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What we think we know

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Author Topic: What we think we know  (Read 2792 times)
Majeston
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« Reply #30 on: April 20, 2007, 05:35:23 pm »

Quote
author=Daffy Duck link=topic=488.msg9438#msg9438 date=1177104255]
  In smoke or fog, turn on a flashlight - I get a beam, same with laser pointer.  Yet, it's a wave.  I'm also familiar with the 'slit experiment' (interference) on how waves can act as particles, and vice versa.  So, somewhere in there, has to be the stumbling block that I'm desperately trying to trip over.

Daffy,

from what I quoted,  light is NOT a wave but sometimes appears as one due to numerous distortions,  some of which

we have not identified or discovered.  Perhaps that is the stumbling block.

.
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« Reply #31 on: April 24, 2007, 09:03:26 pm »

Merl,

isn't it interesting that the light article that you posted used sodium atoms to slow it down and the Urantia

material named sodium and calcium as the 2 elements that attach themselves to light.


Quote
=Merlin
 I know better physicists (younger ones too) that have literally LOST THEIR MIND and have switched to mathematics instead of physics in the process.

 Grin
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19Merlin69
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« Reply #32 on: April 28, 2007, 06:33:46 pm »

This whole thing is quite confusing.  I did not know that we did not know how much light weighs. I knew from the Urantia papers that light had weight and also if gravity bends light then it must have weight.  Why don't we know how much light weighs?

Photons are massless - therefore "weightless".  The reason gravity affects them is because E=Mc2 says that mass and energy are interchangeable.  Now, because we can convert energy into mass, we know that photons have a "potential mass".  So, while they weigh nothing as a photon, once they are converted into matter, they acquire a weight.  Unfortunately - we can not convert one photon into a single fundamental particle...  it takes MANY.

I am also confused by the statement that Merl makes that potential energy adds heat.  How can something that is potential add something that is not yet manifested?  This whole thing about slowing light down or even stopping it is very very puzzling. 

Actually, even though Daffy retracted his comment, he was initially correct.  Because of the laws of thermodynamics we know that, in a closed system - all energy is accounted for.  In my comment, I said that potential energy adds "Heaft".  In the case of conversion to matter it adds mass, in the case of converting matter to energy it adds more energy.  So, in the example we were discussing, the energy expended by the lasers and the cesium gas field were input into the total system of trapping and suspension of the flat wave.  This can be evidenced by sifting the data and noticing that the standing wave is 3% larger than predicted and 21% more reactive once reanimated.  To the layman, this would be like beaming Spock to the surface and getting a chubby Scotty fired up on three pots of coffee back instead.

It brings to mind  a few Urantia quotes but I don't know if or how they really have any bearing.  Merl of course will tell me I'm being bizarre again and there is no proof, Wink  but it appears that cold rather than heat is what brings matter into existence above the level of course of spirit(intelligent) initiation.  So.  let's just skip intelligence and deal with cold since we are talking about slowing down light by the use of cold.

I really have no idea what you mean with those comments, but I'll endeavor to remain focused on the "cold aspect" of your questions.

Merl,  explain how these quotes apply or don't apply if you will to slowing down light and converting energy to matter.  Also I think ultimatons are what we have discovered and named neutrino's.  Some points to consider when we observe these light "waves" The waves apparently are an illusion..

Well, let's see a comparison then.

P461:3, 41:5.7 Solar energy may seem to be propelled in waves, but that is due to the action of coexistent and diverse influences. A given form of organized energy does not proceed in waves but in direct lines. The presence of a second or a third form of force-energy may cause the stream under observation to appear to travel in wavy formation, just as, in a blinding rainstorm accompanied by a heavy wind, the water sometimes appears to fall in sheets or to descend in waves. The raindrops are coming down in a direct line of unbroken procession, but the action of the wind is such as to give the visible appearance of sheets of water and waves of raindrops.

