Category Archives: physics

Why I Haven’t Been Writing Lately

Hi guys,

I am really sorry I haven’t been writing at all in the last months. I am afraid this tendency is very likely to continue in the near future. There are several reasons for this. The first one is exhaustion: when I get home in the afternoons I am so tired I cannot start to write. However, the main reason I’ve been off blogging is that I have been otherwise occupied.

What comes now is somewhat technical so sorry if it makes no sense to you. Maybe this is just me clearing my thoughts.

During Christmas I had this idea concerning limits on information processing capacity. I instantly thought of black holes, as they impose a limit on storage capacity given by the surface of their event horizon. Then I realised that the limit on information storage is not given by the surface, but by 1/4th of the surface. That is, the information stored in a black hole is proportional to the are of the circle you would get if you flattened it out.

And this made me think. For some years now I have had this idea going around in my head: without interaction with the Higgs boson, most, if not all of elementary particles (therefore I am not counting protons and the like) would be massless. Zero mass means their speed is equal to the speed of light.

That is: in reality, all particles are really moving at the speed of light and none at less. This means that the “natural” way to look at the universe is from the point of view of a particle that is moving at the speed of light.

However, that cannot be done. When you try, you find out that every particle that is moving towards you has infinite mass and, well, things just break down. Which suggests that using Lorentz transforms straight with classical particles does not work. Well, it does not “suggest” it: it is a known fact that you are not allowed to do that. One thing you do find out, nevertheless, is that space flattens out: that is, one of the dimensions disappears. A black hole turns into a pancake.

Isn’t that curious? It seems like looking at things from the perspective of a photon gives us the right answer for the amount of information in a black hole: the area of its flattened surface.

So I decided to pursue this line of reasoning. But my theoretical physics is a little rusty, so I have had to refresh my QFT. Doing things in a rough, classical way proved to be hopeless, which is not surprising since:

a) QFT works and classical mechanics doesn’t.

b) QFT gives less nonsensical answers to looking at particles from a system that moves at the speed of light.

QFT is not my favourite theory in the world, but so far it’s the only one that works, so I have been forcing myself to re-learn it (it was a long while ago that I quit my PhD in high energy physics). So I’m basically spending all my afternoons going through the book that elkement recommended and doing the problems and so on. So far it’s been kind of fun. When I’m done I guess I’ll go into “QFT in a nutshell” and the other one I forgot and then I’ll review Kip Thorne’s Gravitation, which is a lot of fun. And then I’ll get started with string theory maybe.

I have also been working on finding an information-based treatment of space-time, so that I can get rid of scale invariance (space looks the same at all scales) and also re-write the equations of QFT in a format that only makes reference to information. Since everyone is pretty convinced space and time are not fundamental but arise from interactions, it stands to reason that a space-time-independent formulation of QFT will help to solve the issue.

So far I have been successful in going to dimension to information (with the drawback of having to choose a scale s, like in renormalization) and the next step is to reformulate differential calculus in an information-pure language so that I can then reformulate geometry and the basic equations of QFT and hopefully GR.

And that’s the memo.

In a nutshell: sorry guys, I’ll be gone for a while. Maybe six months, maybe more. However, it is possible that when I’m finally back I’ll have something really awesome to share. Though the probability is quite low (in general, the ratio of people who make a breakthrough to the people who merely try is pretty small. Also, the ratio of aficionados who make a breakthrough to aficionados who try is even smaller.)

Oh, one more thing: on the Hawking black hole thingy. Yes, there are black holes. All he’s saying is that, given enough time, they evaporate (which we already knew) and they leave no remnant (which is open to debate: Lubos Motl doesn’t agree, for example.) If they leave no remnant then eventually everything comes out, so nothing really stays in the black hole. Since the definition of black hole is that things cannot escape from it, in this sense there are no black holes. However, if you think of a black hole as something that will suck you in, turn you into pulp and only let you escape billions of years later as radiation mesh, then there are black holes.

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Why the Many-Worlds Interpretation Makes Time Travel Possible

I’ve been obsessed with time travel since I watched “Back to the Future” and possibly before that. To a curious mind, not being able to go back to, say, the time of the dinosaurs and actually see them is incredibly frustrating. Despite my fascination and probably everyone else’s, time travel wasn’t seriously entertained as a possibility until the early twentieth century, when our new theories about space-time seemed to allow a new batch of crazy possibilities.

Emmett Brown

Unfortunately, having crazy hair and talking very fast doesn’t make you smart.

The whole “serious science” talk about time travel got started with General Relativity. To be more precise, with Special Relativity it already became demonstrably true that time travel is possible, though only to the future: if you travel at close to the speed of light, you will age less than the people around you and thus will be able to see the future. Unfortunately, you may not be able to go back, which makes the whole thing a lot less attractive.

The idea of backwards time travel, however, turned out to be lot more problematic. In this case and despite what Doc Brown said in Back to the Future, it’s not enough to travel at 88 mph on a Delorean to disappear into the past. However, General Relativity does provide us a way to go back: since space-time is curved, one can imagine different regions of space-time located at different being connected by “bridges,” which are normally referred to as wormholes.

Time travel hypothesis ; using wormholes.

Time travel hypothesis ; using wormholes. (Photo credit: Wikipedia)

So yes, General Relativity allows for time travel, apparently. But combining Relativity with Quantum Mechanics does not. In 1993, Matt Visser proved that the only method for keeping the two mouths of a wormhole open (feeding it exotic matter) will either collapse the wormhole or make the mouths repel. So there went most people’s hopes for time travel, including mine.

Of course, there were already some of very powerful arguments already against the possibility of time travel, of which I will mention a couple. The first is by Stephen Hawking, who uses a modified version of the Fermi Paradox: he argues that the fact that we’re not seeing any travellers from the future means time travel is not possible: otherwise, the place would be packed with people from other epochs! The second is the classic grandfather paradox: if you could go back to the past you could kill your grandfather and thus never be born, which is impossible since you have been born.

