Posts Tagged ‘Physics’
This book is an epistemological nightmare. Rizzi asks the reader to take on radical and unfounded views, sometimes without even a loose explanation or logical construction beyond “That makes sense, right?”
Even though I disagree with nearly every tenet of Rizzi’s philosophy, I still would give it a respectable two or three star rating if it weren’t for:
- His obvious lack of a copyeditor;
- His entire disregard for even addressing other points of view;
- His attempt to tackle complex issues with a poorly developed philosophical toolbox; and, most importantly,
- His total lack of logical flow or structure beyond asking the reader to accept things on his authority.
Though no doubt a great physicist, Rizzi seems to have lost his notion of rigor in trying to invent a new realist approach to the philosophy of science. His biggest flaw, in my opinion, is in his confusion of the nature of words; he oftentimes seems to think that he can pull universal truth out of the English language.
Unfortunately for him, the English language is neither an authority on nature nor a system he’s totally mastered himself.
All in all, avoid this book — especially if you don’t have the scientific grounding to understand why it’s wrong on your own.
So I have plans to attempt graduate mechanics this coming fall semester. As such, I’d like to have to not worry about my Quantum I class and have accordingly started to watch some Oxford lectures on undergraduate QM. I think I’ll try to occasionally summarize what we’ve gone over on this blog, mostly for my own benefit of being able to repeat what I should have digested. I’ve only watched the first three lectures, so there’s not much, but here it goes.
So instead of dealing with probability in “normal” ways like other branches of science and math, quantum mechanics uses a method of complex probability amplitudes. These amplitudes are represented by complex numbers, and it turns out that for a given probability amplitude (from a properly normalized set of amplitudes), we can calculate the probability of the associated event by taking the modulus squared. I’m not sure yet where these amplitudes come from… perhaps just from experiment? That’s a question to have on hold as I move through the lectures, I guess.
Suppose there’s some sort of quantum state that I want to measure, and that there are certain allowed (and distinct?) states for this quantity which form a basis for a vector space . Then we say that there is a ket (which is just a vector) such that
We call a vector a ket in this notation. Coincidentally, there’s a corresponding object called a bra:
Which is just a covector (or 1-form) that exists in the adjoint space (or dual space) . As it goes with these things, covectors “eat” vectors and turn them into 0-forms (numbers), so we can also think of bras as complex-valued functions over ; in other words, . It additionally turns out (importantly) that
Which falls out naturally, because when we multiply them out at we would expect, we’re left with the 0-form
Because every allowable outcome should be represented by its probability amplitude , and so the sum of their squared moduli will be equivalent to the probability of the entire sample space — namely, .
More later on operators, observables, and basically most of Lecture 3.
I know it’s been a long time since I’ve blogged, but I’ve been in a fit of arguing with some of my religiously inclined friends lately and there’s something I have to get off of my chest (and onto the Internet). I’m calling it the “obvious design” argument for a God. It goes like this: the Universe is so beautiful, so rationally explainable, and so crafted to sustain life that it is surely crafted by a single God. The argument is akin to opening a cigar box of 50 toothpicks and, upon seeing that they are perfectly aligned, parallel, and evenly spaced, claiming that they were put that way by a person (because the probability of any other explanation is absurdly improbable).
It kind of makes sense when you think of it in terms of toothpicks, but there’s a fundamental flaw in using this argument to sustain a God: you can only observe one Universe, but you’re free to observe as many boxes of toothpicks as you want. We know exactly what a cigar box of assorted toothpicks should look like; it should be chaos, and almost certainly not lined up in parallel. But we don’t know what a Universe should look like free of design, because we only have one to look at, and furthermore we are removed from even conceiving of such an alternate universe because we aren’t built to envision it.
The common example given in favor of obvious design is something along the lines of: “what are the chances that gravity is inverse-square? It could just as easily be cubic or worse, but someone — some God — has set it to be inverse square, which allows our world to exist.” But again, the fundamental flaw: we only have one Universe to work from here. Sure, our Universe is inverse square. If it wasn’t, you’re right — we probably couldn’t exist. But that means we wouldn’t even be here to observe it.
