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Journal: Trolls on /. get moderated 5, Insightful, Rant 9

Journal by Quantum Jim

I'm a Christian. I respect the opinions of rational non-Christians and am open to the fact that not every intelligent person will agree with me. I don't try to force my religion on people who don't want to hear about it. But I don't like it when people bash Christianity without cause on slashdot. Everyone (rightly) derides politicians for the "Muslims are terrorists" slur but it seems like open season on Christianity sometimes around here. This post is titled "When Wealthy Christians and Crackpots Attack!" but he doesn't talk about Christians in his post at all! There's nothing really substantive or particularly insightful - just one statement as a few instances to support it. He talks about Scientology and Uri Gellar. The Church of Scientology are not Christians (they believe Christ is a delusion IIRC from reading about them). Uri Gellar is Jewish according to wikipedia. Stuart Privar seems to be a creationist, but there is nothing about Christianity in either article that I read. Furthermore, not all Christians are creationists either except in the broadest sense - not the common use of the term. Using such broad, imprecise language in his little post just seems like a potshot or trolling.

Biotech

Journal: Question: Soap After Sports - Antibacterial or Regular? 9

Journal by Quantum Jim

Got a little rant and a question for anyone reading. Again, a popular science article exaggerates the conclusions. A recent /. story mentioned Anti-Bacterial Soap No Better Than Plain Soap. Now most of the comments seem to sermonize against all antibacterial products. I don't completely disagree, but the article doesn't support extreme opinions. Of course, the story in question only concerned itself with one type of antibacterial soap and with one use of that soap: namely washing hands before eating food. Allison Aiello sums it up:

The soaps containing triclosan used in the community setting are no more effective than plain soap at preventing infectious illness symptoms, as well as reducing bacteria on the hands.

Now for my question. I practice Judo and Brazilian Jiu-Jitsu a lot. I used to use a regular soap in the shower, but I caught some severe conjunctivitis three times in the same eye in the past six months despite trying to be clean. The pink eye was very bad, my eyelids swelled up, and the doctor needed a broad-based antibiotic to take care of them. That indicates to me that the infections were caused by bacteria - probably staph.

I am scared to death of MRSA. Now I use antibacterial Dial bar soap as well as some anti-dandruff shampoo to discourage colonies of fungi - with the intention of preventing ringworm (and dandruff I suppose). That seems to have been working better, but this article concerns me. The article didn't research body washes for athletes, but it does raise the question whether or not antibacterial soap is useful for cleaning up after practices. Which type of soap would be best for cleaning up after athletic activities and why - regular or antibacterial soap?

Math

Journal: My /. fortune is mistaken 4

Journal by Quantum Jim

My /. fortune was:

(1) X=Y ; Given
(2) X^2=XY ; Multiply both sides by X
(3) X^2-Y^2=XY-Y^2 ; Subtract Y^2 from both sides
(4) (X+Y)(X-Y)=Y(X-Y) ; Factor
(5) X+Y=Y ; Cancel out (X-Y) term
(6) 2Y=Y ; Substitute X for Y, by equation 1
(7) 2=1 ; Divide both sides by Y
-- "Omni", proof that 2 equals 1

However, you can only cancel out the (X-Y) if X != Y because if they are equal then the expression is zero! Indeed, the rest of the steps can be left, so you end up with:

2(x-y) = (x-y)
0 = 0

Friends don't let friends divide by zero!

User Journal

Journal: Got silver in my first judo shiai 1

Journal by Quantum Jim

I competed in the Pennsylvania Open Judo Championships yesterday. It was a double elimination shiai (tournament) hosted at Master Eugene's school in Cranberry. This was the first time I participated in - and even witnessed - a judo competition.

I won a silver medal, and my record was 3-1. I entered the 175-151 senior men intermediate division. Here are videos of my matches:

  1. I submitted J.R. DeFilippo (Kim) with okuri eri jime (sliding collar choke).
  2. I pinned Rob Lynn (Joseki) with tate shiho gatame (high mount).
  3. Mark deRouville (Brick) threw me with drop seoinage for gold.
  4. I submitted Matt Fisher (Penn State) with koshi jime (clock choke) for silver.

Even though I ate a big pasta dinner last night and didn't even try to make weight for the tournament, I still weighed in at 152 pounds and weighed 151 after going to the bathroom before my matches. Therefore the guy who won (152 pounds) and I were the lighest judoka in the bracket.