Sounds like it was written prior to the understanding of quantum uncertainty...  If memory serves correctly, it was.   Yes, light definitely DOES move in waves - there is absolutely no way to contradict that.  It is because photons are massless (and a seemingly infinite amount can pack into a finite space) that they defy much of the "common sense" logic applied by the UB.  this section of the text is incontrovertably incorrect.

P461:4, 41:5.8 The action of certain secondary and other undiscovered energies present in the space regions of your local universe is such that solar-light emanations appear to execute certain wavy phenomena as well as to be chopped up into infinitesimal portions of definite length and weight. And, practically considered, that is exactly what happens. You can hardly hope to arrive at a better understanding of the behavior of light until such a time as you acquire a clearer concept of the interaction and interrelationship of the various space-forces and solar energies operating in the space regions of Nebadon. Your present confusion is also due to your incomplete grasp of this problem as it involves the interassociated activities of the personal and nonpersonal control of the master universe -- the presences, the performances, and the co-ordination of the Conjoint Actor and the Unqualified Absolute.

What concerns me about this section is that it is purportedly written by the "folks that know the truth" and all they do is retort regarding our misunderstandings...  Then, they themselves (purportedly) get it dead wrong...  Doesn't inspire confidence in me old friend...  There are phenomena in physics {still} but this is not one of them.

P475:10, 42:5.1  4 The so-called ether is merely a collective name to designate a group of force and energy activities occurring in space. Ultimatons, electrons, and other mass aggregations of energy are uniform particles of matter, and in their transit through space they really proceed in direct lines. Light and all other forms of recognizable energy manifestations consist of a succession of definite energy particles which proceed in direct lines except as modified by gravity and other intervening forces. That these processions of energy particles appear as wave phenomena when subjected to certain observations is due to the resistance of the undifferentiated force blanket of all space, the hypothetical ether, and to the intergravity tension of the associated aggregations of matter. The spacing of the particle-intervals of matter, together with the initial velocity of the energy beams, establishes the undulatory appearance of many forms of energy-matter.

I need to stop now, else it will look like I'm being rude...  The aether?  Oi vey - that was a concept of the 1800's that was long since dispelled by the time of the UB.

Really - we need to stop trying to debate concepts of science with the UB, it's so incorrect that I'm stunned most of the time.  Like you said previously - stick with it on spiritual principles.
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« Reply #33 on: April 28, 2007, 07:01:51 pm »

Merl,

it's fine,  you can be rude if you need to.

You've made many assertions but you have not provided any proof,  in fact all I get back is one theory after another

with no proof.  What's with that?  It seems quite obvious that light is not a wave just as has been stated.  It states

as far as I can tell that due to the spacing of matter (most likely atoms;  electrons,  protons, neutrino's),  among other

influences not observed by us,    that it

appears as waves.  That doesn't seem to difficult to visualize.


P173:3, 15:6.8 Many comets are unestablished wild offspring of the solar mother wheels, which are being gradually brought under control of the central governing sun. Comets also have numerous other origins. A comet's tail points away from the attracting body or sun because of the electrical reaction of its highly expanded gases and because of the actual pressure of  light  and other energies emanating from the sun. This phenomenon constitutes one of the positive proofs of the reality of  light  and its associated energies; it demonstrates that  light has weight .  Light is a real substance, not simply waves of hypothetical ether.

Merl,

I don't understand why the comet's tail is a proof that light has weight.  Do you?  Can you explain it?
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« Reply #34 on: April 28, 2007, 07:05:57 pm »

Yes - heaft was a typo...  Daffy got it translated correctly: heft - "weight, solidity, and visceral power"  My bad.


Does this in any way shed 'light' on why the reconstructed wave was not an exact copy of the original - it was 'weaker' because you can't get 100% back out?  Then again, the stopped system has this extra potential (above and beyond the original sodium atoms + the original stopped wave).  And then that was excited with a second laser (I assume adding more energy)...What was left over in the sodium atoms that wasn't there in the beginning?"