I’ve devised what I think is a cute exercise to present to the next person who argues this with me, and I hope I can illustrate it to the present reader (you) well enough with words, because I think it’s a good example.
“Suppose just for the moment that there are 20 possible configurations of the Universe, and only one of them can sustain life. [At this point, I pull a 20-sided die from my pocket.] Suppose that single life-configuration is represented by the number 20 on this die. [I drop the die theatrically.] What does the die say?”
Now there’s a chance that the d20 will read 20, and the arguer will read it to me and I will say “Good. Now roll it again.” Eventually it won’t be a 20, and then they’ll read it to me and I’ll say:
“No it doesn’t.”
“What? Yes it does, look.”
“We aren’t allowed to look, Arguer, because it’s not a 20, and it follows that you don’t exist in this Universe. So you can’t read it.”
If I wanted to draw it out, we could roll it again and again until we get a 20. I’ll then coyly point out that it seems to have been a 20 every time we rolled (if I wanted to pull out this last point at the risk of rolling a success in the beginning, I’ll use a smaller die or more success conditions).
The point, see, is that chance has nothing to do with it. The Universe is here. We’re in it. And that’s just how it is. If I draw a card from a standard deck and get the Queen of Hearts, I don’t say: “ah! The chances of me drawing this card are less than 2%! That should rarely ever happen!”
Anyway, if you’re reading my blog, you probably didn’t need to hear this, and it’s probably not coherent anyway. Good night.
So I’m building this application to use in our lab at Clemson to keep tabs on all the sensors around the equipment. I’m not going to copy over the whole post here but for anybody who has an interest in following my coding endeavors can check out my post at http://ionsurfing.wordpress.com/2009/12/30/mockupsunusable-alpha-screenshots-for-tactile/. I’ve got some nice screenshots and explanations of where I’m going with the program. I think the biggest challenge will be finding a good way to deal with human interaction using an old-style touchscreen. Any and all suggestions on libraries to look into or thoughts on UI challenges are welcome. :)
By the way, thanks to Mairin for her Inkscape mockup class at FUDCon… I actually used it!
Last year, I learned about the layman’s essence of quantum mechanics, and I wrote a post about it on this blog. This semester, my big topic in physics class has been the Lagrangian and Lagrangian Mechanics. So, like last time, I’m going to write a nice lengthy post about it because:
- It might help someone else who wants a basic introduction, and
- It will definitely help me sort it out in my head, seeing as how my exam is this Tuesday.
Recall: Kinetic and Potential Energy
You might remember in previous physics classes a discussion concerning kinetic and potential energy. Recall that for any conservative force, E = T + U, where E is the total energy of the system, T is the kinetic energy, and U is the potential energy (I’ll use these conventions for the rest of this post).
You also might remember that using conservation of energy made some problems much easier to solve compared to using Newtonian methods. Consider, for example, the point-particle baseball thrown directly up in an air-resistance free world; we can find the maximum height by recongizing that at its maximum height the ball has zero velocity relative to the ground. Thus it has zero kinetic energy (because T=(1/2)mv2) and so its potential energy U=mghmax is equal to the total energy of the system. As a consequence, we can find the ball’s maximum height by setting E = E, or, equivalently, Umax = Tmax.
mghmax = (1/2)mv02
Where v0 is the initial velocity of the thrown ball. Note that we could also find the initial velocity by knowing the final height….
Principle of Least Action
To derive the basics of Lagrangian mechanics, we need to understand the calculus of variations, which is a topic beyond the scope of a blog post (and certainly beyond the scope of barebones HTML formatting).
En anglais, the principle of least action says this: a body moving from point A to point B will take the path that minimizes required action. Calculus of variations teaches us how to minimize an action integral in the general case. Now we can apply that to physics.
The Lagrangian L (usually written as a script L) is defined as:
L = T – U
Aside. I think it’s also valid to define L = U – T since we’ll be setting derivatives of the same function equal to each other so that signs will be irrelevant.
