Understanding the Universe by Don Lincoln

Recommend, review, and discuss science related books that you have read, movies/tv programs you've watched, or Podcasts you listen to.

Understanding the Universe by Don Lincoln

Postby Cyndi Loo on December 21st, 2005, 4:10 pm 

This is another great book. It has more information between its cover than I have found in any other book to date. The author, Don Lincoln, is an experimental physicist at Fermilab. The chapter devoted to Accelerators and Detectors is outstanding. He explains not just the theories behind quarks and leptons, but goes into great detail about what they are composed of and even more intriguing, how they react to each other and the energy around them. Truly amazing to find in a book! Most authors give theory only. Mr. Lincoln gives a firsthand perspective to subjects others can only read about! Very nice! There is a whole chapter devoted to Higgs. There are many, many detailed diagrams. This book is making it to the shelves of my personal library.

A dream come true would be if Mr. Lincoln signed into SCF and chatted!
Cyndi Loo
 


Response to review of Understanding the Universte

Postby Lincoln on December 29th, 2005, 3:18 pm 

Dear Ms. Loo,

Thank you for your kind words about my book "Understanding the Universe." I had hoped that the added experimental detail would be received well by the curious lay reader.

On a separate note, if chatting with me on this bulletin board constitutes a dream come true, then I might suggest you could dream bigger.

Best regards,

Don Lincoln
User avatar
Lincoln
Resident Expert
 
Posts: 11095
Joined: 29 Dec 2005
Location: Deep in a lab...


Postby Cyndi Loo on December 30th, 2005, 6:18 pm 

Dear Mr. Lincoln,

With regard, there are few who dream larger than Cyndi Loo. Even fewer who ask as many questions.

Thank you for taking the time to post. In truth, it would be difficult to find a lay person as interested in quantum as I am. Finding a book such as your's is the only opportunity I will ever have to learn what I so very much want to know about quantum. It is difficult to find anyone with as strong of interest in particles as I have, and even more difficult to find anyone willing to discuss, or really in my case to consider answering my thought. Your book has been an amazing experience to read and I have learned much.

Thank you for writing it, and thank you for posting.

Cyndi
Cyndi Loo
 


Postby Lincoln on December 30th, 2005, 6:26 pm 

You are welcome.

If you have specific questions, I can answer them, at least until other obligations become pressing. Or I could suggest alternative sources of information.

Best regards and Happy New Year,

Don L
User avatar
Lincoln
Resident Expert
 
Posts: 11095
Joined: 29 Dec 2005
Location: Deep in a lab...


Postby Cyndi Loo on January 2nd, 2006, 3:20 pm 

It is my hope your holiday season was warm, happy, and filled with warm and happy family and friends! Thank you Don L for the opportunity to discuss and to learn. It is so very much appreciated!

Indeed I do have thought I have been hoping someone would consider answering! If I ask too many questions, please do not hesitate to bring this to my attention, as I can become very involved in thought. Any thought you would like to contribute to the board would be of great interest to me as well. I would consider it a priveledge to read it, and attempt to discuss it. In fact, Rettaw and Josh may also be interested as well. They have both been formally educated in quantum, and their thought tends to be more mainstream than mine, which can sometimes be a little off because as I have stated I am self-educated! Hope it's okay!

Recently I read the strong nuclear force, the weak nuclear force, and the electromagnetic force are all one force which is modified by different particle interactions in quantum scale. If this is so, could it be that gravity (in quantum scale) might also be the result of particle interaction, or even a result of the three forces formed by the particle interaction? Also, has Fermillab established any combinations of particles that result in these changes in this force?

One thing I found particularly fascinating about "Understanding the Universe from Quarks to the Cosmos" was that particles do not decay in the traditional sense of the word. They actually decay or evolve into another type of particle, and actually have been established and defined into which particle they will become. Would you mind sharing how this process was discovered? I am very fascinated by it.

While I have many, many more questions, I do not want to take up too much of your time, so I will start with these and if you have time, later progress from there.

Thank you again. You are very much appreciated!

Cyndi
Cyndi Loo
 


Questions, questions, questions

Postby Lincoln on January 3rd, 2006, 1:13 am 

Dear Ms. Loo,

I do not ordinarily enter online forums, as I get a lot of email since the book came out, but your questions are ones of general interest and so I will address them.

The first question you asked pertains to the unification of the electromagnetic, weak and strong forces and you were wondering if gravity could join the troika. I am afraid I must say that you were misinformed. In the late 60's, several physicsts (of which a subset...Weinberg, Glashow and Salam...shared the Nobel Prize in 1979) were able to show that the electromagnetic and the weak nuclear force were, in fact, different facets of a single force, termed the electroweak force. The details of this are pretty arcane, but they showed at high energies that there were four massless particles that carried different aspects of the electroweak force. As the temperature is lowered, the four particles change their properties (think water freezing into ice) and thus it appears at lower energy that there are two distinct forces, each with unique properties. The mechanism that governs the details of how the two forces "freeze" is the Higgs idea, proposed by Peter Higgs (and others) in the mid 60's.

The fact that the electromagnetic and weak force have been showed to be the same leads one rather quickly to the proposition that perhaps the strong force might be yet another aspect of a single, more fundamental force. As of this writing, this is only an idea. There exists no experimental evidence supporting it. Nonetheless, many physicists believe that further research will reveal this more fundamental force...call it the strongelectroweak force. The technical term is grand unification.

Taking the analogy one step further, physicists suspect that perhaps all four forces (strong, weak, electromagnetic and gravity) will be shown to be different aspects of a single unified force. This idea is purely informed speculation and has resisted mathematical treatment. The idea of superstrings...again just a wild idea that may or may not be true...is the theory for which this unification idea has been best worked out. There are other approaches people are working on, but superstrings is perhaps most attractive.

However, to recap...the weak and electromagnetic force have been shown to actually be the same thing. The other two forces await unification and this may or may not ever happen.

Your second question is an excellent one and one that is best served with a picture. However, I will try to answer using words. As you say, a particle decay at the quantum level is different than you would think using the ordinary meaning of the word decay. It is not the case of a big rock splitting into two smaller rocks. Rather a particle ceases to exist and is replaced by its daughter particles. Take for instance, the case of mu lepton (muon) decay. The muon disappears and is replaced by a W particle and a muon neutrino. The W particle subsequently disappears and is replaced by an electron and an electron anti-neutrino.

http://www.departments.bucknell.edu/phy ... index.html

So your question is when and how was this determined. The history is a bit fuzzy, as there wasn't a single "aha!" moment. Without carefully perusing the literature, probably the first nigglings of this idea was Dirac's prediction (sorta-kinda) of the antimatter electron.

