More (indirect) evidence for Dark Energy

[derekmcd]

<h1 class="style1"><font size="3" color="#000000"><strong>Hawaii Scientists Find Direct Evidence of &ldquo;Dark Energy&rdquo; in Supervoids and Superclusters</strong></font></h1><p><em>A team of astronomers at the University of Hawaii Institute for Astronomy (IfA) led by Dr. Istv&aacute;n Szapudi has found direct evidence for the existence of &ldquo;dark energy.&rdquo; Dark energy works against the tendency of gravity to pull galaxies together and so causes the universe&rsquo;s expansion to speed up. The nature of dark energy (what precisely it is, and why it exists) is one of the biggest puzzles of modern science.</em></p><p><em>This is arguably the clearest detection to date of dark energy&rsquo;s stretching effect on vast cosmic structures: there is only a one in 200,000 chance that the detection would occur by chance. </em></p> <p><em>&ldquo;We were able to image dark energy in action, as it stretches huge supervoids and superclusters of galaxies,&rdquo; Szapudi said. Superclusters are vast regions of space, half a billion light-years across, that contain an unusually high concentration of galaxies, while supervoids are similarly sized regions with a below-average number of galaxies. They are the largest structures known in the universe. The team made the discovery by measuring the subtle imprints that superclusters and supervoids leave in microwaves that pass through them. </em></p> <p><em>&ldquo;When a microwave enters a supercluster, it gains some gravitational energy, and therefore vibrates slightly faster,&rdquo; explained Szapudi. &ldquo;Later, as it leaves the supercluster, it should lose exactly the same amount of energy. But if dark energy causes the universe to stretch out at a faster rate, the supercluster flattens out in the half-billion years it takes the microwave to cross it. Thus, the wave gets to keep some of the energy it gained as it entered the supercluster.&rdquo;</em> </p><p>&nbsp;</p><p>Rest of story at link below:&nbsp;</p><p>http://www.ifa.hawaii.edu/info/press-releases/szapudi-7-08/</p><p>&nbsp;</p><p>Here is the Arxiv pre-print which will appear in the Astrophysical Journal Letters within the next 2 months:<font size="2"></font></p><p>http://arxiv.org/abs/0805.3695</p> <div class="Discussion_UserSignature"> <div> </div><br /><div><span style="color:#0000ff" class="Apple-style-span">"If something's hard to do, then it's not worth doing." - Homer Simpson</span></div> </div>

 

[derekmcd]

<p>I think calling it "direct" evidence might not be appropriate and misleading.&nbsp; In reality, I think it is just more compelling evidence to support a positive cosomological constant.&nbsp; It's not really direct evidence in the way of find out what exactly is causing this phenomena.</p><p>One could only hope the LHC could open some doors up here... that would be "direct" evidence. </p><br /> <div class="Discussion_UserSignature"> <div> </div><br /><div><span style="color:#0000ff" class="Apple-style-span">"If something's hard to do, then it's not worth doing." - Homer Simpson</span></div> </div>

 

[michaelmozina]

<p>Keep in mind that I'm "laying low" at the moment and I have no desire or intention to get into a whole discussion about "dark energy".&nbsp; I am however curious about the "method" being used here and I wondered if you could help me out.&nbsp; Again, I don't want this to become adversarial in the least and I'm only interested in the mechanics of the method itself, not the topic of 'dark energy". </p><p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>&ldquo;When a microwave enters a supercluster, it gains some gravitational energy, and therefore vibrates slightly faster,&rdquo; explained Szapudi. &ldquo;Later, as it leaves the supercluster, it should lose exactly the same amount of energy.</DIV></p><p>I follow the argument to this point.</p><p>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>But if dark energy causes the universe to stretch out at a faster rate, the supercluster flattens out in the half-billion years it takes the microwave to cross it. Thus, the wave gets to keep some of the energy it gained as it entered the supercluster.</DIV></p><p>My confusion may have a lot to do with not properly undestanding the "lingo" here but what exactly do they mean about it "flattening out"? &nbsp; Do they mean that they "spread out"? &nbsp;&nbsp; I didn't think that grouped clusters of galaxies spread out.&nbsp; I don't quite understand what they mean here and maybe you could clerify this point for me.</p><p>Again, please keep in mind that I'm not interested in discussing the "cause" of anything, just the mechanics of what they are suggesting is occuring.&nbsp; What do they mean when they say that the supercluster "flattens out"? </p> <div class="Discussion_UserSignature"> It seems to be a natural consequence of our points of view to assume that the whole of space is filled with electrons and flying electric ions of all kinds. - Kristian Birkeland </div>

