If something gives off light, is it losing mass?

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BoJangles

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<p style="margin-top:0cm;margin-left:0cm;margin-right:0cm" class="MsoNormal"><font face="Calibri" size="3">If something gives off light&nbsp;/ <span style="font-size:11pt;line-height:115%;font-family:'Calibri','sans-serif'">Em radiation </span>, is it losing mass?</font><font face="Calibri" size="3">&nbsp;</font></p><p style="margin-top:0cm;margin-left:0cm;margin-right:0cm" class="MsoNormal"><font face="Calibri" size="3">I&nbsp;searched Google but couldn&rsquo;t find the answer.</font></p><p style="margin-top:0cm;margin-left:0cm;margin-right:0cm" class="MsoNormal"><font face="Calibri" size="3">My instinct says it should, though my understanding of light being massless says it shouldn&rsquo;t.</font></p><p style="margin-top:0cm;margin-left:0cm;margin-right:0cm" class="MsoNormal"><font face="Calibri" size="3"><edit></font></p><p style="margin-top:0cm;margin-left:0cm;margin-right:0cm" class="MsoNormal"><font face="Calibri" size="3">Oops *slaps head*</font></p><p style="margin-top:0cm;margin-left:0cm;margin-right:0cm" class="MsoNormal"><font face="Calibri" size="3">E=mc^2</font></p> <div class="Discussion_UserSignature"> <p align="center"><font color="#808080">-------------- </font></p><p align="center"><font size="1" color="#808080"><em>Let me start out with the standard disclaimer ... I am an idiot, I know almost nothing, I haven’t taken calculus, I don’t work for NASA, and I am one-quarter Bulgarian sheep dog.  With that out of the way, I have several stupid questions... </em></font></p><p align="center"><font size="1" color="#808080"><em>*** A few months blogging can save a few hours in research ***</em></font></p> </div>

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DrRocket

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>If something gives off light&nbsp;/ Em radiation , is it losing mass?&nbsp;I&nbsp;searched Google but couldn&rsquo;t find the answer.My instinct says it should, though my understanding of light being massless says it shouldn&rsquo;t.<edit>Oops *slaps head*E=mc^2 <br />Posted by Manwh0re</DIV></p><p>Light is not massless.&nbsp; Light has zero rest mass, but mass and energy are the same thing.&nbsp; The energy of a photon is given by the expression E = h*nu where E is energy, h is Planck's constant and nu is the frequency of the light.&nbsp; Also E=mc^2, and&nbsp;you can solve those two equations for the mass.</p><p>So, yes if something releases a photon it loses energy and therefore loses mass.&nbsp; Conversely, if it absorbs a photon the energy increases and so does the mass.&nbsp; In fact, if you take a substance and heat it, the heat is reflected in increased energy of the&nbsp;atoms and the mass increases slightly.</p><p>Where I live it is pretty cold outside at the moment.&nbsp; If your weather is similar you can lose weight by going outside without a coat.&nbsp; But eating ice cream won't work even if it cools you down a bit. <br /></p> <div class="Discussion_UserSignature"> </div>

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BoJangles

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<p>So to calculate the energy loss of the sun (&nbsp;EM only ) would i need to know all the frequencies its emitting ?</p><p>--</p><p>Right now , we have light cloud cover and its about 25 degrees. Though that's fairly mild, it may get up into the 30's around xmass through the day.</p><p>I&nbsp;live around here.</p><p>http://maps.google.com.au/maps?f=q&hl=en&geocode=&q=runaway+bay+QLD+4216&sll=-27.91707,153.396349&sspn=0.037921,0.076904&ie=UTF8&t=h&ll=-27.917449,153.390255&spn=0.01896,0.038452&z=15&g=runaway+bay+QLD+4216&iwloc=addr</p><p>&nbsp;</p> <div class="Discussion_UserSignature"> <p align="center"><font color="#808080">-------------- </font></p><p align="center"><font size="1" color="#808080"><em>Let me start out with the standard disclaimer ... I am an idiot, I know almost nothing, I haven’t taken calculus, I don’t work for NASA, and I am one-quarter Bulgarian sheep dog.  With that out of the way, I have several stupid questions... </em></font></p><p align="center"><font size="1" color="#808080"><em>*** A few months blogging can save a few hours in research ***</em></font></p> </div>