English: Stephen Hawking during the press conf...

Stephen Hawking after destroying my childhood dream. (Photo credit: Wikipedia)

You will be amazed, then, to hear that my recipe for time travel solves all of these technical hurdles and skilfully avoids all the paradoxes. It just requires a huge amount of one single thing: luck.

Here’s the idea. There is a non-zero probability that, for example, a pink elephant materializes in the middle of your room. The chances are slim, admittedly, but they are there. Not only that: if you believe in the Many-Worlds Interpretation, then in fact one such elephant has materialized in your room in some parallel universe you’ll never get to see, since you’d need a humongous amount of luck.

Now, that elephant could also have materialized at the time of Julius Caesar’s assassination, for example. In fact, the MWI tells us that one of them did, though sadly we are not in that branch of time, so we don’t get to hear about how Caesar got flattened by a huge pachyderm. And where I say “elephant” I could also say “you:” there is a non-zero chance of you having materialized during Caesar’s murder. This means that you have actually materialized, but you will never get to experience that because it would require a huge amount of on thing: yes, luck.

English: Pink Elephant No, it's not a festive ...

Yup, Caesar was murdered by this in a parallel universe. (Photo credit: Wikipedia)

The main idea is that nothing (except for overwhelming odds) prevents you from disappearing here and magically appearing in the past, thus feeling the continuity a time traveller would feel. Hence, no wormhole is required and therefore we just don’t care what happens to wormholes. So there, Matt Visser.

How does this theory avoid both the grandfather and Hawking’s pseudo-Fermi paradoxes? Well, here’s the thing: in this scenario, it doesn’t matter if you kill your grandpa. In fact, you can kill all of your family for all I care. All this means is there will be a bunch of universes where you will never be born. In fact, there has really been no change: the possibility of your magically appearing and killing a lot of people was there from the start. You haven’t affected the universe in any way.

So why isn’t our planet full of visitors from the future? Simple: since there are a myriad of presents, the odds of a visitor from the future landing in ours are astronomically small. In fact, they become astronomically small because of the fact that the probability of someone appearing out of nowhere is very, very close to zero. Remember, it’s the same as for the pink elephant.

Summarizing:

  • Time travel is possible.
  • You will never experience it unless you’re very, very lucky.
  • There is actually no travelling involved, since it is already hard-wired into the make-up of our universe.
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A Physics Challenge: Explain Pauli’s Exclusion Principle

I was recently teaching a grade 12 physics class and had to explain why only two electrons can be in the same orbital. My explanation went a bit like this (follow the links for explanations of the concepts):

Diagram showing the possible spin angular mome...

Diagram showing the possible spin angular momentum values for 1/2 spin particles (for example, electrons) (Photo credit: Wikipedia)

Electrons are spin-1/2 particles. Particles with half-integer spin are called Fermions. Fermions have a really strange property: no two fermions can be in the same quantum state. Because of this, we can only have two electrons in the same energy level: one with its angular momentum pointing down (you can imagine it spinning clock-wise on itself) and one with its angular momentum pointing up (or spinning counter-clock-wise). After that, you’re out of options: the next electron has to be in a different energy level, since electrons are only allowed two possible directions of spin

.

The question that followed left me at a loss for words:

Why can’t two fermions occupy the same quantum state?

The physicists amongst you will have an answer ready: because of Pauli’s exclusion principle. For those of you who never heard about it, Pauli’s exclusion principle says that no two fermions can be in the same quantum state.

However, as an explanation this is not great. Basically what we are saying is: “no two fermions can be in the same quantum state because there is a principle that says that no two fermions can be in the same quantum state.”

Again, the physicists amongst you may have another answer ready: Pauli’s exclusion principle is, after all, a consequence of the spin-statistics theorem. What happens is that particles with a half-integer spin must have an antisymmetric wavefunction. This means that, if we exchange any two particles, the sign of the wavefunction must invert.

English: Asymmetric wavefunction for a (fermio...

English: Asymmetric wavefunction for a (fermionic) 2-particle state in an infinite square well potential. (Photo credit: Wikipedia)

For those of you who are not physicists, this is harder to explain. The idea is that the probability of finding a certain particle in a certain state is given by this mathematical monster called the wavefunction. We calculate probabilities by taking its square (not exactly, but close enough.) A wavefunction can describe not only one particle, but several. In fact, in quantum field theory we don’t talk about particles but fields and the particle number can oscillate. When our wavefunction is antisymmetrical, it means that, by exchanging any two particles, we get a minus sign. That is:

Wavefunction (electron 1 in state 1, electron 2 in state 2) = -Wavefunction (electron 1 in state 2, electron 2 in state 1)

Now, what happens if two electrons are in the same state? Then we have:

Wavefunction (electron 1 in state 1, electron 2 in state 1) = – Wavefunction (electron 1 in state 1, electron 2 in state 1)

However, electrons are indistinguishable particles, so electron 1 = electron 2. Therefore, we have:

Wavefunction (electron 1 in state 1, electron 1 in state 1) = – Wavefunction (electron 1 in state 1, electron 1 in state 1)

There is only one number that’s equal to its inverse: zero! This means that the wave function for two fermions in the same state has to be zero. Since the wave function is the square root of the probability, we have that the probability of finding two fermions in the same state is zero. Therefore, no two fermions can be in the same state.

However, we still haven’t explained anything. Because the next question is:

OK, but why does the wavefunction of a fermion have to be antisymmectric?

And here I have to say I’m stumped. Yes, I know how to derive this mathematically from Dirac’s equation, but I have no idea how to explain it in any mildly intuitive way. I have also been looking online for an easy-to-understand explanation and found absolutely nothing.

Hence, I want to propose a challenge for my physicist readers: can you come up with an intuitive, math-free way of explaining Pauli’s exclusion principle?

I can’t offer a prize, but I can offer my undying gratitude and a link to you in my next (and this) article.

Also, you will have contributed to enlightening a very curious 18-year-old.

That’s gotta be worth something.

Here’s a new take on the issue from my new blog.

