Self Evaluation 3.

I feel like this blog evaluation period has pretty much been status quo. My second evaluation period was a major increase from the first evaluation, but I feel this period has been about the same as the second, but no better.

Post frequency: About 3 per week, sometimes 2, sometimes 4, but on average, 3. I've exceeded the minimum posts per week - about the same frequency as previous grading periods. This exceeds C level, but I don't think is A level according to the standards. I definitely could use improvement in this category.

Wrapping this up. Mostly.

Well, it's that time of year - the end of the semester. Except this time, I'm graduating! I'm approaching a busy summer - moving, traveling, and at the end, I'm getting married!

For those of you that didn't know, I've been writing this blog as a requirement for a class. I've also very much enjoyed writing it, but I may not have time to continue it, at least not in the detail that I'd like. I'll probably still post on this from time to time, but for the most part, you will not see too many more posts on this blog. Definitely if something new happens in the world of quantum mechanics, and I have the time, I'll add a post.

I'd like to time a moment to thank my readers, which were separated into two groups - the ones that had to read my blog (and others) because they were in the class, and the ones that wanted to. An extra special thanks to the readers that took the time to read my blog, even when it wasn't required!  I'd also like to thank Mr. James Redford for a LENGTHY discussion about Tipler's theory of everything - it was my first real blog debate I had.

It's been great, and I hope to see you all around, but for now, good bye!

Tunneling

I'm going to discuss yet another strange prediction of quantum mechanics - quantum tunneling. This effect allows scientists to image very tiny objects (atom sized objects) via a device called a scanning tunneling microscope (like the image to the left). That image is several atoms arranged in a ring, those bumps you see are the atoms! I direct you to Nano Nook for another example image.

So what is quantum tunneling? Well, think back to the potential that goes into Schrodinger's equation. Speciffically, I want you to consider a potential that looks like this.

You can visualize this like two hills that are sitting next to each other. Image you're sitting in the valley on the left, but you haven't eaten all day an you're exhausted. All your friends are waiting in the valley to the right, but you can't get there! You don't have enough energy! Well, this is the classical physics way of looking at things - no matter how hard you try, you don't have enough energy to make it up and over the hill.  Well, quantum mechanics says, you don't have to! Since your wave function extends in space, a small part of it overlaps with the other valley! What does this mean? There's a finite chance that you could be in the hill to the right! This is what quantum tunneling says, and this effect has been measured and is currently used a device called the scanning tunneling microscope (as well as MANY MANY other technologies.) Here's a gif I stole from wikipedia that shows this happening... sadly I didn't have time to make a simulation of my own.

Here you see a quantum particle penetrating a wall.

So how does the scanning tunneling microscope work? It's actually reasonably complicated, but the basic principle is as follows. A tungsten tip is held above the surface that you wish to image. There is nothing but vacuum between the tip and the surface, so normally, there's nothing to allows the electrons to flow to the surface. Fortunately for us, there's a finite probability that the electrons will "tunnel" to the surface, and this effect allows us to image the surface to extreme detail. Pretty cool, huh?

Not quantum, but I couldn't resist.

General Relativity, the theory of gravity that has existed since the early 1900s has been exceptionally difficult to prove. Early in the 20th century, several of it's major predictions have been proven, but it has taken a while to prove it's most basic predictions.

General Relativity treats time and space as interwoven (ever hear the term, the fabric of space-time?) and describes gravity as the curvature of space time. It's a very complicated and sophisticated theory - much too difficult for me to explain in detail.

Gravity Probe B, a NASA project to test General relativity was sent into orbit to measure the unconfirmed effects of GR. These were the geodetic effect (how objects curve space-time), and the frame dragging effect (essentially, the motion of an object around a rotating gravitating object is different than predicted by Newtonian gravity). Well, the geodetic effect was confirmed to an uncertainty of less than 0.5% in 2008, but what about the frame dragging effect? This effect is TINY, and requires extremely precise instrumentation. Well, NASA just released results that confirm the frame dragging effect to an uncertainty of less than 1%

What does this mean for you? Well, as it turns out, there a technology that many of us use every day that uses GR. That's GPS. GPS is already incredibly accurate (a couple of centimeters!), but these new advances may improve  the accuracy even more, allowing even better positioning. Being able to accuracy located objects from space is extremely important and has widespread applications.

I'm excited, I'm a big fan of General Relativity and an very excited to see this effect finally proven!

References:
NASA on Gravity Probe B

Potentially exciting news in the world of particle physics!

This happened about a month ago, and I've been doing some reading in my spare time about it, but I think now's the time to make a post about it.

It's big news for particle physicists, but I doubt you've heard this on the evening news. The Tevatron particle accelerator at Fermilab in Illinois has data that potentially points to the existence of a NEW fundamental particle.

Currently, physicists describe all the fundamental interactions in nature (except for gravity) by something called the Standard Model. It's done well for the time it's been around, but most physicists believe it's incomplete. Fermilab may have found proof of this.

A particle accelerator is a large device that sends two beams of charged particles in opposite directions. When these beams collide, the particles in the beam break apart and energy is released. This energy sometimes reforms into different types of particles, and the rules governing this are contained in the Standard Model.

Take a look at the graph above. The red line is what they would expect to see with the collisions they were doing. The black dots are the data collected. The blue line is a curve fitted to the bump in the dots - this is what they are excited about. Because that bump isn't predicted, it could mean a new particle previously unknown to physicists!

Of course, there's another possibility - this is statistical deviation from what we expect. The probability of this being the case is about 1 in 45. I like those odds, but they are far from conclusive. Only time will tell! This problem looks like it will be solved in the coming months by data collected at the LHC in Switzerland and France.

References:
http://resonaances.blogspot.com/2011/04/update-on-forward-backward-asymmetry.html
http://www.significancemagazine.org/details/webexclusive/1058929/Does-God-throw-loaded-dice-Fermilab-rewrites-the-laws-of-physics.html

Schrodinger's cat - is the paradox gone?

For a long time, Schrödinger's cat has been everyone's favorite example of quantum mechanics. Who doesn't like cats (aside from the people that don't)? It's become an icon for quantum mechanics, but a new proposal for an experiment may expose the cat while he's in the box. This preprint, due to be published in Physical Review A. Remember my post about the quantum drum? If you don't here's a quick summary.

