Nature of dark matter and dark energy

PD wrote:
[snip]
I don't think it is that mysterious how it could transmit waves. We
know how sound waves travel through solids.

And sound transmission through solids exhibits frequency-dependent
dispersion and all sorts of effects that are related to the medium that
are NOT seen with light transmission through the vacuum.

This is an excellent point that materials made up of "real" matter have
frequency-dependent dispersion. This is what causes white light to
split up into the spectrum when passing through a prism. The key
question is why the diffractive index is frequency dependent. I think
it must have something to do with how the atoms of the prism are
interacting with the EM wave.

However, when we consider the vacuum being made up of an aether solid,
we have a completely different case where (once again), the EM waves
utilize the aether particles as the medium and interact with nothing
else. Therefore, the aether has a privileged position as a solid in
that it should perfectly transmit all frequencies at the same speed
(nothing to interfere with the wave) for an indefinite duration. If you
could build a prism of high density aether, you would see that it would
bend a ray of light, but not disperse it.

I think this could be trivially proven by constructing a computer model
of a perfect solid composed of weakly interacting particles which
transmits all energy and has zero frictional losses (due to their being
nothing but pure real empty vacuum between particles). Such a model
would show that any wave of any frequency would travel at idential
non-dispersing speeds through the solid with perfect fidelity.

I think this is also important in that the tired-light theory of
redshift has been discounted because of these supposed dispersion
effects through the aether. If it could be shown that the aether would
not have any frequency dependent dispersion, this would help support
the tired-light theory of redshift. In this case, the aether would not
transmit light perfectly but would cause all frequencies to equally
redshift as it travels further.

If it does so, then we would expect that the cosmic background
radiation would equal the planck curve exactly because all we are
seeing is the results of the spectrum of all of the surrounding suns
(which start out as planck curve) being consistently redshifted to the
point where we can barely see it as the CMBR.

What we are really looking at in the CMBR are the countless galaxies
filling the skies in an infinite direction. If it weren't for the
redshifting, the entire night sky would be bright in every direction
since visible white light would emanate from every possible location in
the sky.


This is exactly how light
travels through the aether. Since the aether particles are the smallest
units of matter with nothing else to interfere, I would not expect
there to be any frictional losses.

I beg pardon? You've supposed that aether particles are bound states of
protons and electrons. Bound states of protons and electrons most
certainly do exhibit frictional losses. (Consider any state -- solid,
liquid, gas -- of hydrogen. Consider a neutron star interior, if you'd
like.) So you'd have to explain why in *this* particular bound state,
your aether, the frictional losses suddenly drop to *zero*.

The aether particles appear in a
true vacuum and we know a vacuum presents no frictional loses.

We know *experimentally* a vacuum presents no frictional losses. You
have to demonstrate theoretically how a lattice of bound states of
protons and electrons *could* present no frictional losses.


You, yourself say that it has been experimentally observed that a
vacuum presents no frictional losses, what other proof do you need that
particles separated by nothing but vacuum (as would be the aether
particles) exhibit no frictional losses?

Another property of the aether as a "solid" would be that its thermal
termperature as defined by the amount of random motion due to the
kinetic energy of the particles would probably be close to zero as it
is comparitively stationary compared to the motions of real particles
passing through the aehter. Remember we are talking about a crystalline
locked structure which can't bump around like real matter particles
can. Since the aether is relatively solid and motionless, this
contributes to the possiblity that motion is transmitted with perfect
fidelity and zero losses since there is very little random motion in
the matrix to disturb the wave.

[snip]

I think you would have to admit that this isn't an explanation but
rather a description of how boyancy works. It explains "how" but not
"why" it works.

Nonsense. I'd be happy to explain in more detail "why" buoyancy works
that way. Would you like me to take you step by step through that
thinking?

Sure, I like to see you give it a try. Just make sure you don't end up
explaining only the effects of boyancy as you did before. Is there some
mathematical proof that predicts boyancy and can exactly account for
the force as being equal to the difference in density? That would be
interesting, but I have never seen such an explanation, just a lot of
handwaving.


I was just trying to show that an explanation of
dielectrophoresis does at least explain exactly "why" the boyancy
effect occurs as a reverse process of downward gravity which can be
mathematically proven.