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A Crash Course on Dark Matter

Have you ever wondered how we can calculate the mass of the Sun? We of course can’t go there and put it on a scale. So how on Earth do we find out?

The answer lies in Newton’s law of gravitation. According to it, the more mass an object has, the more it pulls others around it; the farther these are, the weaker the pull. If we want to know the Sun’s mass, then, all we need to find out is the force it exerts on some planet of known mass.

Now, how do we find that force? This part is a little trickier, but it can be explained using an example from everyday life. Have you ever spun a yoyo around? If you have, you’ll have realized that the faster it spins, the more force you need to do to keep it from flying off. In fact, there is a precise mathematical formula that relates the force to the speed, so that if you know one, you can find out the other.sun

So how do we find the mass of the Sun? We measure the speed at which some planet is spinning around it and use that to find the force binding both; from that, we calculate the mass of our star. Ta-dah!

This extremely simple technique can be put to good use for calculating other stuff besides the mass of the Sun. For example, we know the distance between the Sun and the center of our galaxy and we know how fast we are moving around it. Knowing this, we can estimate the total mass of our galaxy.

Of course, that is not the only way. Another possibility is to just count the amount of stars we see and multiply that number by the average mass of a star.

What’s funny is that, if you use both methods and then compare, you get different results. But not just a little different: you find out that, if you just count stars, your estimate is wrong by 100%!

English: The contents of the Universe as measu...

English: The contents of the Universe as measured with WMAP and computed by NASA/WMAP Science team. (Photo credit: Wikipedia)

Physicists, however, being the resourceful creatures they are, are not daunted by this. Instead, they put their analytical minds to work and start deducing what they can from the information they have. For example:

  • There must be some kind of particle we’re not seeing.
  • This particle has mass, since it pulls things gravitationally.
  • This particle does not interact with light or we’d be seeing some trace of it. No interaction with light means no electromagnetic interaction.
  • This particle must be absolutely everywhere and distributed relatively evenly. Otherwise we’d see unexplained movements towards “hot spots” instead of a general increase in the gravitational pull.

These new theorized particles cannot be seen and therefore are “dark.” Hence the name “dark matter.”

The idea of dark matter was first suggested 80 years ago by Jan Oort, but things didn’t advance much until recently, when people started building detectors hoping to catch one of these critters in the act. In the last 20 years these have sprouted like mushrooms: we have DAMA/LIBRA from Italy, CoGeNT, CDMS, Xenon-10, Xenon-100 and CREST. The last player in the game is LUX, who is the protagonist of today’s story.

But a little background first.

Dark matter detection is a relatively straightforward matter (no pun intended): even though dark matter particles are not subject to the electromagnetic interaction, they are still capable of hitting a nucleus and making it recoil. The idea, then, is simple: get a bunch of atoms, wait for one of them to be hit by something you can’t readily explain, count the occurrences and be done. Of course, in reality things are never that simple, since there are many sources of noise, so that separating actual recoils from random sources is more than a little hard.

However, it so happens that, since more than 10 years ago, DAMA/LIBRA has been observing a yearly fluctuation in their number of recoils. Their explanation for it is that they have detected a dark matter particle with a mass around 10 GeV. When they announced this, of course, nobody believed them. That is, until CoGeNT, which had a much smaller background noise, detected exactly the same. After that, people started getting excited: did we finally get a glimpse of the elusive dark matter particle?

English: CDMS (cryogenic dark matter search) p...

English: CDMS (cryogenic dark matter search) parameter space exclusion of DAMA result represented in green parameter space. (Photo credit: Wikipedia)

It turns out that no, we didn’t. LUX, a state-of-the-art detector in the US, just released a paper that completely eradicates any possibility that what DAMA and CoGeNT observed is actually a dark matter signal. The result is we’re more confused than ever, since nobody seems to have a clue about what’s causing the yearly fluctuation, but it’s certainly not dark matter.

That’s physics: new data comes in, people get excited and, at the end, the most boring scenario is usually the case. Surprises are few and far between but, when they come, are they worth it.

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The Secret for Happiness Physicists Don’t Want You to Know

Before I start: I implore you read this article until the end, especially if you’re a long-time reader of this blog. I also urge to please not skip. But, if you have to choose between skipping and not reading the ending, by all means skip.

If you’ve been following this blog for some time, you’ll have seen me write about physics often. You’ll have also seen me write about happiness. Today and despite the lack of relationship between these two areas, I’d like to try to mix and match. More specifically, I’d like to share recent advances in physics that have made this discipline into a key tool for achieving happiness. Read on to find out how.

By Shang

By Shang

It all starts with superstring theory, which you may have heard about. This theory sees the universe as being made of tiny strings that vibrate at different frequencies, each of which corresponds to an elementary particle.

Another, not-so-well-known aspect of string theo

Sugar Soliton

Sugar Soliton (Photo credit: oskay)

ry is something called T-duality. A duality is something which allows us to relate two completely different areas, in such a way that predictions in one are automatically translated to the other. In the case of T-duality, we translate between the microscopic and the macroscopic world. The idea is that the math that allow us to describe the infinitely small are exactly the ones that describe the infinitely big: in fact, there is no distinction whatsoever. Both the infinitely small and the infinitely big are one and the same thing.

Many physicists may not have realized this yet, but what they have discovered is that there is an almost mirror-like correspondence between our everyday reality and the microscopic, quantum one.

This is important. It is important because it means that it is possible to apply the seemingly magical predictions of quantum theory – such as entanglement – to our everyday realm, and then to use them to our advantage.

Before we do that, though, a few thoughts on happiness.

It seems obvious that, in order to achieve happiness, one must be able to maintain a positive state of mind, somehow cancelling the effects of negative thoughts and external influences that affect us in a harmful way. The outside universe lies, unfortunately, beyond our direct control, so focusing on managing one’s state of mind is the best policy.

