On Sun, 16 Mar 2025 3:36:57 +0000, LaurenceClarkCrossen wrote:

"Where Does E = mc² Really Come From? | The Hidden Origins of
Mass-Energy Equivalence"
https://www.youtube.com/watch?v=xsL2nWsFgc4

The video explains how relativity assigned momentum to electromagnetism
without mass and then inferred from that that it has mass.
This is a clear case of petitio principii.
(When it can't have mass because of the mass-velocity relationship.)

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"Where Does E = mc² Really Come From? | The Hidden Origins of
Mass-Energy Equivalence"
https://www.youtube.com/watch?v=xsL2nWsFgc4

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Den 16.03.2025 04:45, skrev LaurenceClarkCrossen:

On Sun, 16 Mar 2025 3:36:57 +0000, LaurenceClarkCrossen wrote:

"Where Does E = mc² Really Come From? | The Hidden Origins of
Mass-Energy Equivalence"
 https://www.youtube.com/watch?v=xsL2nWsFgc4

The video explains how relativity assigned momentum to electromagnetism without mass and then inferred from that that it has mass.
This is a clear case of petitio principii.

The fine art of missing the point! :-D

It isn't relativity (SR) that "assigned momentum to electromagnetism",
it was Maxwell who did that. That was the main point in the video!

E = mc² because mass-less EM-radiation has kinetic energy and momentum!

Look at the explanation of Einstein's 1906 paper in the video.

I will give a simple variant of it, using only
Newtonian mechanics and Maxwell's theory.

Given an empty box with length L and mass M.

A photon (or EM-pulse) with energy E and momentum p = E/c
is emitted from one end of the box and absorbed in the other.

When the photon is emitted, the recoil will give the box a speed
v = p/M. When the photon hits the other wall a time t = L/c later,
the box will stop. It has then moved a distance d = Lv/c, so the
centre of mass will have moved a distance d = Lv/c.

According to NM a mass m moving at the speed c will have the momentum
p = mc. So we can set Mv = mc, or v/c = m/M and d = Lm/M.

If we move a mass m the distance L relative to a mass M, the mass
centre will move a distance d = Lm/M.

Conclusion:
When a photon with momentum p = E/c move from one side of the box
to the other, this will move the centre of mass the same distance
as if a mass m with the momentum mc moved from one side of the box
to the other.
E/c = mc -> E = mc²

-----------------

This was according to NM and Maxwell. To show that E = mc² is valid
according to SR is a bit more complicated, but it is done.

My point was to show that the real reason for why mass and energy
are equivalent is that mass-less EM-radiation has energy an momentum.

--
Paul

https://paulba.no/

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On Sun, 16 Mar 2025 19:16:31 +0000, Paul.B.Andersen wrote:

Den 16.03.2025 04:45, skrev LaurenceClarkCrossen:

On Sun, 16 Mar 2025 3:36:57 +0000, LaurenceClarkCrossen wrote:

"Where Does E = mc² Really Come From? | The Hidden Origins of
Mass-Energy Equivalence"
 https://www.youtube.com/watch?v=xsL2nWsFgc4

The video explains how relativity assigned momentum to electromagnetism
without mass and then inferred from that that it has mass.
This is a clear case of petitio principii.

The fine art of missing the point! :-D

It isn't relativity (SR) that "assigned momentum to electromagnetism",
it was Maxwell who did that. That was the main point in the video!

E = mc² because mass-less EM-radiation has kinetic energy and momentum!

Look at the explanation of Einstein's 1906 paper in the video.

I will give a simple variant of it, using only
Newtonian mechanics and Maxwell's theory.

Given an empty box with length L and mass M.

A photon (or EM-pulse) with energy E and momentum p = E/c
is emitted from one end of the box and absorbed in the other.

When the photon is emitted, the recoil will give the box a speed
v = p/M. When the photon hits the other wall a time t = L/c later,
the box will stop. It has then moved a distance d = Lv/c, so the
centre of mass will have moved a distance d = Lv/c.

According to NM a mass m moving at the speed c will have the momentum
p = mc. So we can set Mv = mc, or v/c = m/M and d = Lm/M.

If we move a mass m the distance L relative to a mass M, the mass
centre will move a distance d = Lm/M.