Everyone had to wear a white or a blue belt - or a white or blue gi - during our matches. Even the black belts generally conformed to this rule; although, a lot of people just ignored it too. The competition ran late by over an hour, and I didn't feel like I had much energy while waiting. Somehow I had more than enough cardio, since I didn't really break much of a sweat or work that hard even during the one match I lost. Everyone else seemed exausted, so I guess I didn't work hard enough. I hope the reason is that I was just very efficient and/or had good cardio. Mentally I was drained by the end of the day, though.

I had fun during the judo shiai. JR trains at Kim's in Brendwood too. Rob Lynn invited me to train with him in Altoona, but that's a long drive unless I can get someone else to come with me. Matt Fisher trains at the Penn State Judo Team. I'm not too concerned about my loss to Mark deRouville, since he is the NJ State Champion and also placed in every skill division in his weight class. But I will learn from my mistakes and beat him next time. Good guys; it was an honor to meet them. I hope next time during the shiai I can relax more, and maybe win by ippon with a throw at least once. :)

User Journal

Journal: My First Firefox Extension: "Personal Toolbar Button"

Journal by Quantum Jim

I wrote my first Firefox 1.5 extension called "Personal Toolbar Button." Of course, it simply adds a toolbar button that toggles on/off the "Personal Toolbar" toolbar. This is where I keep all my bookmarks, but too many toolbars wastes useful screen real estate. Install it at extension's web site. (Thanks Mozilla.org!)

I was inspired by the web developer extension which uses the same trick to toggle its toolbar. I created a new GUID for the extension using an online UUID generator. This tutorial at Mozillazine provided the template for the extension. Roachfiend's tutorial filled in the gaps on how to package it as an installable XPI. Oh, and I used the DOM Inspector to figure out which CSS declarations/IDs to use.

The entire project took me about two hours because I kept making stupid mistakes. I originally wanted to write an extension for a programmable set of buttons for Firefox's toolbar, but I quickly realized that was too ambitious. Programming the extension was fun and a very practical use of my time - at least for me. All in all, I'm very pleased with the result. I hope someone else finds this project useful as well...

User Journal

Journal: My ear is dog food (cauli surgery) 1

Journal by Quantum Jim

Had surgery on my ear today. I first injured my ear hurt my ear back in March. I was rolling with a judo shodan (black belt) and tapped him with a choke. Then during standing randori, he schooled me with a billion uchi mata throws. The result was a broken toe and cauliflower ear. Pictures provided upon request. :x

This was my first surgical procedure. It was weird. I felt naked under my gown. My weight was 154 lbs, heart rate 55 bpm, and blood pressure 125/65. The nurse inserted the most painless needle ever into a vein my hand. Then she retracted the needle and replaced it with a plastic catheter. That was actually more annoying than the needle.

I recieved a general anesthetic. It was strange... I don't remember being giving the anesthetic nor falling asleep, but I work up in a different room. The doctor removed the fluid and blood clots, then sewed it back up. He stitched it back up along with a tube to hold the skin and cartilage so they heal together. As the anesthetic wears off it gets more and more painful, but I have a prescription for the good stuff. :p

The doctor said he saw a lot of crushed and fractured cartilage in there. He doesn't want me doing any more BJJ or judo for about 2 weeks after I see him on Friday. However, I hope to do some non-contact drilling and rolling as soon as I can.

User Journal

Journal: 2 is the loneliest number 3

Journal by Quantum Jim

I competed in the Kumite Classic this past Saturday (May 27, 2006). It is a no-gi submission wrestling and a gi-required Brazilian Jiu Jitsu tournament. (A gi is the typicially white uniform some martial artists wear.) My record was:

  • Men's Gi White-Belt 145 lbs: 1-1 (Second Place)
  • Men's No-Gi Intermediate 145 lbs: 1-1 (Second Place)

My record is now 7-6. I had a lot of fun at the tournament, but I am not satisfied. Man, I'm a little pissed for not getting first place. I have a lot to work on.

Gi Division

In my first gi match, I defeated Matt Jubara by scoring 16 points. He was very strong and very tough. You can watch a video of Jubara vs me.

My second gi match was against Mat "Rosco" Rosborough for the championship. He was very tough too. We went into overtime, and I eventually ran out of gas in the tank. It was very long: the match lasted over 8 minutes... I have to work on my cardio so I can roll for 10 minutes or more at a high intensity. Watching it, I don't think my technique was as smooth as I would like. You can view a video of Rosco defeating me.

No-Gi Division

In my first no-gi match, I faced a karate guy (I could tell because he wore black karate gi pants and no shirt); although, he said he did study grappling. Donnie took care of him a few years ago in the advanced division. Now he was back, but in my intermediate bracket. Oh well. I owned him and finished the dude with a RNC. Watch a video of my easy no-gi match.