One thing you need to realize is that at the frontier of science, all we have are models. So we can draw the muon decay chain described above. But what we **REALLY** know is what goes in and what goes out. Thus we must admit that our model (the disappear and reappear idea) may be incomplete. After all, the quantum world is difficult to envision. For instance, it may appear that further study reveals that the muon (a charged particle, with some amount of "muon-ness") passes its charge to the W particle (a charged particle without muon-ness) and its muon-ness to the muon neutrino (an electrically neutral particle that has muon-ness). Further study could reveal that the muon is a composite particle and when it decays, these two aspects "break up" and flow in different directions. Note that this is an unorthodox idea and not one I am espousing. But I am unaware of any experimental evidence that would forbid it.

Note further that superstrings allows rather naturally for this idea. You can think of the muon as a string vibrating with two notes, one A-flat and the other D-sharp. If the muon splits into two strings, each vibrating with an individual note, this is analogous to the muon sending the charge one way and the muon-ness another. Again, this is an unproven idea.

So unraveling this question requires further study. It may be that our model is wrong.

One case of our model likely being right is the case of conversion of matter/antimatter into energy and back again. Take the case of a matter quark and antimatter quark combining and annihilating into energy (a photon). This photon can then decay (disappear) and form an electron/antimatter electron pair. This is a pretty simple case and it progresses as discussed here. However, further study has revealed that what happens both at the annihilation and decay vertex is more complicated than this simple picture, although the picture contains the essential features of what is going on.

I hope this second answer wasn't so confusing. It would be best explained at a blackboard, as there are many subtle aspects of both the question and answer. I think the best "short answer" is that the "decay = disappear" idea is an excellent model that serves us well, although we are always aware that further measurements may reveal the idea's short comings.

Cheers...

D
User avatar
Lincoln
Resident Expert
 
Posts: 11095
Joined: 29 Dec 2005
Location: Deep in a lab...


Postby BioWizard on January 3rd, 2006, 3:18 am 

Dear Dr. Lincoln,

While I am no physicist and cannot adequantley contribute to this discussion, I would simply like to extend a welcome on behalf of SCF. It is certainly an honor to have you with us.

Best regards,
Bio
User avatar
BioWizard
Forum Administrator
 
Posts: 12763
Joined: 24 Mar 2005
Location: United States
Blog: View Blog (3)


Postby Cyndi Loo on January 3rd, 2006, 8:40 pm 

Thank you, Mr. Lincoln. I cannot fully express my great appreciation for your time, and most certainly for your answers. It is really great to have a reply to my thought. If you ever have time and want to discuss anything quantum, I most certainly would welcome the opportunity to do so. You truly are appreciated. It is rare anyone takes the time to discuss quantum with me. Of all the sciences, it is my favorite.

Your thought pertaining to Grand Unification echoes my more recent thought and I am very glad to read your statement pertaining to it. As I have stated, I am self taught and sometimes I have difficulty truly knowing if I am on the right path. I have images of the quantum world, they are perhaps not as mainstream. It is nice to read a "place" where string theory and quantum connect in your statement, as I have had some difficulty bringing the images together in my mind. I did wonder if perhaps you are a person who thinks in pictures, not words? I think in pictures and really appreciate images and diagrams. Your book is amazing. I am looking forward to the next one!

Cyndi
Cyndi Loo
 


Postby Lincoln on January 3rd, 2006, 11:42 pm 

Ms. Loo...

I will answer questions as time allows. But someone other than me must supply the questions.

As far as thinking in pictures...In my case, that is largely correct. Equations are best, but I usually don't understand them viscerally until I can draw an accompanying cartoon. The problem is that the cartoon is inevitably wrong in some way or another, as analogies frequently are. But with the cartoon in hand, I can understand the equation with greater clarity and this improved clarity can manifest itself in an improved picture. I rely heavily on analogies and pictures in my explanations. Both suffer greatly from a lack of both accuracy and precision that sometimes causes my colleagues to shudder, but they are very useful for conveying the most fundamental points, especially to an audience that is uninterested in the gorier details.

The next book is only in the mulling-over stages, so it will be some time before you can expect it on a store shelf.

Cheers...

D
User avatar
Lincoln
Resident Expert
 
Posts: 11095
Joined: 29 Dec 2005
Location: Deep in a lab...


Postby Cyndi Loo on January 4th, 2006, 8:48 pm 

WOW! Someone like me. Cartoons, I never would have thought of that. I have been trying to associate mathematics with something I can understand. The diagram in your book lays out the math in a box. This was really great. You also included the equation(s) corresponding with the mathematics in the box. That was really great too. It made me truly consider why it is I can understand the math in the box, but cannot understand the equation(s). I am really glad you decided to enter Science Chat Forum, and am completely thrilled at the continuing opportunity to ask questions! Thank you!

Pertaining to the accelerator, I was wondering how it is Fermilab controls the number of atoms in the process? I mean how do you know how many atoms you are sending through the accelerator? How do you know what the results are, and second how are you able to record the results?

IBM has been experimenting with photons transfering their energy. I have read similiar things with electrons, and I had thought this was an established occurrance in quantum because so many books refer to it. I think IBM is trying to transfer information (via photons), but I am not entirely certain. The situation they are experiencing is the process is limited in scope, in that they are only able to send the energy so far before it ends.

If models are all we have in science, then where do mathematics actually fit into this equation? I had thought physics was the one place we could indeed establish somewhat of a solid acceptance of fact because of mathematics. Is this not so with quantum particles as well?

You have been very gracious and I truly do appreciate it. Tomorrow I will prewrite some additional thought and post it. I would have been more prepared tonight, but did not want to take advantage or impose on your time. Thank you for the continuing opportunity to learn!

Cyndi Loo
Cyndi Loo
 


Postby Lincoln on January 5th, 2006, 12:16 am 

I'm extremely peeved. I just typed a long (and, in my opinion, eloquent) answer to your questions. Apparently the bulletin board timed out and when I hit "submit", it wanted me to log in and, in doing so, lost the long answer.

I don't know the rules for this web site, but it won't take too many times of that occurring for me to not bother, as I answer questions in the brief quiet moments.