Physicists put a 30 micrometer (human hair is about 100 micrometers thick) long piezoelectric paddle into a quantum superposition state - it was vibrating and not vibrating at the same time. As soon as they measured it though, its wave function collapsed to either of the two states, but some careful measurements showed that it was truly in a superposition state.

Hear is where the story gets interesting. Some physicists aren't satisfied with this, and want to take it a step further! What if we can make a measurement of the drum while it's in a superposition state without causing it to collapse? This is precisely what they are trying to do. Physicists Kurt Jacobs, Justin Finn, and Sai Vinjanampathy propose an experiment with an isolated wire put into a superposition state (vibrating in opposite directions - at the same time). They aren't stopping here, however. They wish to track and control the quantum state without collapsing the wave function. If they can achieve this, this would be revolutionary in quantum theory in general, and more specifically quantum computing. Quantum computing can theoretically achieve computational efficiency and speed leaps about bounds faster than current computers. Unfortunately, this experiment is a few years off, as the team doesn't have sensitive enough equipment.

Where does this leave Schrödinger's cat? Well if this experiment works as hoped, he'll be either dead - or alive - forever.

Be careful what you believe.

Being skeptical is a good thing for scientists, but when is it going too far?

We are taught to question what we are told, yet we are expected to accept whatever is taught to us in school. Are we supposed to just take in the knowledge and accept it as fact? Well, a little yes, and a little no.

Should we question everything, nothing would get accomplished - there's many many many lifetimes of research that has been done, and sometimes you have to accept things an trust that it was done correctly. Hopefully someone else will independently corroborate those results. Basically, it's perfectly okay to be skeptical about things, just don't take it to far. How far is too far? Well, take a look at this. For those of you not wanting to read, I'm going to post snippets here.

Basically, this guy says all the current mysteries of the universe, including quantum mechanics can be explained by "expanding mass". Load of crap if you ask me, and by the looks of it, he doesn't understand basic physics.

"...Can light from a distant source be simultaneously both a “wave of pure energy” and a “quantum-mechanical photon particle”, only physically “choosing” one or the other based on how it is later observed? Can a magnet cling energetically to a fridge against the constant pull of gravity, yet need no explanation for this endless energy? "

All experiments point to the first being a reality, but I understand his skepticism - it's difficult to swallow. The second sentence is what bothers me. He claims to accept the previously uncovered laws of physics, yet seems to be missing something. The first law of thermodynamics says that energy cannot be created or destroyed. That's precisely why a magnet sticks on the fridge. "Work," in the fundamental sense requires something be moved to a different potential energy, that kinetic energy can only come about by a change in potential energy. It just so happens magnets have greater potential energy for their size, and dominate gravity. No new energy is being added into the system. He's completely misunderstanding the fundamental laws of physics (which have NEVER been observed to be violated.)

So then he goes on to claim he can explain everything with a simple theory. Well based on what I'd seen so far, I wasn't expecting to find much, but I wanted to keep an open mind. You can read the whole article if you like, but I'm only going to highlight a few points he makes.

"Today we think of matter as passive lumps of mass..."

Well that's kinda redundant. Mass is understood to be a number associated with a type of particle. Just as an electron always has a +1e charge, so does an electron always have the mass of one electron - this hasn't changed, and his statement is dumb. Continuing his thought...

"... with various ethereal energy phenomena actively driving everything. But what if, instead, it is matter itself that is active – both atomic and subatomic matter – and there are no separate “energy” phenomena at all?"

That's like saying, "What if people don't move with their legs, what if their legs just move and intrinsically people move with them!"

Worthless. He then talks about his theory...


"The simplest example of this is a rethink of gravity, where all atoms actively expand very slowly and in unison. Nothing would appear any different over time, but standing on an enormous expanding planet means we would certainly feel this expansion beneath us – as a force pushing upward under our feet."

Okay, I'll bite. These atoms just continuously expand? Since gravity appears to be constant, they MUST be accelerating at a constant rate, and must have been doing this for a long time. In order for us to feel a force equal to that of gravity, they must be moving pretty damn fast, just according to Newton's third law of motion (If a body applies a force on another body, that body exerts an equal and opposite force on the first body.)

He presents no calculations, no testable predictions, he just says, oh this theory explains what we see! Obviously our current theories are wrong! It gets much worse.

I guess the moral of the story is, be somewhat skeptical, but be on the lookout for crackpots like this and take everything at face value. There seem to be a lot of people that think String Theory is proven and accepted - it isn't, it's got a LONG way to go if it's ever to be proven. But still I think people believe it is because they are not skeptical enough. Sorry, a little ranty and long winded, but that article bothered me. I honestly was surprised that was posted on that blog - they seemed more reputable than that.

No potential = boring?

Back on the topic of quantum mechanics theory real quick - let's review. Remember back when I talked about what the Schrodinger equation meant? That it had to do with the kinetic energy plus the potential energy, and the choice of potential energy is what moves the particle forward in time? Yeah, well, no one ever said quantum mechanics was easy...

Anyway, I'm going to discuss the most boring potential - none. That is, what happens to a particle is I just put it down free from the influence of other forces? Let's consider the classical picture first. Say you go out to the middle of space, far from the solar system, and far from the influence of anything. You set down a marble. What does it do? It sits there. You turn your back for a few minutes and turn back, oh, it's still there! This isn't a surprise, it's what we see every day.

So what's different about quantum mechanics? Take a look for yourself!

Recall that if the probability density is very narrow (sharply peaked), the particle is most likely at that position, but as the probability density spreads out, the probability for the particle to be observed somewhere way off to the left is nearly as high as the probability of it being in the center.

What can we gather from this? Well, remember in one of my first posts that says if I drop a ball, I'm not necessarily going to find it at my feet? Well, this is exactly that problem! I put a particle at a very specific spot, but if I check back later, it's not necessarily going to be at that spot!

Quantum Mechanics and Free Will

Here is a short video of Michio Kaku explaining what quantum mechanics says about free will.

 

There you have it. Assuming quantum mechanics is correct, there's no such thing as determinism. We only see determinism at large scales because we are looking at the effects of trillions upon trillions of random events. The physics we see and experience in every day life are known as emergent phenomenon - patterns emerging from an underlying structure to the universe. The rules that govern this structure may not be deterministic (and all evidence points to this...), but it's these rules that give the nearly deterministic reality we witness and experience every day.