 

[DrRocket]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>Keep in mind that I'm "laying low" at the moment and I have no desire or intention to get into a whole discussion about "dark energy".&nbsp; I am however curious about the "method" being used here and I wondered if you could help me out.&nbsp; Again, I don't want this to become adversarial in the least and I'm only interested in the mechanics of the method itself, not the topic of 'dark energy". I follow the argument to this point.My confusion may have a lot to do with not properly undestanding the "lingo" here but what exactly do they mean about it "flattening out"? &nbsp; Do they mean that they "spread out"? &nbsp;&nbsp; I didn't think that grouped clusters of galaxies spread out.&nbsp; I don't quite understand what they mean here and maybe you could clerify this point for me.Again, please keep in mind that I'm not interested in discussing the "cause" of anything, just the mechanics of what they are suggesting is occuring.&nbsp; What do they mean when they say that the supercluster "flattens out"? <br />Posted by michaelmozina</DIV></p><p>They are saying that if the group&nbsp;of superclusters is moving apart, due to expansion of the universe or any other cause, then the concentration of mass is reduced and therefore the curvature of space-time is reduced.&nbsp; That results in less redshift coming out of the gravity well than the blueshift that occurred when it entered a considerable period of time earlier.</p><p>I don't understand why dark energy or accelerated expansion is necessary for this mechanism to work.&nbsp; It seems to me that all that is needed is for the expansion rate to be high enough that there is a significant change in the curvatue over the time period required for light to cross the region of the grouped clusters.&nbsp; Accelerated expansion would tend to amplify the effect.<br /></p> <div class="Discussion_UserSignature"> </div>

 

[michaelmozina]

I think that answers both of my basic questions.&nbsp; "Flatten"="Spread" and yes, superclusters do spread apart. <div class="Discussion_UserSignature"> It seems to be a natural consequence of our points of view to assume that the whole of space is filled with electrons and flying electric ions of all kinds. - Kristian Birkeland </div>

 

[michaelmozina]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>I don't understand why dark energy or accelerated expansion is necessary for this mechanism to work.&nbsp; It seems to me that all that is needed is for the expansion rate to be high enough that there is a significant change in the curvatue over the time period required for light to cross the region of the grouped clusters.&nbsp; Accelerated expansion would tend to amplify the effect. <br /> Posted by DrRocket</DIV></p><p>FYI, I agree with you on both points. </p> <div class="Discussion_UserSignature"> It seems to be a natural consequence of our points of view to assume that the whole of space is filled with electrons and flying electric ions of all kinds. - Kristian Birkeland </div>

 

[DrRocket]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>I think that answers both of my basic questions.&nbsp; "Flatten"="Spread" and yes, superclusters do spread apart. <br />Posted by michaelmozina</DIV></p><p>No, flatten = reduced curvature.&nbsp; The spreading out of the superclusteres reduces the density of mass in the area and that reduces the local&nbsp;curvature of space.</p> <div class="Discussion_UserSignature"> </div>

 

[michaelmozina]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>No, flatten = reduced curvature.&nbsp; The spreading out of the superclusteres reduces the density of mass in the area and that reduces the local&nbsp;curvature of space. <br /> Posted by DrRocket</DIV></p><p>Fine, have it your way.&nbsp; &nbsp;&nbsp; I think I do finally grasp the concepts now and that was my primary motive.&nbsp; I think I also grasp why they used the term "flattening' now as well based on your curvature explanation.&nbsp; Thanks for the detailed explanation.&nbsp; </p> <div class="Discussion_UserSignature"> It seems to be a natural consequence of our points of view to assume that the whole of space is filled with electrons and flying electric ions of all kinds. - Kristian Birkeland </div>