I know it's not your fault, but I just don't have the gumption to type something similar again.

Perhaps later.

D
User avatar
Lincoln
Resident Expert
 
Posts: 11095
Joined: 29 Dec 2005
Location: Deep in a lab...


Postby mabus on January 5th, 2006, 12:40 am 

The session expiration on our message board is a full 1 hour, so it's not possible that the board would have cut you off unless it took you over an hour to write your post. Still in response to this issue we've doubled the session timeout to two full hours between session expirations.

The likely culprit in the incident you experienced was probably a momentary disconnection from the internet. Most of us nowadays have an "always on" DSL or Cable connection and because of that convenience, do not notice these minor brief disconnections, as the modem {or router} automatically reconnects quietly in the background without our noticing. But when you are replying on a message board {any message board where a log in was made} the account will be affected. This occurs because when you log in, you do so with one IP, and while writting your reply, you disconnect and reconnect, in the background. The IP you reconnect with is different, so when you try to send the post it trips up. This will happen on any message board and is beyond anyone's ability to remedy, as it is occuring on your computer. A good solution for you when you write a long post you'd had to have to rewrite, is just before you hit send, press "select all" with your mouse and click on "copy" as a failsafe. This way if you lose it it's a snap to get it back.
User avatar
mabus
Active Member
 
Posts: 1562
Joined: 05 Apr 2005


Postby BioWizard on January 5th, 2006, 1:22 am 

I sometimes write extra long replies on a text editor first, and then copy/paste into the reply box and hit submit, to avoid the risk of losing any replies to a reset connection. But most of the time, I use the ctrl+a and ctrl+c technique.
User avatar
BioWizard
Forum Administrator
 
Posts: 12763
Joined: 24 Mar 2005
Location: United States
Blog: View Blog (3)


Grumble....

Postby Lincoln on January 5th, 2006, 8:38 am 

Thanks to Bio and mabus....

Once it was clear that there is a timeout, both of your suggested solutions were pretty clear, as they are the usual cut-and-paste techniques. But that didn't help for the specific message. (And the muse had been so friendly...sigh...)

I'm usually sitting on a 100 Mb line (one of the benefits of being at a national lab), so the issue was long compose time. Multitasking often makes for longer compose times than an hour.

In any event, once you know that there are time out issues, there are always work-arounds. I was especially irritated that the design of the board didn't allow for hitting "back" on the browser so as to allow a capture and reinsert. Another useful feature might be a time-out countdown clock.

Live and learn, I suppose....

D
User avatar
Lincoln
Resident Expert
 
Posts: 11095
Joined: 29 Dec 2005
Location: Deep in a lab...


Let's try it again...

Postby Lincoln on January 5th, 2006, 9:54 am 

Hi...

After some sleep, I'll take a stab at answering Cyndi's questions again. Time constraints will make them briefer than the originals.

So the first question was on how we know how many atoms we have in our accelerator. First, as you no doubt know, people don't really accelerate atoms. The whole "atom smasher" thing is a misnomer. Atoms are electrically neutral bits of matter, consisting of equal numbers of electrons and protons and associated neutrons. To accelerate a subatomic particle, you need to use electrically charged particles. In our case, we use bare protons and their antimatter equivalents. Other accelerators make different choices.

So there are number of ways we can count the protons in our accelerator. The first uses magnetic induction (Faraday, 1831). A current is simply the amount of charge passing a point per unit time. Thus the beam, which is circulating charge, creates a current. Current creates a magnetic field, which causes a voltage in a loop of wire, placed near the beam. By measuring the voltage in the wire, you know the current. Since you know the charge on a proton, you know the current and you know the number of times the protons circulate in the accelerator per second, you can work out how many protons there were there.

Another option is kind of cute. First you measure the probability that protons and antiprotons interact. This is done independently of any current experiment. Then you measure how many collisions per second you have in your detector. Once you measure your collision rate, and you know the probability of protons and antiprotons to interact, you can form the ratio to determine the number of protons.

Regarding the QM question, yes people are working on entangling/transporting photons. It's not fundamentally different than doing electrons...just technically more difficult. Note for the future that "nature of quantum mechanics" questions are better suited for a QM researcher. I can answer questions, but the answers will be more pedantic and won't have the "insider's flare."

So the last question...models vs. equations...this is a very interesting and exceedingly misunderstood aspect of science. (And this is the answer which was most inspired last night. Let's see if the Muse hung around overnight...)

In science, there is nothing of substance except ideas, which are manifested as models. You see a phenomenon and you have an idea about what is going on. Equations are nothing more than the model expressed in a concise and powerful language. You could also express the idea in iambic pentameter. The thing that an equation brings to the model is the vast machinery of mathematical manipulation. Equations and mathematics are the most efficient way yet developed to manipulate an idea and explore its implications.

Take as an example Newton's Law of Universal Gravity (NLUG). He developed an idea that the force that governed the motions of the heavens is identical to the force of gravity on earth. This is a model. This model can be explained in those words, or amplified in a larger way..stating that the parameters of relevance are the masses of the bodies involved and that the makeup of the bodies don't matter (e.g. a planet made entirely of copper or feathers undergoes the same force). You could go further and use the words that the force between two astronomical bodies is proportional to the product of their masses, divided by the square of their distance. Or you could simply distill all of these words to the elegant: F = G m1 m2/ r^2. Basically, I've said the same thing over and over again. But the equation says the idea concisely. It also says it in a unambiguous way, detailing the important parameters (mass, distance and the fundamental strength of the force) and how they matter. This equation is crucial because you can now easily make predictions that can be tested. But it's only an equation. The underlying idea (or model) is what matters.

While I'm on my soap box, there is a disservice done to the smarter of our students when the scientific method is taught in school. You are taught the whole hypothesis, testing, theory and law thing. A theory is a well-tested idea, while a law is a super-duper-well-tested idea. But it's still an idea. A single measurement (done properly and confirmed) can kill or at least reveal the holes in any law. Further the word theory is a very dangerous one, because it has a "normal" as well as "scientifically technical" meaning. It is only because of this fact that fundamentalists can attempt to disparage the theory of evolution (as in "Well, that's YOUR theory...") But in our context, model and theory are mostly synonymous...with a theory being a model with supporting measurements.