Then we can use the Euler-Lagrange formula (a result of calculus of variations) to say that for each generalized coordinate (xi) in our configuration space:
dL/dxi = d/dt [ dL/dxi' ] (*)
If you have trouble reading that, just look up the Wikipedia article on Euler-Lagrange; I don’t feel like going through the trouble of LaTeX’ing on this not-yet-configured machine just to point out that the partial derivative of the Lagrangian with respect to the generalized coordinate xi equals (under the condition of minimizing the action integral) the time derivative of the partial derivative of the Lagrangian with respect to xi‘ (or xi dot, the derivative of xi with respect to time).
These mysterious generalized coordinates can be whatever you want them to be as long as they can fully describe the system you’re concerned with. With a simple pendulum, you might just have the angular coordinate phi, which can alone describe any state of the pendulum. With a pendulum on a spring, you might have phi and x, the length of the spring. With an Atwood machine, you might just have one coordinate again that describes the length of the rope on one side (which describes the entire system given an ideal rope).
The set of your generalized coordinates forms the basis of a configuration space in which every possible state of the system is in the set spanned by those coordinates… I think. We didn’t really cover that in class too much.
Equations of Motion
So anyway, now we have these equalities as defined by the equation (*), and each equality for some coordinate y should include y” (because we’ve taken a time derivative of y’). Now we can re-arrange these as second order differential equations! Hurray!
Background Story/Flavor Text
So I’m working on getting this ammeter to interface with Linux system for the lab, and it turns out that this thing supports the Standard Commands for Programmable Instruments (SCPI). A few hours, Google searches, and Perl scripts after I started, I’d done what I would call a reasonable job of communicating with this device and pulling data from it.
So what is SPCI, and how does it work?
Connecting the Interface
SPCI is just a standard set of commands, not a defined interface. But it turns out that when you’re communicating with electronics SPCI is often used over serial connections like GPIB or RS-232. In my case, I was forced to use RS-232 because of hardware limitations.
Now, you can just read and write directly with the device handle. In my case using RS-232, I ended up discovering that
was right for me.
The entire set of commands is found in this documentation from the IVI foundation site. The commands are organized in a directory like structure. If I want to execute the command to ask how many errors messages are sitting in the buffer, for example, I’ll execute this:
What this effectively seems to do is…
- Go to the “root” directory [:]
- Look in the SYST(em) folder [SYST]
- Look in the ERR(or) folder [:ERR]
- Execute the COUNT command [COUNT]
- Note that this is a query; i.e. returned data is expected [?]
Each command has as:
:SYSTEM:ERROR:COUNT? :System:Err:Count? Syst:ERROR:COUNT?
Note that you can vary capitalization without consequence, you can choose to ignore that prefixed colon, and you can even mix around when you use long and short forms.
I used SCPI to communicate with a Keithley 6485 Picoammeter. I doubt seriously that many people reading this will ever need to repeat this task, but it’s all I have to present some examples.
To turn off the zero check on the picoammeter and take the current reading, we could execute these commands:
Syst:ZCh 0 Read?
Note that I could have used “OFF” in place of “0″; either is a legitimate boolean value for “false”. Meanwhile, a script running in the background that looks something like this:
#!/bin/bash cat /dev/ttyS0 >> datafile
Will magically receive a line of data from the machine that we can interpret with a simple Perl script.
This is the kind of thing I should use Twitter for, but I’m just too verbose. For the few onlookers interested in an update on the life of Matthew, though, here it is.
- I’m interning at MUSC, doing medical physics research on dosimetry. Really, it’s just me dissecting some software from a Brazilian research lab and processing numbers, but it makes me feel like I’m at least doing something productive.
- I’m working at Masters Studios over the summer as well. I actually kinda ran the studio this past week because Master Phil was out. Next week I’m back to just one or two evening classes to teach a week. Over and over I’ve volunteered to redo the crappy website for them, and I keep hearing for the past one or two years that someone’s been working on it already. I think at this point the site would already have to be re-updated to keep up with the times.