 

[yevaud]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>Fine, have it your way.&nbsp; &nbsp;&nbsp; I think I do finally grasp the concepts now and that was my primary motive.&nbsp; I think I also grasp why they used the term "flattening' now as well based on your curvature explanation.&nbsp; Thanks for the detailed explanation.&nbsp; <br /> </p><p>Posted by <em>michaelmozina</em></DIV></p><p>Just think a Geodesic.&nbsp; Less curvature of space means less distance travelled. </p> <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>

 

[michaelmozina]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>Just think a Geodesic.&nbsp; Less curvature of space means less distance travelled. <br /> Posted by yevaud</DIV></p><p>I guess I understand how this method could be used to observe basic expansion as DrRocket suggested, but I'm still a little murky on how they could tell that anything was actually accelerating from this data.&nbsp; I guess it's time for me to actually read the paper. </p> <div class="Discussion_UserSignature"> It seems to be a natural consequence of our points of view to assume that the whole of space is filled with electrons and flying electric ions of all kinds. - Kristian Birkeland </div>

 

[emperor_of_localgroup]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>I guess I understand how this method could be used to observe basic expansion as DrRocket suggested, but I'm still a little murky on how they could tell that anything was actually accelerating from this data.&nbsp; I guess it's time for me to actually read the paper. <br />Posted by michaelmozina</DIV><br /><br /><font size="2">Sorry about this post. I'm deleting it. Please ignore my rants and keep the thread alive.&nbsp;</font></p><p><font size="2">I was reading a book by Lee Smolin and many new thoughts came to me. </font></p><p><font size="2"><font color="#ff0000"><br /> </font></font></p><p>&nbsp;</p> <div class="Discussion_UserSignature"> <font size="2" color="#ff0000"><strong>Earth is Boring</strong></font> </div>

 

[UFmbutler]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>What bothers me&nbsp; most about this 'direct' or 'indirect' evidence of dark energy or dark matter&nbsp; is these so called energy was always there, billions of years. We have been observing the deep sky with very high powered telescopes for over a century. We now suddenly discover an anomaly in supernova and other space objects.&nbsp; Why do I have a suspicion that if there were no theory on dark energy, we wouldn't &nbsp;have an anomaly in anything observed. What happened to finding 'anomaly' first and then explain in a theory?May be my cracked theory is right. Nothing exists until we look for it.&nbsp; <br /> Posted by emperor_of_localgroup</DIV></p><p>Dark matter wasn't proposed until an anomaly, the galaxy's flat(more than it should be) rotation curve, was observed.&nbsp; Dark energy was introduced in part because of the observed anomaly that the expansion of the universe is accelerating.&nbsp; This is the scientific method.&nbsp; A theory was proposed, and now evidence is being gathered to either support or refute it.&nbsp; Why would we be looking for things we have no reason to believe exist?&nbsp;&nbsp; </p> <div class="Discussion_UserSignature"> </div>

 

[derekmcd]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>I don't understand why dark energy or accelerated expansion is necessary for this mechanism to work.&nbsp; It seems to me that all that is needed is for the expansion rate to be high enough that there is a significant change in the curvatue over the time period required for light to cross the region of the grouped clusters.&nbsp; Accelerated expansion would tend to amplify the effect. <br /> Posted by DrRocket</DIV></p><p>I think that is the whole point of these findings.&nbsp; In a flat, matter dominated universe, the expansion wouldn't be enough to notice these effects.&nbsp; As far as I know, the Hubble Constant is only constant over space, but not time.&nbsp; It's actually slowing down.&nbsp; The latest WMAP measurements have the universe as flat.&nbsp; If it was matter dominated as they thought over 10 years ago, our observations would be different.&nbsp; In a universe dominated by dark energy and an observed acceleration, the CMB anistropies due to late-time integrated Saches-Wolfe effect simply agree with dark energy and accelerated expansion.</p><p>The speed at which these superclusters' gravity wells are flattening out couldn't be explained in a flat, matter dominated universe... the Hubble expansion wouldn't fit the observations.&nbsp;</p> <div class="Discussion_UserSignature"> <div> </div><br /><div><span style="color:#0000ff" class="Apple-style-span">"If something's hard to do, then it's not worth doing." - Homer Simpson</span></div> </div>