What you haven't shown is how the same interaction can pull in both
directions. You'll note that dielectrophoresis does not say that there
is a force pulling both in the direction of increaseing field AND in
the direction of decreasing field.

No, you read this wrong. It is exactly my point that the same diverging
field can both attract and repel simultaneously depending on the
permittivity of the object in the field.
Look at the figu

http://www.blazelabs.com/pics/emep.gif

This shows both the attraction and repelling of an object depending on
the permittivity compared to the surrounding medium. If Ep Em then
the force is in the direction of the decreasing field. If Ep Em, then
the force is toward increasing field. This can happen at the same time
in the same field with 2 different kind of objects.


[snip]
OK, you'll have to explain in more detail (mathematically would be
good) how the sign of the interaction changes with range. I'm not
saying it can't, but you need to be able to explicitly account for it.


How about this ...

I am assuming that the empty void of space has a higher aether density
than space which is filled with matter. Therefore, any matter appearing
within the void will be repelled away from the void in the presence of
any surrounding gravitational field. This is the repelling interaction.

The sign of the interaction changes when you enter an area of space
which is filled with matter. While we might consider the spaces between
our glalactic neighbors to be a pretty good vacuum, it contains far
more matter than the void and reduces the average density of what looks
like "empty" space to be lower than that of a solid mass. Now we have
the reverse situation where the surrounding medium is less dense than
clumps of real mass. Now the sign of the interaction works in reverse
causing clumps of mass to fall into each other attempting to create an
area of higher density.

So the void effectively tries to form a
clump or a bubble and everything else gets pushed out as far as it can.
This would be analogous to blowing bubbles inside of a closed box where
the inside of the bubbles are the voids which are trying to reduce
their surface area, and the galaxies are the bubble walls. This is
exactly the pattern that is observed.

You'll note in the soap bubble analogy there are two *different*
substances at play that have *different* operating interactions
governing their behavior. (There is no surface tension in the gas in
the bubble volume; there is no molecular dispersion in the fluid of the
bubble wall.)

All analogies have their limitations, so I was more calling your
attention to the shapes which are formed and what happens when many
bubbles which are trying to minimize their surface area (as would an
interstellar void).

[snip]
And you'll note that a gravitationally *attracting* dark matter that
interacts with conventional matter holds together consistently as a
model. A *repulsive* dark matter has some of the difficulties I was
alluding to. Also, be careful to distinguish dark matter from dark
energy. The two are *completely* different beasts.

I wouldn't say that there is a repulsive dark matter. There is no
inherent force of attraction or repulsion, only the effects of boyancy
control which direction matter heads and this is only dependent on the
density of the particle in question and the density of the surrounding
medium.

I think one of the coolest things about how I am modeling dark matter
and dark energy is that they aren't completely different beasts. It
unifies them under the same gravitational force. Gravity creates dark
matter by compressing the aether around massive objects. It is also
responsible for the repelling of galaxies from each other due to a
boyancy effect. I think this is a powerful unification and is a very
elegant model compared with the theories which can only treat these two
mysterious phenomenon as two completely different effects with
unrelated causes. In fact, it is the only model I have ever heard that
could draw any kind of line between these two phenomenon.

Another thing about the comments about dark matter being explained by
relativity - if this is true, then how is it that hubble is able to map
the higher density of the dark matter around galaxies? We've clearly
measured something there, not nothing which would be true if the
relativity explanation were true.




These theories are part of my theory of everything which can be found
at:
http://www.geocities.com/franklinhu/theory.html

fhudark

wrote:
PD wrote:
[snip]
I don't think it is that mysterious how it could transmit waves. We
know how sound waves travel through solids.

And sound transmission through solids exhibits frequency-dependent
dispersion and all sorts of effects that are related to the medium that
are NOT seen with light transmission through the vacuum.

This is an excellent point that materials made up of "real" matter have
frequency-dependent dispersion. This is what causes white light to
split up into the spectrum when passing through a prism. The key
question is why the diffractive index is frequency dependent. I think
it must have something to do with how the atoms of the prism are
interacting with the EM wave.

More precisely, how the charged particles (the proton and the electron)
in the atom are interacting with the EM wave.