Because particle physics is on the frontier of knowledge, our understanding is not as strong as our understanding of NLUG, for instance. So we have our model (the so-called standard model) of particle physics, which we test, using equations and experiments. It's not fair to say "it's only a model" and we shouldn't believe it. It's actually a damn good model and can make some predictions to better than 7 significant figures of accuracy. But it's true that it's only a model. It doesn't explain everything. So some day it will be superceded by a better model, with a broader region of applicability (like General Relativity superceded NLUG). In the meantime, we use our model to guide our thinking.

The bottom line is that an equation is nothing more than a very powerful statement of our current model. Further, it's difficult to make further progress until the model can be expressed as an equation. But there's nothing deeply fundamental about it. On the other hand, it's true that the field of physics is more precise because of this clear association between our ideas and mathematics.

Sorry...not as eloquent as last night. I think the Muse is sleeping in...

Time to go and smash some atoms....

D
User avatar
Lincoln
Resident Expert
 
Posts: 11095
Joined: 29 Dec 2005
Location: Deep in a lab...


Postby Cyndi Loo on January 5th, 2006, 8:36 pm 

Bio and Mabus, thank you for increasing the time limit on a single post to 2 hours. It would completely crush me to loose Mr. Lincoln.

Mr. Lincoln, Thank you so very much for taking the time to post. One thing I have had some success with when writing longer posts on SCF is to write them in Word, copy them, and then paste them into the post. This process has worked well for me.

Pertaining to the muse, the muse was up because I have found your thought both eloquent and amazing! Thank you.

Cyndi
Cyndi Loo
 


Nothing of Substance except ideas

Postby Cyndi Loo on January 5th, 2006, 9:06 pm 

WOW! How absolutely profound. Nothing of substance except ideas. I love this. In fact, I would be willing to suggest many, many people are going to love reading your thought pertaining to ideas and mathematics. It blurred the line for me somewhat, perhaps math is not as out of reach as I had thought! Thank you!

In truth, Mr. Lincoln, your book is so packed with amazing information I truly do not know where to begin in asking questions.

Often I read posts pertaining to quantum in which there is some confusion over spin. It was especially interesting to read in your book how spin is opposite as in mirror like opposite. I guess this would go along somewhat with the thought of matter and antimatter being mirror like if you really consider them. It was especially interesting to read how there is an imbalance between matter and antimatter in that one seems to be slightly more than the other. My thought did arrive at one would have to be slightly more than the other, although I never have found any direct support of this until I found it in your book. (Thank you, again, Mr. Lincoln!)

It is COMPLETELY fascinating how within the weak nuclear force the distance between the particles determine how strong the weak nuclear force is, as in the closer together the particles the stronger the force. This is intriguing because it supports the idea of particle interaction controlling the energy around it. It is interesting (as you have stated in the book) how relativity does not seem to find a comforatable place in quantum. I have some extremely radical thought about this, but will not disrespect you by posting it! LOL

Cyndi <--------- known to be full of quantum air at times! LOL

Thank you, Mr. Lincoln.

C
Cyndi Loo
 


Be very careful

Postby Lincoln on January 6th, 2006, 9:47 am 

Hi Cyndi...

First, since we seem to have gotten past the first few emails, call me Don. Secondly, I could form my answers better if I knew more about your background. Formal education level is most important, followed by years since school and informal learning in the intervening time. You don't have to tell me, because the web is way too open, but for the record, I have been framing my answers aimed at a 35-ish year old person, with some high-school science, perhaps a freshman college physics class, no math beyond algebra or geometry or so, and an avid reader about many things, not just science. If that's too far off in any direction let me know, and I'll adjust. If you knew more math or science, I could be more succinct.

In any event, your topics....

Spin is very hard to understand. Nobody understands it (with all due respect to my quantum mechanics researcher colleagues). The math is clear enough. But the cartoon is fuzzy. Spin arose because initially we discovered that the electrons around the atoms acted in some respects like planets around the sun. The quantum in quantum mechanics comes in part from the fact that these planets were only to orbit at specific fixed distances, each of which had an additional unit of angular momentum. An electron could be in an orbit with 1 unit of angular momentum or 2 or 3, but not 1.5.

When a photon leaves an atom (which is how adjacent atoms interact), it changes the angular momentum of the atom by 1 unit. So the electrons could jump adjacent orbits. Or, as it turns out, the electron itself could change its spin. It was determined that the spin of an electron could be + or - 1/2. That way, the change in angular momentum could be from the electron going from +1/2 to -1/2 or vice versa.

So far so good. But it became clear that the idea of an electron being a little ball of charge, spinning madly, became untenable. Spin then became an intrinsic bit of the electron, like its charge or mass. So here's the weird thing. Spin is **NOT** supposed to be thought of as an "electron is a top". Yet spin can be changed by simultaneously changing the electron's orbit, so there is some sort of way in which the electron's spin and the electron's orbital motion are in some way the same. More detail than that will have to come from one of the many quantum mechanics popularizations.

Regarding the weak force being distance-dependent....this is true of all of the forces. The biggest deal with the weak force comes not so much the distance, but rather the mass of the particle that carries it. Consider, if you will, the idea that the electromagnetic and weak force are fundamentally the same. How is it then that the electromagnetic force extends forever, while the weak force extends only 10^( -18 ) meters or so? It is because the photon is massless, while the W and Z bozon have a mass of about 100 times the mass of the proton. A high mass object isn't allowed to live for very long.

So this is one of those rare times that 1920's quantum mechanics ideas and particle physics have a clear and unambiguous linkage. It comes down to the Heisenberg uncertainty principle. This principle says that energy doesn't have to be conserved, as long as the period of non-conservation is short.

In order for a particle (say a neutron) to decay via the weak force (into a proton), a W particle must be emitted. The problem is the masses of the neutron and proton are very similar (and small)...about 2 MeV. The mass of a W particle is very large...about 80,000 MeV. Thus in order to decay from a neutron to a proton, the neutron has 2 MeV to work with. But it needs 80,000 MeV to make the particle that is needed for the neutron to decay. So it can't pay the bill, so to speak, and the neutron can't decay. So here's where Quantum Mechanics comes in...Not all W particles have a mass of 80,000 MeV. In fact, the range of the mass of observed W bosons is about 2,000 MeV...meaning that 70-ish% of the W bosons have a mass somewhere between 78,000 and 82,000 MeV. Yes that means that 30% of the time a W boson has a mass outside this range. However having a mass of only 2 MeV is very, very, very weird. So it doesn't happen very often, and hence the decay takes a very long time (900 seconds, which is forever in particle terms).