Without complicating this unnecessarily, let's just stick with the added energy input in the form of the second laser and residual electron voltage from the sodium.  Summative to be sure.  For an analogy, think of a latex ballon filled with helium.  Not only do you have to input enough "physical helium" to fill the balloon, you have to put it in with enough pressure to exceed the atmospheric pressure of the surrounding space.  Also, and this is the most oft forgotten part, your pressure has to be greater than the resistance supplied by the latex material.  All of that elastic retraction is stored in the energy of the helium, not the latex.  That is kinetic energy.  So, in this story, we are stopping something with lasers and cooling.  We wouldn't be stopping it if it wasn't trying to move - right?  When the energy is removed from the laser it not only has the momentum it possessed prior to being stopped - it also has the kinetic energy usurped from the lasers that were 'stalling' it.  Instantaneously, the material LEAPS TO LIFE again once the laser is shut off.  A large part of the energy is lost due to the 'leap', but some still remains...  Energy Conservation is a beautiful thing.  Grin


Majestron:

Quote
A given form of organized energy does not proceed in waves but in direct lines.

That's the part I'm having trouble conceptualizing, even though I fully? understand and "know" it.  Like in an ocean wave, the wave is moving, but the individual water molecules are mostly just rising and falling.  SO, are photons rising and falling, travelling in a straigh line, or both?  They're obviously moving, slapping me in the retina, since I can read the drivel I type.

Don't get hung up on this - it's incorrect.  Energy of every sort moves in both straight lines and waves.  The two are not mutally exclusive.  All objects move in straight lines until they are acted upon by another object from within or without their system of existence.  Light around a sun bends due to gravity, but in this case only it's rotational symmetry is altered, not necessarily its trajectory.  It is still moving in a straight line from a 90o view!  Same goes for magnetic field lines...  Their paths are altered by the electromagnetic force, but they travel in geodesics...  Staright lines that arc in circles.  Ultimately, if we acknowledge that particles and waves do not change trajectory without being physically contacted, we are forced to admit that the fabic of space-time must warp for the effects to occur.  Make sense?

Now - as for the "waving" that you are trying to make analogous with water:  Stop it.  You are unintentionally confusing yourself.  Water waves do not help in this case.  Perform a little experiment before you reply:

Go outside tonight.  Take a healthy flashlight with you.  Light a cigarette (I do not condone smoking) and blow the smoke into the beam of light you have focused onto the darkest spot you can find (not your neighbor's bedroom window).  Watch the action of the smoke in the waves of light emanating from the end of the flash light.  Note the actions further from the light's end.  If you can manage, watch the action of the smoke outside of the beam and in the reflected light off the driveway or wall...  Contemplate what you saw and reply.  It helps if you have a Maglight quartz-halogen rechargeable with focusable beam, but any flashlight with a littel A$$ behind it will do the trick.



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« Reply #35 on: April 28, 2007, 07:12:40 pm »

Merl,

I added something to the previous post about the comet being a proof while you were replying.
will you look back on that?
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« Reply #36 on: April 28, 2007, 07:13:31 pm »

Merl,

it's fine,  you can be rude if you need to.

You've made many assertions but you have not provided any proof,  in fact all I get back is one theory after another

with no proof.  What's with that?  It seems quite obvious that light is not a wave just as has been stated.  It states

as far as I can tell that due to the spacing of matter (most likely atoms;  electrons,  protons, neutrino's),  among other

influences not observed by us,    that it

appears as waves.  That doesn't seem to difficult to visualize.

"Difficult to visulize" is not a litmus test for being correct.  If it were, the planet would be round - not sphereoid, the orbits would be circular - not elliptical, galaxies would revolve as solar systems do - not as they do and gravity would be based upon the inverse square rule - not symmetric geomterical deformation of a non-existent fabric.  