 

[DrRocket]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>I think that is the whole point of these findings.&nbsp; In a flat, matter dominated universe, the expansion wouldn't be enough to notice these effects.&nbsp; As far as I know, the Hubble Constant is only constant over space, but not time.&nbsp; It's actually slowing down.&nbsp; The latest WMAP measurements have the universe as flat.&nbsp; If it was matter dominated as they thought over 10 years ago, our observations would be different.&nbsp; In a universe dominated by dark energy and an observed acceleration, the CMB anistropies due to late-time integrated Saches-Wolfe effect simply agree with dark energy and accelerated expansion.The speed at which these superclusters' gravity wells are flattening out couldn't be explained in a flat, matter dominated universe... the Hubble expansion wouldn't fit the observations.&nbsp; <br />Posted by derekmcd</DIV></p><p>As I understand it this experiment is a direct observation of the integrated Sachs-Wolfe effect, which is basically a somewhat less than average redshift in the direction of high galactic density -- basically a blue shift superimposed on the average redshift.&nbsp; The mechanism is that photons enter a gravity well, are blue-shifted and then are red-shifted again when they come out.&nbsp; But if the gravity well has flattened due to expansion of the universe while they are in the well the red-shift as they come out does not quite compensate for the blue shift on entering.&nbsp; That mechanism only requires a measurable expansion while the photons are traversing the gravity well.&nbsp; It does not explicitly require acceleration of the expansion, although acceleration of the expansion would help to provide enough flattening while the photon is crossing the gravity well.</p><p>I know what Wiki says, but I don't always trust Wiki.&nbsp; What is missing from my perspective is the justification that only through accelerated expansion could there be enough expansion while the photons are crossing the gravity wells to cause the integrated Sachs-Wolfe effect.&nbsp; I don't buy a simple line in the sand between matter-dominated and dark energy dominated.&nbsp; There is too much room in that spectrum.&nbsp; </p> <div class="Discussion_UserSignature"> </div>

 

[derekmcd]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>As I understand it this experiment is a direct observation of the integrated Sachs-Wolfe effect, which is basically a somewhat less than average redshift in the direction of high galactic density -- basically a blue shift superimposed on the average redshift.&nbsp; The mechanism is that photons enter a gravity well, are blue-shifted and then are red-shifted again when they come out.&nbsp; But if the gravity well has flattened due to expansion of the universe while they are in the well the red-shift as they come out does not quite compensate for the blue shift on entering.&nbsp; That mechanism only requires a measurable expansion while the photons are traversing the gravity well.&nbsp; It does not explicitly require acceleration of the expansion, although acceleration of the expansion would help to provide enough flattening while the photon is crossing the gravity well.I know what Wiki says, but I don't always trust Wiki.&nbsp; What is missing from my perspective is the justification that only through accelerated expansion could there be enough expansion while the photons are crossing the gravity wells to cause the integrated Sachs-Wolfe effect.&nbsp; I don't buy a simple line in the sand between matter-dominated and dark energy dominated.&nbsp; There is too much room in that spectrum.&nbsp; <br /> Posted by DrRocket</DIV></p><p>I think that they are recognizing variations in the redshift much the same way they did with type Ia SNe.&nbsp; The farther back you look when the universe was matter dominated, the expansion was actually slowing down as expected due the Hubble constant slowing down (it's constant through space, but not over time).&nbsp; When observing more local supercluster/voids when dark energy took over, the variations are different and the correlation is made that there is an accelerated expansion.</p><p>IIRC, SNe at say a redshift of Z=2, the SNe are what you would expect given the Hubble constant at that time.&nbsp; However at Z=1, they are dimmer than expected, therefore the expansion must be accelerating during that time.&nbsp; (I don't know what the actual redshift number is for when we passed from a decelerating to an accelerating universe... i think it is ~Z=1.5)</p><p>I would assume they are finding the same patterns using the the anisotropies of the CMB.&nbsp;</p><p>I'd say that's some mighty compelling evidence for a positive Lambda.&nbsp; Two completely independent observations that agree the Universe started to accelerate at a given time.&nbsp; Now if we can just figure out what the heck is causing it. </p> <div class="Discussion_UserSignature"> <div> </div><br /><div><span style="color:#0000ff" class="Apple-style-span">"If something's hard to do, then it's not worth doing." - Homer Simpson</span></div> </div>