However, when we consider the vacuum being made up of an aether solid,
we have a completely different case where (once again), the EM waves
utilize the aether particles as the medium and interact with nothing
else. Therefore, the aether has a privileged position as a solid in
that it should perfectly transmit all frequencies at the same speed
(nothing to interfere with the wave) for an indefinite duration.

Not obvious, and you're begging the question again. The question is WHY
do the charged particle bound states in the aether NOT cause
dispersion, when the charged particle bound states in atoms DO cause
dispersion? Why should they be different?

If you
could build a prism of high density aether, you would see that it would
bend a ray of light, but not disperse it.

I think this could be trivially proven by constructing a computer model
of a perfect solid composed of weakly interacting particles which
transmits all energy

"Weakly interacting" and "zero frictional losses" are mutually
contradictory.

and has zero frictional losses (due to their being
nothing but pure real empty vacuum between particles). Such a model
would show that any wave of any frequency would travel at idential
non-dispersing speeds through the solid with perfect fidelity.

Then I think you'd better produce that model, because nothing that
you've said indicates that this is even remotely possible.


I think this is also important in that the tired-light theory of
redshift has been discounted because of these supposed dispersion
effects through the aether. If it could be shown that the aether would
not have any frequency dependent dispersion, this would help support
the tired-light theory of redshift.

No, you misunderstand. The whole point of "tired light" is the PRESENCE
of dispersion. If there is no dispersion, then there is no "tired
light" model of redshift.

In this case, the aether would not
transmit light perfectly but would cause all frequencies to equally
redshift as it travels further.

If it does so, then we would expect that the cosmic background
radiation would equal the planck curve exactly because all we are
seeing is the results of the spectrum of all of the surrounding suns
(which start out as planck curve) being consistently redshifted to the
point where we can barely see it as the CMBR.

And here you're wrong too. A lower temperature Planck curve is not the
same as a redshifted Planck curve. The two have different shapes.


What we are really looking at in the CMBR are the countless galaxies
filling the skies in an infinite direction. If it weren't for the
redshifting, the entire night sky would be bright in every direction
since visible white light would emanate from every possible location in
the sky.


This is exactly how light
travels through the aether. Since the aether particles are the smallest
units of matter with nothing else to interfere, I would not expect
there to be any frictional losses.

I beg pardon? You've supposed that aether particles are bound states of
protons and electrons. Bound states of protons and electrons most
certainly do exhibit frictional losses. (Consider any state -- solid,
liquid, gas -- of hydrogen. Consider a neutron star interior, if you'd
like.) So you'd have to explain why in *this* particular bound state,
your aether, the frictional losses suddenly drop to *zero*.

And you didn't answer this crucial point.


The aether particles appear in a
true vacuum and we know a vacuum presents no frictional loses.

We know *experimentally* a vacuum presents no frictional losses. You
have to demonstrate theoretically how a lattice of bound states of
protons and electrons *could* present no frictional losses.


You, yourself say that it has been experimentally observed that a
vacuum presents no frictional losses, what other proof do you need that
particles separated by nothing but vacuum (as would be the aether
particles) exhibit no frictional losses?

Nope. See the problem is, you are hypothesizing a charged particle
aether which, by its nature, simply CANNOT behave the way that is
observed experimentally. You can't simply wave a wand and say, "But we
observe it to behave that way, therefore it MUST behave that way." You
have not considered the possibility that if the hypothesized charged
particle aether cannot be expected to behave that way, then this is
evidence that there is no charged particle aether.

Look, this is like supposing that there are giant 20-ton beasts with
five legs and nine toes on each foot. If I ask, "Where are the
footprints?" and you say, "It must not leave footprints somehow," and I
say, "How can you expect a 20-ton beast with five legs and nine toes on
each foot to not leave footprints?" and you say, "Because we don't see
any footprints with nine toes and five legs," then I'd be right to
laugh at you.


Another property of the aether as a "solid" would be that its thermal
termperature as defined by the amount of random motion due to the
kinetic energy of the particles would probably be close to zero as it
is comparitively stationary

How do you know THAT?
And if there is a medium that passes on electromagnetic radiation, you
do know that this involves motion of the particles in the medium don't
you? You do know about how other waves are conducted in media, don't
you?

compared to the motions of real particles
passing through the aehter. Remember we are talking about a crystalline
locked structure which can't bump around like real matter particles
can.