As for not supplying any proof - that's absurd and you must be in a lousy mood tongiht.  I'm not having this argument with you.  Light moves in waves, as does plasma, as does all matter under the influence of the EM field.  EVERYONE knows it in the scientific community and to request evidence to "prove" it is like asking for proof that space is cold or steel is hard - it's a well known fact.
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« Reply #37 on: April 28, 2007, 07:30:13 pm »

Merl,

I added something to the previous post about the comet being a proof while you were replying.
will you look back on that?


Photons do not have mass Buddy...  They have momentum.  The formula for understanding that is: E2 = m2c4 + p2c2 .  So - because photons have no mass, we wind up with:  m=0 so E = pc or p = E/c.  For items of mass, we wind up with E=mc2.  Using unsubstantiated comments from the UB as proof that the UB is correct and physics in general is incorrect isn't working so well.  Instead of accusing me of "not supplying proof", why don't you substantiate some of the UB's theories with well demonstrated science and then present it.  When you do that, then you can accuse me all day long if I do not respond in kind.  Until then, I hope you have a good evening (and your demeanor improves).

Nitey nite...
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« Reply #38 on: April 28, 2007, 11:19:34 pm »

Quote
Deafening silence...

Wizard, I want you to know that, even if I don't post here, I'm still lapping up every word. I understand that my lack of understanding everything you are expounding upon prevents me from responding intelligently!  So please don't let the silence stop you!.

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« Reply #39 on: April 29, 2007, 10:00:52 am »

Wizard, I want you to know that, even if I don't post here, I'm still lapping up every word. I understand that my lack of understanding everything you are expounding upon prevents me from responding intelligently!  So please don't let the silence stop you!.

I seek to explain the {apparently} inexplicable.  The primary reason for me spending time here is so that I can make science interesting to those who gave up on it years ago.  A secondary reason is to demonstrate that much of what we are being told by the mainstream (in almost every field) isn't necessarily true anymore...  Why don't you hit us with your thoughts and give those of us who are contributing, the opportunity to explain what you do not comprehend.  We do delve into the theoretical an awful lot but we are pretty good at fleshing out the observational and well understood stuff too.

So, with that said - let's have it...  Give us a thought, a pondering or a concept that you cannot wrap your brain around and we'll do our very best to explain it so that you get it.
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« Reply #40 on: April 29, 2007, 09:07:44 pm »

Quote
The primary reason for me spending time here is so that I can make science interesting to those who gave up on it years ago.  A secondary reason is to demonstrate that much of what we are being told by the mainstream (in almost every field) isn't necessarily true anymore...

I have always had a strong layman's interest in physics. It is one of my life's regrets that I did not study physics in high school (because my friends said it was too 'hard'.) A big mistake. But now, what with all the books I keep around the house and the programs I watch on the Science channel, my 17 year old son has decided to study physics in high school next year and I hope to be his biggest cheerleader on the subject!

Quote
So, with that said - let's have it...  Give us a thought, a pondering or a concept that you cannot wrap your brain around and we'll do our very best to explain it so that you get it.

I've done that on the other thread with my question on Quantum Non-locality. It is a subject of extreme interest to me and I will respond to your recent post soon!

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« Reply #41 on: May 01, 2007, 09:23:17 pm »

Quote
Go outside tonight.  Take a healthy flashlight with you.  Light a cigarette (I do not condone smoking) and blow the smoke into the beam of light you have focused onto the darkest spot you can find (not your neighbor's bedroom window).  Watch the action of the smoke in the waves of light emanating from the end of the flash light.  Note the actions further from the light's end.  If you can manage, watch the action of the smoke outside of the beam and in the reflected light off the driveway or wall...  Contemplate what you saw and reply.  It helps if you have a Maglight quartz-halogen rechargeable with focusable beam, but any flashlight with a littel A$$ behind it will do the trick.