So how does this translate into distance? Since Heisenberg's principle says that a big fluctuation in energy can only happen for a very short time, the W boson can exist for only a very short time. Since they are travelling at the speed of light, you can do the math. The lifetime of the W boson, times the speed of light, gives a handle on how far it can go. And, it turns out, 1/1000 the size of the proton is about the right distance.

Finally, on the substance = ideas point, be very, very careful. More than once, I've been contacted by a person who takes that point too close to heart. They don't have strong math skills, but they're imaginative. They figure that the idea is enough and they get some cockamamy idea that is completely in disagreement with data. But their ignorance and poor math skills is a blessing for them, as they can remain unaware that their idea is excluded by data (and, of course, "the man"....i.e. me...is keeping down their brilliant insight.) The fact is, we need equations to calculate...at least until someone figures out another tool with the power of math. So equations and data are both crucial. But within the context of speaking with a layperson about science, their relatively low math skills do not have to be an insurmountable obstacle. They can often get the essential idea, even though they will not appreciate the implications in the way someone who speaks "math" will.

I guess the bottom line is that the math language can be a barrier to some people's understanding of the more fundamental idea. So we can explain the idea using words. But it is the equation that speaks most simply and that is why practioners must continue to master this language.

Oh yeah..and if I may correct a small misconception in your last post...quantum mechanics and special relativity have been seamlessly integrated. There is no tension between the two ideas. Quantum mechanics and GENERAL relativity have never been integrated, except possibly in superstring theory.

D
User avatar
Lincoln
Resident Expert
 
Posts: 11095
Joined: 29 Dec 2005
Location: Deep in a lab...


Spin

Postby Cyndi Loo on January 7th, 2006, 12:00 pm 

Thank you, Don. Your thought is appreciated.

Quantum is my favorite science. I am particularly interested in particles as you may have guessed from reading my posts. I do have some college, and I am self taught. I am interested in many areas of science. SCF has contributed to my continuing desire for knowledge, something I have not been able to find on other science boards. Most boards would not take the time to explain and post any educating or lengthly answers. In response, I try to do the same for other posters when I have an answer that will explain a thought. When I do not have an answer to explain a thought, or I am unable to cypher my thought in a way that anyone other than myself will be able to understand, I find links and post them. More so lately, I have found I am beginning to be able to post explanations and have not had to rely so much on links, although I do sometimes post both.

You are correct, and as I have stated I am not certain I am able to learn math. If I could learn math, I would attempt to go back to college. I do not understand what you mean when you refer to cartoons in relation to math?

Pertaining to spin, I do not find it so complicated. It could be the way I "see" particles in my thought contributes somewhat to all of the questions I have about particles and spin. I am a person who believes once we understand particles completely, then the universe will be ours. I do not believe quantum is strange. I believe there are still many interactions yet to be explained. As in spin, a +1/2 and a -1/2 spin, up and down, can either equal zero or one depending on if they are orbiting around something or not. I believe there will be many things that some people may attribute to strangeness that are really not strange. Perhaps just misunderstood.

One thing I am curious to know is when a particle physicist observes two particles with opposite spin, how does he determine if they are zero or one? Does he observe to see if they are rotating around something and then determines they have a spin of one, or does he first have a way to observe (perhaps through the accelerator) the two particles and then calculate the spin to determine if they are rotating around an object?

As of now, on Sunday I will be unable to post.

Thank you again!

CL
Cyndi Loo
 


Equations and ducking spin.

Postby Lincoln on January 9th, 2006, 9:41 am 

Hi Cyndi...

Regarding cartoons and math....perhaps the most succinct way I can state this is that words, cartoons and mathematics are all ways to express an idea. While words are powerfully descriptive, they are generally not nuanced enough to convey the details of the idea, unless they are essentially reciting an equation. An equation is the strongest, as not only is it totally explicit, it also comes with the vast and unparalleled machinery of mathematics, which allows you to (mostly) trivially explore the implications of the idea. For me, the equation does not always give me the intuition necessary. For that, I go to cartoons, analogies and diagrams. Once I have understood the strengths and weaknesses of how an idea corresponds to a particular analogy or cartoon, I gain enough wisdom to see what mathematical steps are needed. After all, you can do an unlimited number of mathematical steps to an equation...only a few advance your knowledge. It is the synergism of math and cartoons that illuminates my way.

I've met people who claim to understand it all via cartoons and analogies. Upon deeper probing, I've never found them to be correct. As much as I love analogies, there is always a point at which the analogy breaks down. They should only be thought of as guides. It is training that helps the user understand the limitations of their analogies.

I've also known people who claim that as long as they can put the idea into the math language, they understand the idea. Some of these people are pretty smart. In my opinon, many of them have good enough math skills to compensate for a lack of understanding. In high school, this was me. Once I could turn a word problem into an equation, I could solve it. But there were classes of word problems that were sufficiently difficult to set up that, while I could always get the right answer, I didn't always understand all of the nuances.

In fact, because I was so much better at mathematics than my contemporaries and, at least in high school, than some of my teachers, I came to rely too much on mathematics. It was only much later that I realized that mathematics for scientists is not an end in and of itself, but rather only a means to an end. It's kind of like having a recipe for a potion of eternal life, written in Sanskrit. Learning Sanskrit is important...but once you've read the recipe, the language is no longer something you should care much about. Of course if there are other recipes, then you keep up with it.

Mathematicians and scientists view math in very different ways. Mathematicians explore their (very beautiful and elegant) language, mostly for the sake of the internal beauty. Scientists view it as a tool to get at the thing they really care about...the idea.

This is not to say that math is unimportant. It is critical and I know of no other tool that works as well. But, for me, it is cartoons and analogies that allow me to understand at a visceral level.

Of course, that's just me....

Your spin question is a good one, but not one I can answer quickly. There are chapters in books on the subject. But first some very brief points.

People build up an idea of the spin of various particles by working slowly and building an interlocking mosaic of information. Each tile in the mosaic (eventually) fits snugly with the others. But there is no single measurement or cartoon that makes it all obvious at one time. It took a hundred years to work it all out. Even today, we make measurements to verify that the spin of the top quark is actually 1/2, as expected. It's a century of leap-frog progress.

The spin of a particle is unrelated to its orbital motion. So whether or not it is orbiting has no real effect on the spin. I could write a book on spin (which nobody would read) and maybe I could explain the topic in lay terms. But since the bulk of the lay audience doesn't care enough about spin to understand its nuances, I don't ever expect a lay audience book on the topic. And I certainly can't explain your question in a few-hundred word bulletin board post.