In my second no-gi match I faced Rosco again. This time I scored a super sweet judo throw. I was actually trying for Harai Goshi, but Randy told me the throw was really Harai Makikomi (on further reflection, it probably was harai goshi). It was mostly instinct: I was setting up a throw and just saw the opening. In judo, that would have been ippon. However, this is grappling so no soup for me! Rosco rolled when we landed and I felt off balance in side control. Somehow I ended up with reverse guard and tried for a toe hold, but I screwed it up. Still, with 45 second to go the score was tied and I was winning with an advantage. However, I was still tired and lost when he passed my guard as I opened it to attack. Randy uploaded a partial clip of Rosco vs Me in no-gi. (I wish he got the whole thing so I could go over my many mistakes.)

Analysis

Ironically if I just stalled from guard a little bit then I would have won. However, that is stupid and not honorable. No excuses: I lost twice to the same guy in both championship matches. I have to work on my control, my cardio, and my leg locks. I have to be able to finish long matches grapple at 110% throughout the fight. This month I shall try to improve these aspects of my game.

There is more about the tournament at the CMU Grappling Club's tournament page or my training log.

User Journal

Journal: Q: Caffeine and Athletic Performance? 4

Journal by Quantum Jim

"One of the main reasons for caffeine giving you a wake-up call is that it forces the liver to hydrolise glycogen into glucose." (src) Glycogen "is the main form of carbohydrate storage in animals and occurs primarily in the liver and muscle tissue." (src) Granted those two sources are not good references. I need to do additional research. However, if true, would diet caffeinated beverages not work for diabetics (since the caffeine increases their sugar level)? Also, would caffeinated beverages degrade athletic performance by depleting your muscle glycogen supplies? More investigation is called for. Any insight anyone?

User Journal

Journal: CMU Grappling Video

Journal by Quantum Jim

CMU Grappling kicking ass, taking names - Highlights from our tournament in December via Google Video. I'm Jimmy. :-) There is another tournament in March, but I haven't decided whether I will compete in it. Many of my friends are going to enter, but I am burnt out from tournaments. I'd really like to skip one - just for once - and catch my breath. Oh, and I've been diverting my whining to a different journal to spare you, my /. friends and other readers. :-)

User Journal

Journal: Better But Still Stressed Out 2

Journal by Quantum Jim

On Exams. I feel better though still stressed out. In the real world, I refer to documentation all the time even for basic stuff just to confirm things. Why do profs expect you to know everything from memory?

On Championships. Wow. I was afraid this might happen. Many of the people that I roll with during practice really want to prove themselves.

The first person I fought beat himself up for a few days afterward. I tried comforting him and instructing where he went wrong. Now he really wants a rematch even though I just want to have fun!!!

The guy who took third wanted to spar very hard Wednesday, because we didn't get to fight at the tournament. I think he wanted to know whether he could have beat me if he won his match. Instead I gather it clouded his judgement. During randori I tapped him twice. However, I was really sad and just played around for the rest of the session.

I grapple just to have fun and lose weight. That's it. I'm very worried that now I'm expected to do well at every future lesson and tourney, and everyone will be gunning for me! That is very stressful and not fun at all. :-/

On the other hand it was actually a relief yesterday when I went to the advanced BJJ practice, since I got decidedly crushed when rolling with the blue belts. I usually go on beginner BJJ day with most of the other white belts, and I was beginning to get nervous when my luck would run out!

Unexpected Consequences Odd that is felt better losing than winning. On the bright side, a clothing manufacturer wanted to sponsor me.... Methinks the advertiser is a tad too enthusiastic, or that he couldn't get Fedor to do endorce his product, or that he tipped the bottle too much. Still gave me a chuckle! :-D

Ya Drew! Thanks to a buddy of mine who also fought, you can download a quicktime highlight clip set to some funny music. Feel free to download more videos from our club if you wish.

I promise more Geeky stuff later...

User Journal

Journal: First place yet still depressed (more non-nerd stuff) 4

Journal by Quantum Jim

I won first place in both the gi and no-gi lightweight novice divisions in the Ultimate Force 2005 grappling tournament. I fought twice with my kimono on and twice without. Therefore, I went 4-0 today. Pictures and video forthcomming.

I should feel great; however, I don't. I spent all week stressing over my weight (I was 160, now I'm 152) and having nightmares about losing in the first ten seconds. It is a relief that I don't have to worry any more!!! However, I am still a little nervous since now I must to well for now on. I will have to fight in more experienced weight divisions like intermediate or beginner in the future... I feel like everyone expects me to do good, and I keep thinking I will choke.

