Momentum

[sparhawk]

I was starting to learn some physics from books (my main source is "Feynmann lectures Volume 1" and "Essentials of modern physics"), and so far it went ok. I just have a problem with understanding what momentum really is. Maybe somebody has a good explanation. I know the formula F=ma, but that doesn't help much. Especially with angular momentum, I have a problem getting the idea. I tried to find some good physics forum but I haven't found one. Maybe I also post in the usenet group sci.physics, but the issue there is that there are a lot of nutheads and a high spam frequency, so I don't really like to post in newsgroups anymore.

 

The reason why i started to do this is, because I read a lot of books about astrophysics and the universe on a laymans level, but they are no longer enough for me. I know most of the concepts in a general way, so most of these books no longer provide some new insights for me, and I thought the only way to go deeper and get a better understanding is, if I learn the math behind it, and see for myself. Relativity is rather simple in terms of math and I was quite pleasently suprised when I learned about the Lorentz transformation and realized that it is essentially the same mathematics that I rehashed a few years ago for the game development 3D math. It was really a fun experience when I read about several concepts and suddenly realized that I already knew a great deal about it, because I learned all that stuff when I really tried to get into 3D math as well, only I never connected it to physics.

 

Funny thing is, that I remember reading about 3D math, and in one book it explained that for some obscure mathematical reason you have to use a 4x4 matrix but the fourth column should be set to 0 0 0 1 and it never explained why this is the case. Now when I read about Lorentz I suddenly understood why this is so, and I always like it when such things suddenly come together on a broader basis. I guess this is what scientists refer to when they talk of the beauty of symmetry.

 

Well, I disgressed a bit, but the bottom line is that I knew the formulas for momentum but they don't mean much to me. I usually try to understand what a formula means, because this also helps me to remember it better, then just learning a formula and memorize it.

[demagogue]

Momentum is a stranger concept the more I read about it, too ... I mean, anything dealing with mass and movement generally gets stranger. And it all started off so simply. I mean, I think I generally get kinetic energy and rest energy. But when you don't take formal courses on it, there are gaps.

 

I remember with special relativity, as you speed A up relative to B, and they have an elastic collision, even though the mass of A is increasing relative to B (b/c it'd take more and more energy to speed it up the same amount), time is going proportionally slower, so the energy exchange (the kinetic energy A would transfer to B in an elastic collision) ends up being the same. And -- in a probably very similar moment that you had -- that made me think just what the hell is momentum, then, anyway? Is this all just about how energy (in its various guises) is transfered around in "transactions"? And now I think about all the math in terms of "transactions", like all the particles or widgets come together and agree to an exchange according to the rules, and then go their merry way. It helps me "get" the math, but not so enlightening what a transaction really is.

 

I read in the newspaper yesterday about the CERN cyclotron getting ready to go on-line, and how they hope to discover the Higgs particle, which is apparently the cornerstone to why things have mass and the last major missing piece to the Standard Model. And I realized that everything I think I know about "mass" seems so naive. I keep thinking no matter how much I read, I still have so far to go to have a good sense about what they're really talking about.

Edited May 21, 2007 by demagogue

[sparhawk]

But when you don't take formal courses on it, there are gaps.

 

Yeah. The problem is, that I can't really, because I don't have the papers to go to a university. I could go there as a "listener" (don't know the proper english word for this) so I could participate in all the courses if there is free room, but I would not be able to make exams even if I were good at it. That's school system for you.

 

I remember with special relativity, as you speed A up relative to B, and they have an elastic collision, even though the mass of A is increasing relative to B (b/c it'd take more and more energy to speed it up the same amount), time is going proportionally slower, so the energy exchange (the kinetic energy A would transfer to B in an elastic collision) ends up being the same. And -- in a probably very similar moment that you had -- that made me think just what the hell is momentum, then, anyway? Is this all just about how energy (in its various guises) is transfered around in "transactions"?

 

Yeah. That sums it up pretty neatly. I think I have a good understanding on how special relativity works. It doesn't really take to much advanced math and the ideas are rather straigthforward to follow. I'm working though a university level physics book, which I got recommended by a collegue who has a Ph.D. in particle physics, and even worked on scientific projects in russia, so at least I have a good source to ask. When I look at the examples in the book, then I can solve most of them (at least up to the part that I'm now).

 

And now I think about all the math in terms of "transactions", like all the particles or widgets come together and agree to an exchange according to the rules, and then go their merry way. It helps me "get" the math, but not so enlightening what a transaction really is.

