object_ at relative rest (as Einstein did, but this wording is
>>> obsolete), but NOT "of the mass".  Mass is a quantity, not a object; a
>>> quantity has no content.
>>
>> You are nit-picking again!
>
> No, to distinguish between the concepts here is vital for a proper
> understanding.
>
>> Of course "mass" is the mass of an object.
>> and E = mc² is the energy content of the mass of an object.
>
> NOT E = m c², but E₀ = m c², is the _energy_ of an object with mass m at
> relative rest, its *rest energy*.
>
>> It is quite common to write things like:
>>     "Let the speed of the mass m be v".
>
> Maybe in colloquial or popular-scientific (con)texts; but this is a
> scientific newsgroup, and it is not only good form but required to be
> precise here and in this regard.
>
>> Everybody will understand that m is the mass of an object.
>
> Irrelevant.  The problem is that *you* do not understand it correctly
> despite the many explanations and references that I gave (you) already.
>
>> And so do you. So why the nit-picking ?
>
> It is not nitpicking, but requiring a clarity of expression to arrive at a
> proper understanding of a subject.
>
>> This is a post in a Usenet group, not a scientific paper.
>
> This is a _scientific_ newsgroup.
>
>> 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.
>
> If there is confusion: "rest" here is not meant as in "and all the rest",
> but as in "at rest", i.e. "not moving".
>
> See also: <https://en.wikipedia.org/wiki/Invariant_mass#Rest_energy>
>
>> The energy of a moving object with mass m is:
>>     E = γmc² = mc² + (γ-1)mc²
>
> That is the *total energy* of *any* object with mass m, including one that
> is moving in the chosen rest frame (then we have γ > 1).
>
> [The total energy also includes the potential energy, but coordinates can be
> chosen such that the latter is zero.]
>
>> The term mc² is the invariant energy content of the object with mass m,
>
> One can say that; but as I already pointed out, that wording is both
> obsolete and imprecise.
>
>> the term (γ-1)mc² is the kinetic energy of the object with mass m.
>
> If the potential energy is zero.
>
>> The energy content E = mc² of the object with mass m
>> is a property of the object with mass m.
>
> *No, it is the other way around*: The mass m of an object is a measure of
> its rest energy or, as Einstein wrote in "Does the Inertia of a Body Depend
> Upon Its Energy Content?" its "energy content" -- by which he meant "its
> energy content _at relative rest_":
>
> ,-<https://web.archive.org/web/20240708111817/https://einsteinpapers.press.princeton.edu/vol2-trans/188>
> |
> | [...], we are led to the more general conclusion: The mass of a body is a
> | measure of its energy content; if the energy changes by L, the mass
> | changes in the same sense by L/9 * 10^20, if the energy is measured in
> | ergs and the mass in grams.
>
> [Unfortunately, since the commercialization of the Digital Einstein Papers
> we are required to refer to archived versions or unofficial
> translations/copies :-(]
>
>> But a frame dependent entity
>
> _quantity_, not entity
>
>> like kinetic energy or relative speed is not a property of the moving object.
>
> Self-contradictory.
>
>> They are properties of the relationship between the object
>> and a frame of reference.
>
> /Non sequitur./
>
>> The kinetic energy which can have any value depending on
>> the arbitrary choice of frame of reference, is not part
>> of the energy content of the object.
>
> That depends on how one defines that.  "Energy content" is an obsolete term
> to begin with.
>
> However, if one simply substitutes "total energy" for "energy content", then
> the total energy of an object depends on the choice of rest frame; and the
> "energy content" that Einstein means is just that of an object/body (with
> non-zero mass) *at relative rest* -- in modern terminology, the
> object's/body's *rest* energy.
>
>> So the mass isn't conserved, [...]
>
> There is no and has never been a disagreement among the two of us about that.
>
>>> Again: NOT the mass is partially converted to kinetic energy, but the rest
>>> energy E_0 = m c^2 *equivalent to* the mass m.
>>
>> 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 = 3.089167695E-28 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 = 3.089167695E-28 J
>
> You keep missing the point.
>
>> 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.
>
>> You are free to choose your wording.
>
> No, one is NOT free to choose one's wording if one wants to participate in a
> fruitful scientific discussion.  That is a fundamental misconception.
> Scientific terms have meaning, and the meaning of certain terms has been
> agreed upon, like total energy, rest energy, mass, kinetic energy, and
> potential energy.
>
> What actually happens here is that rest energy is (partially) converted to
> other forms of energy.  This is equivalent to a reduction in mass; precisely
> what Einstein wrote in his paper, and in a sense precisely what he suggested
> in that paper as an experimental test:
>
> | Perhaps it will prove possible to test this theory using bodies whose
> | energy content is variable to a high degree (e.g., salts of radium).
>

"Ex falso quodlibet" is a lesson, not a fact.