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vogon13

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<p>&nbsp;</p><p>The mass is the E=MC^2 equivalent of the energy of motion (thermal agitation) of the objects atoms and molecules.</p><p>&nbsp;</p><p>The object would continue to emit photons of longer and longer wavelength as it cooled, with the process essentially stopping at absolute zero.</p><p>&nbsp;</p><p>The object may continue to emit something as a result of proton decay, but I gather this not a certainty yet.&nbsp; If it is found out to be true, eventually the object would vanish over longish periods of time.&nbsp; Maybe 10^100 to 10^300years.&nbsp; Make some popocorn, grab some tea and key posting here while you wait.</p><p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <div class="Discussion_UserSignature"> <p><font color="#ff0000"><strong>TPTB went to Dallas and all I got was Plucked !!</strong></font></p><p><font color="#339966"><strong>So many people, so few recipes !!</strong></font></p><p><font color="#0000ff"><strong>Let's clean up this stinkhole !!</strong></font> </p> </div>

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DrRocket

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>So to calculate the energy loss of the sun (&nbsp;EM only ) would i need to know all the frequencies its emitting ?--Right now , we have light cloud cover and its about 25 degrees. Though that's fairly mild, it may get up into the 30's around xmass through the day.I&nbsp;live around here.http://maps.google.com.au/maps?f=q&hl=en&geocode=&q=runaway+bay+QLD+4216&sll=-27.91707,153.396349&sspn=0.037921,0.076904&ie=UTF8&t=h&ll=-27.917449,153.390255&spn=0.01896,0.038452&z=15&g=runaway+bay+QLD+4216&iwloc=addr&nbsp; <br />Posted by Manwh0re</DIV></p><p>It is probably easier just to look up the energy ouput from the sun.&nbsp; </p><p>From Wiki (&nbsp;http://en.wikipedia.org/wiki/Orders_of_magnitude_(energy) )&nbsp;3.86&times;10<sup>26</sup> J, the total energy output of the Sun each second </p><p>OH MY GOD !&nbsp; You are upside down !</p><p>And you are measuring temperature in centigrade.&nbsp; We don't wear shorts here when it is 25 degrees, which it is now.</p><p><br /><img src="http://sitelife.space.com/ver1.0/Content/images/store/12/7/0c2ae3c5-1666-4dc6-976e-560aeb8abfee.Medium.jpg" alt="" /></p><p>However you don't need the cold, you have pets that can help you lose weight -- all of it.</p><p><br /><img src="http://sitelife.space.com/ver1.0/Content/images/store/0/4/40226bd1-2adb-4f84-a47a-f20526faa902.Medium.jpg" alt="" /><br /></p> <div class="Discussion_UserSignature"> </div>

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BoJangles

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<p>pןɹoʍ ǝɥʇ ɟo puǝ ǝsɹɐ ǝɥʇ</p> <div class="Discussion_UserSignature"> <p align="center"><font color="#808080">-------------- </font></p><p align="center"><font size="1" color="#808080"><em>Let me start out with the standard disclaimer ... I am an idiot, I know almost nothing, I haven’t taken calculus, I don’t work for NASA, and I am one-quarter Bulgarian sheep dog.  With that out of the way, I have several stupid questions... </em></font></p><p align="center"><font size="1" color="#808080"><em>*** A few months blogging can save a few hours in research ***</em></font></p> </div>

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SHU

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<font size="2">Many years ago, my high school physics class taught me that as an electron gives off a photon, it moves into a lower orbital and vice versa.&nbsp; My question, at the time,&nbsp;was how many possible orbitals does a hydrogen atom have?</font><br />

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Bflowing

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>Many years ago, my high school physics class taught me that as an electron gives off a photon, it moves into a lower orbital and vice versa.&nbsp; My question, at the time,&nbsp;was how many possible orbitals does a hydrogen atom have? <br />Posted by SHU</DIV><br /><br />Not a scientist, but look at hydrogen's spectra, that may give you an idea.</p><p>Can an atom spontaneously emit a photon, or that it require a photon to hit it first?&nbsp; Not counting radioactive elements.</p> <div class="Discussion_UserSignature"> </div>