 

Yes. That's exactly my understanding as well. When I look at the description and the conservation of momentum, then it seems to be mostly that. A collision and a special name for the exact moment of the collision. Well, at least I'm not the only one.

 

I read in the newspaper yesterday about the CERN cyclotron getting ready to go on-line, and how they hope to discover the Higgs particle, which is apparently the cornerstone to why things have mass and the last major missing piece to the Standard Model.

 

Cool! I read several times in some books that it was scheduled for summer 2007, but I hadn't heard when it should really start. I wonder how long it will take until we hear about the results. In the german paper of Scientific American they said that they are expecting to create microscopic black holes, which I would really like to hear about.

 

And I realized that everything I think I know about "mass" seems so naive. I keep thinking no matter how much I read, I still have so far to go to have a good sense about what they're really talking about.

 

A few days ago I saw a rather strange doku about physics. They tried to squeeze good old quantum physics to explain consciousness. I always dislike this approach, because it always feels as if some people have a shady understanding of quantum physics and a shady unterstanding of consciousness, and from this they conclude that there must be a connection.

 

Anyway, there was one really good line of thinking though. We don't really exist. When you look closer and closer, the more space you can see between all the supposed objects, and if you get very close, there is suddenly nothing except a probabillity for a wave that can collapse into what we experience as a particle and mass. Really quite strange to think about it in this way.

[OrbWeaver]

A few days ago I saw a rather strange doku about physics. They tried to squeeze good old quantum physics to explain consciousness. I always dislike this approach, because it always feels as if some people have a shady understanding of quantum physics and a shady unterstanding of consciousness, and from this they conclude that there must be a connection.

 

Right. Such theories are nonsense, they are unsupported by evidence and just use "quantum physics" as a synonym for "Wooo! It's magic!"

[demagogue]

Yeah, I concentrated in cognitive science in undergrad, and I don't remember a single moment where QM effects were ever taken seriously for a second.

 

The basic unit of functional organization in the brain is the neuron (anything lower than that just doesn't have functional relevance to how information moves or is "processed" throughout the brain, hence, cognition). And just about everything you'd want to explain about the neuron itself is safely covered by classical electromagnetism and fluid mechanics, basically charges and concentrations, nothing very fancy, and then there's nothing remaining left to explain. All the hard questions are about how neurons are organized to work together, not really how individual neurons work ... which we actually know a good deal about.

 

So I don't know what they think QM is really contributing. Well, I think the idea started because people got the idea that superpositions didn't collapse until they were "observed", so they figured there must be some connection between the observing-process (consciousness) and QM state collapse, and then they must have figured it works in the other direction, too. Or something... the whole idea is so out-of-touch with anything going on in cogsci that I don't know what they think they're doing.

 

 

... still waiting for that answer to "momentum", though.

Edited May 21, 2007 by demagogue

[Maximius]

QM is sometimes used to build models of freely formed thoughts, the idea is that if an idea is the result of a quantum event, its not a part of the deterministic chain of events and therefore we can claim that such thoughts enjoy a degree of freedom not found elsewhere. Even if this is so, the question remains why would a random thought event be any more freedom producing than a determined one. If at any point my actions can be randomly skewed from what my desires wish them to be, it sound rather unfree to me. Like someone who suffers from arbitrary seizures can be said to lack a degree of freedom.

Edited May 22, 2007 by Maximius

[sparhawk]

Right. Such theories are nonsense, they are unsupported by evidence and just use "quantum physics" as a synonym for "Wooo! It's magic!"

 

The bad thing about this is that it lends credit to this idea for laymens ears, because they have no idea on what scale QM is. The usual reasoning is, that, because of the Heisenberg's Uncertaintity Priniciple, we can determine that we have a free will and that this effect also gives rise to consciousness.

[sparhawk]

QM is sometimes used to build models of freely formed thoughts, the idea is that if an idea is the result of a quantum event, its not a part of the deterministic chain of events and therefore we can claim that such thoughts enjoy a degree of freedom not found elsewhere.

 

Yes. That is the reasoning behind it, but I think that it's wrong for two reasons.

 

The first reason is simply a hunch. I kn ow that we have a problem understanding QM properly, because we only can talk about it in statistics. To me this indicates that there is a fundamental principle, which we may not yet understand. I can not fully accept that the whole universe works just on statistical chances.