Spooky Navigation?

In the previous couple posts, I've discussed the subject of quantum entanglement - the idea that quantum particles that are separated by even a large distance are connected and can communicate instantaneously. This is such a weird idea, but can it possibly have any affect on you?

Well, as it turns out, researchers are discovering more every day how much quantum entanglement affects things you wouldn't even guess. Take this for example. Some scientists are doing research to see if quantum entanglement affects the way birds navigate the globe. For more detail, see the article, but here's a brief summary.

Basically, there's a molecule called a cryptochrome in a bird's eye, and roughly it works like the following. There are pairs of electrons in that have opposite "spin" (a quantum mechanical property). When one of the electrons is struck by light, it is sent flying off. Because of this motion, magnetic fields have the ability to affect it's spin. Some scientists believe this triggers a chemical response that alerts the bird of a magnetic field. The question is, how is this signal triggered? Well, physicist Hans Briegel and his colleagues believe it may have something to do with quantum entanglement! Based off of some calculations, it doesn't look like it's the case, but they haven't been able to study how the actual molecule works inside a real bird. They did, however, find that entanglement DOES make a difference in other molecules of biological significance.

So entanglement may or may or may not affect a bird's sensitivity to magnetic fields, but it would appear quantum effects do! In fact, many researchers are looking into the effects of quantum mechanics in biology, pretty neat I think!

Spooky Action at a Distance

The great Albert Einstein never fully accepted Quantum Mechanics, quoted as saying, "God does not play dice with the universe."

One of his biggest issues with the theory is quantum entanglement. I spoke briefly about it in the previous post, but essentially it boils down to this. Quantum particles that are in an "entangled" state instantaneously "know" information about the other particles in the state.

Lemme give you an example. One of the simplest (in a way...) quantities an electron can have is called spin. This spin can be one of two things - up or down (The details of this are not important...) Now, say I put to electrons into an entangled state so that if I measure one of them as up, the other is down, and vice versa. Well, the laws of quantum mechanics say that this happens extremely fast, perhaps instantaneously! Imagine this - I take one of these entangled electrons in a space ship and bring it 5 light years away (that's the distance light goes in 5 years! A long way!) and leave the other on earth. Quantum mechanics predict that if I measure one electron as up, then if someone way back on earth makes a measurement at the exact same time as I do on my space ship, he'll measure the other electron as down.

What does this mean? The particles somehow communicated, over a distance of 5 light years instantaneously. Relativity predicts that no information can travel faster than the speed of light, yet quantum particles can still somehow communicate with each other of massive distances at many many times the speed of light. This effect has been verified to at least 10,000 times the speed of light! Entanglement is a very active research topic because of its huge potential for new technology, and I'm going to post a more about it's applications in my next several posts.

China Builds Teleporter!

That got your attention, didn't it? Well, it's true, just probably not what you're thinking. For a while I've been droning on about quantum superposition and how something is in all possible states at once until it's measured. Well, here's a direct application - that's what quantum teleportation is based off of.

I originally found this article from Time magazine while searching for information about what China has been doing in the field of quantum mechanics. China has successfully transported information at a distance of 16 km at light speed.  This is the largest distance that quantum information has been transmitted. Surely an impressive feat, and the Chinese appear to be best at it right now. What's the application? Well, China wants to use this technology for secure light speed communications. Now, thanks to the laws of quantum mechanics, this information is tamper proof. If someone intercepted the stream, the Chinese would know about it, thus making it a secure form of communication. Currently, this quantum teleportation has only 89% fidelity at this distance, making it shaky at best for communication purposes, but it's certainly a start.

You may be asking, can we do this with matter?  In a manner of speaking, it has. This article discusses a state of an atom being transported to another atom 3 feet away. This is certainly far from what a Star Trek transporter can do, and it's doubtful that we'll ever be able to have that ability, but it's cool none the less and definitely shows what an achievement the Chinese have made.

This technology is being researched and funded by the Chinese military, so it's natural to wonder: does this give them an advantage over other countries? How far is the USA from such achievements? Will the USA catch up? I do not know the answers to these questions.

Schrödinger's Cat

This is certainly a well known topic in quantum mechanics, but I feel like very few people understand it. I certainly don't claim to be an expert in the subject, but in this post I'm going to discuss what the Schrodinger's cat thought experiment means.

The original thought experiment was devised by Erwin Schrodinger to address a particular interpretation of quantum mechanics. In the early days, people did not like the idea that something could be in a superposition of possibilities, but the more experiments done, the more this seems to correspond to reality. Without further ado, I give you my explanation of the Schrodinger's Cat thought experiment.

There you have it. I will likely address this topic again (I will certainly discuss the many different interpretations of quantum mechanics in the future.). What do you think? Is the world really like this? Why/Why not?

Expectation Values

Yes! I've finally made it to this point. Normally, this is early on in a quantum mechanics course, but I've had to get through some material in order to make this make sense. Expectation values are important. Very important. We talked about the wave function, and that's important. I've told you it contains information about how to get real things we can measure, but how?

One answer, a very important one, is called an expectation value. As it turns out, expectation values do not come from quantum mechanics, the concept is actually much older! Expectation values come from probability theory, which was originally invented to predict the odds in gambling. The basic idea of expectation values are extremely valuable in determining likely outcomes, but we're here to talk about quantum theory.

Anything that a physicist can measure (and some things they can't directly measure) has a mathematical object associated with it called an "operator". When the operator is combined with the wave function in a special way, the answer is the average value of that operator, called the expectation value of the observable. What's an example?

So I've shown you a couple different wave functions - the infinite square well (particle in a box) and the harmonic oscillator (the spring). Well, say I had a particle that had a wave function like that. If I'm in a lab and I measure the position of the particle I get one value. Then I reset the experiment and try again, well quantum mechanics says I'm likely to get a DIFFERENT value, even though I performed the same experiment. We just have to deal with that - it's quantum mechanics! What if I want to perform an experiment many times, is there anything that I can measure? Yes there is! If I AVERAGE the results from those experiments, I'll obtain the expectation value, which, as I said before, we can calculate!

Why is this important? As it turns out, expectation values obey classical laws of physics. Once you've used quantum mechanics to predict the expectation values, that's it. 

So what's with this wave function?