Suffice it to say that we know the spin of the electron from (among other bits of information) the Stern-Gerlach experiment. From looking at photons converting to electrons and antimatter electrons (and studying the angular distribution of the electrons), we can infer the spin of the photon. Once you know that, you can use that information to infer the spins of other particles. And so it goes...

D
User avatar
Lincoln
Resident Expert
 
Posts: 11095
Joined: 29 Dec 2005
Location: Deep in a lab...


Postby Cyndi Loo on January 9th, 2006, 8:12 pm 

Hi DL!

Well I have found something you have posted incorrectly......someone WOULD read a book pertaining to just spin, I would read it and be thrilled to have it. Thank you for your thought pertaining to math. Perhaps I will try to learn it again.

I prewrote the following:

Wow, I did misstate Relativity instead of Special Relativity. General Relativity does include gravity whereas Special Relativity does not include gravity. Therefore, Special Relativity can be used in quantum, whereas General Relativity can only be used in classical thought. No one has yet (to my knowledge) been able to correspond General Relativity with The Standard Model (quantum). General Relativity can be combined PARTIALLY with The Standard Model, which is known as "The Standard Model with Gravity." The Standard Model with Gravity does include all the known forces and particles.

Quantum physics and gravity both have their own separate formulas and these formulas seem to be incompatible with each other as they are currently represented in mathematics. Until this incompatability is resolved, I guess The Standard Model with Gravity is the best we can do for now. Would you agree?

Having said all of that, I do know at Fermilab, the particles actually increase in mass as they travel around the accelerator before they collide. My guess is this would be Special Relativity somehow related to The Standard Model with Gravity.

We could consider Lorentz Violations, but we have agreed to focus specifically on particles, not theorem, so I will move on. [Unless you change your mind about this, then we could possibly go on to consider how violations of Lorentz in quantum may be an indication of gravity or possibly more of the quantum yet to be discovered, both amazingly interesting!]

In an earlier post, you discussed particles determining the force around them. At first I did not understand this, but now I believe I do. While it could be particles interact with the force around them to determine how the force will behave, I can see where it may have its limitations, especially now that you have explained decay as particles changing into energy and then into another set of particles and then into energy and then into another set of particles. It seems like decay would not support the thought of particles determining the force around them because they change into energy, the energy changes back into particles, although a different set (or generation?) of particles. So there still is some confusion (on my part) as to what is actually occurring here. [Conservation laws?]

Or perhaps decay does support the idea of particles determining the force around them in that they decay into energy and then a specific set of particles and then into energy and then into another specific set of particles based upon the original type of particles involved at the beginning of the decay process with the weak nuclear force.

If my understanding is correct, some particles decay into other particles and do not return to the original particles. Whereas others decay into their anti particle and then the anti particle decays back into the particle, I read when this occurs it is called oscillation.

The rate of decay determines it parity. A quick decay rate decays into two particles, while a slow decay rate decays into three particles. This as truly astounding to read in your book, as it did solve the matter/anti matter mystery, as well as some ongoing personal thought I had posted in the physics sub forum a while back.

An off thought I had this morning before class while reading about probability: Could probability be representative of the overall percentages of the different types of particles floating around in the universe? I mean, is there a way using mathematics to change the probability numbers into actual statistics representing the different ratios of particles in the known universe? Or perhaps this is one of my way out there thoughts? If so, my apologies.

Again, thank you so very much, Mr. Lincoln!

Cyndi
Cyndi Loo
 


Postby Lincoln on January 10th, 2006, 9:22 am 

Huh...

In the future, we should probably keep the number of topics in posts to be a smaller number. That last one is long and a bit wide-ranging.

Make no mistake...learning math takes time. But it's necessary to REALLY understand science. On the other hand, you can still get 90% of the ideas without it, as long as you have a good translator.

Special relativity is a piece of the Standard Model (SM). It is also a piece of General Relativity (GR). SM is the theory of the very small and very fast. GR is the theory of the very large and very massive. SM has, as part of its fundamental premise the idea that everything comes in small and discrete lumps. GR's premise is that space is smooth, continuous and without any lumpy structure. They just cover different realms. Physicists believe that there should be a single over-arching theory that encompasses both. So far, there has been no true success, although there has been some progress on quantum gravity and superstrings have had mathematical success. Neither of them have any experimental support. In the meantime, SM and GR are held to be separate.

Lorentz violations are possible, but people have looked for them and not found anything. We will continue to look, but don't hold your breath. We could talk about it, but you should realilze that with only so many minutes on Earth, you have to pick and choose where you spend those minutes. Lorentz violations has never struck me as a promising place to advance the body of scientific knowledge. There are those who disagree...

I would disagree with you that the mass of a particle increases as it goes faster. I know that this is the way it is frequently taught in popularizations and in introductory physics classes, but this is a pedagogical choice. It is one of those analogies that break down upon further inspection. It's a layer of truth that illuminates an important point to a novice, but stands in the way to a deeper understanding. The more serious scholar needs to put that idea aside for further successful inquiry. The inertia of a particle increases with velocity, not its mass. There is one and only one mass...the so-called rest mass. Relativistic mass is a convenient mathematical construct that is useful. But it isn't really fundamental. See the relevant appendix in my book for a longer discussion. [This point has caused me some grief, as I have received a number of communications from people who have "disproved" relativity and hoping to have me get them published. But my assertion is really true. Ask any real physicist and they will be able to tell that you about "gamma times m", the so-called relativistic mass, is just a mathematical construct.]

I do not understand at all your discussion about particles determining the force around them.

There is the matter/antimatter oscillation phenomena. It's pretty interesting and (to me) very counter-intuitive. But it's a clear prediction of quantum mechanics, and it has been demonstrated unambiguously. Very cool.

Parity plays a role in decay, but by no means should it be thought of as dominant. You're talking about the weak force, in which a neutral K meson can decay. Because a neutral K meson can have positive or negative parity, it can decay into either two or three pi mesons. Because making each daughter particle takes energy, making three is harder than making two. Thus the requirement that the K mesons decay into two or three particles plays a role in the K meson's lifetime.

But in the event that there is plenty of energy to go around, parity does not matter nearly as much. The most relevant feature is energy balance. Take the "mass energy" of the parent particle and the sum of the mass energy of the daughters. If those two are close, the decay is more improbable than if they are not. (If the sum of the daughters exceeds the parent, it doesn't happen at all.) In addition, the strength of the forces involved comes into play. But parity is only a big deal in very specialized places.