Merl,
I tried this but used a 100,000 c.p. spot.
What I observed was that the smoke became trapped in the beam and then smoothed out into a line and it seemed to be pushed away.
What does that tell me?  Dunno,  maybe like the calicum or sodium attaching itself to photons (("This calcium atom moves outward by alternate jerks of forward propulsion, grasping and letting go the sunbeam about twenty-five thousand times each second. And this is why stone is the chief component of the worlds of space. Calcium is the most expert solar-prison escaper." ))

Now,  let me ask you this Merl,  if that above statement is true,  and I believe it is even though you state that we haven't observed it,  then in the example of the laser they are using a sodium cloud to slow down light to a standstill;  even though it is named in the Ubook that sodium and calcium atoms do the same thing as far as attaching themselves to photons;  it implies that the calcium atom is better at doing it.  It would seem to me that the same experiment could be done more efficiently if they were using a calcium cloud instead of sodium.  What would be the feasibility of carrying out the same experiment with calcium?

Do we have the technology to verify that calcium attaches and releases itself 25,000 times a second from a photon?

Quote
P461:3, 41:5.7
Solar energy may seem to be propelled in waves, but that is due to the action of coexistent and diverse influences. A given form of organized energy does not proceed in waves but in direct lines. The presence of a second or a third form of force-energy may cause the stream under observation to appear to travel in wavy formation, just as, in a blinding rainstorm accompanied by a heavy wind, the water sometimes appears to fall in sheets or to descend in waves. The raindrops are coming down in a direct line of unbroken procession, but the action of the wind is such as to give the visible appearance of sheets of water and waves of raindrops.

Quote
Don't get hung up on this - it's incorrect.  Energy of every sort moves in both straight lines and waves.  The two are not mutally exclusive.  All objects move in straight lines until they are acted upon by another object from within or without their system of existence.  Light around a sun bends due to gravity, but in this case only it's rotational symmetry is altered, not necessarily its trajectory.  It is still moving in a straight line from a 90o view!  Same goes for magnetic field lines...  Their paths are altered by the electromagnetic force, but they travel in geodesics...  Staright lines that arc in circles.  Ultimately, if we acknowledge that particles and waves do not change trajectory without being physically contacted, we are forced to admit that the fabic of space-time must warp for the effects to occur.  Make sense?

Quote
 Light moves in waves, as does plasma, as does all matter under the influence of the EM field.


Merl,
you've thrown a red herring into the mix;  the EM field.  Skip the EM field and then what do you have?  No waves right?



P476:1, 42:5.1  5
Quote
The excitation of the content of space produces a wavelike reaction to the passage of rapidly moving particles of matter, just as the passage of a ship through water initiates waves of varying amplitude and interval.


I don't know why you are so easily getting upset.  You are a theoretical physicist and I would think you would be all over this stuff.  There is enough there to keep you busy for a lifetime.  By your own admission physics is so full of errors and assumptions and theories and changes in position every time there is a new discovery that if you applied the same frustration to the Ubook that you do to physics you would have been selling burgers at McDonalds years ago.  I was just watching the Science channel;  Extreme Universe; Planet Hunters,  and it was amazing that they couldn't find a planet until some guy from Europe or something found the wobble because the planet was rotating about every 3 days instead of the 10 years or so that our guys were looking for.  You talk about inspiring confidence,  well,  let's use the mirror a bit.

Look,  I don't belong in your class.  I have no foundation for the science and math that you are dishing out.  I surmise that even other physicists have a problem with your stuff.  The only thing I have is an interest in science;  astronomy;  religion and other such fields but mainly as they pertain to the information in revelation.  The only reason I can even participate in these discussions is because of the Ubook and there are a fair amount of scientific minds with a laundry list of credentials attached to this revelation that can see it for what it is.