Sorry for the lack of posts recently. Between preparing new quantum mechanics simulations, school getting busier, and the fear of losing my income because of some bickering about budgets, I haven't found the time to post. I return with a "short" post about classical-quantum correspondence.

What does this mean? Well, in the real world, we observe things and we can say where things are and what they are doing. However, when we talk about the quantum world, suddenly there this uncertainty! What's the deal?

Why don't small systems behave like what we are used to seeing? Well, as I'm going to show you, they do! Here's a very concrete example of a quantum system that ALMOST looks classical. We return once more to the particle attached to a spring.

As you will see in the videos below, the first is the wave function doing it's wiggly thing. I'm showing this purely to show that the quantum world is a bit more complicated that the classical world, and that a real and imaginary part of the wave function contributes to the probability. The other video shows the main point of this.

 

 Wave Function

Probability Density along with classical path.

You'll notice it isn't melting as it always has been before. I'm not cheating, this is an actual possibility in quantum mechanics. It's called a coherent state, and I picked it because it's a state that very closely follows classical behaviour, but there's still uncertainty in the particles' position.

The vertical line is the probability for a classical particle in the same system. It may not be obvious, but if all of its probability is on a single vertical line (known to physicists as a delta function), then it is at that location with 100% probability! The quantum version isn't just a straight vertical line because of uncertainty! The larger the physical system that that particle is in, the more likely the wave function will look like a vertical line. This is roughly what the concept of quantum decoherance is. The writer of Nano Nook knows a great deal about this, so hopefully we will chime in to correct me or clarify if I said something wrong. Enjoy the movies!

Self Evaluation 2

My regular readers can skip this post unless for some reason you are wildly interested in how I rate my blog for my science communication class.


I have kept up what I started with since my last evaluation. Before, I graded myself as an A. I believe I have improved greatly since then in several ways.

Feedback

The poll has been very illuminating. I got 6 votes.

0 votes for "Need to explain more" (phew!)
2 votes for "Needs more application"

1 vote for "Boooooring!"
3 votes for "Posts are too damn long"

I want to thank the voters for the feedback.

What's changing? Shorter posts for sure.  I've had the two votes for needs more application for a little while and have added more posts with application or things people care about (I think). How have I been doing? There was one vote for "Boooooring!", which is fine, I can't appeal to everyone. But I ask the one who voted on that, how can I make my content less boring? If it's just the topic that bores you, I guess there's not much I can do. If you think my blog has potential, what content would make it more interesting to you?

Thanks again for the feedback, I'll add a new poll soon!

EDIT: 3/23/2011
I received one more vote for "Posts are too damn long." Thanks for the input! 

Religion is NOT science - part 2

Wow.

I had no idea of the discussion that would ensue. Mostly from people not reading my post, or putting words in my mouth. 22 comments, and possibly more physics content than the rest of my blogs posts thanks to a Mr. James Redford. That went way out of hand, and off topic, but I think the discussion has finally been brought to an end.

So instead of the part two I was originally planning, I'd prefer to summarize the previous (long!) post, and listen to what you guys have to say. So here goes.

My intention was not at all to bash religion. I thought I made that clear, but evidentally it wasn't clear enough. Let me make it clear. This post is not about whether or not religion is correct, necessary, a waste of time, or the most fruitful pursuit. This post is about how science and religion should remain separate entities. My reasoning for this is as follows. Religion is based upon faith in the unobserved (directly observed and quantifiable). Science requires quantifiable observations to make conclusions; otherwise it's just speculation. A scientific theory must be testable - religion is not. There's no way to disprove the existence of God or Gods (and arguably no way to prove them either.). Thus religion is not science. That's my point, and details are detailed in my previous post.

Regarding another topic. This was flushed out in the discussion, but I want to mention this once more here. A question was asked, (and I'm paraphrasing) if religion isn't science, where does that leave string theory? Regarding string theory as a theory. In my definition (the commonly accepted definition) of a scientific theory, string theory simply isn't one. It doesn't make any new predictions that can falsify it in the near future. It can be lumped into two categories.

1. A developing theory. This means it has potential to eventually become a true theory, but currently isn't one. This doesn't mean that it can't be applied to science or that work in the theory is pointless. Indeed string theory has been successful in a few areas of physics. Physicists are using string theory as a tool to learn more about quantum theory through something known as the AdS/CFT correspondence. I might discuss this at a later point, but it's an advanced topic - yes, it puts the subject of my this blog to shame as far as difficulty. String theories been used in other useful areas, but that's a whole other topic.

2. Philosophy. This means it could very well be true, but we can't prove it right or wrong right now. What does it mean for everything to be made of strings? Are there really 11 dimensions? What does this mean for the world? We can discuss implications as long as we understand these questions are philosophy - not science.

That concludes my posting about religion on this blog. Though I attempted to handle in an unbiased way, it still got slightly out of hand (yet yielded some interesting discussion!). I would really like to continue this discussion, but if I do, it'll be in the comments on this post, not in a future blog post (unless something changes and I'm compelled to do so for some reason...)

Cold Fusion Followup.

So, not much has been posted recently about it, but there are a few updates. This site seems kinda shady to me, just from the layout, but they've been giving updates on the situation. So what's new?


Looks like there's an upcoming test in the US. Of course, the device will still be kept under wraps until he is successfully able to file for a patent (his first attempt failed.). Hopefully this will allow scientists in the US to witness this device actually producing power. We'll see.

A one megawatt reactor is being constructed in Greece. From Free Energy Times, it looks like the start up date for this reactor is in October. A 1 MW reactor by October? I'm rather skeptical, but if this pans out, this could really change things.

Currently, a one year study on the reactor is being performed at the University of Bologna in Italy. The goal of this research is to better explain the theory behind the reactor.

Finally, I'd like to point out that they are trying to stay away from the term Cold Fusion for obvious reasons. Instead, they've been calling it LENR (low energy nuclear reactions) or chemically catalyzed nuclear reactions. Rossi has been documenting his reactor very well (as well as he really can whilst still keeping it secret...) on his blog, the Journal of Nuclear Physics (Not a peer reviewed journal; moderate skepticism is necessary; take what it says lightly please!)

Religion is NOT science - part 1

I'm probably going to step on some toes with this one, be warned. 