However, minds are unruly. The more we try to get rid of a certain bad memory, the more it comes back to haunt us. Indeed, just like trying to not think about a pink elephant will cause us to immediately picture one, trying to get rid of a bad thought actually reinforces it. And, even though there seems to be no way out of the paradox, we fortunately have quantum physics.

There are two key concepts from quantum mechanics that may help us here: solitons and entanglement.

picture to show how spatial solitons behave li...

picture to show how spatial solitons behave like a normal electric field focused by a lens (Photo credit: Wikipedia)

A soliton can be viewed as a stable perturbation. Imagine a chaotic mess of waves in the sea; now imagine that, amongst that, a recognizable shape emerges and starts moving through the chaos at a constant speed, seemingly ignoring the turmoil around it. That is a soliton. Solitons are created from the intersection of two powerful forces: from one side, dispersion or the tendency of every object to spread and disappear. From the other, non-linearity: the fact that materials are not smooth but bumpy and unpredictable. It is the combination of these two effects, each pulling in a different direction, that creates a soliton.

Understanding how solitons behave is key for achieving happiness, because it so happens that negative thoughts or states of mind behave exactly like them. In fact, according to T-duality, they are solitons: there is no difference between a negative thought and a perturbation moving through a non-linear solid.

Our knowledge of solitons tells us that negative thoughts, if left to their own devices, would tend to disintegrate because of dispersion. However, the non-linearity of their medium (our minds) acts as an opposite force, providing them with the means for propagation to the extent of making them seem indestructible.

On the other hand, happy thoughts and states of mind tend to disappear quickly. They are not solitons: like solitons, they are subject to the forces of dispersion. Unlike them, our mind’s topology does nothing to cancel that tendency. The absence of the balancing force makes dispersion queen, and so we see our happiness vanish in an instant. This is why we are mostly victims of negative thoughts and moods and seem to be constantly struggling against something.

Entanglement is another important concept of quantum ph

A numerical simulation of the Korteweg-de Vrie...

A numerical simulation of the Korteweg-de Vries equation. Two soliton waves colliding. (Photo credit: Wikipedia)

ysics that will help us in our route to happiness. It happens when two quantum systems emerge from the same place and become linked (entangled) forever. Anything that is done to one system will affect the other, no matter how far apart they are.

The concept of entanglement can, thanks to T-duality, be applied to our minds too: entanglement happens between our thoughts and their source, creating an ethereal bond that is very difficult to break and which causes our pain to persist more than we’d like.

In order to achieve happiness, then, we will have to go through these steps:

  • Destroy the soliton-nature of our negative thoughts .
  • Disentangle the negative thoughts from their source.
  • Turn our positive emotions into solitons.
  • Entangle our positive thoughts with our inner core.

    Quantum Entanglement

    Quantum Entanglement (Photo credit: jk-digital)

Entanglement, for one, is easy to break. All that needs to be done is a quantum measurement. For example, if two electrons are entangled in such a way that their spins are correlated, measuring the spin in one will automatically determine that of the other; however, further measurements will have no such effect. The electrons will have been disentangled. In this sense, the best policy to disentangle our negative thoughts from their source would be to perform a quantum measurement on them, that is, to analyze them and weigh them, to dive right into them. By doing this, the entanglement is broken and the negative thought loses is power. The thought becomes separated from its source and thus unable to hurt us. However, it may still survive for some time if we don’t break its soliton-nature.

Breaking a thought’s soliton-nature is a more complicated matter. We cannot change the forces of dispersion, since they are inherent to matter and thought. Therefore, we have to modify the non-linear nature of our medium, that is, the mind where the thought runs amok. We need to re-orient the topology of our mind so that it stops counteracting the dispersion effect and starts to aid it. There are two ways to do this.

The first way is the most effective but also the most risky. We must analyze our thought patterns regarding the negative thought we wish to eliminate; then, we must elaborate a strategy that does exactly the opposite: for example, if we previously rejected, we must now embrace; what previously feared, we must now look forward to. This is extremely hard to do, since it requires control of our emotions. It is also susceptible of achieving the opposite of what we intended. However, the long-term benefits of this approach make its practice extremely recommendable.

The second way involves considerably less risk but it is somewhat slower: it consists of leaving the mind blank. This can be done by staring at a candle or concentrating on your breath and is the way Buddhists have been dealing with their emotions for millennia. There are two drawbacks to this technique: the first one is that leaving the mind blank requires considerable effort; the second one is that the effects will be slower to appear, since we are not aiding in the destruction of the thought, but merely not preventing it. That is, by leaving our mind blank we destroy the non-linearity of our thought-medium, which is therefore unable to cancel the dispersion effects that drive our negative thought to disappear. However, we do not invert the shape of the medium and thus do not accelerate the dispersion process.

These techniques are only a small taste of a new wave of physics-based recipes for happiness. The revolution has started and more and more secrets are seeping quietly from the outer edges of theoretical physics. In the next article we will tackle how to entangle our positive thoughts with our core, so that they may not be affected by external disruptions.

 

Crap, that was hard to write. It honestly made me feel a little sick. Anyway, I hope I didn’t fool you and you realized the article was complete horseshit from beginning to end.

If I did fool you, however, you may want to go on reading so that you know what I was doing, why I was doing it and how I did it. Even if I didn’t fool you it may be entertaining. So let me explain.

I wrote this article with several goals in mind: first, I wanted to see if I could come up with a Chopra-like article. I’m still not sure I did. Second, I wanted to do a bit of a “Derren Brown” kind of thing: here’s the trick and here’s how it’s done. In my case, I took three concepts that I deemed obscure enough for some of my readers to not know (or not be familiar enough with): entanglement, T-duality and solitons. Where I cheated the most was with T-duality, which is only metaphorically related to what I said. Basically, T-duality is a property of certain string configurations that relate position to momentum states and that allow us to consider distances below the Planck length. If that just sounded like Greek to you it’s because it probably cannot be explained in a line. Anyway, what T-duality definitely does not allow is to establish a correspondence between quantum and everyday phenomena, especially not our thoughts. The same goes with entanglement, which I described in an extremely vague way and then used in a more-than-questionable manner, using the fact that “entangled” in normal language is the same word as “entangled” in a quantum sense, even though they have nothing to do with each other meaning-wise. The part about solitons was just stupid, but at least my description of the phenomenon was relatively accurate. Associating a topology with our mind and calling it a “non-linear medium” was an exercise in imagination and pretentiousness. I was by the way inspired to do this by Lacan, who did actually speak of the topology of people’s minds and is still for some reason studied in psychology degrees.