I even found myself rationalizing my wins. With my kimono on, the first person I defeated was a lot lighter than me and actually wanted me to go up a weight class. He is my friend and I look up him; I still feel he has better technique than me. In the championship gi match, my opponent was also a friend. I actually think fighing people I know is more fun, but he had trouble getting intense for the match. I ended up winning by scoring 12 points more than him (a technical submission).

Without the kimono I almost lost both matches; however, I won at the end partly because my opponents were wrestlers not grapplers. Their technique was very bad, and I just held out until they made a mistake. I tapped both of them; however, they were in much much better shape than me. I was very intimidated and expected to lose.

Does this take away from my victories? This is the first time I ever won first place at any sport. I want to be proud, and I bragged a little. But too much pride is often a sin (and not solely for religious reasons). I feel humbled by my opponents, yet nervous about the future. I'm even sad a little for hurting them enough to submit during the matches! (Not enough to quit, but still is worries me.)

I began studying Brazilian Jiu-Jitsu only to lose weight. Now I have, but I still feel fat. My self image is shot even though I won first place twice. Does anyone else feel not as good as they thought they would after winning?

User Journal

Journal: Second Place at Grappling Tournament 5

Journal by Quantum Jim

Today, I got second place in the novice lightweight weight class at Mark Shrader's Third Annual Grappling Tournament. First, congratulations to the first place winner: Jay Morris. He is an awesome wrestler and grappler, and I wish him luck with his MMA career (no, we weren't fighting MMA).

Despite losing I shouldn't feel bad. In nearly six months of training I worked hard enough to lose 45 pounds (I'm 154 now); clothes that were too small for years are now too big. That was why I started grappling, after all. I only entered the tournament for the experience and not to place. I fought a tough opponent and still came out with a medal.

However, those are rationalizations. The only reason I got a metal is that there were only two people in my weight class: the champion and me. In other words, I lost and still received a metal. I was beaten in skill and strength. Even worse, during an exhibition later on, I tapped out to exactly the same submission from the same opponent. They weren't short matches, but they weren't especially long either. I'm angry at myself for losing in that way.

Every fight is won before anyone steps on the mat through how they prepare. Instead of dwelling on the past, I should direct my energies on the future.

  • Deluding myself, I though I was improving against the people I usually train against. I guess my pride was hurt a little. I need to train against different people so I don't get used to anyone.
  • The submission that got me was a guillotine. I need to learn to master, avoid, and counter them.
  • I also have to work on initiating things from the guard. My confidence with guard work was virtually nill even before the tournament.
  • I was out wrestled, so improving my stand-up is also a priority.
  • I did not feel winded or tired at all during the match, instead I was simply overpowered. I need a better lifting routine to get stronger. However, I should maintain this weight at least (154). Therefore, I still need to do more jogging and cardio as well to lose the dead weight.

I was debating throwing the silver metal away (which says made in China on the back). However, I'll keep it to motivate me to work on these goals.

User Journal

Journal: Secrets of the Universe (Or Why E = mc^2) 6

Journal by Quantum Jim

Every wonder why E = mc^2? It has always bugged me why it was so . Hardly any college introductory physics courses go into why. In fact, hardly any college courses derive the formula and just assume it is correct. I hardly ever accept anything on face value: I like running experiments, confirming observations, compiling source code, and deriving formulas. By doing so, I get a better understanding of the stuff I use. That is a worthwhile endeavor.

Now I finally figured out why E = mc^2, all by hand. It doesn't take much more than what you learn after a single year of a single college physics courses (Physics I + II) and a year and a half of calculus (Calc I + II + III). I highly encourage anyone who has taken those classes to try it out. It is very enlightening!

The Speed of Light Is a Constant

To start, you have to accept the following axiom.

The laws of the universe are valid in all inertial reference frames.

That seems super obvious, but there are interesting concequences. You see, one law of the universe is that the strength of electric fields is a certain constant in space. This is represented by the variable e - AKA the "Permittivity of free space" - and the higher e is the weaker the electric field.

Another property of the universe is the strength of magnetic fields. This term was mostly subsumed into the permittivity constant since magnetic fields are created by electric fields, so you don't really need to consider it. This magnetic constant was should be a geometric factor (4*pi) but is usually multiplied by 10^-7 for practical reasons.