I was reading a post on fellow science communication blog They Let You Graduate?.  The author of this blog typically tends to anger me after reading his posts, but I'm fairly certain that's the very reason he's writing it. Whatever you think of his blog, he certainly does stir up deep thoughts in my head. His recent post was discussing the the movie Expelled, a documentary about how scientists that believe in the possibility of intelligent design (not necessarily creationism, I suppose it's different somehow...) are being discriminated against in academia. 

Consequently, that's not what my post is at all, but it did get me thinking about something that's dwelt on my mind for some time. People don't get what science means. People don't get what theory means. Yet people try to use science to prove unprovable things, and act as if it's perfectly valid! Now, I probably have a more liberal definition than most of what I call science. In a recent discussion in my science communication class, I stood firmly on the belief that science could exist independent of society, in an idealized sense. I believe science is a pure, unbiased entity. But when it comes down to it, this kind of science doesn't exist very often. I want to reserve the term to describe purely the "endeavor to uncover the mysterious truths of the universe." 

But we all know science doesn't end up being that. When I refer to science in this post, I speak of the socially, economically, political beast that requires certain ground rules. Here are my simple rules, and I reserve the right to edit this post if I change my mind (I'll leave original stuff intact though, I don't believe in covering up true mistakes.)

1. The only scientific absolute is that there are none.

2. A theory is a well established, physically motivated set of rules that describes something about how we perceive the world to work. 

3. In order to be a theory, it must make testable predictions, and there must be some way to prove it wrong. 

For example, I could write down a set of rules, but if I cannot determine whether or not they are correct, it's simply not science, it's just a guess! When a scientist talks about a theory, he doesn't mean, "this is our guess at how it works," he measn "this explains a particular set of observations, but could be proven wrong by x.". A well established theory is considered "fact" if it is unlikely to be proven wrong. The word fact here doesn't mean absolute certainty (absolute certainty is unscientific.), it is simply used to describe a well established theory because the colloquial use of the word theory is very very different from the scientific use.

This brings us to our main issue: Science and Religion. I should be perfectly transparent, so that should I introduce bias into my posts, hopefully you can take that into account. I am an atheist. This does not mean, however, that I think religion is a useless institution, nor do I believe the world would be better off without it. Quite the contrary, I believe religion is necessary, but this isn't the point of the post - I just wanted to make sure you understand where I am coming from.

What motivated me to write this post was a physical theory I read about some time ago.  A mathematical physicist cosmologist Frank J. Tipler devised a physical theory of everything - how everything works at a fundamental level. This is the holy grail for physicists! So what's the problem? 

Religion is the problem with this theory. There are two major physical theories that dominate our understanding of the way the universe works, namely Einstein's general theory of relativity, and quantum mechanics. Quantum mechanics (the very subject of this blog!) has been exceptionally successful when dealing with small objects (and sometimes large objects!). General relativity, on the other hand, describes LARGE objects well, but really doesn't naturally extend to small objects because it isn't a quantum mechanical theory. This is a problem. Both theories cannot be correct, because quantum mechanics can't deal with gravity, and relativity can't deal with small things. The solution to this issue is known as quantum gravity. The issue? It doesn't work. More explicitly, if one tries to make certain calculations with the naive mating of relativity with quantum mechanics, you get infinity as you answer. I don't know about you, but anything infinite in this universe just doesn't make sense. Tipler's explaination? God. He says, accept the infinities in the theory, call it complete, and explain the infinities as the presence of God. 

Contrary to the belief of some people, you cannot disprove the existence of God or Gods. I don't like it, but I don't have to! I can't disprove the existence of Santa Claus either. My point is, it's not science! If it isn't falsifiable, it's not science!

I suppose you may be thinking, okay Dan, this is one crackpot theory, maybe you can put science into religion somewhere? My answer to you would be, notice how the title is "Religion is NOT science - part 1"? Well, you'll just have to wait for part two. Next I'm going to discuss what I'm simply going to call "quantum theology," to generally discuss attempts to mix religion and science (though there is a book by the same name).

The Quantum Spring.

Sorry for the delays! As it turns out this was becoming challenging to make an animation for, but I finally got it!

Alright, so here it is, the quantum spring. First and foremost, this is one of the more useful solutions to Schrodinger's equation.  Why? As it turns out, a lot of things behave like little springs! Anything that is held in place by some kind of force vibrates very slightly, the physics that describes that is the quantum harmonic oscillator. This means the quantum spring can be used to make calculations about solid materials. Understanding materials improves our every day lives!

Just as all quantum mechanics, it comes from a normal physical theory made weird by Schrodinger's equation. Remember the potential energy part? Well here's where it comes from in the case of the spring. With the infinite square well, I just said that it would take infinite energy to penetrate the walls, but in this case, I'm tying my particle to a little spring. This could be describing an electron wiggling around near an atom, or anything else that is small and vibrating! If you've ever studied physics in high school, then you've surely heard of Hooke's Law. This is a physical law that describes the motion of something attached to a spring. It simply says:

F = kx

The force on the particle is proportional to the distance it is from where it feels no force.

If this is confusing, think about this. Say you hang something from a spring. It'll bounce up and down going above and below a center point. We call this point the equilibrium point. I know you've all seen it in real life, but here's what I'm referring to.

Now what happens to the quantum picture? Well, we take Hooke's law and using some fancy math, turn it into a potential energy equation that we can shove into Schrodinger's equation. When we solve the equation, we find out what happens to a particle that we attach to a spring. I made these videos with Python using scipy and matplotlib, two open source modules that are easy to use and very fast! Feel free to ask me if you want my code, all my code is open source. Here's my videos, I added color this time! What you will see is the particle bouncing back and forth due to the spring pushing and pulling it.

Probability Density - Remember, I started the particle out as a bell curve, meaning I'm guessing it's right about the center of the peak, but there's some uncertainty in its position.

Wave Function. The "real" part is blue, the "imaginary" part is red.

Pretty trippy, eh?

These don't really get old for me. I think quantum mechanics is cool, and as we go on, it'll get weirder and cooler (for me, and I hope, for you.). Can anyone name some possible applications for a particle on a tiny "spring"? I've intentionally left some out. I'll give you a hint, your gps wouldn't work nearly as well without it!

Also, next up: Expectation Values, Delta Potential, Quantum Tunneling, and Quantum Theology (yeah, you heard me correctly!)

Cold Fusion? Again?