 

[derekmcd]

<p>And yet there is more:</p><p><strong>This arxiv paper</strong> that the article is referring only alludes briefly and indirectly to dark energy as the main thrust of the paper was in describing the galaxy.&nbsp; I think the article sufficiently elucidates why this is (indirect) proof. </p><p>http://www.space.com/scienceastronomy/080825-galaxy-cluster.html</p><p><font face="Verdana, Helvetica, sans-serif" size="3" color="#1b4872"><strong>Giant Galaxy Cluster Seen in Early Universe</strong></font> </p><p><em><font face="arial" size="2"><font face="arial"><p class="MsoNormal">Astronomers have glimpsed the largest cluster of galaxies ever seen in the distant, early universe. </p> <p class="MsoNormal">The discovery of this far-off group, estimated to contain as much mass as a thousand large galaxies, offers further proof of the existence of the enigmatic force called dark energy. </p> <p class="MsoNormal">"This is the most luminous, and therefore probably the most massive, cluster of galaxies discovered at this epoch," said Georg Lamer of the Astrophysikalisches Institut Potsdam in Germany, who led the team that discovered it. "The light we observe started about 7.7 billion years ago. This is about half of the age of the universe, so it is from quite long ago, and quite far away."</p> <p class="MsoNormal">When astronomers look at distant objects, they are looking back in time, in this case seeing objects that are 7.7 billion light-years away.</p> <p class="MsoNormal">Lamer and his team discovered the cluster, known by its catalogue number, 2XMM J083026+524133, by chance while they were surveying a portion of sky for a catalogue of X-ray sources. Using the European Space Agency's orbiting X-ray observatory XMM-Newton, they spotted an extremely bright object without any galaxy visible in optical light nearby. </p> <p class="MsoNormal">After noticing the aberrant object, they took a deeper exposure with the Large Binocular Telescope in Arizona and determined that the source of the light was a far-off group of galaxies containing the mass of about 1,000 Milky Ways.</p> <p class="MsoNormal">The astronomers say the discovery offers further proof of the mysterious force called dark energy that scientists think propels the acceleration of the universe's expansion. Dark energy is believed to account for about 70 percent of the universe, with the remaining portion made up of normal matter and its enigmatic sister, dark matter.</p> <p class="MsoNormal">"The existence of the cluster can only be explained with dark energy," Lamer said.</p> <p class="MsoNormal">Since dark energy is contributing to the stretching of the universe, and speeding up the process of galaxies receding from each other, it hampers the growth of massive galaxy clusters in more recent times. </p> <p class="MsoNormal">To test dark energy, scientists compare frequency of these massive clusters today with earlier times. If there were no dark energy, they would expect clusters to grow relatively quickly, so the largest clusters we see now would be very small at half the age of the universe, and there would be no gigantic clusters.</p> <p class="MsoNormal">"The fact that we do find these clusters is a clear confirmation of dark energy," Lamer told SPACE.com. "This was a very long time ago and it's actually about as massive as the most massive ones we observe today. Without dark energy we would observe much more massive clusters and many more of these massive clusters than we actually do."</p> <p class="MsoNormal">The discovery will be detailed in a forthcoming issue of the journal Astronomy & Astrophysics.</p></font></font></em></p><p>&nbsp;</p> <div class="Discussion_UserSignature"> <div> </div><br /><div><span style="color:#0000ff" class="Apple-style-span">"If something's hard to do, then it's not worth doing." - Homer Simpson</span></div> </div>

 