The reason this is important is that light is a wave. If you solve Maxwell's equations for an electromagnetic field (in space), you find that the speed of light only depends on the permittivity of space, e, and the strength of magnetic fields in space. In fact, the final result describing the speed of light is simple:

c^2 = 1/(e*u)

c
Speed of light
e
Strength of Electric fields (Permittivity)
u
Strength of Magnetic fields (Permeability)

Such a simple result is rarely a fluke. It also makes little sense. For many years, scientists tried to disprove this result with many experiments. Their skepticism was based on the prevailing theory of the day: that light is not only a wave but a particle too. It is like Jello: while hot it looks like a liquid and waves can be seen. While cold, Jello looks like a solid and can hold its shape. Light is similar - in certain circumstances is acts like a wave and others it acts a particle. This violates the principle of relativity.

The Principle of Relativity

Relativity is a basic observation. Say you are in a bus, and you walk from one end to the other. You don't feel like you are traveling very fast... only a few miles per hour. And to the rest of the people in the bus, you are moving that slowly. However, to people on the street, you are moving very fast. Your speed, to them, is your velocity (relative to the people on the bus) plus the velocity of the bus (relative to the people on the street). Take this example:

Look at this picture (from this page).

O
Represents the "stationary" reference frame with respect to us (you and me).
O'
Represents the "moving" reference frame wrt O (and us).
v
Velocity of O' relative to O.
x, y, z
Coordinates according to O.
x', y', z'
Coordinates according to O'.
t
Time in O (not shown in diagram) since some start event.
t'
Time in O' (same as O).

We are only going to consider one dimention, so y, z, y', z' can be ignored for now. Time (t) and accelerations are the same in each frame (O and O') if V is a constant - i.e. O' doesn't accelerate and moves with a constant speed in a constant direction (wrt O.) Say we have a point called P with coordinate x' in O' and is not moving. Relative to O it is moving with speed v (i.e. the same as O'). To figure out what point P has in O - called x - you use:

x = x' + v*t'

y = y'

z = z'

t = t'

Velocity times time is the distance O' moved, and x' is the distance P is in O', so added together you get the distance P is from O.

From the vantage point of O', things are just the opposite. You come up with the following equations, which can be derived from the equations above:

x' = x - v*t

y' = y

z' = z

t' = t

Just use algebra to figure out those. That second set (and the following set) seems almost trivial, but there are important effects later. There is one more set of equations to note:

ux = ux' + v

uy = uy'

uz = uz'

These are the velocities of a particle at the point if it was moving instead of stationary wrt O'. We used u to differentiate it from the speed of the reference frame, v.

Those are the Galilean Transoformation Equations and are the main result of the Principle of Relativity. See if you can understand that before going on. It is pretty standard and makes sense if you think about it.

How the Speed of Light Mucks Everything Up

The speed of light depends on the strength of electric fields in space, as shown above. But in two reference frames, the speeds observed have to be different according to relativity. If c is the speed of light, and it travels only in the x-direction:

c = c' + v (Not true as explained below!)

Thus, each frame must see a different speed of a light beam. But Maxwell says the speed is a property of the universe (as I said before), so c = c'. One of them is wrong. After lots of experiments, it seems Galileo's Relativity is WRONG! The speed of light, no matter how it was measured, was the same for all frames of reference. So we have the following axiom:

The speed of light is 186,282.397 miles/second for ALL reference frames.

So how do we fix Relativity, since it seems to work in most cases? There must be a correction factor that has to be added in. Let's call that factor, gamma or g. That means the transformation equations will look something like:

x = g*(x' + v*t')

x' = g*(x - v*t)

Those are the same equations as above, just with the correction factor added. But what is the correction factor? Let's perform an experiment to find out!

Now, even though O' is moving, lets start it at the same place as O. So this start occurs where t = t' = 0. At this time, a light pulse is emitted from the origin of the frames (remember, they are at the same place right now) and moves in the x-axis direction. According to O it moves a distance of:

x = c*t

But according to O' it moves a distance of (note c'=c):

x' = c*t'

Plugging these into the equations above:

c*t = g*(c*t' + v*t')

c*t' = g*(c*t - v*t)

Subsitituting:

c*t = g*(c + v)*t'

c*t' = g*(c - v)*t

This is a system of two equations. Solving one for t' (say the second one) and substituting into the first one can help you solve for g:

t' = g*(c - v)*t/c

and

c*t = g*(c + v)*t'

c*t = g*(c + v)*g*(c - v)*t/c

c = g^2*(c + v)*(c - v)/c

c^2 = g^2*(c^2 - v^2)

1 = g^2*(1 - v^2/c^2)

g^2 = 1 / (1 - v^2/c^2)

g = 1 / (1 - v^2/c^2)^.5

That is what g actually is. For small values of v, it is about zero. But if you travel facter than light, it grows to infinity! That was an early indication you couldn't travel faster than light.