Conclusion:
When a photon with momentum p = E/c move from one side of the box
to the other, this will move the centre of mass the same distance
as if a mass m with the momentum mc moved from one side of the box
to the other.
E/c = mc -> E = mc²

-----------------

This was according to NM and Maxwell. To show that E = mc² is valid according to SR is a bit more complicated, but it is done.

My point was to show that the real reason for why mass and energy
are equivalent is that mass-less EM-radiation has energy an momentum.

You still say "duh" (:-D) at the end of your sentences. Did you go to
college on a football scholarship?

It is okay to call some quality of electromagnetism momentum without
mass. However, to avoid confusion, perhaps we should use a different
term.

It is the inference from there to mass that is false.

To presume energy has mass because it imparts momentum is absurd.

Sound moves objects without momentum because it has no mass. Neither
does light.

Kinetic energy has no mass, and it imparts momentum.

To claim light has both mass and not mass is absurd.

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Paul.B.Andersen <relativity@paulba.no> wrote:

Den 16.03.2025 04:45, skrev LaurenceClarkCrossen:

On Sun, 16 Mar 2025 3:36:57 +0000, LaurenceClarkCrossen wrote:

"Where Does E = mc? Really Come From? | The Hidden Origins of
Mass-Energy Equivalence"
https://www.youtube.com/watch?v=xsL2nWsFgc4

The video explains how relativity assigned momentum to electromagnetism without mass and then inferred from that that it has mass.
This is a clear case of petitio principii.

The fine art of missing the point! :-D

It isn't relativity (SR) that "assigned momentum to electromagnetism",
it was Maxwell who did that. That was the main point in the video!

E = mc? because mass-less EM-radiation has kinetic energy and momentum!

Look at the explanation of Einstein's 1906 paper in the video.

I will give a simple variant of it, using only
Newtonian mechanics and Maxwell's theory.

Given an empty box with length L and mass M.

A photon (or EM-pulse) with energy E and momentum p = E/c
is emitted from one end of the box and absorbed in the other.

When the photon is emitted, the recoil will give the box a speed
v = p/M. When the photon hits the other wall a time t = L/c later,
the box will stop. It has then moved a distance d = Lv/c, so the
centre of mass will have moved a distance d = Lv/c.

According to NM a mass m moving at the speed c will have the momentum
p = mc. So we can set Mv = mc, or v/c = m/M and d = Lm/M.

If we move a mass m the distance L relative to a mass M, the mass
centre will move a distance d = Lm/M.

Conclusion:
When a photon with momentum p = E/c move from one side of the box
to the other, this will move the centre of mass the same distance
as if a mass m with the momentum mc moved from one side of the box
to the other.
E/c = mc -> E = mc?

-----------------

This was according to NM and Maxwell. To show that E = mc? is valid
according to SR is a bit more complicated, but it is done.

My point was to show that the real reason for why mass and energy
are equivalent is that mass-less EM-radiation has energy an momentum.

Radiation pressure, as predicted by Maxwell,
was confirmed experimentally be Lebedev in 1901.
(so well before relativity)
It is also indispensable for getting the thermodynamics
of black-body radiation right.
(also well understood, by 1901)

It did take Einstein (1905) however
to get the mass-energy equivalence right.

Jan

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Den 16.03.2025 21:51, skrev LaurenceClarkCrossen:

On Sun, 16 Mar 2025 19:16:31 +0000, Paul.B.Andersen wrote:

My point was to show that the real reason for why mass and energy
are equivalent is that mass-less EM-radiation has energy an momentum.

You still say "duh" (:-D) at the end of your sentences. Did you go to
college on a football scholarship?

Yes, of course. How could I else have learned to write :-D ?

It is okay to call some quality of electromagnetism momentum without
mass. However, to avoid confusion, perhaps we should use a different
term.

It is the inference from there to mass that is false.

So from my statement:
"mass-less EM-radiation has energy and momentum"
you infer that mass-less EM-radiation has mass.

Well done. :-D or "duh" if you prefer.

Sound moves objects without momentum because it has no mass.

Know what?
I won't bother to explain why this statement is nonsensical
by a number of different reasons.

You invariably understand nothing of what I say anyway.

Or better: you invariably understand nothing.

I will say this, though: duh! :-D

--
Paul

https://paulba.no/

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