[michaelmozina]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>The astronomers say the discovery offers further proof of the mysterious force called dark energy that scientists think propels the acceleration of the universe's expansion. Dark energy is believed to account for about 70 percent of the universe, with the remaining portion made up of normal matter and its enigmatic sister, dark matter. "The existence of the cluster can only be explained with dark energy," Lamer said. Since dark energy is contributing to the stretching of the universe, and speeding up the process of galaxies receding from each other, it hampers the growth of massive galaxy clusters in more recent times. To test dark energy, scientists compare frequency of these massive clusters today with earlier times. If there were no dark energy, they would expect clusters to grow relatively quickly, so the largest clusters we see now would be very small at half the age of the universe, and there would be no gigantic clusters. "The fact that we do find these clusters is a clear confirmation of dark energy," Lamer told SPACE.com.</DIV></p><p>From a skeptics perspective, this argument amounts to "Look, there's a big cluster of older galaxies.&nbsp; Dark energy did it!".&nbsp; There's absolutely no correlation at all between the age or the size or the cluster and the existence of dark energy. It's a complete non-sequitur. </p><p>&nbsp;</p><p>&nbsp;</p> <div class="Discussion_UserSignature"> It seems to be a natural consequence of our points of view to assume that the whole of space is filled with electrons and flying electric ions of all kinds. - Kristian Birkeland </div>

 

[UFmbutler]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>From a skeptics perspective, this argument amounts to "Look, there's a big cluster of older galaxies.&nbsp; Dark energy did it!".&nbsp; There's absolutely no correlation at all between the age or the size or the cluster and the existence of dark energy. It's a complete non-sequitur. &nbsp;&nbsp; <br /> Posted by michaelmozina</DIV></p><p>That's not a skeptic's perspective, thats the perspective of someone who didn't read the paper/article.</p> <div class="Discussion_UserSignature"> </div>

 

[derekmcd]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>From a skeptics perspective, this argument amounts to "Look, there's a big cluster of older galaxies.&nbsp; Dark energy did it!".&nbsp; There's absolutely no correlation at all between the age or the size or the cluster and the existence of dark energy. It's a complete non-sequitur. &nbsp;&nbsp; <br /> Posted by michaelmozina</DIV></p><p>Do you even understand the correlation they are making?&nbsp;</p> <div class="Discussion_UserSignature"> <div> </div><br /><div><span style="color:#0000ff" class="Apple-style-span">"If something's hard to do, then it's not worth doing." - Homer Simpson</span></div> </div>

 

[R1]

<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>I don't understand why dark energy or accelerated expansion is necessary for this mechanism to work.&nbsp; It seems to me that all that is needed is for the expansion rate to be high enough that there is a significant change in the curvatue over the time period required for light to cross the region of the grouped clusters.&nbsp; Accelerated expansion would tend to amplify the effect. <br />Posted by DrRocket</DIV><br /><font size="2">&nbsp;</font></p><p><font size="2">Good point.&nbsp; It almost seems that the expectation would have <em>otherwise</em> been that the supercluster's 'well' would not have flattened?&nbsp; On a standard&nbsp;yet 'high' expansion rate within the 'well', the mechanism appears to work equally as well&nbsp;to me, I see what you mean (but would we question why superclusters appear to be inflating?). </font></p><p><font size="2">So I wonder if perhaps what was needed was various extensive calculations, given that these are large time spans, in order to accomodate all&nbsp;relevant changes within the system.&nbsp;&nbsp;This may be how&nbsp;the possible&nbsp;acceleration was&nbsp;observed.&nbsp; It probably came up in the results that in the given time spans acceleration was necessary to overcome the well's [negative acceleration] gravity?</font></p><p><font size="2">On a similar thought what I don't&nbsp;easily understand is why the wave's energy would revert to its initial condition.&nbsp; With a large t needed to traverse the well, I would think considerable total change to the well occurs either way, even a possible contraction, should there not even be any expansion.&nbsp; So my first thought is that this frequency restoration is meant to work only in reasonably small systems?</font></p> <div class="Discussion_UserSignature"> </div>