If they're locked into the structure, how do they pass on a wave? You
do know about how other waves are conducted in media, don't you?

Since the aether is relatively solid and motionless, this
contributes to the possiblity that motion is transmitted with perfect
fidelity and zero losses since there is very little random motion in
the matrix to disturb the wave.

[snip]

I think you would have to admit that this isn't an explanation but
rather a description of how boyancy works. It explains "how" but not
"why" it works.

Nonsense. I'd be happy to explain in more detail "why" buoyancy works
that way. Would you like me to take you step by step through that
thinking?

Sure, I like to see you give it a try. Just make sure you don't end up
explaining only the effects of boyancy as you did before. Is there some
mathematical proof that predicts boyancy and can exactly account for
the force as being equal to the difference in density? That would be
interesting, but I have never seen such an explanation, just a lot of
handwaving.

In the interest of space, I'll do that in a separate post.



I was just trying to show that an explanation of
dielectrophoresis does at least explain exactly "why" the boyancy
effect occurs as a reverse process of downward gravity which can be
mathematically proven.

What you haven't shown is how the same interaction can pull in both
directions. You'll note that dielectrophoresis does not say that there
is a force pulling both in the direction of increaseing field AND in
the direction of decreasing field.

No, you read this wrong. It is exactly my point that the same diverging
field can both attract and repel simultaneously depending on the
permittivity of the object in the field.
Look at the figu

http://www.blazelabs.com/pics/emep.gif

This shows both the attraction and repelling of an object depending on
the permittivity compared to the surrounding medium. If Ep Em then
the force is in the direction of the decreasing field. If Ep Em, then
the force is toward increasing field. This can happen at the same time
in the same field with 2 different kind of objects.

Right, but what you're supposing is the *same* interaction acting in
*two* different directions on the *same* object.



[snip]
OK, you'll have to explain in more detail (mathematically would be
good) how the sign of the interaction changes with range. I'm not
saying it can't, but you need to be able to explicitly account for it.


How about this ...

I am assuming that the empty void of space has a higher aether density
than space which is filled with matter. Therefore, any matter appearing
within the void will be repelled away from the void in the presence of
any surrounding gravitational field. This is the repelling interaction.

The sign of the interaction changes when you enter an area of space
which is filled with matter. While we might consider the spaces between
our glalactic neighbors to be a pretty good vacuum, it contains far
more matter than the void and reduces the average density of what looks
like "empty" space to be lower than that of a solid mass. Now we have
the reverse situation where the surrounding medium is less dense than
clumps of real mass. Now the sign of the interaction works in reverse
causing clumps of mass to fall into each other attempting to create an
area of higher density.

Sorry, this made no sense. Try again. And where is the math?


So the void effectively tries to form a
clump or a bubble and everything else gets pushed out as far as it can.
This would be analogous to blowing bubbles inside of a closed box where
the inside of the bubbles are the voids which are trying to reduce
their surface area, and the galaxies are the bubble walls. This is
exactly the pattern that is observed.

You'll note in the soap bubble analogy there are two *different*
substances at play that have *different* operating interactions
governing their behavior. (There is no surface tension in the gas in
the bubble volume; there is no molecular dispersion in the fluid of the
bubble wall.)

All analogies have their limitations, so I was more calling your
attention to the shapes which are formed and what happens when many
bubbles which are trying to minimize their surface area (as would an
interstellar void).

And I pointed out to you that the *reason* why those bubbles behave the
way they do is because of the presence of two substances with different
interactions. You can't just wave your hands and say "Same thing, but
without the things present in bubbles that make it happen there."


[snip]
Another thing about the comments about dark matter being explained by
relativity - if this is true, then how is it that hubble is able to map
the higher density of the dark matter around galaxies? We've clearly
measured something there, not nothing which would be true if the
relativity explanation were true.

What makes you think relativity would say there is nothing there?

PD

wrote:

Nonsense. I'd be happy to explain in more detail "why" buoyancy works
that way. Would you like me to take you step by step through that
thinking?

