That is mumbo jumbo, the longer in sun,
the deeper the surface warms, and the longer
in dark, the more heat lost.

Can you describe more clearly how the
temperatures would still be as extreme to the
same depth below the surface?

On Fri, 06 Apr 2007 04:31:54 +0000, mmeron wrote:

In article <pan.2007.04.07.02.03.39.593714@REMOVETHISix.netcom.com>, Bill
Ward <bward@REMOVETHISix.netcom.com> writes:

On Thu, 05 Apr 2007 23:41:51 +0000, mmeron wrote:

In article <pan.2007.04.06.23.40.44.501861@REMOVETHISix.netcom.com>,
Bill Ward <bward@REMOVETHISix.netcom.com> writes:

This can also be observed with a simple vacuum radiometer, consisting
of a paddlewheel with 4 horizontal spokes with paddles on the end of
each spoke, free to rotate in an evacuated transparent globe. Each
paddle is reflective on one side and black on the other. When exposed
to bright light, the silver side reflects the photons, while the black
side simply absorbs them. As a result of the net momentum transfer
(2mv - mv), the silver side retreats from the light, rotating the
wheel. (Note - gas filled versions rotate oppositely.)

That simple demonstration proves that light (photons) carries momentum.

Since momentum = mass times velocity,

No, momentum is not defined as mass times velocity. It *evaluates* to
this in the simple case of a massive particle in the Newtonian limit
but not in general.

Then could you expand on that a bit? How would you correctly phrase what
I was trying to say? Are the conclusions changed in any way?

Sure, I'll expand a bit. First, just as an aside, I'll mention that it is
not uncommon (in fact it is very common) for definitions to change over
time in a way which broadens their scope (while not negating their meaning
within their original domain). Thus, for example, the functions sine and
cosine, which were originally defined in terms of ratios of sides of a
right triangle, acquired over time much broader definitions which allow
for their applications in domains way beyond those envisioned by their
creators (as functions over the complex domain, for example).

So, coming back to the original topic, thus it is with momentum, as well.
It is true that momentum was originally defined by Newton as mv. But,
Newton didn't define momentum for all possible physical systems, only for
moving masses. Over time,when the scope of physics grew, there was need
for a broader definition and this came from the Lagrangian formulation of
mechanics. In this formulation the connection between symmetries and
conservation laws become apparent (check out Noether theorem) and we got
to define momentum as the vector property of a physical system which
couples to symmetry under space translations. That's the "high brow"
formulation, technically it means that the momentum of a system is given
by the derivatives of the Lagrangian with respect to velocities.

Now, this definition is much broader than the original and it applies to
all physical systems, not just moving masses. For moving masses, using a
Lagrangian based on Newtonian mechanics, you recover p = mv (which is
now a derived result, not a definition). But, you also get momentum for
systems or parts of systems devoid of mass. Specifically, *within
classical physics", that is before we get to either relativity or QM,
electromagnetic radiation *does* carry momentum, even though it *does
not* carry mass.

So, coming back to the beginning, yes, some of the conclusions do
change. That light exerts pressure, this is an evidence for light
carrying momentum. But it is *not* evidence for light having mass. In
the general formulation, mass and momentum are somewhat related but it
is not a one to one relationship and one can be present without the
other.

And, in fact, the definition of mass changed as well. But that's
another story.

Thanks for the clarification. Things have changed since I first studied
physics. I think most of the confusion is explained by the following
snippet:

http://en.wikipedia.org/wiki/Mass#Relativistic_relation_among_mass.2C_energy_and_momentum

<Begin quote>
Some authors define a quantity known as the relativistic mass, which is
basically the quantity E/c2. This allows E = mc2 to be true in all cases,
and makes the "equivalence" of "mass" and energy true by definition,
though neither quantity is frame-independent. "Relativistic mass" was used
in many early writings on relativity, and it is still used in books for
laymen as well as introductory physics classes. However, the concept is
downplayed or discouraged by many physicists nowadays, for reasons
explained in the article on mass in special relativity.
<end quote>

By defining mass as rest mass, then obviously photons are massless. That
was not the case in my physics courses. Then, a photon's rest mass was
zero, but it had relativistic mass, because of the energy it carried.

But Pluto was a planet back then, too.

Thanks for your modern physics lesson, Mati. I appreciate your patience.

In article <pan.2007.04.07.02.03.39.593714@REMOVETHISix.netcom.com>, Bill
Ward <bward@REMOVETHISix.netcom.com> writes:

On Thu, 05 Apr 2007 23:41:51 +0000, mmeron wrote:

In article <pan.2007.04.06.23.40.44.501861@REMOVETHISix.netcom.com>,
Bill Ward <bward@REMOVETHISix.netcom.com> writes:

This can also be observed with a simple vacuum radiometer, consisting
of a paddlewheel with 4 horizontal spokes with paddles on the end of
each spoke, free to rotate in an evacuated transparent globe. Each
paddle is reflective on one side and black on the other. When exposed
to bright light, the silver side reflects the photons, while the black
side simply absorbs them. As a result of the net momentum transfer
(2mv - mv), the silver side retreats from the light, rotating the
wheel. (Note - gas filled versions rotate oppositely.)

That simple demonstration proves that light (photons) carries momentum.

Since momentum = mass times velocity,

No, momentum is not defined as mass times velocity. It *evaluates* to
this in the simple case of a massive particle in the Newtonian limit
but not in general.

Then could you expand on that a bit? How would you correctly phrase what
I was trying to say? Are the conclusions changed in any way?

Sure, I'll expand a bit. First, just as an aside, I'll mention that it is
not uncommon (in fact it is very common) for definitions to change over
time in a way which broadens their scope (while not negating their meaning
within their original domain). Thus, for example, the functions sine and
cosine, which were originally defined in terms of ratios of sides of a
right triangle, acquired over time much broader definitions which allow
for their applications in domains way beyond those envisioned by their
creators (as functions over the complex domain, for example).

So, coming back to the original topic, thus it is with momentum, as well.
It is true that momentum was originally defined by Newton as mv. But,
Newton didn't define momentum for all possible physical systems, only for
moving masses. Over time,when the scope of physics grew, there was need
for a broader definition and this came from the Lagrangian formulation of
mechanics. In this formulation the connection between symmetries and
conservation laws become apparent (check out Noether theorem) and we got
to define momentum as the vector property of a physical system which
couples to symmetry under space translations. That's the "high brow"
formulation, technically it means that the momentum of a system is given
by the derivatives of the Lagrangian with respect to velocities.

Now, this definition is much broader than the original and it applies to
all physical systems, not just moving masses. For moving masses, using a
Lagrangian based on Newtonian mechanics, you recover p = mv (which is
now a derived result, not a definition). But, you also get momentum for
systems or parts of systems devoid of mass. Specifically, *within
classical physics", that is before we get to either relativity or QM,
electromagnetic radiation *does* carry momentum, even though it *does
not* carry mass.

So, coming back to the beginning, yes, some of the conclusions do
change. That light exerts pressure, this is an evidence for light
carrying momentum. But it is *not* evidence for light having mass. In
the general formulation, mass and momentum are somewhat related but it
is not a one to one relationship and one can be pre