- I got out of Fedora stuff for a while as I adjusted to summer, but I’m kinda trying to get back into it. I’m not sure that I want to keep doing all docs stuff, so I’ll pull back on that once I can find someone to hand off the user guide to and then I’ll get into packaging. I’ve been reading up on the packaging guidelines tonight.
- I’d like to reconnect with some friends over the summer. There are a few people I’ve been independently talking to about getting together, so hopefully that’ll all fall into place. I was going to do something with Araba too, but I have a feeling she’s already gone back to Cambridge without saying bye… (*frown*)
- I’ve been blogging more frequently!
- Rob and I are working on Nevhma, a Sugar activity for the XO-1 for the math4 project. It’s a little Tron-like game where you run around a coordinate plane to hit benchmark points.
- Sherwin and I are still working on our project which has about 6 different names now. He’s actually done way more effective work than me since I started worrying about MUSC stuff, but hopefully I’ll be able to get my part done by the end of the summer and we can release Beta 1.
That’s all I can think of right now. Hopefully I’ll find another Csifa soon, and take a photo if I can.
Disclaimer: I know, I know. This is about a piece of software for Windows. It’s not like I enjoy using Windows or that I even have it installed on any of my personal machines (I don’t). Read further, and you’ll see why I have to use Windows in my situation for a month or so. And if you’re reading this on Fedora Planet or something, please don’t post something like “Don’t put Windows stuff on Fedora Planet”. We’re all about Freedom, right?
So I started this internship doing medical physics at MUSC in Charleston, SC. I’m doing work in Radiology, and I’m required to use a program called CALDose_X to calculate radiation fractions imparted to patients. The program is closed source and maintained by a nuclear physics lab in Portugal. It can be found at http://www.grupodoin.com.
The program is useful for its purpose, but it’s otherwise kind of clumsy. Exceptions aren’t handled very well, several features seem to be inconsistent with each other, and something is screwed up with how is recognizes the presence of a .NET framework on your machine (which is one reason that I couldn’t get it working under Wine).
The program is made for doctors to do single examinations with, but I’m using it to find trends in data. Since it takes a while to fill out their little GUI form, I was finding it very tiresome to compute simulations for different values. And since it was closed source with poor documentation, I couldn’t readily write any scripts to interface with it.
That’s when I had the idea to write a macro. There are several macro recorder programs available for a fee for Windows, but I found something even better: AutoHotKey. It’s free and open-source, and has an extensively documented scripting language that lets you interact directly with GUI elements (not just relying on screen coordinates). Additionally, you can compile AHK scripts into Windows executables for use on any machine. It also includes a window inspector to reveal the IDs of GUI elements so that you can interact with them in your scripts.
All-in-all, I was very pleased with this program. I can’t stress how well it was documented. Writing a perl script to interface with some open source code – or at least some APIs – would have been nice, but this is a great solution for when that’s not available under Windows.
PS: Do we have anything like this under Linux? (Not that there would be as much use for it when everything can be so elegantly linked…)
WordPress Drafts: Lessons Learned (or, Reality, Quantum Mechanics, and the Romanticism of Modern Physics)
I had the pleasure a few weeks ago to attend an in-department lecture/debate on opposing interpretations of quantum mechanics. The quantum mechanics was interesting, but one of the philosophical tangents was what stuck in my head for the rest of the night. We’ll talk about it all in the next few paragraphs.
Before we attacked quantum mechanics, Dr. Hartmann opened with some thoughts on how different interpretations can lead to the same experimental results. To paraphrase: consider the basic Newtonian physics we learn in high school (or earlier). This sort of physics is on the whole inferred from a priori observation of our environment, and on childhood assumptions about the nature of reality. Things like F=ma and Newton’s famous laws of motion are essentially common-sense.
But mechanics does not stop with Newton’s formalization of a priori perception. An important abstraction that we learn in high school is to energy. The familiar quantities of kinetic and potential energy make solving certain problems child’s play compared to the Newtonian physics that would be required to do the same thing.