Sure, I like to see you give it a try. Just make sure you don't end up
explaining only the effects of boyancy as you did before. Is there some
mathematical proof that predicts boyancy and can exactly account for
the force as being equal to the difference in density? That would be
interesting, but I have never seen such an explanation, just a lot of
handwaving.


OK, no handwaving.
I'll take it gradually, only doing a little step in each post. As the
posts develop, you'll see the whole derivation.

Take a swimming pool full of water. In the middle of that pool of water
there is a chunk of that water, around which I can mentally wrap an
imaginary cylinder. The cylinder has circular ends of area A at top and
bottom, and the height of the cylinder is h. As we've imagined it, this
cylinder has a volume A*h. The mass of the water inside this imaginary
cylinder is the density times the volume, or p*A*h, where p is the
density of the water. The weight of the water in this cylinder is the
mass times g, the acceleration of gravity, or p*A*h*g.

Now, since the pool is still and the water is not circulating, this
cylinder of water is not moving. It is suspended in the surrounding
water. (If you doubt this, note that we took an arbitrary chunk of
water in the pool -- not all of the water can be sinking, and not all
of it can be rising.) Since it is in equilibrium, the net force on the
water must be zero. But we know gravity is acting on that cylinder of
water, pulling it downwards. So there *must* be a force acting upwards
on this cylinder -- which we'll eventually find out is the buoyancy
force.

OK so far?

PD

PD wrote:
[snip]
Since it is in equilibrium, the net force on the
water must be zero. But we know gravity is acting on that cylinder of
water, pulling it downwards. So there *must* be a force acting upwards
on this cylinder -- which we'll eventually find out is the buoyancy
force.

OK so far?

PD

Do we know that the force of "gravity" is pulling it downwards?
Experimentally, if the cylinder of water is sitting in the middle of
the pool, at appears that simply no forces are acting on the it. If you
could prove with a weight scale that the force of gravity is still
active while the cylinder of water is immersed in only water, then you
would have a point about there being a downward gravity force. If
dilectrophorisis is the explanation, then the cyclinder of water would
truly have no force exerted on it and would truely weigh nothing and no
forces are active on it which explains why it neither rises or falls.
There would be no need for an upward acting force of boyancy.

So far, the explanation sounds like a handwave, I would expect an
explanation that does as good a job as dilectrophorisis by showing the
source and vectors of the forces involved and the magnitude.

wrote:
PD wrote:
[snip]
Since it is in equilibrium, the net force on the
water must be zero. But we know gravity is acting on that cylinder of
water, pulling it downwards. So there *must* be a force acting upwards
on this cylinder -- which we'll eventually find out is the buoyancy
force.

OK so far?

PD

Do we know that the force of "gravity" is pulling it downwards?

Well, we know that, if instead of a swimming pool, we have a beaker on
top of a scale, that the weight that the scale reads is exactly
proportional to the amount of water that is in it. If I add an
imaginary cylinder's worth of water to the beaker, the scale reading
will increase by exactly the weight of the water added. If gravity were
not pulling down on that added bit of water, then the scale reading
would not increase.

Certainly we know that at least *some* of that water has the downward
force of gravity on it, because the scale deflects. And since where we
wrapped our imaginary cylinder was arbitrary, we'll just say we choose
the chunk of water that we *know* weighs something. (Of course, you
know I'm pulling your leg a little here. Any bit of the water is
indistinguishable from any other part of the water. It's impossible, of
course, to draw a line between the water that gravity is acting on and
the water that gravity is not acting on.)

So we'll imagine our imaginary cylinder of water is part of the water
that sits in a beaker on top of the scale, which is reading the weight
of all the water in the beaker, the cylinder's worth included.

OK so far?

Experimentally, if the cylinder of water is sitting in the middle of
the pool, at appears that simply no forces are acting on the it. If you
could prove with a weight scale that the force of gravity is still
active while the cylinder of water is immersed in only water, then you
would have a point about there being a downward gravity force. If
dilectrophorisis is the explanation, then the cyclinder of water would
truly have no force exerted on it and would truely weigh nothing and no
forces are active on it which explains why it neither rises or falls.
There would be no need for an upward acting force of boyancy.