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DrRocket

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>Not a scientist, but look at hydrogen's spectra, that may give you an idea.Can an atom spontaneously emit a photon, or that it require a photon to hit it first?&nbsp; Not counting radioactive elements. <br />Posted by Bflowing</DIV></p><p>It requires an electron in an excited state (so that it has a lower state to go to), when that electron moves to a lower energy state a photon is emitted with precisely the energy of the difference between the two states.&nbsp; To get to the higher state from a lower state a photon is absorbed.&nbsp; There may be some time involved between the absorption and emission of a photon, as in the pumping of a laser rod.&nbsp; And the emission may be spontaneous or stimulated, again as in a laser rod.&nbsp; <br /></p> <div class="Discussion_UserSignature"> </div>

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Saiph

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how'd you get the text upside down?! <div class="Discussion_UserSignature"> <p align="center"><font color="#c0c0c0"><br /></font></p><p align="center"><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">----</font></em></font><font color="#666699">SaiphMOD@gmail.com </font><font color="#999999"><em><font size="1">-------------------</font></em></font></p><p><font color="#999999"><em><font size="1">"This is my Timey Wimey Detector.  Goes "bing" when there's stuff.  It also fries eggs at 30 paces, wether you want it to or not actually.  I've learned to stay away from hens: It's not pretty when they blow" -- </font></em></font><font size="1" color="#999999">The Tenth Doctor, "Blink"</font></p> </div>

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vogon13

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<p>&nbsp;</p><p>Pluck anomaly or a feature ??</p><p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <div class="Discussion_UserSignature"> <p><font color="#ff0000"><strong>TPTB went to Dallas and all I got was Plucked !!</strong></font></p><p><font color="#339966"><strong>So many people, so few recipes !!</strong></font></p><p><font color="#0000ff"><strong>Let's clean up this stinkhole !!</strong></font> </p> </div>

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amaterasu

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Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>how'd you get the text upside down?! <br />Posted by Saiph</DIV><br /><br />&iquest;sıɥʇ ǝʞıl 'ǝɥ-ǝɥ&nbsp; d-: <div class="Discussion_UserSignature"> </div>

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BoJangles

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i just googled upside down html, i guess&nbsp;its just a&nbsp;combination of fonts to achieve it <div class="Discussion_UserSignature"> <p align="center"><font color="#808080">-------------- </font></p><p align="center"><font size="1" color="#808080"><em>Let me start out with the standard disclaimer ... I am an idiot, I know almost nothing, I haven’t taken calculus, I don’t work for NASA, and I am one-quarter Bulgarian sheep dog.  With that out of the way, I have several stupid questions... </em></font></p><p align="center"><font size="1" color="#808080"><em>*** A few months blogging can save a few hours in research ***</em></font></p> </div>

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UncertainH

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>In fact, if you take a substance and heat it, the heat is reflected in increased energy of the&nbsp;atoms and the mass increases slightly.Posted by DrRocket</DIV></p><p>I don't understand how heating a substance would increase its mass. When I googled this I found: http://www.mansfieldct.org/schools/mms/staff/hand/atomsheat.htm&nbsp;which states that the mass does not change. Do you have a reference that would explain the mass increase ?</p><p>&nbsp;</p><p>&nbsp;</p>

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BoJangles

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<p>hrm ill try to answer this one, heat = kinetic/potential energy = energy = mass. well at least this is what im thinking after&nbsp;watching a Richard A. Muller lecture&nbsp;; now i will step aside and let someone who actually knows tell us. </p><p>---</p><p>Richard A. Muller&nbsp;lecture on heat and atoms as refrenced above, if you work it out let me know </p><p>http://video.google.com.au/videosearch?q=physics+10+&hl=en&emb=0&aq=f#</p> <div class="Discussion_UserSignature"> <p align="center"><font color="#808080">-------------- </font></p><p align="center"><font size="1" color="#808080"><em>Let me start out with the standard disclaimer ... I am an idiot, I know almost nothing, I haven’t taken calculus, I don’t work for NASA, and I am one-quarter Bulgarian sheep dog.  With that out of the way, I have several stupid questions... </em></font></p><p align="center"><font size="1" color="#808080"><em>*** A few months blogging can save a few hours in research ***</em></font></p> </div>