Sorry, another break from our study of quantum mechanics. I couldn't resist when I came across a very interesting story. A h/t to Weird Things for posting this about a month ago. Greg Fish's post discusses a pair of Italian experimental physicists that claim to have developed a reactor capable of creating power with very little energy input. Since a month ago, news has spread about this experiement, but is it real or are we looking at a repeat of the claims started Pons and Fleischmann's famous cold fusion experiment? This remains to be seen, but the idea is certainly interesting.

I would like to direct you to this article from Popular Science. The claim is that Andrea Rossi and Sergio Focardi have successfully constructed a reactor capable of 12,400 kW from a 400 W input on a tabletop device. Instead of using palladium electrodes like Pons and Fleischmann's apparatus, this device supposedly fuses nickel with hydrogen and produces copper and energy.

A translated interview with Andrea Rossi sheds a little light on the device, but they are keeping details quiet until they have a better understanding on the theory behind it. There still isn't much information about this out there, but I'm keeping my eyes open and will post an update as soon as I can. This is certainly intriguing. If anything positive comes out of this, it will certainly be exciting, but I for one remain extremely skeptical, and will remain skeptical until either we see these in action or the theory behind it is explained.

It'll blow your mind - part 2

Well I read the full paper and I must say, it's a difficult topic. Those who have personally asked me how you can actually measure something being in two states at the same time will hopefully find an answer here.

Quantum mechanics has been well established by experiment. The theory behind this systems involved in this experiment are well understood. That being said, it is a comparison between the gathered data and what they theory predicts that leads the physicists who performed the experiment to conclude that they are observing a macroscopic quantum effect (the drum both vibrating and not at the same time.). Let me try to explain.

The experimental set up is a extremely cold piezoelectric oscillator electrically coupled to a quantum bit (or, qubit). If none of those words make sense, let me break it down for you. A piezoelectric material is a material that produces electricity from being bent or vibrated. You have seen piezoelectric materials in many places, perhaps the most familiar being in a butane lighter. When you click the lighter on, you are actually compressing a piezoelectric element that makes a little spark. The next word I would like to explain is the oscillator. An oscillator is something that vibrates in a predictable manor. Think of the surface of a drum. When you strike a drum, the surface moves up and down at a predictable rate - a drum is an oscillator. In this experiment, the piezoelectric oscillator is just a little piece of metal that produces an electric current when it vibrates. The physicists know at what rate (frequency) it can vibrate.

Next up is the qubit. A quantum bit is essentially a 1 or a 0 that obeys the laws of quantum mechanics. That is, a qubit is in two states simultaneously until measured. I do not pretend to be an expert in quantum computers, for some more information, I recommend Michael Nielsen's quantum computing for everyone. The basic idea behind this experiment is that when the oscillator vibrates, it affects the qubit. This allows the two systems to be entangled. Knowing the state of one means you know the state of the other. This way, the oscillator can be isolated (so that nothing is allowed to interact with it), and it's state can be inferred by qubit measurements.  Pretty cool.

Now, the most important part of the experiment is the cooling. The colder something is, the less it's molecules that make it up move, the less they move, the lower the energy. They cooled the oscillator down to EXTREMELY low temperatures so that it would have the lowest possible energy it can have (called it's ground state.). This corresponds it the lowest possible rate at which it can vibrate. They made measurements of the ground state vibration rate and the next to the lower vibration rate. The qubit's state was either 0 for the ground state or 1 for the first excited state.

Here's the part that's difficult to swallow. We can't actually look at the oscillator while we run this experiment because this would count as a measurement. Remember, measurements collapse the wave function to a single outcome. This is boring and there's no way we can observe quantum behaviour if we are constantly observing something. So how did they know they observed a large object obeying quantum mechanics? Well, they repeated certain measurements on the qubit. By repeating the measurements, they were able to measure the probability and the state transition times for the qubit. By comparing these probabilities and transition times to both the theoretical and experimental predictions of the qubit's behavior, they determined that they qubit was in a quantum superposition state (both 1 and 0 at the same time.). But, the qubit and the oscillator are linked, so knowing the state of one tells you the state of the other! Thus, they report with high confidence that the oscillator, which would be actually visible with the naked eye (but still very tiny) was in a quantum superposition state (being both in the ground state and first excited state at the same time!).

This is a major discovery! Provided others can replicate similar results in different experiments, this will confirm that everything, not just small objects obey the laws of quantum mechanics. Even trillions of atoms cannot escape the strangeness of the quantum world.

Comments? Questions? Mistake in my post? Open discussion encouraged!

Up next, the quantum mechanical spring, then a discussion and some demonstrations of expectation values!

Site News

Just a quick post here. It has been brought to my attention by my readers that my poll wasn't working. I believe I have fixed this. I'd love to get some feedback from you guys, so vote away! You won't hurt my feelings if my posts are "booooring," but you you select that option (or any other for that matter), I'd like some input on how to improve. Thanks!

Another matter my readers have mentioned to me is that my previous post was rather confusing. This is a difficult subject, but I'm going to go through the journal article once more to seek a better explanation. Stay tuned!

Old news, but it'll blow your mind...

... or at least it should. It blew mine back when I read it. Here is an article from Nature documenting a research effort in quantum mechanics. The research that this article discusses shows that even large objects can exhibit the weird quantum effects I've been talking about. I recommend reading the article, even though I'm not entirely pleased with some of the terminology (quantum mechanics is a tricky subject, and requires precise words to describe it.). If you're feeling lazy at the moment, my summary is below.

Andrew Cleland and his team of researchers at UCSB successfully measured an object large enough to be see with the "naked eye" exhibiting one of the most strange and difficult to swallow aspects of quantum mechanics. A quantum object can be in a state where it's moving, and a state where it's not - at the SAME time! These scientists were able to measure this in a tiny paddle that is 30 micrometers (that's about one thousandth of an inch!) in length. Here's a picture below:

This object is huge, at least in quantum terms. It's built out of trillions of atoms! What they observed is the object being simultaneously in a vibrating and stationary state at the same time! They did this by cooling the drum to 2 tenths of a degree Fahrenheit above the lowest possible temperature (absolute zero). This brought the molecules in the drum to their very lowest energy state. They were able to verify that it was not vibrating at all. With a quantum mechanical circuit, they could also bump up the energy level to make the drum vibrate at a VERY specific energy level. They put their circuit into what's called a quantum superposition state (a quantum state that is actually a mixture of two states, e.g. moving and not moving). The circuit was a superposition of telling the drum to be stationary, and to vibrate. What was the result? Exactly that! They were able to measure the drum as vibrating and not vibrating at the same time!