So far, the explanation sounds like a handwave, I would expect an
explanation that does as good a job as dilectrophorisis by showing the
source and vectors of the forces involved and the magnitude.

PD wrote:
[snip]
So we'll imagine our imaginary cylinder of water is part of the water
that sits in a beaker on top of the scale, which is reading the weight
of all the water in the beaker, the cylinder's worth included.

OK so far?


You may continue, as I wish to see what the rest of your explanation
is. However, I am still unconvinced that there is a force on the
imaginary cylinder. If I put the pool of water into the space shuttle
and said that I see the Earth below, so that must mean that there is a
force on the cylinder pointing to the Earth, that would be not be
right. The situation in the space shuttle and on the surface of the
Earth is indistinguishable by any experiment I can think of (that
doesn't involve surrounding the cylinder with air).

wrote:
PD wrote:
[snip]
So we'll imagine our imaginary cylinder of water is part of the water
that sits in a beaker on top of the scale, which is reading the weight
of all the water in the beaker, the cylinder's worth included.

OK so far?


You may continue, as I wish to see what the rest of your explanation
is. However, I am still unconvinced that there is a force on the
imaginary cylinder. If I put the pool of water into the space shuttle
and said that I see the Earth below, so that must mean that there is a
force on the cylinder pointing to the Earth, that would be not be
right. The situation in the space shuttle and on the surface of the
Earth is indistinguishable by any experiment I can think of (that
doesn't involve surrounding the cylinder with air).

I'll address your second point first. I think you'd better see if an
experiment has been done. While a submerged styrofoam float will make
its way to the surface of the water on Earth, it will *not* move toward
the surface on the Shuttle. (This is actually an area where a lot of
interesting little experiments have been done on the Shuttle. Be
prepared to be surprised by the *real* behaviors there.) At the end, if
you're still with me, I'll be able to tell you why this happens.

Heading backwards, you are absolutely right that there is no *net*
force on the cylinder of water. If there were, it would accelerate in
one direction or another, and both because we chose the chunk of water
arbitrarily and because the water is not circulating like crazy, we
know that this is not happening.

But we have clearly shown that gravity *does* exert a force on this
chunk of water, just like it acts on all the other chunks of water (and
the scale reads the sum of all the weights of all those chunks of
water), and we already figured out how much this force is: p*A*h*g --
the force of gravity acting on that chunk is precisely the weight of
that cylinder of water.

So there must be *another* force acting on that cylinder of water, so
that the *net* force is zero. Since the gravitational force acting on
the cylinder of water is downward, this other force must be upward.
What could be the agent of this force? Well, what's in contact with
that chunk of water? (The only non-contact force present, gravity, has
already been accounted for.) The only thing that's in contact with that
cylinder of water is the rest of the water on the *outside* of that
cylinder.

This is not unreasonable. We know that all fluids (including gases and
liquids) exert a pressure against whatever surface they're in contact
with. Hoover Dam was designed to withstand that pressure, we feel the
pressure on our eardrums when we dive to the bottom of the pool, and
deep-sea submarines have to withstand the pressure of the ocean
squeezing in on their hulls.

So the water on the *outside* of the cylinder must be squeezing in on
our cylinder of water, pressing in on all sides. It is pressing
horizontally inward on the curved sides of the cylinder, and it is
pressing down on the top of the cylinder, and it is pressing up on the
bottom of the cylinder.

For reasons that will become clearer in a moment, let's imagine that we
can paint the surface of our imaginary cylinder black, so that we can't
see inwards.

OK, so we have two forces at play on our cylinder of water:
1. Gravity, which acts on the contents of the cylinder and which points
downward, and whose magnitude we know: p*A*h*g.
2. The pressure of all the water on the outside of the cylinder,
squeezing inward on the cylinder.

There is nothing else in physical contact with the cylinder and no
other non-contact force evident. We most likely have a full inventory
of forces.

With me so far?

PD

PD wrote:
[snip]

There is nothing else in physical contact with the cylinder and no
other non-contact force evident. We most likely have a full inventory
of forces.

With me so far?