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origin

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<p>I would say in most (non-nuclear)&nbsp;cases when an object gives off light it does not lose weight.&nbsp; Every object you see is 'giving off light' in a sense.&nbsp; A green piece of paper is emitting photons in a green wavelength.&nbsp; The paper is not losing weight, the electrons in the molecules that make up the green pigment are absorbing photons and&nbsp;emitting photons, there is <em>no net mass loss or gain</em>. </p><p>When a piece of metal is heated to&nbsp;a glowing red.&nbsp; The metal is giving of vast amounts of photons but it is not losing weight.&nbsp; The metal assorbs&nbsp;energy which heats the metal and then the heat is emitted by conduction, convection and ratiation - the radiation&nbsp;is in the form of photons.&nbsp;&nbsp;Again there is no <em>net loss of mass</em>.</p><p>If you look at a snapshot in time it could be that the mass of objects gain or lose small amounts of mass due to the absorption and emission of photons but to say an object loses mass when it gives off light is misleading, over a period of time the mass is not decreasing.</p><p>Clearly in nuclear reactions this is not the case - part of the mass is being converted directly into electromagnetic radiation.<br /></p> <div class="Discussion_UserSignature"> </div>

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aphh

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>i just googled upside down html, i guess&nbsp;its just a&nbsp;combination of fonts to achieve it <br /> Posted by Manwh0re</DIV></p><p>This was an interesting and educating thread for the first year physics student. Thanks! <br /><br />The upside down text is the result of Unicode, which the browsers seem to support very well. Unicode is a universal set of graphical symbols containing some 90 000 different symbols. To have a Unicode support a special Unicode compatible font is required.</p><p>Looks like the browsers come with Unicode compatibility.&nbsp;</p>

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aphh

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>I would say in most (non-nuclear)&nbsp;cases when an object gives off light it does not lose weight.&nbsp; <br /> Posted by origin</DIV></p><p>Paper does not give off light, it merely reflects existing light. If the light source truly gives off light, it would self-illuminate. Energy is used and lost so using the principles from above mass is lost aswell.&nbsp;</p>

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DrRocket

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>I don't understand how heating a substance would increase its mass. When I googled this I found: http://www.mansfieldct.org/schools/mms/staff/hand/atomsheat.htmwhich states that the mass does not change. Do you have a reference that would explain the mass increase ?&nbsp;&nbsp; <br />Posted by UncertainH</DIV></p><p>The effect is very small.&nbsp; But heating a substance increases the internal energy and E=mc^2.&nbsp; The change in mass can be calculated as delta m = delta E / c^2. </p><p>I suspect that the site you found was concerned with students not being confused by a very very old theory that postulated that heat was some sort of fluid that flowed into and out of a substance as it was heated and cooled.&nbsp; They are clearly thinking in a classical mode and the effect that causes mass increase is definitely relativistic.&nbsp; It is so small an effect under most circumstances as to not be noticeable.&nbsp; </p> <div class="Discussion_UserSignature"> </div>

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DrRocket

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>The effect is very small.&nbsp; But heating a substance increases the internal energy and E=mc^2.&nbsp; The change in mass can be calculated as delta m = delta E / c^2. I suspect that the site you found was concerned with students not being confused by a very very old theory that postulated that heat was some sort of fluid that flowed into and out of a substance as it was heated and cooled.&nbsp; They are clearly thinking in a classical mode and the effect that causes mass increase is definitely relativistic.&nbsp; It is so small an effect under most circumstances as to not be noticeable.&nbsp; <br />Posted by DrRocket</DIV></p><p>From a Wiki article on mass and energy in relativity:</p><p>"This formula also gives the amount of mass lost from a body when energy is removed. In a chemical or nuclear reaction, when heat and light are removed, the mass is decreased. So the <em>E</em> in the formula is the energy released or removed, corresponding to a mass <em>m</em> which is lost. In those cases, the energy released and removed is equal in quantity to the mass lost, times <em>c</em><sup>2</sup>. Similarly, when energy of any kind is added to a resting body, the increase in the mass is equal to the energy added, divided by <em>c</em><sup>2</sup>."</p><p>http://en.wikipedia.org/wiki/Mass-energy_equivalence<br /></p> <div class="Discussion_UserSignature"> </div>