By the way...the matter/antimatter asymmetry is by no means understood. We know of mechanisms whereby matter is preferred slightly to antimatter. But everything we've studied thus far doesn't provide enough asymmetry. We know that in the beginning for every billion antimatter particles, there were a billion and one matter particles. However, our studies thus far cannot explain this relatively large asymmetry. So this remains a mystery.

I don't understand your probability query. Probability is nothing more than a ratio of how many of something that happened to how many could have happened. In the context of particle physics, it can answer the question "If you grab a random quark, what is the probability that it is an up quark?" The answer would simply be the ratio of the number of up quarks to all quarks.

D
User avatar
Lincoln
Resident Expert
 
Posts: 11095
Joined: 29 Dec 2005
Location: Deep in a lab...


Postby Cyndi Loo on January 10th, 2006, 3:50 pm 

With respect, Mr. Lincoln, I did send you a PM when you first began posting inquiring as to your preferences pertaining to these posts. I have just forwarded another PM inquring the same. Perhaps if you would forward me the guidelines in which you prefer to post, I will be better able to accommodate them. And the subjects in which you will discuss would also be helpful.

Regards,

Cyndi Loo
Cyndi Loo
 


No problem

Postby Lincoln on January 10th, 2006, 3:55 pm 

Hi...

It's not the number of messages...it's just that I can't answer lots of questions at once. You ask good questions and I like to talk to people enthusiastic about physics. One or two per post is probably the most I can handle. I suppose you could send lots of questions, but then each will get less attention than it deserves. Your call.

D
User avatar
Lincoln
Resident Expert
 
Posts: 11095
Joined: 29 Dec 2005
Location: Deep in a lab...


Postby Cyndi Loo on January 10th, 2006, 4:08 pm 

Thank you DL! It could be I do tend to get a little overboard with quantum questions! LOL

It is amazing to be able to hear first hand from someone as knowledgable and gifted as you are pertaining to particle physics. WOW to be able to learn the mass of a particle does not increase in size inside the acclerator. Some people may find me totally out in space, but this is really truly exciting! It is also something only a true particle physicist would know and be able to share. Thank you for explaining the math behind this process. Thank you for explaining how some people could be confused and believe they have disproved Relativity! There are some posters on SCF who attempt to disprove well established and proven science on a regular basis, and you have most likely just saved a lot of explanation in advance! LOL

Math the way you have posted it does actually sound within reach. I am appreciative.

As you have time, I know very little about cool dark energy. If this is something you have an interest in, I am more than willing and very excited to hear anything you would have to share about it!

CL
Cyndi Loo
 


Relativistic mass

Postby Lincoln on January 11th, 2006, 9:30 am 

Hi...

I thought I'd amplify the relativistic mass idea, as my words have been misquoted and mangled in the past. Relativistic mass is a pernicious misconception, ironically most prevalent among the most educated of the lay audience. Partly this is because of how the idea is taught (and how I learned it the first "real" time in college.) Only later, when a deeper grasp of relativity was necessary, did I come to realize how the pedagogical approach necessary to introduce relativity's odd behavior is "not quite right".

In some sense, the discussion is semantic. But the cartoon of increasing mass at high speeds is one of those analogies with limited strength and should be put aside by a serious student of relativity.

Basically the problem is the following. We teach to students the Newtonian concept of momentum, denoted p, which is simply mass (m) times velocity (v). Or, in the concise language:



[or momentum equals mass times velocity for the math-phobic.]

This mass is what you're used to...a measure of how much "stuff" is involved. It is an immutable quantity. However, Einstein showed that this Newtonian idea was wrong, although it works very well at lowish speeds (note lowish still means many thousands of miles per second). He found that the correct equation was



where () holds all of the relativity stuff. And, at low speeds, (gamma) is equal to 1, so Newton's equation is just fine. So here is were the pedagogical approach comes in. Relativity is wierd, gamma is wierd. In order to make students a little more comfortable, we decide to not monkey with the equations and so we define a new quantity, relativistic mass. Relativistic mass is defined:

relativistic mass =

And thus the momentum equation becomes



which is our old Newtonian buddy. So you tell the students that we've just defined a slightly different mass, their equation is what they're used to and everything is both hunky and dory. Relativistic mass does increase with velocity. This is where mid-level students of relativity stop.

The question is "Does relativistic mass have any real significance?" The answer is no. What is really increasing as the velocity increases is inertia. Einstein's equation is right and it is gamma that changes, not mass (the rest mass).

Partially, this is a math thing. There is a property of mathematics, called commutativity, that says when you multiply three things, you can multiply them in different orders and get the same thing.

For instance 5 x 2 x 3 = 30. But you can write that as ( 5 x 2 ) x 3 = 10 x 3 = 30. You can also write it as 5 x (2 x 3) = 5 x 6 = 30. The question becomes, do the things inside the parentheses have a physical significance? Sometimes yes and sometimes no.

The volume of a rectangular cube is length times width times height



In this case, the parentheses denote a physical quantity. (l x w) or (w x h) denote the area of a face of the rectangular solid. So it makes sense to say

V = (area of one face) x h
or
V = (area of a different face) x l

In this case, putting something inside the parentheses really means something.

On the other hand, the volume of a sphere is (or four thirds times pi times r (cubed)).

Now if you can certainly mathematically put parentheses around parts of the equation



But the stuff inside the parentheses doesn't really mean anything.

Similarly in



...which is defined to be relativistic mass, doesn't have a physical significance.

In any event, it is INERTIA that increases as the velocity increases, not MASS.

Now you can't imagine how much this discussion has caused in the past. There are a lot of people out there who figure that if Einstein, laboring as a lowly patent clerk, could come up with relativity then they can work out something even better, sitting in their cubicle. The difference was that Einstein was a far-seeing, visionary genius. Oh, yeah...and his theory of special relativity has been experimentally proven...the ultimate arbiter of a physical theory. But when I tell people that mass doesn't increase without bound, although inertia does, an irritating few take the first half of the sentence and now I'm their best buddy, as they've somehow proven that Einstein was wrong. Now interstellar travel becomes more tenable, blah, blah, blah.... I've even been quoted (against my will and without my permission) in books on the topic, with the quote taken out of context and the clear intent of the original text completely subverted. Hence my long-time hesitation about getting into bulletin boards.