I gave you this statement to which you replied .........The aether?  Oi vey -
quote from: Majeston on April 19, 2007, 12:34:36 am
P475:10, 42:5.1  4
The so-called ether is merely a collective name to designate a group of force and energy activities occurring in space. Ultimatons, electrons, and other mass aggregations of energy are uniform particles of matter, and in their transit through space they really proceed in direct lines. Light and all other forms of recognizable energy manifestations consist of a succession of definite energy particles which proceed in direct lines except as modified by gravity and other intervening forces. That these processions of energy particles appear as wave phenomena when subjected to certain observations is due to the resistance of the undifferentiated force blanket of all space, the hypothetical ether, and to the intergravity tension of the associated aggregations of matter. The spacing of the particle-intervals of matter, together with the initial velocity of the energy beams, establishes the undulatory appearance of many forms of energy-matter.

what I was pointing out was this so-called undifferentiated force blanket of space and the following sentences.  The Ubook very clearly states that the hypothetical aether that you are Oi Veying about from the 1800's does not exist.  Perhaps one problem here are your "trigger" words.

Quote
=urantia
P476:2, 42:5.1  6
Primordial-force behavior does give rise to phenomena which are in many ways analogous to your postulated ether. Space is not empty; the spheres of all space whirl and plunge on through a vast ocean of outspread force-energy; neither is the space content of an atom empty. Nevertheless there is no ether, and the very absence of this hypothetical ether enables the inhabited planet to escape falling into the sun and the encircling electron to resist falling into the nucleus.

Now,  if you can  please tell me why the absence of this hypothetical aether keeps the planet from falling into the sun or the electron from falling into the nucleus.

Thank you "buddy".  Smiley







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« Reply #42 on: May 01, 2007, 09:53:37 pm »

P173:3, 15:6.8
Many comets are unestablished wild offspring of the solar mother wheels, which are being gradually brought under control of the central governing sun. Comets also have numerous other origins. A comet's tail points away from the attracting body or sun because of the electrical reaction of its highly expanded gases and because of the actual pressure of  light  and other energies emanating from the sun. This phenomenon constitutes one of the positive proofs of the reality of  light  and its associated energies; it demonstrates that  light has weight .  Light is a real substance, not simply waves of hypothetical ether.

Merl,

I don't understand why the comet's tail is a proof that light and its associated energies have weight.  Do you?  Can you explain it?

                                                       
                                               

                                                         
Quote
Photons are massless - therefore "weightless".  The reason gravity affects them is because E=Mc2 says that mass and energy are interchangeable.  Now, because we can convert energy into mass, we know that photons have a "potential mass".  So, while they weigh nothing as a photon, once they are converted into matter, they acquire a weight.  Unfortunately - we can not convert one photon into a single fundamental particle...  it takes MANY.

I don't understand why we can't convert one photon into one particle and why it takes many.  Additionally,  when we do convert photons into matter what do they become?

Thanks Merl
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« Reply #43 on: May 03, 2007, 07:58:59 pm »

.




Jet Breaking the Sound Barrier






.
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« Reply #44 on: May 04, 2007, 11:36:44 am »

Sonic Boom, Sound Barrier, and Condensation Clouds 
 Prandtl-Glauert Condensation Clouds

  Nowadays there are many photographs on the web which depict condensation clouds similar  to that seen at the right. Excellent sources of such photos include the sites by  Peter Steehouwer,  Evert Konigsveld,  Jeff Wilkinson,  and the  ChamorroBible site  and, of course, my own Gallery of Fluid Mechanics.    Unfortunately, there is also a great deal of confusion (on other sites and forums) as to the physical  origin of these clouds. Because these clouds tend to be seen when the aircraft flies at near-sonic  speeds, it is frequently said that they "visualize shock waves" or are due to the  aircraft "bursting through the sound barrier". Neither statement is true, although the  second at least suggests that the phenomena occurs in the near sonic or, in the language of aerodynamics, transonic, regime. The point of this page is to give a short, non-technical discussion of the physical origins of this  phenomenon.