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lildreamer

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>The effect is very small.&nbsp; But heating a substance increases the internal energy and E=mc^2.&nbsp; The change in mass can be calculated as delta m = delta E / c^2. I suspect that the site you found was concerned with students not being confused by a very very old theory that postulated that heat was some sort of fluid that flowed into and out of a substance as it was heated and cooled.&nbsp; They are clearly thinking in a classical mode and the effect that causes mass increase is definitely relativistic.&nbsp; It is so small an effect under most circumstances as to not be noticeable.&nbsp; <br />Posted by DrRocket</DIV><br /><br />Hi DrRocket</p><p>slightly off topic so forgive my ignorance but if h*nu=Mc^2 then if we were to substitute the mass of a stellar black hole, would we not end up with a extremely large frequency.&nbsp; Just thinking off the top of my head - if that frequency is beyond what we currently can&nbsp;&nbsp;"see" would that not constitute the whole idea about black hole...since we can't see it....? just a thought???</p> <div class="Discussion_UserSignature"> </div>

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DrRocket

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>Hi DrRocketslightly off topic so forgive my ignorance but if h*nu=Mc^2 then if we were to substitute the mass of a stellar black hole, would we not end up with a extremely large frequency.&nbsp; Just thinking off the top of my head - if that frequency is beyond what we currently can&nbsp;&nbsp;"see" would that not constitute the whole idea about black hole...since we can't see it....? just a thought??? <br />Posted by lildreamer</DIV></p><p>When you apply this idea to general massive bodies you get a relation that reflects the quantum mechanical wavelength associated with that body, not a wavelength of light emitted by it.&nbsp; So the frequency has little to do with "seeing" the body.&nbsp; In the case of a photon the quantam mechanical wavelength and the wavelengthe of the light are the same thing.</p><p>For bodies other than photons the wave nature was first proposed by deBroglie.&nbsp; Here is a Wiki article on the subject. http://en.wikipedia.org/wiki/De_Broglie_hypothesis</p><p>This is an interesting topic, but it has little to do with black holes.&nbsp; Black holes are a general relativistic effect that occurs with high mass density.&nbsp; Basically it is a case of having sufficient mass density that there is some spherical surface at which the escape velocity is the speed of light.&nbsp; There is a bit more to it, but it turns out that if you calculate the escape velocity using ordinary Newtonian gravity for the mass contained within sphere and find the radius at which the escape velocity is c, then that surface is the event&nbsp; horizon for the black hole.<br /></p> <div class="Discussion_UserSignature"> </div>

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lildreamer

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Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>When you apply this idea to general massive bodies you get a relation that reflects the quantum mechanical wavelength associated with that body, not a wavelength of light emitted by it.&nbsp; So the frequency has little to do with "seeing" the body.&nbsp; In the case of a photon the quantam mechanical wavelength and the wavelengthe of the light are the same thing.For bodies other than photons the wave nature was first proposed by deBroglie.&nbsp; Here is a Wiki article on the subject. http://en.wikipedia.org/wiki/De_Broglie_hypothesisThis is an interesting topic, but it has little to do with black holes.&nbsp; Black holes are a general relativistic effect that occurs with high mass density.&nbsp; Basically it is a case of having sufficient mass density that there is some spherical surface at which the escape velocity is the speed of light.&nbsp; There is a bit more to it, but it turns out that if you calculate the escape velocity using ordinary Newtonian gravity for the mass contained within sphere and find the radius at which the escape velocity is c, then that surface is the event&nbsp; horizon for the black hole. <br />Posted by DrRocket</DIV><br /><br />Thankyou for your reply.... <div class="Discussion_UserSignature"> </div>