Let's review for a second. Why do we generally see small things follow the laws of quantum mechanics, but big things behave normally? This is because if something is really small, it doesn't interact with other things nearly as much. Think about someone you know (maybe yourself!) that had an extremely messy room. You couldn't walk around in their room without running into junk that was scattered about. Now think of the cleanest person you know. Perhaps you could walk across the entire room without running into anything! Back to the story, you are like the person in the messy room, and an atom is like a person in the clean room. An atom can move around a lot without hitting anything, but you cannot. Everywhere you walk, you run into air (air is made of trillions of molecules!). If you zoom in to an atom in the air, it's relatively far from the others. When you heat things up, the atoms move around a lot more, causing them to interact with other atoms. When you cool things down, they do the opposite, they hardly move at all, and hardly ever interact with the atoms around them. This is what they did, the slowed down all the molecules in the drum until they were barely moving.

This is really really cool and weird at the same time, you may ask what applications there are for this. The truth is, there aren't any right now, there's still working on that part. For those of you technically inclined, and with access to Nature, you can find a *.pdf of the article here. Anyone else think this is really really cool, or is it just me?

More on the "Particle in a Box"

The infinite square well problem previously discussed as typically called the "particle in a box" problem. This doesn't really make much sense in terms of the previous problem as it's more like a "particle on a line". Well, this problem is called the particle in a box problem because that's exactly what it describes and is used for. In this post, I will talk about one of the applications of this simple model. But first a video. Remember in the last post how I had the particle sitting there, it's it's probability distribution kinda melted? Well, here's the same thing, but now the particle is confined to a flat sheet instead of a wire.

Now, I find that really cool. You can really see the wavelike nature of the particle bouncing off the walls and running back into itself! It kinda looks like ripple on a pond, but water waves are made out of trillions of parts, but this is just one! What happens if I give it some initial momentum? Take a look.

The wave function also looks like this. Here's a couple more videos, one moving fast, and one moving slowly.

Here's the slow mover.

So what are these good for? Why do we care how a particle trapped in a box behaves besides the fact that it looks cool?

Well here's the biggest application I know of. Have you ever studied the ideal gas law? If you haven't, don't worry. It's a rather simple relationship between pressure, temperature, and volume.

PV = NkT

If you've seen it in the past, that's probably written a bit different than you're used to. This is how physicists express it, and since I'm a physicist... Anyway, P stands for pressure, V for volume, N for number of particles, k is called Boltzmann's constant, and T is absolute temperature. This equation says if you put a gas, like air, into a container you can calculate the pressure if you know how much air is in there, the temperature, and the volume. Also if you know the other three variables, you can figure out the last one. This equation is used a lot in many engineering and science fields.

Since I bring this up, was this equation originally derived from quantum mechanics? The answer is no. It wasn't. So why do I bring this up? Read on. This equation can be derived by experimental measurements on gases that are nearly "ideal".  An ideal gas is essentially a gas that doesn't affect itself, even when it is smashed down to a small area. Gases like Helium, or other noble gases, are very well approximated by the ideal gas law in certain cases. Using a gas such as this, a experimental physicist or chemist can derive this law. This law can also be derived using classical physics methods called "statistical mechanics", which uses probability and statistics to determine the properties of large collections of stuff. The reason I bring this up though is that you need quantum mechanics to get a full thermodynamic description of an ideal gas. That is, you need quantum mechanics to accurately derive its entropy. Entropy is a measure of the disorder of a system. Once you have the entropy, you can calculate other thermodynamic properties. I think the most remarkable thing you can do is re-derive the ideal gas law! Once you have the entropy, it's relatively easy to get the ideal gas law out of it. And where does all of this come from? That's correct, the particle in a box problem. Next time you think you don't deal with quantum mechanics always, think again, it's everywhere!

That's it for the infinite square well for a while, I may revisit it in the future, as it's such an important problem. Next up, I'm going to talk about something a bit more current and down to earth, stay tuned!

The Infinite Square Well

We've gotten past some of the fundamentals of quantum mechanics. Now it's time to begin one of the first problems encountered by physics students when studying quantum mechanics. It's the first not just because it's the simplest, but because it's important. It gives a solid example, and a way of thinking about many quantum mechanics problems.

So what is it? Well, the infinite square well is a particular choice of the Hamiltonian, or, the system. We have the usual kinetic energy term, but we have a particular potential. Imagine there's a particle. It could be an electron, a proton, a hydrogen atom. Anything small will do. We put this electron inside a very thin wire, so thin that it can only move forward or backward, not left or right or up or down. The electron can move perfectly freely inside the wire, but when it comes to one of the ends, it cannot help but bounce back. Think about you running in along a track. You keep running until you hit a wall. Since you're bored and got nothing else to do, you run the other way, until you hit the wall on the other side. You keep repeating this until you have enough bruises...

 

This is what the infinite square well represents. It's just an electron that's trapped along a line. We call it the infinite square well, because the wall is a barrier with infinte potential. That means you have to have infinite kinetic energy to go through! That's a pretty solid wall. It turns out, this is a decent model for electrons in a piece of metal. Here's where I think it gets cool. We solve Schrodinger's equation (SE from now on) and we get | psi >. At least, we get a way of determining how an initial state evolves with time. Let's say we put the electron in a wire and have a decent idea of where it is. It's probability density should look like a bell curve (known as the gaussian or normal distribution in probability theory.). Basically that says it's most likely at the center of the bell curve.

Here's a Gaussian curve. I made my initial state a bit skinnier because I think I know where I put the electron better. Let's see what SE predicts will happen to the probability density (just think of this as a guess at where the electron is, the higher the value, the more likely it could be there when we measure it.)

Pretty cool, huh? The longer you wait, the less chance you have a guessing where it it correctly. The probability density melts as time marches on. Sometimes you can see little peaks of possible places it could be. The peaks at the end are a glitch in the video that I can't seem to fix. Those frames should be at the beginning. But remember, when you solve SE, you get the wave function, not the probability density function. So what does the quantum state look like? Well hold on, this looks pretty weird I think.