Truths is discovered /
lies are invented /
when a lie's discovered /
that's a truth.


Ex falso nihilum.

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#668106

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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#668068

Am Sonntag000004, 04.01.2026 um 20:51 schrieb Paul.B.Andersen:
> Den 01.01.2026 17:19, skrev Stefan Ram:
>> "Paul.B.Andersen" <relativity@paulba.no> wrote or quoted:
>> :that mass could be converted to energy as
>> :predicted by Einstein's E = mc².
> 
> I resent very much that you:
> 1. Break threads so it is impossible to see to what you are responding.
> 2. Paraphrase and not quote.
> 
> I can guess that you were responding to my statement:
>   "The atom bomb proved in a very convincing way
>    that mass could be converted to energy as
>    predicted by Einstein's E = mc²."
> 
> This statement isn't very precise, but not wrong.
> So let's look at a more precise statement about
> what is happening in an atomic fission bomb:
> 
> One possible fission process is:
> 
> 1n + U-235 → Ba-141 + Kr-92 + 3n
> 
> The atomic weight (mass) 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
> 
>>
>>    I can spot three mistakes here right off the bat.
>>
>>         First, the phrase "mass could be converted to energy" is based on
>>    a misconception, since mass already /is/ a form of energy - there's no
>>    "conversion" happening. It's like saying, "water can be turned into a
>>    liquid" - no, water /is/ a liquid.
> 
> Note that m = 3.089167695E-28 kg is the _lost_ mass,
> it doesn't exist any more.
> So where has it gone?
> It is converted to E = mc² ≈ 2.776404839E-11 J of _kinetic energy_.
> Kinetic energy is not mass. Thus "convert".
> 
>>
>>         Second, "E=mc^2" only applies to systems at rest. In general,
>>    it's "E^2=(mc^2)^2+(pc)^2", where "p" is the system's momentum.
>>    (That basically says mass is the magnitude of the four-momentum.)
> 
> 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.

So let's keep energy and regard matter as some strange form of energy.

I actually had this idea long ago and wrote kind of book about it:

https://docs.google.com/presentation/d/1Ur3_giuk2l439fxUa8QHX4wTDxBEaM6lOlgVUa0cFU4/edit?usp=sharing

(As proof of concept I had 'Growing Earth' in mind.)


TH

...

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#668089

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.


-- 
Paul

https://paulba.no/

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#668091

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".

That is what *you* mean by it *here*, NOT what it *generally* means.

What *you* mean *here* is more precisely called "_Lorentz_-invariant".


F'up2 sci.physics.relativity
-- 
PointedEars

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

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#668094

Thomas 'PointedEars' Lahn wrote:
> Paul.B.Andersen wrote:
>> Invariant means "the same in all frames of reference"
>> or "independent of speed".
> 
> That is what *you* mean by it *here*, NOT what it *generally* means.
> 
> What *you* mean *here* is more precisely called "_Lorentz_-invariant".

It turns out, though, that the mass of a massive particle (sic) is
*generally* frame-invariant (not just under a Lorentz boost) as it is
proportional to the norm of the 4-momentum:

With the general spacetime metric

  ds² = c²dτ² = g_μν dx^μ dx^ν = dx_ν dx^ν,

where τ is proper time, and [g]_μν is the metric tensor, we have

           dτ = dt √[(1/c²) ẋ_ν ẋ^ν],

where t is coordinate time, and ẋ^ν := dx^ν/dt.

The *4-velocity* is defined as

  [u]^μ := d[x]^μ/dτ = dt/dτ [ẋ]^μ.

For timelike worldlines, its norm squared is always

  u_ν u^ν = (dt/dτ)² ẋ_ν ẋ^ν = 1/[(1/c²) ẋ_α ẋ^α] ẋ_ν ẋ^ν = c².