In my next article I will give you the tell-tale signs of pseudo-scientific rubbish so that you may learn to spot it yourself. Or, if you’re materially inclined, to make a living from it.

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No Such Thing as Causation

A recurrent argument for the existence of God is that of the “uncaused cause.” What caused the Big Bang? Did this all come from nothing? There must have been something to set it all in motion, a First Cause. God.

Unfortunately, this line of reasoning uses a concept that may sound uncontroversial but is in fact quite problematic: causation. Here I will argue two things:

  1. There is no such thing as causation in the universe.
  2. There is no suitable definition of causation.

The first one is easy to argue by taking a physicalist approach. By this, I mean that the state of the universe at any given time is determined and is such that it can be derived using some set of fixed rules. This doesn’t mean there really are a set of rules written in the sky or that electrons are little people who read those rules and comply.

Causality

I don’t know why this photo is called “causality” but there are robots on it. (Photo credit: Clement Soh)

The thing about the laws of physics is that they’re a bunch of differential equations. In order to solve a differential equation one needs two things: the equation itself and something called a “boundary condition.” A boundary condition is just the requirement that the function have a certain value at some point. For example, in order to solve the differential equations for a harmonic oscillator I have to specify where it was at the beginning. However, I could also specify where it was after 10 seconds or 30,000. I just need to set one instant and the rest of the motion becomes determined.

In this sense, then, how can I say the present causes the future? Boundary conditions may be set at the past or at the future; once that’s done, the rest is determined. It makes as much sense to say the past causes the future as to say the futures causes the past.

If you adopt a relativistic approach, things are even clearer: in relativity, time and space are just part of a 4-dimensional space and are exactly as real. In this sense, our universe is just a frozen 4-dimensional shape and, therefore, no causality applies, since there is no evolution.

Hence, there is no such thing as causality in the universe.

However, one can still try to find a finding a working definition of causation which preserves what we understand by it. It is a tricky issue, which still has philosophers scratching their heads as I write this.

The first idea one comes up with is that some event A always happens before some other event B; furthermore, if we want this to be more than correlation, B shouldn’t happen unless A happened before. That is, A is necessary for the occurrence of B.

However, this does not apply to the vast majority of situations one can think of. For example, let’s take lighting a match. We could say that friction causes the match to light: it happens before and, without it, the match won’t light. However, this doesn’t always work. If the match was doused in water, for example, the match still won’t light. Therefore, requiring a cause to be sufficient is not feasible.

There is a way around this, suggested by Mackie. He says that a cause is an “insufficient but necessary part of a sufficient but unnecessary condition.” That is: friction is necessary but insufficient, whereas the absence of water and gusts of CO2 are the rest of the sufficient but unnecessary condition.

The Lorenz attractor is an example of a non-li...

The Lorenz attractor is an example of a non-linear dynamical system. Studying this system helped give rise to Chaos theory. (Photo credit: Wikipedia)

Of course, there is a problem, thanks to chaos theory. Chaos theory applies to any system of, say, more than five particles. The idea is that complex systems are so sensitive to initial conditions that their behavior becomes impossible to predict after enough time. What this means is that, in principle, a match could spontaneously light up without us scratching it against any surface, so that friction is not necessary. It could also happen that we have all of our sufficient conditions in place and the match still didn’t light. So our sufficient condition is not sufficient.

If you don’t like chaos theory and think that I’m using the wrong physics, the issues I just pointed out still apply when using quantum mechanics (and then some).

It may be able, however, to define some kind of probabilistic causation. This type of causation is evidently not as useful as the previous one. It certainly seems less impressive to think of a deity setting the universe in motion “with a 52.3 chance.” A probabilistic causation would work like this: given a controlled environment, one will observe fixed probabilities for the occurrence of certain pairs of events.

Whether this qualifies as causation is open to debate, but let’s assume it does. This account has the usual problems: isolation is hard to define and to apply and the probabilities will be real numbers, which have infinite precision and are therefore impossible to check. One can get around those by specifying reasonable accuracies and error margins, just like scientists do every day.

Bayes theorem

Bayes theorem (Photo credit: disownedlight)

There is another issue, though, which concerns the very nature of probability. When we say that an event has a probability of 72% of happening we don’t mean that, if we try 100 times, it will happen 72. We mean that, as the number of tries approaches infinity, the ratio between the number of events and the number of tries will approach 0.72. But this doesn’t have to happen: in fact, I could spin heads or tails a million times and always get heads. There’s nothing in the laws of probability to prevent this. Of course, if that happened I’d be quite suspicious, with my level of certainty that the coin is rigged approaching 100% as each spin yields tails. But the thing is I have no way to check. Probabilistic causality does not work either.

So, should we throw causality and be done with it? I don’t think so. There is room for causation, as long as we realize it is nothing but a shortened way of speaking about statistical correlations between events that happen because of how matter is organized in space-time. But taking the idea of cause and effect too far will lead us to nonsensical conclusions, because causation as a concept is unsound when it is applied outside its area of definition.

I hope this article caused you to have a good time. However, we can never be sure.

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Entangled Particles May Be Connected by Wormholes

I recently read (and only partially understood) a very intriguing paper by Juan Maldacena and Leonard Susskind. These are big names: Maldacena is responsible for the AdS/CFT correspondence, which allows us to use regular quantum field theory to treat quantum gravity problems (it’s closely related to the Holographic Principle, which you may have heard of); Susskind is one of the fathers of String Theory and is credited with introducing the idea of the Landscape (the string-theory version of the multiverse).