In more advanced physics, we can abstract mechanics ever further to Lagrange and Hamiltonian mechanics. Here, in the land of manifolds with tangent spaces, we can solve problems well beyond the scope of our other methods. At the same time, though, these methods could be overkill for a simple pendulum.
The idea is that different representations of reality can lend themselves to solving different problems. When Dr. Daw spoke, he reinforced these ideas. He also proposed that the a priori observations at the base of Newtonian physics are “reality”. In his interpretation, all the further abstractions take us away from reality. Furthermore, these other methods lose validity and meaning if they can no longer be traced back to “reality”.
I disagree with this on a fundamental level, and I’m happy to know that some of the other professors agree with me here (although others don’t). While I appreciate the role of Newtonian physics, I’m not of the opinion that human sensory perception can scientifically define universal reality. Perhaps it would be useful to check that our more advanced interpretations of physics agree with our older ones, but if they don’t, that doesn’t necessitate fault. I can imagine a universe which doesn’t agree with my childhood assumptions of reality – and even though I don’t see this everyday with my eyes, that shouldn’t mean that I can discount this theoretical reality. The optical perception of a coffee-filled glob of carbon should not be counted on to reveal fundamental truths of reality.
Intepretations of QM
The mainstream, popular interpretation of quantum mechanics – and the one the general public is familiar with – will, for simplicity’s sake, be called the Copenhagen interpretation in this blog. I hear that this term is misleading – that there are, in fact, several Copenhagen interpretations – but I don’t really care.
But according apparently, physics is a bit like Perl – there’s more than one way to do it. Interestingly, there’s a way to do quantum mechanics not with the use of probability and apparent chance but with completely deterministic wave physics. It’s called pilot wave theory, and it was thought up by de Broglie and refined by a few other physicists in the past century. A primer on the theory and its history can be found on Wikipedia (http://en.wikipedia.org/wiki/Pilot_wave).
Dr. Daw gave the impression while he was talking that he feels like the Copenhagen interpretation is the result of romanticism kicking into physics. I’ll admit that there is something romantic about the Copenhagen interpretation. It’s mysterious and beautiful, and quite different. I happen to appreciate Capra’s views on the separation of physics from classical western philosophy and the parallels between eastern mysticism (taoism, zen, hinduism, et cetera) which he explains in The Tao of Physics, a book I’ve blogged about before.
Because I have a particular affinity for the orient, I very much like the Copenhagen intepretation. I acknowledge, though, that this is human bias. But I hope that both interpretations are correct. This is a totally valid outcome – just like Newtonian, Lagrangian, and Hamiltonian physics are all valid representations, I think it would be acceptable for both the Copenhagen and Broglie-Bohm…
That’s the end of this post.
I guess that’s what happens when you save something as a draft and forget about it. You have no idea what you were writing.
Review of Night Thoughts of a Classical Physicist, focusing on the analogs between Jakob and his era.
Night Thoughts of a Classical Physicist picks a unique subject and setting through which revolutions of thought permeated every facet of the West. The beginning of the twentieth century marked a global transformation in many facets of humanity, and science was not exempt from cultural upheaval. Changes both political and social ensued in parallel with revolutions in scientific thought, and McCormmach tells the story of a man left behind – a Classical Physicist permanently intertwined with the past. The story of Professor Viktor Jakob represents the struggle of the world to keep up with the sweeping changes of a new, faster globe and the intellectual modifications that accompanied it.
The physics presented in the novel – although nonetheless historically accurate – served a purpose beyond simply representing a branch of natural science. The paradigm shift in physics of the day was an analog of the worldwide metamorphosis of civilization. Jakob embodied these parallel transfigurations in his thoughts on both art and science. To him, theatre and physics as well as music and mathematics were entangled in a single human experience. In this sense, his scholarly lineage could nearly be traced to the Enlightenment era. The ideas of unity, closure, determinism, and the importance of the individual that accompanied Enlightenment philosophy manifested themselves in his interpretation of science. Jakob’s pursuit of a solution for the world-ether typified his mindset towards the world. Even deterred by the likes of Planck (pg. 139), Jakob continued to dream of a grand scientific unification.