Another result is that, since the space direction (x) changes, the time direction must also change. This makes sense, since speed is distance over time. If the speed is constant, but the space dimention changes, then time should do. You can solve this by using the two equations above again:

x = g*(x' + v*t')

x' = g*(x - v*t)

But because we know what g is, we can solve for t now:

x = g*(x' + v*t')

and

x' = g*(x - v*t)

x' = g*(g*(x' + v*t') - v*t)

x'/g = g*(x' + v*t') - v*t

v*t = g*(x' + v*t') - x'/g

t = g*(x'/v + t') - x'/(v*g)

t = g*(x'/v + t') - g*x'/(v*g^2)

t = g*(x'/v + t' - x'/(v*g^2)

t = g*(t' + x'/v*(1 - (1 - v^2/c^2)))

t = g*(t' + x'/v*v^2/c^2)

t = g*(t' + v*x'/c^2)

Together with the distance-equation, these form the new relativity equations, called the Lorentz Transformations:

x = g*(x' + v*t')

y = y'

z = z'

t = g*(t' + v*x'/c^2)

g = 1 / (1 - v^2/c^2)^.5

And from the other point-of-view:

x' = g*(x - v*t)

y' = y

z' = z

t' = g*(t - v*x/c^2)

g = 1 / (1 - v^2/c^2)^.5

Lorentz Velocity Transformations

But wait: there's more! Velocity is the derivative of distance with respect to time. Time and distance are distorted between the two reference frames, so velocities measured between the two should also be distorted. Say a particle moves with a velocity u (components ux uy uz) in O, and say that it moves with a velocity u' (components ux' uy' uz') in O'. It is the same particle looked at from two vantage points O and O'. How is the velocity in O' related to the velocity in O? First note the definitions:

ux = dx/dt

uy = dy/dt

uz = dz/dt

and

ux' = dx'/dt'

uy' = dy'/dt'

uz' = dz'/dt'

Let's begin by looking at the x-direction velocities. Note the following identity from the chain rule:

dx/dt' = dx/dt * dt/dt'

or

dx/dt = dx/dt' / dt/dt'

ux = dx/dt' / dt/dt'

We want the derivatives of the varibles in O wrt variables in O', since that's how the Lorentz transforms are defined. The velocity ux is dx/dt of course. Now taking the derivatives of the transforms and plugging them into the equation yeilds:

dx/dt' = d/dt' (g*(x' + v*t'))

dx/dt' = g * d/dt' (x' + v*t')

dx/dt' = g * (dx'/dt' + v*dt'/dt')

dx/dt' = g * (ux' + v)

and

dt/dt' = d/dt' (g*(t' + v*x'/c^2))

dt/dt' = g * d/dt' (t' + v*x'/c^2)

dt/dt' = g * (dt'/dt' + v*dx'/dt'/c^2)

dt/dt' = g * (1 + v*ux'/c^2)

Therefore

ux = dx/dt' / dt/dt'

ux = (ux' + v) / (1 + v*ux'/c^2)

Compare with the Galilean result, ux = (ux' + v). There is a correction term, and it is caused by the time distortion of Relativity. What about y-direction and z-direction velocities? Well, the two will have the same form, since anything in one direction perpendicular to the direction of motion - x-direction - isn't special in any other direction perpendicular to the direction of motion. (Can you see why?) So let's solve for the y-direction, and the z-direction follows the same logic:

dy/dt' = dy/dt * dt/dt'

or

dy/dt = dy/dt' / dt/dt'

uy = dy/dt' / dt/dt'

also

dy/dt' = d/dt' (y')

dy/dt' = dy'/dt'

dy/dt' = uy'

and remember

dt/dt' = g * (1 + v*ux'/c^2)

Therefore

uy = uy' / g / (1 + v*ux'/c^2)

And in the z-direction

uz = uz' / g / (1 + v*ux'/c^2)

It is interesting that the changes to the Galilean result in the y/z-directions depend on the distortion from the x-direction (and the ux' velocity). This is complete counter-intuitive at first glance, but makes sense after thinking about it. The distortion is from movement in the x-direction of the O' frame, so that is what the change depends on. In summary (from both points of view):

ux = (ux' + v) / (1 + v*ux'/c^2)

uy = uy' / g / (1 + v*ux'/c^2)

uz = uz' / g / (1 + v*ux'/c^2)

and

ux' = (ux - v) / (1 - v*ux/c^2)

uy' = uy / g / (1 - v*ux/c^2)

uz' = uz / g / (1 - v*ux/c^2)