The second reason is that QM works on an extremly small scale. QM effects take place far below the scale of even atoms. In order for such a small effect to have an effect on something huge as a neuron, we would need to observe a really big statistical flux. And then we are only talking about a single neuron, whereas the human brain is made out of millions of neurons. A conscious thought or decision requires probably several thousands of neurons working together to make it's effect known, so we are comparing scales on the order of a grain of sand to the solar system (or probably even more). I have yet to see how this is supposed to work. And even if that were true and QM really had an effect on such large objects, then it doesn't really follow that we have any freedom. After all, QM follows rules, even though we may not be able to predict a specific outcome.

 

Even if this is so, the question remains why would a random thought event be any more freedom producing than a determined one. If at any point my actions can be randomly skewed from what my desires wish them to be, it sound rather unfree to me. Like someone who suffers from arbitrary seizures can be said to lack a degree of freedom.

 

Yes. Exactly what I meant above.

[sparhawk]

Yeah, I concentrated in cognitive science in undergrad, and I don't remember a single moment where QM effects were ever taken seriously for a second.

 

 

So I don't know what they think QM is really contributing. Well, I think the idea started because people got the idea that superpositions didn't collapse until they were "observed", so they figured there must be some connection between the observing-process (consciousness) and QM state collapse, and then they must have figured it works in the other direction, too. Or something... the whole idea is so out-of-touch with anything going on in cogsci that I don't know what they think they're doing.

 

That "observer" thing for the collapse of the wave is IMO one of the worst ideas that physicists came up with, and it doesn't really work well. After all, on the level of QM, where does one observer end and the object start? On a molecular leve we might even make a distinction between two objects, but on lower levels it doesn't make much sense to me. If you lean against the wall and then look at the atomic scale where do you end and the wall start? So how would the wave know which particular "observer" it should use to collapse?

 

... still waiting for that answer to "momentum", though.

 

I hope I get a usefull answer. Yesterday I started to download the sci.physics newsgroup, but it took so long that I had to stop. Problem is that there is so much crap, so I don't really expect to get much usefull out of it, but it's worth a try. I guess I just have to ponder about this for some time, and after some time I will get this understanding magically. At least this is a good approach in such cases.

[Ishtvan]

In a "special relativity & waves" class, we used a semi-layman book on special relativity, and it argued that in relaitivity, momentum and energy become the same thing, and then went on to call it "momenergy."

 

Personally, I'm still puzzled about how momentum is conserved in an inter-subband optical transition in a quantum well. In the bulk interband transition, you can draw a straight line (neglecting the tiny photon momentum) that connects two points with the same momentum on the E-k diagram. In fact, this is how you uniquely determine which two states are going to participate in the transition for a given photon energy.

 

In the quantum well intersubband transition case, how do you conserve the z component of momentum (calling the growth direction z)? k_z has two different values for the two quantum well states, so how do you make up that momentum difference with just a photon?

[OrbWeaver]

That "observer" thing for the collapse of the wave is IMO one of the worst ideas that physicists came up with, and it doesn't really work well.

 

That's because it is greatly misunderstood. The uncertainty principle has a precise mathematical definition, relating to the measurement of conjugate quantities, and has nothing to do with a conscious, human "observer".

 

Personally, I'm still puzzled about how momentum is conserved in an inter-subband optical transition in a quantum well. In the bulk interband transition, you can draw a straight line (neglecting the tiny photon momentum) that connects two points with the same momentum on the E-k diagram. In fact, this is how you uniquely determine which two states are going to participate in the transition for a given photon energy.

In the quantum well intersubband transition case, how do you conserve the z component of momentum (calling the growth direction z)? k_z has two different values for the two quantum well states, so how do you make up that momentum difference with just a photon?

 

Yeah, I was wondering about that just the other day.

[sparhawk]

That's because it is greatly misunderstood. The uncertainty principle has a precise mathematical definition, relating to the measurement of conjugate quantities, and has nothing to do with a conscious, human "observer".

 

One should think that professionals of that field would know abuot this.

 

Yeah, I was wondering about that just the other day.

 

[greebo]

One should think that professionals of that field would know abuot this.

Having a higher education doesn't necessarily stop you from believing in crazy things. The amount of post-graduate medicine students believing in Bach flowers and other esoteric crap is disturbing me.

[sparhawk]

Probalby you are right. Never underestimate the stupidity of people.