There are two lines. One of the "real" part of the wave function, the other is the "imaginary" part. Don't worry too much about this, this has to do with the imaginary number "i" that I mentioned before. The wave function is very strange. I think that's cool. So now you know what happens to an electron when you set it down. But what if you give it a push? The probability density:

And the wave function (just showing the real part this time):

 Let's talk about this for a second. First the probability density. It makes sense given what you just saw, right? You give the electron a kick to the right, it bounces off the wall and comes back. But what happens when you get near the wall? It gets a squiggly. Ever hear about atoms, light and other small objects acting like both waves and particles at the same time? This is where you can see it! When the electron gets near the wall, the waves that make it up interfere with each other, causing this weird squiggly effect you see when it gets near the wall! The wave function is a bit more obvious. It already looks like a wave. When parts of it bounce off the wall, they interfere with other parts. I think it looks pretty cool, what about you?

So that's it in a nutshell, there's more details that I might revisit at a later time, but they aren't that important right now. The videos were created with Python, using scipy, matplotlib, and mencoder. The source code is available if you're interested. As usual, comments and suggestions are encouraged!

Next up is the quantum mechanical version of the spring. I think this one is both really cool and important.

Schrödinger's Equation - Part 2

Okay, so last post we briefly introduced Schrödinger's equation. Mainly, we introduced the left hand side, which consists of the Hamiltonian, and the wave function. As a reminder, here is the equation once more.

On to the right hand side!

Schrödinger's Equation - Part 1

This is the start of where all the real quantum mechanics happens. Schrödinger's equation equation is what we use to calculate useful information about a quantum object or system of objects. Here it is...

 

Don't be afraid of it, it is difficult to solve, but not too difficult to understand. Through the next couple articles, I'm going to explain what it means, and why you should care.

A requirement and self evaluation

Just kidding. I have one more post that is off the intended track. For those that do not know, I've started this blog as a requirement for my science communication class here at the Colorado School of Mines.

If interested, read on.

Giving back

Greetings readers!

I have spent the last few posts discussing both introductory quantum mechanics material (the primary focus of this blog), as well as a more recent development in quantum theory and its applications. Quantum mechanics is a notoriously difficult topic. People like to use the words to make something out to be unexplainable or seem revolutionary. While quantum theory has been around for around a century, it is still a sort of buzz word. People hear quantum mechanics and tend to think it's magic, or that it's something only geniuses know.

Scientists as a whole have not done an excellent job in fixing this issue. The commonly implemented  "deficit" model of science communication is certainly prevalent in discussion of quantum mechanics. Sure, there are popular shows on the history channel, such as The Universe, and books such as The Elegant Universe that make certain aspects of quantum theory accessible to the layman. The question is, how many sources are there for the same material taught in a quantum physics class at a university? So far, I have found very little of it out there. The major sources lie on two extremes - the scientists unloading their research on the public, and the physics popularizers taking these ideas and condensing them into a simple idea. On one extreme, you have unintelligible papers filled with equation after equation. On the other, you feel like the information you've received has been so condensed that it is meaningless. Generally I find both of these extremes discuss the difficult concepts, and if you really want to understand the basics, you've got to head back to school and get a degree in physics.

I have found very little published in the middle, and my goal is to provide a source of basic quantum mechanics, and to apply these small steps towards bigger problems so that the next time you hear something about quantum mechanics in the news, in a book, in a movie, or on another blog, you can put it into context and grasp what it's actually saying.

While I have in mind what I would like to accomplish, I would like to take a step back and get feedback. I'm a physicist. I love physics, and applications or no, I find the subject absolutely fascinating. The problem is, this can blind me to what my readers are interested in. In science communication, information must be sent through multiple channels, and in multiple directions. If I am to accomplish my goals, I need engagement and feedback from my readers. I assume you have interest in quantum mechanics, at least on some level or you wouldn't be reading this. My question to you is, what additional content are you interested in? Find an interesting article? Send me a link! Confused about any of my posts? Let me know! Find an error in any of my posts? Rub it in my face!

One other thing. I try to keep up on other blogs, but if you find something similar to what I'm doing, I'd love to connect with other sources. If you're active on another blog, forum or other pipeline for science communication, link to my blog! I'd love to get more viewers and more feedback.

We will return in the next couple days with a post about the famous Schrodinger's equation. The first post will be an introduction, then I will delve into its uses and applications. I first have to go through some simple examples before we build up the know-how to tackle more interesting applications like atoms, molecules, and beyond.

Something from "nothing" - the Casimir Effect.

As promised, I'm taking a small break from introductory quantum mechanics, and discussing a topic that has some very real consequences in real life. This is one of the more strange predictions of quantum theory, so hold on. Ever heard of zero point energy? If you have it's related to the Casimir effect.

The Heisenberg Uncertainty Principle, Part 2

Welcome to part 2 of my explanation of the Heisenberg uncertainty principle. Today, I'm going to introduce the concepts of a quantum "state", an "ensemble" of states, and probability density. Only with this framework can you accurately describe what the uncertainty principle. But first, a video. This is from a TV show that tried to popularize mathematics, by showing its uses. Being employed as a mathematician, a lot of their explanations bugged me. This one especially bugs me.

Why? Read on.

The Heisenberg Uncertainty Principle, Part 1

Hold on readers, these next couple posts are going to be rough. The Heisenberg Uncertainty principle is fundamental to understanding quantum theory, but is a rather confusing topic. It isn't extremely complicated, but it is VERY subtle and easily misunderstood. Through the next couple posts, I hope to illuminate this highly misunderstood topic. Let us begin this venture with a short clip from one of my favorite television shows.

So what is quantum mechanics?

People throw the words "quantum mechanics" around without really understanding what it really means. What is quantum mechanics? Why is it necessary?  These are the questions I will be answering.

Greetings to the curious

Hello readers. If you have a fascination with Quantum Physics, but do not have the time, energy, or background to study the subject in depth, you are in luck! At least, that is my hope. The purpose of this blog is to describe quantum mechanics with as little math as possible. While Quantum Mechanics requires extensive knowledge of Linear Algebra, Calculus, Partial Differential Equations, Group Theory, as well as other advanced topics in Mathematics, I believe the principles can be understood with little to no math. That is my main goal.