So, when Maldacena or Susskind publish a paper, people listen. When they do so together, people listen more. And what they had to say in this case was pretty, pretty wild. Remember my last article on entanglement? Well, they suggest that entanglement and wormholes may be one and the same thing. That is, there is a wormhole uniting every single pair of entangled particles and we can think as the two sides of a wormhole as entangled black holes.

I will do my best to explain this but, given that the details of the paper went way over my head, I may not do a very good job (or you may think I did when I actually explained it all wrong). Anyway, let’s get to it.

A Lorentzian wormhole (Schwarzschild wormhole).

A Lorentzian wormhole (Schwarzschild wormhole). (Photo credit: Wikipedia)

As you probably know, a black hole is a region of space where light itself cannot escape. There are two defining regions of a black hole: the event horizon and the singularity in the middle. The event horizon is not a physical place, but a mathematical boundary: it is the region where the escape velocity becomes greater than the speed of light. That is: if you fall beyond the even horizon and you want to escape the black hole, you have to move faster than light, which is impossible. Hence, once you go through the event horizon, you’re pretty much done for.

The singularity, on the other hand, is a point that lies in the middle of the black hole, where the density of matter becomes infinite and, thus, so does the curvature of space-time. Everything that goes through the event horizon ends up in the singularity sooner or later.

A black hole can be depicted using something called a Penrose diagram, which can be thought of as a perspective view of space-time, where infinities are projected onto points on the sides. You can see a Penrose diagram for a black hole below these lines.penrose_DM

It turns out, though, that the black hole depicted above is not the whole story. In fact, it is possible to mathematically extend its description to create something called an eternal black hole, which looks like this:penrose_Schwpar

There are many interesting aspects in this diagram, but I will focus on one. As you can see, now beyond the even horizon there are two regions: left and right exterior. However, this does not mean your usual left and right. In fact, the right exterior represents the whole of our universe outside the black hole, whereas the left exterior represents a whole different universe outside another even horizon “on the other side of the black hole”, whatever that means. That is: the black hole connects two different universes. The bridge that connects these two black holes is called an Einstein-Rosen bridge or a wormhole, in the popular literature.

So you can look at our eternal black hole from two different perspectives: either as a black hole that exists in two different universes or as two black holes in two universes that have exactly the same state. This means that the state of one black hole is correlated to the other, so that a change in the first one instantly affects the second one. Sounds familiar? Of course! Entanglement. That is: we can understand the connection between two black holes (the wormhole) as an entanglement between them.

From the idea that two black holes connected by an Einstein-Rosen bridge (wormhole) are in fact entangled, Susskind and Maldacena put forward a daring hypothesis: what if the converse was also true? What if the entanglement/wormhole duality goes both ways and can be applied to any entangles set of particles? If this were true, any set of entangled particles would actually be connected by a wormhole.

I hope your mind is as blown as mine.

Simulated gravitational lensing (black hole go...

Simulated gravitational lensing (black hole going past a background galaxy). (Photo credit: Wikipedia)

This, of course, is not established science. For example: how exactly does the wormhole get formed in, say, the two spin-1/2 particles of my previous article? Susskind and Maldacena say in this case it would be “extremely quantum” but that doesn’t really answer the question or put forward any plausible mechanism for it. We will have to wait for a long while if we want to have a more coherent formulation of the principle, if it is indeed valid.

So, here it is. Some cutting-edge, extremely recent piece of physics that has researchers everywhere scratching their heads (Lubos Motl in particular seems to be having a ball). Bear in mind my understanding of these ideas is flimsy at best, so I’m pretty sure I have misrepresented them completely. However, I couldn’t resist the temptation to talk about something that sounds extremely crazy and that, if true, will push our understanding of fundamental physics.

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Entangled

You may have heard about quantum entanglement. It’s this really mysterious, complicated thing only people with a physics degree can understand.

Except that it’s not.

Quantum entanglement is the (admittedly weird) property that some groups of particles have, where measuring a certain property in one of them automatically determines the properties of the others. But you’ll probably want an example.

Imagine we have a couple of electrons. We measure their total spin upwards (a measure of where their magnetic field is pointing) and find out that it is zero. Since we know that our electrons’ spin is either ½ or -½, we now know one of the electrons must have spin ½ whereas the other one must have spin -½ (since ½ – ½ is zero). What we don’t know is which one is which.

Diagram showing the possible spin angular mome...

Diagram showing the possible spin angular momentum values for 1/2 spin particles (Photo credit: Wikipedia)

We express this mathematically (yes, math. Don’t panic!) like this (I’m omitting constant factors):

|\Phi >= |1/2>|-1/2> + |-1/2>|1/2>

Now, before you panic, this is really easy to understand. The first Greek letter just means “state of the system.” The line after the equal signs tells us what state our system is in. In this case, it tells us that our two electrons are in either one of these states:

  1. The first electron has spin ½ and the second one has spin -½ (|1/2>|-1/2>)
  2. The first electron has spin -½ and the second one has spin ½ (|-1/2>|1/2>)

In fact, what this means is that our electrons are in a superposition of these two states, which means both possibilities happen at once until we make a measurement.

Now imagine I take these two electrons and separate them 200 kilometers. If I don’t make a measurement on them, they will still be in that same state.

And now I make a measurement on the first electron. Imagine that I get ½ as a result: this means the first electron has spin ½, so the second electron has to have spin -½! That is, the second electron’s spin has been automatically set to -½ from my making a measurement 200 km away, without any other human intervention.

Of course, if the spin of the first electron had been -½, the other electron’s spin would have been set to ½.

I decided to use a pattern sometimes associate...

An artistic depiction of entanglement. (Photo credit: Wikipedia)

So that’s it: entanglement just means that, when I measure a particle’s properties, it determines the properties of some other particle it was related to previously, even if the two particles are separated by a great distance. This just happens because particles (and groups of particles) can be in many states at once and these states may be correlated. No big deal!