Momentum changes

Momentum is highly depended on velocity. So does it change too? Let's perform an experiment and find out! :-) Here's the skinny:

Look at this picture in the O frame and this picture in the O' frame from this page.

a
Ball thrown by O
uax
x-velocity of "ball a" wrt O before the collision
uay
y-velocity of "ball a" wrt O before the collision
uax'
x-velocity of "ball a" wrt O' before the collision
uay'
y-velocity of "ball a" wrt O' before the collision
wax
x-velocity of "ball a" wrt O after the collision
way
y-velocity of "ball a" wrt O after the collision
wax'
x-velocity of "ball a" wrt O' after the collision
way'
y-velocity of "ball a" wrt O' after the collision

and

b
Ball' thrown by O'
ubx
x-velocity of "ball b" wrt O before the collision
uby
y-velocity of "ball b" wrt O before the collision
ubx'
x-velocity of "ball b" wrt O' before the collision
uby'
y-velocity of "ball b" wrt O' before the collision
wbx
x-velocity of "ball b" wrt O after the collision
wby
y-velocity of "ball b" wrt O after the collision
wbx'
x-velocity of "ball b" wrt O' after the collision
wby'
y-velocity of "ball b" wrt O' after the collision

also

uy
Velocity each person measures throwing their ball in their reference frame (x-componet=0)

My notation is slightly different from the picture. Note the differences!

Here is what the situation is. Say the person at O throws a baseball straight out (y direction) relative to her. Say the person' at O' also throws a baseball' straight out (-y' direction) relative to her'. Each ball has constant velocity (no gravity), and each person throws the ball with the same velocity as measured in their reference frame. Well, relative to the person at O, the baseball' moves in a diagonal line.

(Think of it this way. If you throw a ball up in a car, it seems to go straight. To a person on the sidewalk, it is moving in a diagonal. You just don't notice any horizonal direction because you are moving at the same speed in that direction.)

Well, the velocity of the "ball a" thrown by O is:

before the collision

uax = 0

uay = uy

and after the collision

wax = 0

way = -uy

Using the classical definition of momentum p = m * u then the change of momentum observed by O is:

before the collision

pax = 0

pay = m * uy

and after the collision

qax = 0

qay = m * (-uy)

So the net momentum change

Pax = qax - pax = 0 - 0 = 0

Pay = qay - pay

Pay = m * (-uy) - m * uy

Pay = -2 * m * uy

Likewise for "ball b" thrown by O':

before the collision (using the velocity transforms)

ubx = v

uby = -uy / g

and after the collision

wbx = v

wby = uy / g

and the momentums:

before the collision

pbx = m * v

pby = - m * uy / g

and after the collision

qbx = m * v

qby = m * uy / g

So the net momentum change

Pbx = qbx - pbx = m * v - m * v = 0

Pby = qby - pby

Pby = m * uy / g + m * uy / g

Pby = 2 * m * uy / g

This makes no sense! The momentum from one side of the collision is not balanced by momentum on the other side:

Should be zero, but isn't:

Pynet = Pay + Pby

Pynet = -2 * m * uy + 2 * m * uy / g

Pynet = 2 * m * uy * ( 1 / g - 1)

Pynet != 0

Since the net is not zero, momentum was NOT conserved using Lorentz Transforms! To preserve the law of conservation of momentum the definition of momentum must be changed. How should it be adjusted? Well the problems occured when we calculated the momentum of the particle in the O' frame:

Remember this?

Pby = 2 * m * uy / g

The 1/g factor came from the Lorentz velocity transformations. To fix it, we adjust the definition of momentum from:

p = m * u

To:

p = m * u * g

This doesn't affect the "ball a" result since for the O frame, relative to itself, g is zero. Plugging it into the above result allows momentum to be conserved. Cool!

Proving E = m * c ^ 2

In summary so far... The effects of relativity means measurements between O and O' are different. The changes include the Lorentz Transforms of position and velocity. The law of momentum was adjusted:

p = m * u * g

Also note the original definitions of velocity, force and energy (work):

v = dx/dt

F = dp/dt

E = integral of F dx

The first step is to get a more specific equation for Force. Momentum changed, so the force is not just F=ma. Let's put a particle right at the origin of O' and see what happens. This is a modification of Young's derivation of Kinetic Energy. By evaluating the derivate you find:

Note: u=v

F = dp/dt

F = d/dt (m * v / (1 - v^2 / c^2)^.5

F = m * v * d/dt((1 - v^2 / c^2)^-.5) + m / (1 - v^2 / c^2)^.5 * dv/dt

F = m * v * d/dt((1 - v^2 / c^2)^-.5) + m * a / (1 - v^2 / c^2)^.5

F = m * v * (1 - v^2 / c^2)^-3/2 * d/dt(1 - v^2 / c^2) + m * a / (1 - v^2 / c^2)^.5

F = m * v * g^3 * (-1/2) * (-2 * v / c^2) * dv/dt + m * a * g

F = m * a * g * (1 + g^2 * v^2 / c^2)

F = m * a * g * (1 + v^2 / c^2 / (1 - v^2 / c^2))

F = m * a * g * (1 - v^2 / c^2 + v^2 / c^2) / (1 - v^2 / c^2)

F = m * a * g^3 * (1 - v^2 / c^2 + v^2 / c^2)

F = m * a * g^3

Now going back to the definition of energy:

E = integral of F dx

F = m * a * g^3

E = integral of m * a * g^3 dx

E = integral of m * g^3 * dv/dt dx

E = integral of m * g^3 * dx/dt dv

E = integral of m * g^3 * v dv

E = integral of m * v / (1 - v^2 / c^2)^3/2 dv

Note (from integral table):

integal du / (a^2 - u^2)^3/2 = u / a^2 / (a^2 - u^2)^1/2 + C

Using the product rule:

J = m * v

dJ = m dv

dK = dv / (1 - v^2 / c^2)^3/2

K = v / (1 - v^2 / c^2)^1/2

E = J * K - integral of K dJ

E = m * v^2 * g - integral of m * v / (1 - v^2 / c^2)^1/2 dv

Note (from integral table):

integal du / (a^2 - u^2)^1/2 = arcsin(u / a) + C

Using the product rule:

J = m * v

dJ = m dv

dK = dv / (1 - v^2 / c^2)^1/2

K = c * arcsin(v / c)

E = m * v^2 * g - J * K + integral of K dJ

E = m * v^2 * g - m * v * c * arcsin(v / c) + integral of m * c * arcsin(v / c) dv

E = m * v^2 * g - m * v * c * arcsin(v / c) + m * c^2 * integral of arcsin(v / c) dv / c

Note (from integral table):

integal of arcsin(u) du = arcsin(u) + (1 - u^2)^.5 + C

E = m * v^2 * g - m * v * c * arcsin(v / c) + m * c^2 * (v / c) * arcsin(v / c) + m * c^2 * (1 - v^2 / c^2)^1/2

E = m * v^2 * g - m * v * c * arcsin(v / c) + m * v * c * arcsin(v / c) + m * c^2 * (1 - v^2 / c^2) * g

E = m * v^2 * g + m * c^2 * g - m * v^2 * g

E = m * c^2 * g

Almost there! When the velocity is zero, g = 1. Therefore, when the object is at rest, it still has some energy. This is called rest energy. So what is the equation for rest enegy?

E = m * c^2

User Journal

Journal: Juvenile cerebellar astrocytoma (repost for posterity)

Journal by Quantum Jim

I am not a doctor. Cerebellar astrocytoma is a form of intracranial cancer which involves brain cells call astrocytes. It is the third most common type of cancer in juveniles. There are four grades of increasing severity defined by the World Health Organization. Juvenile cerebellar astrocytoma rarely leave the cerebellum. It is a section of the brain located near the brainstem and below the occipital lobe. The cerebellum helps direct balance, attention, and complex motor control (particularly involving vision-related feedback). It also helps a person judge the passage of time and is involved in language processing too.

Astrocytes are not neurons. They are star-shaped glial cells that commonly help form the structure of the brain and provide nutrition from blood vessels. Astrocytes are the largest cells in the brain and outnumber neurons by an order of magnitude. Astrocytes help limit the spread cerain toxic neurotransmitters. Through haemodynamic regulation they can also increase blood flow to areas of intense neural activity in the brain. Functional Magnetic Resonance Imaging (fMRI) of those areas helps biologists understand which areas of the brain corrolate with certain thought patterns.

Astrocytes may also play a role in certain types of neuron-to-neuronsignal transmission by isolating or withdrawing from synapses. They can also form a second communication network within the brain by releasing neurotransmitters in response to certain stimulations. However, it is at least several orders of magnitude slower than the neuronal network.

I love google, wikipedia, and especially the library, where I first learned about these things before the world wide web even existed! :-)

If you hype something and it succeeds, you're a genius -- it wasn't a hype. If you hype it and it fails, then it was just a hype. -- Neil Bogart

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