The clouds appear for the same reason that clouds always form, namely, that the  air has cooled to the point that the ambient water vapor condenses. Flows around bodies and wings  always change the temperature and pressure of the fluid. It is well known that lift is caused by  pressure differences on top or bottom of a wing or body so that it ought to be obvious that the pressure  varies from point to point in a flow around an object. The fact that the temperature changes can be  seen by noting that most fluid flows and nearly every aerodynamic flow are frictionless. In the  language of thermodynamics, the flow is said to be reversible or loss-free. As a result the entropy  of the flow is a constant and the temperature (T) at each point in the flow is necessarily related to the     pressure (p) as follows:

   




 T a p(g - 1)/g, 


 (Pg1)





 for low pressure gases. The constant g is the ratio of specific heats. For  air, g = 1.4 and the exponent on the pressure (p) in the above equation is  approximately 0.29. Thus, the temperature of the air will increase and decrease as the pressure  increases and decreases. Regions of high pressure will necessarily correspond to regions of  high temperature and regions of low pressure will correspond to regions of low temperature.

Lift-Induced Condensation
 An example of condensation due to the pressure variations over wings is illustrated by the various forms of  lift-induced condensation found in my  Gallery of Fluid Mechanics. This type of condensation cloud is formed when an aircraft undergoes a high-lift  maneuver resulting in very low pressures on the upper surface of the wings. The corresponding  temperatures are so low that the water vapor condenses on the upper (low-pressure) side of the wing.  A characteristic of lift-induced condensation is that it is asymmetric, i.e., there will be much more condensation  on the upper side of the wing than on the lower side, and that it is usually associated with high-g turns.

Condensation due to the Prandtl-Glauert Singularity
 In the case of the lift-induced condensation the temperature variations found in  normal flight are exaggerated by the large pressure differences required to  generate high lift. At speeds near that of sound, the temperature and pressure variations  occurring at every speed can also be exaggerated in steady level flight. The mechanism for this near-sonic  exaggeration of the temperature variations is the so-called Prandtl-Glauert singularity which requires  that pressure and temperature perturbations approach   as the flight speed approaches the ambient sound speed. In terms of the temperature, the Prandtl-Glauert singularity  takes the form:

 
 

   
     T - T            

   
   
                 constant       

   
   
    (Pg2)     

   

   
         -----------         

   
   
             ------------------,       

   

   
         U2/2cp        

   
   
               | 1 - (M)2 |     

   



where M= the Mach number = the ratio of the  flight or far-field flow speed (denoted by U) to the sound speed of the undisturbed atmosphere. The  quantities T and cp  are the temperature and specific heat at constant pressure in the undisturbed atmosphere.    The constant in (Pg2) depends on the specific shape and orientation of the  wing or body, but not on the Mach number or aircraft speed. Equation (Pg2) holds for gases at atmospheric  pressure.   








Remark   Unfortunately, I don't know of a simple physical explanation for the existence of the  Prandtl-Glauert singularity which is easily understood by laypeople and even undergraduates  in science and engineering. Perhaps the best route is just to take my word (or, rather, the word  of the great men and women of aerodynamics) that it exists and is of the form given. Of course,  if you are an upperclassman in engineering, math, or physics, my  discussion of aerodynamic similarity laws might help guide you through the mathematical explanation.         





   A more general form of (Pg2) be found by combining the  small disturbance approximation for the temperature with the general expression for the  Prandtl-Glauert singularity, cast in terms of the pressure coefficient. 

The | 1 - (M)2 |  term seen in (Pg2) will be very small when the flight Mach number M  is near one. As a result, the right hand side of (Pg2) will be very large when  M 1 and the  temperature perturbation (T - T) will be correspondingly large.  This is the amplification referred to as the Prandtl-Glauert singularity. If the Mach number is sufficiently close to one, the temperature  perturbations in the low-pressure, low-temperature portions of the flow can become large enough to  cause condensation of the ambient water vapor. If condensation does occur, then the resultant cloud  is referred to as a Prandtl-Glauert condensation cloud. 

 Characteristic Cloud Shape
 The characteristic conical shape of the Prandtl-Glauert clouds is consistent with and can be predicted by  the characteristic flow patterns of near-sonic, i.e., transonic, flow known to aerodynamicists. An  example of the flow over a two-dimensional wing is sketched below. At flow or flight speeds near  the sound speed (M 1)  any bump, e.g., a wing or canopy, causes the pressures and temperatures to drop. The  bump can also cause the flow to become slightly supersonic; this is the case illustrated below. As indicated in the sketch, the region of low pressure and temperature will exist over a  portion of the upper and lower surfaces of the wing and will be terminated by a shock wave.   