I wouldn't be shocked if it turns out that relativity isn't the whole story. But the piece of the story we understand is very solid, well tested, and all of the goofy time and space dilation bits of relativity have been observed. My colleagues and I use time dilation every day to study longer-lived particles...for instance b quarks.

Regarding dark energy, start at
http://en.wikipedia.org/wiki/Dark_energy

Dark Energy is not understood and, truth be known, the data is new enough that debates about what it means (and even if dark energy even exists) are quite tenable. Some exquisite experiments will be performed in the next few years that will better illuminate the situation.

D
Last edited by Lincoln on April 21st, 2006, 8:09 am, edited 1 time in total.
User avatar
Lincoln
Resident Expert
 
Posts: 11095
Joined: 29 Dec 2005
Location: Deep in a lab...


Postby mabus on January 11th, 2006, 10:40 am 

Don;

The above just may very well be the most important post anyone has ever posted on this board. Very informative, thank you.
User avatar
mabus
Active Member
 
Posts: 1562
Joined: 05 Apr 2005


Postby Cyndi Loo on January 12th, 2006, 3:52 pm 

http://www.eurekalert.org/pub_releases/ ... 010605.php

This is an article pertaining to cold dark matter. There is a reference to cold dark matter being structured. I am uncertain what this means. My thought is if cold dark matter is structured, then they are suggesting gravity is involved. With respect Don, what are your thoughts about this subject?

Cyndi
Cyndi Loo
 


Clumpy stuff

Postby Lincoln on January 13th, 2006, 9:38 am 

Hi Cyndi...

First, I should like to say that the post before last, you asked about dark energy. This most recent was dark matter. While the names are similar and both are fascinating, they are unrelated phenomena.

Now on to the structuring.

Dark matter has been suspected for nearly a century. And yet,we don't **REALLY** know that dark matter exists. Let me explain. The first evidence for dark matter was gathered about 1920-1930 by Jan Oort and Fritz Zwicky, with Zwicky's evidence being the stronger (but slightly later). They both noticed that astronomical bodies were moving too fast....Oort the rotation of the Milky Way and Zwicky the velocity of galaxies in the Coma cluster. Without getting into math, the basic idea is that gravity keeps astronomical objects near one another, while large velocities make them want to separate. By balancing these two effects, you can infer how much matter is present in an astronomical body (say a galaxy or a cluster of galaxies). You can also infer how much matter is present, simply by looking at the light coming from the body. You'd think these two should be the same, but Oort inferred that there was twice as much matter in the Milky Way as he could observe, while Zwicky found that there was 400 times as much matter in the Coma Cluster as could be observed. Since they observed matter by looking at its light, this additional matter (which wasn't observed) was therefore dark. As I recall, it was Zwicky that coined the term "Dark Matter".

So dark matter has the following properties. It both feels and contributes to the gravitational field around it. And it doesn't emit light. There have been many candidates...very low-light stars, rogue planets, black holes, massive neutrinos, etc. Studies have been performed that rule out all of these ideas. More exotic ideas involve massive and stable subatomic particles....the so-called lightest supersymmetric particle is a candidate.

Another idea, circa 1983 by Mordehai Milgrom at the Weizmann Institute in Israel, suggests that simply Newton's laws (and by extension Einstein's general relativity) are simply incorrect. At low accelerations, Newton's laws of motion do not apply (while applying just fine at large accelerations.)

So to recap the status...there is CONFIRMED DATA that suggests many astronomical bodies are moving faster than their visible mass allows. There has been SPECULATION that this may be caused by dark matter or modification of Newtonian dynamics (MOND). While neither of these possible solutions have been proven, you can still make progress. Most people believe that the solution to the problem with the data is thus-far-unobserved dark matter. IF that is so, you can use the data to constrain what it must look like. In doing so, physicists have determined that IF dark matter exists, it must be "cold", which is to say it can't be moving fast. But until a (in this case) particle is observed with the right properties, the whole idea is speculative. The data is not speculative and there is a real phenomena to be explained.

So with all that said, the URL you posted isn't very surprising. Since the research group assumes dark matter and dark matter is both (a) dark and (b) feels gravity, it is expected that it would clump together...similar to normal matter. Since it cannot radiate its energy as light, dark matter is different, but in this case not so much. You'd expect dark matter to follow the mass distribution of galaxies and clusters.

The important thing about this URL is that the research group is starting to tease out the details of how the dark matter is clumping. For example, does it form clumps millions of light years or hundreds of millions of light years across? Or what? This URL is announcing a detail of a measurement, not a grand discovery.

Another interesting social thing you're seeing here is the fact that the press (and perhaps the group) is using the public's interest in dark matter/energy to report a small step forward in knowledge as much grander than it is. This is interesting as it misleads the young scientist wannabe (say me at age 14). The result, while important and interesting, is an incremental step in a large and established body of knowledge. But to read it, you'd think it was some mind-blowing breakthrough. This gives the aspiring scientist an unrealistic explanation of how modern science really advances.

In any event, yes dark matter is structured and it is expected to be so. This measurement is an important advance to understanding the broad nature of dark matter.

D
User avatar
Lincoln
Resident Expert
 
Posts: 11095
Joined: 29 Dec 2005
Location: Deep in a lab...


Postby Cyndi Loo on January 13th, 2006, 5:21 pm 

Hi Don! WOW!!! I have really learned a lot. Thank you so very much!

I did not realize dark matter and dark energy were so different. I have always considered them to be related. I had read a while back Dvali thought dark energy was actually a form of gravity, and that gravity was pushing the universe apart. I guess this is why I immediately thought dark matter clumping would be a part of gravity. From what you have just shared, dark matter feels gravity and is dark. WAY Cool!

You refer to supersymmetric particles in "Understanding the Universe from Quarks to the Cosmos." It is astounding to consider there may be particles light years wide, and that they would be stable. Would these type particles be considered as a result of dark matter clumping or would they be something completely different? I guess I kind of have the thought quantum particles form atoms, perhaps dark matter clumping would form supersymmetric particles light years wide......

Thank you for presenting all of the different ideas on a particular subject and your thought pertaining to each one. I am so very appreciative of you, your thought, and your time. It is really truly great to hear your thought and to have an opportunity to learn.

Thank you, Don!

Cyndi
Cyndi Loo
 


Next

Return to Books, Movies, and Podcasts

Who is online

Users browsing this forum: No registered users and 8 guests