Of course, this does seem like a big deal, especially if you’ve grown up to believe that information cannot travel faster than the speed of light. How is it possible for the other electron to “know” that the first one has a certain spin? Doesn’t that go against the locality of the laws of physics? How did the information go from one place to the other instantaneously?

There is a nice way to look at entanglement that avoids all the bizarreness. It involves (how could it not?) the many-worlds interpretation. The idea is simple: at the beginning, when we have two possibilities for the two electrons, we shouldn’t think about particles but about universes. Before we make our measurement, we have two possible universes. In one of them, the first electron has spin ½ and the second one, spin -½. In the other, it’s the opposite. Until we make a measurement, we “coexist” in both universes, which means both universes are similar enough to be able to influence each other. When we make a measurement, we get stuck in one of them. There is no instant transfer of information, no spooky “action at a distance.” The particles don’t “know” squat. We’re just ending up in one universe or the other. This is another reason why I like the many-worlds interpretation: where the other interpretations say “weird, but the math says so” the MWI has a nice, intuitive explanation.

Note: this was a fairly rigorous introduction to entanglement. I gave you the math straight. If you understood this, you understood entanglement, not a watered-down version of it. The many-worlds interpretation view is, of course, subject to debate. The first part of the article is not.

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Why Does Time Move Forward?

Disclaimer: these are not original ideas but are largely based on Sean Carroll’s “From Eternity to Here,” which I highly recommend.

You may have wondered why time seems to move forward and not backwards. Then, of course, you may have wondered what exactly one means by this. In other articles I’ve adopted a more philosophical approach; today I will focus on the physics.

There are several clues that tell us there is a fundamental difference between past and present. For example, we can only remember the past, not the future. We see glasses breaking, but never re-assembling themselves before our very eyes. When we put blue coloring in water and we stir, the coloring dissolves in the water. No matter how long we keep stirring, the two will never separate again.

This would make one think there is something in the laws of physics that differentiates between past and present. Alas, this is not the case (for physicists out there: it depends on how you define “time reversal” and I’m using CPT as a synonym of time-reversal symmetry.) The laws of physics are time-symmetrical. They predict exactly the same in both directions of time.

Let’s see what we mean by this. Imagine I film a pool game, disregarding the players and focusing on the balls themselves. The laws being time-symmetrical means I have no way to tell, upon watching the video, whether it is being played forward or backwards. Both chains of events are compatible with the laws of physics. If I do the same with any interaction between subatomic particles, I will get exactly the same result.

Pool

Pool (Photo credit: davehuehn)

Some astute reader may have been thinking: “you’re wrong! There is a well-established law which is not time-symmetrical: the second law of thermodynamics.” If you don’t know what this is, here’s a brief summary. The second law of thermodynamics states that there is a quantity, called “entropy,” that increases in every isolated process. This gives us an arrow of time: the future is the direction in which entropy increases. There! Done.

Not so fast! Unfortunately, the laws of thermodynamics are not fundamental laws. They are actually consequences of the basic laws of nature (quantum mechanics or Newtonian mechanics, whatever tickles your fancy) together with probability theory. They are a prediction of our time-symmetrical laws, not an independent entity.

But how can something time-symmetrical predict something that is not time-symmetrical? The short answer is it can’t. The only way to achieve this result is to cheat.

But first, an aside on entropy, which is the most important concept we will deal with in this article. Entropy is usually explained to laypeople as a measure of how disorderly a system is. I will try to go a little beyond this simplistic view and give a more realistic account that’s actually in line with the math.

Thermodynamic system with a small entropy

Thermodynamic system with a small entropy (Photo credit: Wikipedia)

Entropy is (related to) the number of ways you can microscopically arrange a system without changing its macroscopic properties. For example, take a room full of air: if I swap one molecule in the top right by another one in the top left, there will be no appreciable difference in the air’s properties: it will have the same pressure, volume and temperature. In this case, a change in the microstate (the position and velocities of each molecule) has absolutely no effect on the macrostate (pressure, volume and temperature).

Each macrostate (set of properties visible with our “naked eye”) is compatible with a certain number of microstates. That is: for each pressure, volume and temperature combination there is a certain set of microscopic configurations that will give us this result. Entropy is defined as the (logarithm of) the number of microstates compatible with the current macrostate. That is, suppose I want to know the entropy of a gas at a certain temperature, pressure and volume: its entropy is the sum of all the possible microscopic combinations that give rise to the observed properties.

If we understand this, it is easy to derive the second law that says that entropy always increases. In fact, all the second law says is that systems tend to be in their more likely state, basically because it’s, well, more likely. But what does the number of microstates have to do with likelihood? A lot, in fact. Imagine a system (a gas in a container) that can be in one of three macroscopic states. For each macrostate, there is a certain number of microstates compatible with it: 1 for the first one, 10 for the second one and 100,000 for the third one. What are the odds of the system being in the third state? 100,000 / 100,011 or 99.98% (the compatible microstates divided by all the possible microstates). As you can see, the third system is the likeliest and is also the one with the highest entropy. Higher entropy equals higher probability.

Entropy ≥ Memory . Creativity ²

Entropy ≥ Memory . Creativity ² (Photo credit: jef safi \ ‘Parker Mojo Flying)

So we’ve cracked it, haven’t we? Systems tend to evolve to likelier states (duh!) which means higher entropy, which means we will always see an increase from lower to higher entropy, which gives us an arrow of time. Right?

Wrong. Because this argument, which works from past to future, should also work from future to past. If I have some state at this moment, logic also dictates that its evolution towards the past increase its entropy, not decrease it! We should see an increase of entropy in both directions from the present, because the laws of physics are time-symmetrical. So, as I said before, our only way of deriving the time-asymmetrical second law is to cheat: entropy will always increase towards the future, as long as entropy in the past was very low. The question now is finding out why on Earth entropy was so low in the past, when it should have been high. We are right where we started!

Not quite, though. Because now we have transformed our original question (“why does time move forward?”) into “why was entropy so low in the past?” which is a lot more specific. If we manage to answer that, we will have finally cracked the mystery that has had the best minds in the planet scratching their heads for centuries.