The *4-momentum* is

  [p]^μ = m [u]^μ,

where m is mass, so its norm squared is

  p_ν p^ν = m² u_ν u^ν = m²c²,

and the mass of a massive particle is the *scalar*, thus frame-invariant,

        m = 1/c √(p_ν p^ν). ∎

LaTeX:

<https://www.HostMath.com/Show.aspx?Code=%5Cbegin%7Balign*%7D%0A%5Cnewcommand%7B%5Ccoloneqq%7D%7B%5Cmathrel%7B%3A%3D%7D%7D%0A%5Cnewcommand%7B%5Cfourvec%7D%5B1%5D%7B%7B%5Cmathbf%7B%231%7D%7D%7D%0A%5Cnewcommand%7B%5Cd%7D%7B%7B%5Cmathrm%7Bd%7D%7D%7D%0A%7B%5Cd%20s%7D%5E2%20%3D%20c%5E2%7B%5Cd%5Ctau%7D%5E2%20%26%3D%20g_%7B%5Cmu%5Cnu%7D%20%5C%2C%20%5Cd%20x%5E%5Cmu%20%5C%2C%20%5Cd%20x%5E%5Cnu%20%3D%20%5Cd%20x_%5Cnu%20%5C%2C%20%5Cd%20x%5E%5Cnu%20%5C%5C%0A%5CLeftrightarrow%20%7B%5Cd%5Ctau%7D%20%26%3D%20%5Cd%20t%20%5C%2C%20%5Csqrt%7B%5Cfrac%7B1%7D%7Bc%5E2%7D%20%5C%2C%20%5Cdot%20x_%5Cnu%20%5C%2C%20%5Cdot%20x%5E%5Cnu%7D.%20%5C%5C%0A%5Cfourvec%20u%5E%5Cmu%20%5C%20%26%5Ccoloneqq%20%5Cfrac%7B%5Cd%5Cfourvec%20x%5E%5Cmu%7D%7B%5Cd%5Ctau%7D%20%3D%20%5Cfrac%7B%5Cd%20t%7D%7B%5Cd%5Ctau%7D%20%5C%2C%20%5Cdot%7B%20%5Cfourvec%20x%7D%5E%5Cmu%20%5C%5C%0A%5Cimplies%20u_%5Cnu%20%5C%2C%20u%5E%5Cnu%20%26%3D%20%7B%5Cleft(%5Cfrac%7B%5Cd%20t%7D%7B%5Cd%5Ctau%7D%5Cright)%7D%5E2%20%5C%2C%20%5Cdot%20x_%5Cnu%20%5C%2C%20%5Cdot%20x%5E%5Cnu%20%3D%20%5Cfrac%7B1%7D%7B%5Cdfrac%7B1%7D%7Bc%5E2%7D%20%5C%2C%20%5Cdot%20x_%5Calpha%20%5C%2C%20%5Cdot%20x%5E%5Calpha%7D%20%5C%2C%20%5Cdot%20x_%5Cnu%20%5C%2C%20%5Cdot%20x%5E%5Cnu%20%3D%20c%5E2.%20%5C%5C%0A%5Cfourvec%20p%5E%5Cmu%20%26%3D%20m%20%5C%2C%20%5Cfourvec%20u%5E%5Cmu%20%5C%5C%0A%5Cimplies%20p_%5Cnu%20%5C%2C%20p%5E%5Cnu%20%26%3D%20m%5E2%20%5C%20u_%5Cnu%20%5C%2C%20u%5E%5Cnu%20%3D%20m%5E2%20c%5E2%20%5C%5C%0A%5Cimplies%20m%20%26%3D%20%5Cfrac1c%20%5C%2C%20%5Csqrt%7Bp_%5Cnu%20%5C%2C%20p%5E%5Cnu%7D.%0A%5Cend%7Balign*%7D>

-- 
PointedEars

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

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#668095

On 1/7/2026 5:12 AM, Thomas 'PointedEars' Lahn wrote:
> Thomas 'PointedEars' Lahn wrote:
>> Paul.B.Andersen wrote:
>>> Invariant means "the same in all frames of reference"
>>> or "independent of speed".
>>
>> That is what *you* mean by it *here*, NOT what it *generally* means.
>>
>> What *you* mean *here* is more precisely called "_Lorentz_-invariant".
> 
> It turns out, though, that the mass of a massive particle (sic) is
> *generally* frame-invariant 

It just turns out that you're talking this
way together with tour fellow idiots,
nothing more. Feynman, for instance, was
talking a different way.

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#668107

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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#668108

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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#668109

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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