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jdweston

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<p>It was recomended to me to post this over here.</p><p>&nbsp;</p><p>T&rsquo;was the night before Everything</p><p>By Daniel Weston</p><p><br />T&rsquo;was the night before, (as if night mattered) <br />and all through the universe,<br />not a fermion was stirring, <br />not a quark or it&rsquo;s inverse.</p><p>Everything was nothing <br />yet in a moment later,<br />the size of a dot, <br />something - an energy radiator.</p><p>Then a phase transition, <br />caused a cosmic inflation,<br />that grew exponentially towards, <br />quark-gluon plasmatiation.</p><p>An excess of quarks as it cooled <br />In the first seconds,<br />by the time down to a billion K, <br />an annihilation dance beckons.</p><p>Time not to rest still way too hot, just not as hot as before,<br />particle energies drop, now the physics we can&rsquo;t ignore.</p><p>379,000 light years later<br />the electrons and then nuclei combine,<br />Still 11,000 plus degrees C, <br />now into atoms it finally sublimes.</p><p><br />Then slowly gravitationally attracted, <br />to nearby each others and more,<br />two, four, eight, a million,<br />soon sextillions and decillions galore.</p><p><br />Then speckles and sparkles,<br />like first falling snow,<br />gives a depth to space, <br />and a pattern to the glow.</p><p><br />When out on the edge,<br />a shutter, and chatter,<br />from the swirls and the collapses, <br />out-shed matter.</p><p><br />When, what to the deep <br />and the deeper should show,<br />But a star that lasts more <br />then a fleeting you know.</p><p><br />With a force super lively <br />and light way too bright,<br />They shine, fade, expand, <br />and explode with the might.</p><p><br />More and more the elements <br />by orbital came,<br />And they spun in layers, <br />and periodic by name!</p><p><br />"Take Hydrogen first! <br />and now Helium! too, <br />make Lithium and Carbon <br />to name just a few!</p><p>Now, Nitrogen!, Now Oxygen! Now Beryllium and Boron!,<br />Now more and more and more they flew on!</p><p>To the column of the group and rows of little balls,<br />Now fusion away! Fusion away! Fusion away all!"</p><p>And then, in a twinkling of stars, <br />and a swill of dust danced,<br />Galactic arms twist to a center, <br />that disappeared into blackness.</p><p>Pulled towards the hole, <br />with one last drift around,<br />Down the chimney the light went <br />with only a slight sound.</p><p><br />Gravity wins or does it really a few great minds must ponder,<br />Does something leak out and flatten the warp, they now all wonder.</p><p>Space-time bends and it twists, <br />but does it break or falter.<br />Can we ever know just one <br />everything equation or another.</p><p><br />With all this and that when you add all the parts,<br />the mass not enough to hold the whole thing should fall apart.</p><p>The numbers not-exact but checked time and time again by the add-ers,<br />There&rsquo;s only one answer (maybe), it's full of Dark matter!</p><p><br />Will it grow forever, <br />until it&rsquo;s runs out and lapses,<br />Just can&rsquo;t stay the same, <br />must at least relapses!</p><p>But what is the mass balance <br />and how will we know,<br />whether times runs forever, <br />or someday backwards to no.</p><p><br />We measured the shift rates and much to our surprise,<br />not only just away they all flew but still accelerating, we weren't very wise.</p><p>So we heard it exclaim,<br />I go &lsquo;perpetually out of sight,<br />"Happy forever to all, <br />and to all a very slowly dimming night!"</p><p><br />---30&mdash;&nbsp;</p>

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BoJangles

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<font color="#5574b9">jdweston</font> why are you splattering threads with that nonsense. <div class="Discussion_UserSignature"> <p align="center"><font color="#808080">-------------- </font></p><p align="center"><font size="1" color="#808080"><em>Let me start out with the standard disclaimer ... I am an idiot, I know almost nothing, I haven’t taken calculus, I don’t work for NASA, and I am one-quarter Bulgarian sheep dog.  With that out of the way, I have several stupid questions... </em></font></p><p align="center"><font size="1" color="#808080"><em>*** A few months blogging can save a few hours in research ***</em></font></p> </div>

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