PD

You're going to say that it is water pressure which is pushing up the
cylinder. I am familiar with this explanation - but what if I take the
cylinder and push it all the way to the bottom of the pool and
completely squeeze out any water from between the bottom of the
cylinder and the pool bottom. Now, there should be zero pressure from
water molecules in the critical upward vector and in fact the
unbalanced downward pressure from the top of the cylinder should keep
it at the bottom of the pool. But if the cylinder contains a less dense
substance, like air, it comes from the bottom like a cork. Where did
the upward force come from, if it didn't come from the bottom of the
cylinder? The upward force is present even when there is no water
underneath the cylinder as is evident by the force required to hold the
cylinder down on the bottom of the pool. Water pressure at the sides
can only contribute to horizontal movement and water pressure at the
top can only contribute to a downward force.

wrote:
PD wrote:
[snip]

There is nothing else in physical contact with the cylinder and no
other non-contact force evident. We most likely have a full inventory
of forces.

With me so far?

PD

You're going to say that it is water pressure which is pushing up the
cylinder. I am familiar with this explanation - but what if I take the
cylinder and push it all the way to the bottom of the pool and
completely squeeze out any water from between the bottom of the
cylinder and the pool bottom. Now, there should be zero pressure from
water molecules in the critical upward vector and in fact the
unbalanced downward pressure from the top of the cylinder should keep
it at the bottom of the pool.

Yes, indeedy. This is precisely the principle of a suction cup, which
squeezes the water out from under it, and the pressure on the top
surface holds it down. This works, as you know, just as well in air,
and in fact I have at home a nifty little neoprene ring with an inner
diameter just big enough for a can of Coke and an outer diameter of
about five inches. It takes just a little math to figure out why it
requires 200 lbs of vertical pressure to raise the Coke, even though
the whole can and ring can be easily slid off the counter top.


But if the cylinder contains a less dense
substance, like air, it comes from the bottom like a cork. Where did
the upward force come from, if it didn't come from the bottom of the
cylinder?

The trick is keeping the water from seeping back under the cylinder. If
you can keep the water from seeping back under (and here all that's
really needed is a rubber O-ring or even a dollop of Vaseline and a
smooth surface on the bottom), then you'll find that even a chunk of
styrofoam will stay on the bottom. But once the water seeps underneath,
then of course all the pressure is transmitted to all parts of the
fluid, even the little bit that seeps underneath, and there will be a
force upward.

The upward force is present even when there is no water
underneath the cylinder as is evident by the force required to hold the
cylinder down on the bottom of the pool. Water pressure at the sides
can only contribute to horizontal movement and water pressure at the
top can only contribute to a downward force.

Yes, exactly! To continue where we were going, we'll suppose that the
pressure pushes inward on all parts of the cylinder, but not
necessarily equally. There is a pressure on the top end of P(top) and
so there is a force downward on the top of P(top)*A. There is a
pressure on the bottom end of P(bottom) and so there is a force upwards
on the bottom of P(bottom)*A. For the sides, it's not clear that the
pressure near the top of the can is the same as the pressure near the
bottom of the can, but it doesn't matter, because whatever the pressure
is at the top left side of the can, there is an equal and opposite
pressure at the top right side of the can (we know left and right are
the same, because the cylinder doesn't accelerate sideways). So there
is no *net* force from side to side due to the pressure on the sides of
the cylinder.

Let's guess that the bottom pressure is larger than the top pressure.
Then the *net* force upward due to the pressure of the water outside
the cylinder is P(bottom)*A - P(top)*A =
[P(bottom) - P(top)]*A. This is precisely the buoyant force.

It is this force that has to balance the weight of the water *inside*
the can, and so we set those to be equal:
[P(bottom) - P(top)]*A = p*A*h*g
or, canceling the A's,
P(bottom) = P(top) + p*g*h.

This last equation says that, yes indeed, the pressure increases
linearly with depth.

We're almost done. OK so far?

PD

On 4 Jan 2006 15:56:37 -0800, "PD" Gave
us:

Yes, indeedy. This is precisely the principle of a suction cup, which
squeezes the water out from under it, and the pressure on the top
surface holds it down.

A suction cup works due to the flexure of the cup, the surface
quality of the cup's surface as well as the surface quality of the
surface it gets applied to. Given the right settings, it will even
work dry.