Physics and the world stage were in two not unalike states at the turn of the century. The rise of Germany in central Europe and the end of the beginnings of industrialization introduced paradigm shifts in life and politics as radical as the new interpretations in physics. It may have been ironic to Jakob that the very same forces in Germany catalyzed both scientific knowledge and military prowess. He prided his and his fellow scientists’ peaceful natures, especially within their profession – but even he could not entirely resist the call of nationalism. His work on acoustics in the field was an example of his contribution to the war.
But nationalism was a phenomenon with which the professor did not always peacefully mesh. Jakob considered himself a worshipper of science, in accord with Einstein’s scheme (108). Jakob has chosen for himself “the life of the discoverer” (109), and accordingly placed physics higher than the state. But interestingly, many of the scientists to whom he would pay reverence – such as Planck – were at least able to support the war with their public attitudes. Jakob’s refusal to sign a single document supporting the war is evidence of his strict, scientific moral code and fear of change. It fits with his description of a classical physics; in his view, the role of virtue and scientific rigidity within oneself is the key characteristic of physics. He admired many of his more esteemed colleagues for their incredible internal strength of character.
Jakob was, indeed, a self-proclaimed Classical Physicist. Unlike the era of his youth, the German students of the twentieth century had (allegedly) not been “drilled in the classics, in the careful thought of the languages and literatures of antiquity” (133). Jakob believed in a strong connection between physics and the classics. With this in mind, one might propose that what bothered Jakob in part about the new age of atomic physics was uncertainty and a disconnect between a priori assumptions and the implications of modern physics. Jakob thought of classical physics as not so much a world-view, but an attitude: a description more of the scientist than the science.
His knowledge of the classical age made it easy for Jakob to recognize the mutation of Greek thought and culture into a tool for nationalism when he and his wife attend a reading of Antigone. European affinity for Greek science and culture is exploited as the company alters details of the tragedy to create sympathy for the German cause. This sort of alteration for the sake of political allusion would begin to permeate many cultures in future decades. Later in the century, this same type of subliminal propaganda would manifest itself in American and Soviet media to generate sympathy for democracy and communism.
It was Jakob’s belief that the loss of the world-ether implied the loss of intelligibility in the physics community (134). Jakob appreciated mechanisms representative of our perception more than he did abstractions into mathematics. Accordingly, he felt that the lack of an absolute reference frame turned physics into a “cold gray cave of abstraction” (ibid). Once more, Jakob reveals his ties to the previous century. Like the romantics of art and literature calling for a return to nature after industrialization, Jakob feels that the loss of sensible physics is a loss of a part of human culture.
The magnitude of destruction experienced in the First World War is certainly akin to a cold gray cave of abstraction. The introduction of twentieth century weaponry and technology made the Great War a monster of a sort not before witnessed in the world. Lengthy, monotonous trench warfare and the introduction of war to the sea and sky made war less personal than ever. In the eyes of many – including Jakob – soldiers started their transformation from people to numbers in that era. In that light, modern warfare may be somewhat similar to modern physics in Jakob’s view.
But more than simply the loss of the world-ether concept, Jakob felt that the branching away from classical physics meant the loss of the individual. Jakob recalls a shift during his career from individuals pursuing physics of their own accord – with their own ideas – to an age where money translates a wealthy student into a fledgling scientist to pursue the goals advancing the reputation of the university director. The idea that money fuels a man’s career is certainly not a new concept, but Jakob seems to feel that this sort of construct contaminates the purity of the physics community.
Jakob’s view of his evolving science and evolving world resonated with the ideas of a finished age. Victor Jakob might have been one of the last of his breed. Perhaps, though, his concern for the individual may have been warranted as we entered a less personal age. Perhaps, even today, there is still a place for the Classical Physicist.
You can find a more traditional book review at the Harvard Press site, http://www.hup.harvard.edu/catalog/MCCNIG.html.
You can also preview the book on Google Books. Search for “Night Thoughts of a Classical Physicist”.