[greebo]

http://demotivators.com/idiocy.html

[Maximius]

The first reason is simply a hunch. I kn ow that we have a problem understanding QM properly, because we only can talk about it in statistics. To me this indicates that there is a fundamental principle, which we may not yet understand. I can not fully accept that the whole universe works just on statistical chances.

 

Its use in analytical philo was primarily to create "What If?" kinds of arguments IIRC, even the people making them would probably happily admit all the criticisms we are discussing here are true, they were just looking at all possibilities. I think some folks outside of A-philo, was it Feynmann who did this?, tried to promote the ideas as being plausible or something but ultimately all such approaches (non-deterministic) rely on incorrect definitions of freedom IMHO.

[Order of the Hammer Bureaucrat]

post-graduate medicine students believing in Bach flowers

Off I go to wikipedia

used primarily for emotional and spiritual conditions

50:50 solution of water and brandy

Aah, there's nothing mysterious about it. Everyone knows Brandy heals most ailments, and spirits are good for "spiritual conditions".

[sparhawk]

On the topic of momentum I found one site which is german though, which has some reasonable explanations, but I guess I have to think more about this. Eventually I will develop a feeling for it, and then it doesn't matter if I really understand it or not.

[Ombrenuit]

Sounds to me with the whole quantum physics/consciousness thing that they are just trying to stuff function into form like Jello molds. I guess it makes sense. If you have one model that fits for one branch, I guess try it on another? I guess we just get a bit too excited when one of the holes fits, but that doesn't necessarily mean all of them do...

[sparhawk]

Yeah. Most of these ideas, either come because the person involved looks at some things that might be perceived as similarity and it doesn't have a clue what it really means, or just because of wishfull thinking. For example from some esotreic people I h=often heard that "energy" thingy. We are all energy and thus we are linked all together, so it's feasable to think that mind reading, precognition, etc. should be possible. After all, it's scientifically proven that E=mc^2, so that means they have to be right. They simply take conveniently what they think they understand (energy is mass) and neglect all the inconvenient parts (energy doesn't have a consciousness). And the same thing happens with QM as well. They take whatever they think sounds good and ignore all the other petty details.

[Ishtvan]

Yeah, it seems like words that instantly set off the lunatic-alarm are: "crystals", "magnets", "quantum state of consciousness", "Knights Templar", etc. It will be interesting to see what lunatics come up with when more modern theories become more mainstream and well understood. M-theory proves existence of the holy grail!

 

My personal lunacy is cycles. A fly that only lives for a few has no idea about night and day cycles. Something that lives for a few days has no idea about the tides and waxing and waning of the moon. Something that only lives for a month has no idea about the rotation of the Earth around the Sun and the seasons. People who can't look at astronomical data have no idea about the very long rotation of the Milky Way galaxy around the galactic nucleus.

 

So do the ever-increasing cycles just stop there because we humans now know everything? I doubt it. Pretty much every physical law can be derived from the least action principle. Whenever there's a minimum in potential energy, nature tends to oscillate around it.

 

I wouldn't be surprised if ultimately the universe is like a giant spring, where some process (dark matter, periodic boundary conditions, the holy grail?) eventually decelerates the expansion of the universe and initiates a Big Crunch so we can start all over again.

[Order of the Hammer Bureaucrat]

Hey, I like crystals.

Minerals, crystals, they look nice when placed on a table or bookshelf.

[sparhawk]

I wouldn't be surprised if ultimately the universe is like a giant spring, where some process (dark matter, periodic boundary conditions, the holy grail?) eventually decelerates the expansion of the universe and initiates a Big Crunch so we can start all over again.

 

I don't like that Big Crunch scenario so much. My personal interpretation is more that the universe started from a black hole that exploded, and I think that these objects are maybe what powers the universe. But essentially it is simialr to a Big Crunch theory, only that it is not a single crunch, more like the bubbles in hot water.

[OrbWeaver]

I wouldn't be surprised if ultimately the universe is like a giant spring, where some process (dark matter, periodic boundary conditions, the holy grail?) eventually decelerates the expansion of the universe and initiates a Big Crunch so we can start all over again.

 

It's actually one of my worst fears that the ultimate collapse of the universe will result in some bizarre "rewinding of time" that will drag us all back into existence again. I can't actually think of anything worse than having to live an infinite number of human lives, rather than just one.

[greebo]

Well, obviously nobody does remember it, so where's the difference to living just this one life?