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!