So, ready for the solution?

Hah! Who said there’s a solution? Unfortunately, this has not been resolved yet. There are several promising lines of inquiry that I may go into some other day, but for the moment nothing is settled. In short: we have some wild guesses but really no idea. Feel free to contribute!

Who said that science claims to know everything?

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Why Finding the Higgs Boson Sucked

I’ve had some people requesting me to explain what the Higgs boson is and why it is important. Here I’ll do my best to clear up some misunderstandings that keep coming up; then I’ll expla

in why we were looking for it and why most physicists felt a tinge of disappointment when we found it.

First things first: the Higgs boson is not something unexpected. It was a prediction of the Standard Model that had been waiting a long, long time to be confirmed. Its detection didn’t shatter any of our preconceived ideas: if anything, it confirmed them. The Higgs boson was the last piece of the Standard Model puzzle. It was not a revolution, but the confirmation of the status quo.

So what is the Higgs Boson? It is a manifestation of the Higgs field. The Higgs field is, just like the Dirac field or the electromagnetic field, a field. Fields are abstract objects extended in space with different values at each point. You can imagine a field as a big, elastic blanket that permeates space: if you tap it, you create ripples through it. Those ripples are the field’s particles.

Peter Higgs (* 1929)

Peter Higgs (* 1929) (Photo credit: Wikipedia)

The Higgs field, however, is a bit strange, because we can actually only see one piece. Now, imagine that this blanket could vibrate in different directions: each direction would be a different component of the field. The Higgs field has four components, but three of them are hidden inside a series of particles, leaving only our beloved Higgs boson.

Before we go on to explain who is eating the missing components of the Higgs field, I need to talk about the weak force. In the Standard Model, forces are nothing but the exchange of a type of particles called bosons between two other particles (see my article on spin). The electromagnetic force, for example, is mediated by the photon. In the case of the weak force, the interaction is mediated by three particles: the W+, W and Z bosons. These particles are really, really massive: they are heavier than a proton. This makes the weak force effective only at very short distances.

It turns out that the weak force wasn’t always the weak force: in fact, the W+, W and Z bosons weren’t always so massive! When the universe was hot enough, the W+, W and Z bosons were massless, just like the photon. In fact, these bosons and the photon were part of a single force: the electroweak force!

However, once a certain threshold in the temperature was reached, the W+, W and Z bosons absorbed three of the Higgs field components, thus becoming massive. The photon didn’t and thus remained massless. How the absorption happened is complicated to explain and involves something called “spontaneous symmetry breaking” which would be too long to deal with here.

The remaining component of the Higgs field became our beloved Higgs particle: a spin-zero field that impregnates the whole universe and interacts with all fermions (particles with half-integer spin, like electrons, muons or quarks), giving them mass.

A complex Feynman diagram involving the Higgs ...

A complex Feynman diagram involving the Higgs boson. Two virtual gluons from colliding LHC protons interacting to produce a hypothetical Higgs boson, a top quark, and an antitop quark. These in turn decay into a specific combination of quarks and leptons that is very difficult to fake in other processes. (Photo credit: Wikipedia)

Before we discuss how the Higgs gives those guys mass, I’d like you to consider the relationship between traveling at the speed of light and having mass. As you know, only massless particles may travel at the speed of light: particles with mass cannot, since accelerating them to that speed would give them infinite mass. Similarly, a massless particle cannot travel at less than the speed of light: doing that would amount to its non-existence. Put otherwise: a photon cannot exist, by definition, in a reference frame where it’s at rest or moving at less than the speed of light.

Now, as I said, the Higgs field permeates space and interacts with every fermion. Fermions, as I told you, are electrons, muons, quarks and the like. It turns out that, according to their own field equations, those fermions should have no mass! But they do. So how do they get their mass? The Higgs field.

Here’s what happens: an electron is trying to go from one place to the other at the speed of light. However, it interacts with the Higgs field, which permeates space. So, every so often, it will interact with a Higgs boson, turning its trajectory into a zig-zag (in fact, every time the electron interacts with the Higgs boson, it will turn into an opposite-handed version of itself, but this is a little beyond the scope of this article). Now, if you look at the electron’s speed, you’ll see it’s not the speed of light anymore, but a little less, precisely because of this zig-zag. And, as we said before, something that travels at less than the speed of light must have mass. That is: the Higgs gives the electron mass by interacting with it and slowing it down, thus making it appear as if it had mass.table

(One little side-note: not all mass in the universe comes from the Higgs boson. A substantial chunk of the mass in an atom comes from the binding energy of the quarks due to the strong nuclear force.)

So why does the Higgs boson suck? It sucks because it exists. Physicists have known for ages that the Standard Model can’t be right, simply because it’s not consistent with Einstein’s general relativity. What we need, however, is some clue on how to move forward. The problem is the bloody Standard Model is never wrong. Never, ever, ever. This is of course very impressive, but it pisses everyone off: without any new, unexpected phenomena, nature is giving us no clues about how to continue.

Many of us were hoping the Higgs wouldn’t show up: that would have given us the hint that something was amiss and it would have been a great starting point to start building something new and better. Alas, we found the Higgs and, as momentous as that was, now we have to deal with the fact that we are left right where we started.

Now, to all science conspiracists out there: remember this. Scientists want their theories to fail. Desperately. If you perform an experiment that proves relativity is wrong, you will get a Nobel price, for sure. So there is a huge incentive not to protect the status quo, but to do the opposite. Scientists try very, very hard to find cracks in their theories. Their fame and their fortune depends on it. The fact that they don’t doesn’t show there’s a conspiracy trying to cover up results: quite the opposite. It just goes to show how frustratingly good some of our theories are. Which makes the people who’d love to make a difference (like me) very, very annoyed.

I highly recommend this article for a better explanation about the Higgs boson. It is much more rigorous than mine, though a little longer. Having read this introduction, you should be able to get it.

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