   

 Sketch depicting the near-sonic flow over a wing. The quantity M is the Mach number which is just the  ratio of the flow speed to the sound speed and the incoming  flow is taken to be subsonic. A few temperature contours can be seen by  running your mouse over the image. 
        As pointed out in my brief discussion of shock waves, the shock decelerates the airflow and heats it. (I have also sketched the isotherms, i.e., the lines of constant temperature similar to those seen on a  weather map, for the same flow. You can see these by running your mouse over  the image.) Because the condensation is likely to be initiated along a constant temperature line, the  front of the cloud ought to inherit the conical shape of the isotherms and ought to be terminated  by a nearly flat shock surface. This, of course, is exactly what is seen in photographs such as that seen  at the top of the present page.

Good examples of the very flat base of the cloud can also be seen in the photo at the  top of the page, in a recently contributed photo of a  transonic F-14,  and in this widely distributed photo of an F4 Phantom.     

The above discussion holds when the flight speed is close enough to one to ensure that the  characteristic transonic flow pattern, complete with terminating shock wave, is established. However,  when the flight or flow speed is just at the outer edge of the transonic regime, shock waves are not generated and the  flow appears to be closer to that seen in incompressible (low speed) flows. Under these conditions,  the amplification due to the Prandtl-Glauert singularity could still be important resulting in condensation.  The difference between this marginal case and the fully developed  transonic flow illustrated in the sketch at the above left is that the temperature and cloud shape  is not likely to have the distinct "conical" shape seen in the sketch and photo above. Examples of this marginal case  are likely to be this image of a  cloud on an F-14  or even the spectacular image of the  B2 stealth bomber.

Conclusions 
 The clouds formed by the Prandtl-Glauert singularity are due to the near-sonic amplification of the pressure  and temperature perturbations which naturally occur whenever air passes over any bump or object.  Thus, an aircraft can fly at one-half or twice the speed of sound and generate no clouds.  However, if the same aircraft flies at 0.95 or 1.05 times the speed of sound, the amplification implicit  in (Pg2) may be enough to cause condensation in the low-pressure, low-temperature portions of the flow. 

Because Prandtl-Glauert condensation can form in both slightly supersonic and slightly subsonic flow, a  sonic boom may or not be  heard. 

The shape of Prandtl-Glauert condensation clouds will reflect the isotherms characteristic of  transonic flow. In many cases, the cloud will have the conical shape seen at the top of this page.  As pointed out in the previous subsection, other patterns could also be observed which are  completely consistent with the near-sonic flow patterns and temperature distributions  known to aerodynamicists. 

A common error is to state that the cloud "visualizes shock waves". As indicated above, the front  of the cloud has nothing to do with the shock wave. As a note to aspiring aerodynamicists,  the cloud also does not correspond to the flow Mach lines which tend to be nearly  vertical in near-sonic flows. Although the shock does not correspond to the leading  edge of the cloud, it does correspond to the termination of the cloud which gives rise to  the characteristic flat base of the cone.

Other earmarks of a Prandtl-Glauert condensation is that it will be reasonably symmetrical with respect to the  top and bottom of the aircraft. This fact, and the fact that Prandtl-Glauert  condensation can be seen in steady level flight, can be used to distinguish it from lift-induced  condensation which tends to be associated with high-g maneuvers and tends to occur primarily on  the upper or low-pressure side of the aircraft. 

Finally, it should be clear that Prandtl-Glauert condensation has nothing to do with "breaking the sound  barrier" and is not a Star Trek-like "burst" through Mach one. An aircraft can generate a  Prandtl-Glauert condensation cloud without ever exceeding the speed of sound. 
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