Science discussion, continued from other thread

[michaeld]

OK! Time to play catch up with this thread. I'll start with some of the interpretation-of-QM posts. This is another one of my favourite topics. :D

Oh, OK. That is the Many Worlds Interpretation, a.k.a., the Everett interpretation. Here, the universe splits in two, with the cat alive in one and dead in the other. These universes cannot interact with each other.

In the Schrödinger's kitty picture in the original post, we are using the Copenhagen weinterpretation, which makes the kitty a wave function of eigenvalues. The squares of the eigenvalues sum to 1:

Er, it's not the eigenvalues whose squares sum to 1. Given a Hermitian observable, an eigenstate is a state for which the value of the observable is well defined, and the eigenvalue is the corresponding value of the observable.

If is a Hermitian observable with a complete orthonormal basis of eigenstates , ,... with corresponding eigenvalues , i.e.

for every i

then we may write a generic state as

where are complex numbers denoting the amplitude (or coefficient) of the eigenstate .

If the state is normalized then the squares of the absolute values (or moduli) of the amplitudes sum to 1:

and the probability of observing the value in a measurement of the observable is . (So the above equation is just saying the probabilities sum to 1.)

In brief: it's the (normalized) amplitudes whose square moduli sum to 1, not the eigenvalues.

(Sorry about the poor notation. Maybe later I'll try and figure out how to import properly Latexed equations here. EDIT: it's now fixed!)

Back to the Many Worlds Interpretation. Here, the kitty is not a superposition of a live and a dead cat, but it is either alive or dead in any given universe.

Oh it's very much a superposition. In fact that's the whole point.

To understand Everett you have to realise that it's not just electrons and small particles that are quantum, but rather everything around us - including we, the observer - are part of a great big quantum system. Let's switch to a much simpler quantum observation. Let's suppose we're measuring the spin of an electron in a certain direction. There are two possibilities - it could be spin up or spin down.

Now what we are measuring is just one little quantum number. But... when we observe this quantum number, a huge number of quantum numbers will be affected. The dial of our macroscopic instrument will read UP or DOWN, and then this image will be imprinted in our brain, and if we go on to tell our friends about the result, write it on the internet or write papers about it, the effect will become even more enormous. Literally trillions and trillions of quantum numbers will be determined by the one original single quantum number we observed.

But of course the rest of the world - outside the single electron - is also a quantum system. So let's summarize the entire state of the rest of the world by . A massive quantum state, containing the information of zillions and zillions of different quantum numbers. The entire state of the universe is then

where is the state of the electron.

(Technically, the entire Hilbert space is a tensor product of the spin-state-space of the electron and the state space for the rest of the world, but we don't need to get into the technicalities here. All that matters is that the entire state is some kind of amalgamation of the state of the electron and the state of the rest .)

Before the measurement, call the state of the rest of the world . After the measurement the rest of the world will be if the electron was measured as spin-up and if it was measured as spin-down. These two states are very different, because a difference in the measurement will make a macroscopic difference in the two worlds and so effect many trillions of quantum numbers.

OK so what do we know? We know that by the system is governed by the rules of quantum mechanics, i.e. Schroedinger's equation

where is the state of the system, is the Hamiltonian.

We also know that if the electron starts in a state of being spin-up-for-certain then the world will inevitably measure the electron as spin up. So the world will go from to whereas the electron will simply stay spin-up. We can represent this as follows.

-----> (1)

Similarly if the electron starts as spin-down-for-certain then this is what the world will measure.

-----> (2)

But what happens now if the electron does not start in a certain spin state? Let's say it's starts with equal probabilities of being UP or DOWN:

.

Then the entire state beforehand can be written

,

which can be re-written

using the distributive law for tensor products.

But now we may use the fact that the equation (*) is linear! Using (1) and (2) we deduce

------> .

That's all there is to Many Worlds. Notice that the final state is a linear superposition of two hugely differing macrostates. These two states are the two different "worlds". The universe in its final state is a linear superposition of two different worlds - each existing just as much as the other one. And that's Many Worlds!

Notice the other very important point here. The term Many Worlds is actually a misnomer, albeit a very intuitive one. In actual fact, there is only one world. And one overall state. But this state

is a combination of two macro-states and that are so "far apart" that they will never see each other ever again, and will keep evolving as though the other one didn't exist. They are completely "out of tune" with each other. On totally different frequencies if you like - so they will never interact. These are the two "worlds", but in actual fact they are in the same world as each other but just don't know it.

That means that according to MW, all these other "worlds" are right here, right now, occupying the same space as you and me. But we just can't feel them, or see them. Our only reason for thinking they exist is by following the rules of quantum mechanics.

Now I find all that very elegant. But what's NOT elegant is the next step some people take. To get rid of the extra "worlds" it is postulated that all the extra "worlds" apart from the one we're in, instantly vanish. This is the "collapse postulate". The argument goes that the final state that the Schroedinger equation predicts

contains two observers - one in and one in . Since we must observe a definite value we must lie in either or and we will never see the other world at all. Therefore why not just get rid of it! So they go from

to either

or

.

This is the collapse postulate. It involves cutting away, by fiat, part of the state of the system when that part becomes no longer relevant to you. Some even claim the collapse occurs as a real physical process - whenever a quantum state is observed. My objections to this:

(1) The collapse is non-local. As Kelly mentions later, you can set up a system of entangled electrons separated by a huge distance. If the collapse postulate is true, when one electron is observed and collapses, that determines the state of the other, which must therefore collapse at precisely the same instant - even if the two electrons are now at other ends of the universe!

(2) The collapse would be non-unitary and (probably) non-continuous. Specifically, it would involve a violation of Schroedinger's equation.

Either of those two properties would certainly be pathological but not totally fatal. Even more seriously though...

(3) It is completely non-objective. When does the collapse occur? When the quantum state interacts with the "macroscopic world"? But what is the macroscopic world? Isn't the macroscopic world just made up of a huge collection of quantum systems? So where does one draw the border between what is quantum and what is classical, for the collapse to occur at? Similar, even more severe, problems occur if you try to define the collapse as occurring when a "conscious observer" sees the result.

Finally...

(4) It is completely unnecessary. It seems highly likely that all the observational evidence supporting QM can be completely explained without invoking any collapse postulate, and simply postulating that everything obeys the Schroedinger equation at all times. Decoherence explains the appearance of collapse and the emergence of the classical world on the macro-scale - and in particular, the fact every measurement appears to have a single result and that we can only observe one "world".

So the collapse postulate, at least as an actual physical process rather than an emergent phenomenon, is unnecessary, hard to objectively define and would be hugely problematic anyway if it were true. The collapse postulate, although historically influential, to me has about the same level of elegance and scientific merit as the conjecture that if you shine photons away from you into empty space they disappear because there will never be anyone able to catch up with and observe them.

Er, I'd better stop here. This was long enough. More later. If I get time I'll try and make the equations look a little more elegant. EDIT: done!

[michaeld]

Testing Latex... .

EDIT: yay, that seems to work!

OK I'm going to go through my previous post and my next post and try to tex things up! This may take a while as I'll only do it as and when I have time rather than all at once.

In case anyone else who knows the Latex language wants to try this with their posts, the site I'm using is texify.com. The easiest way I think is to edit the URL directly. Here is the code I used to make the psi-ket above. Now just edit the latex code to make the equation you want and after testing it out, paste the url in here, between the [ img ] [ /img ] tags (no spaces).

EDIT^2: OH NO!!! I got cut off!! It said I had posted too many images so I lost the edit for the next part of my message. That took me a long time too. The switch is now between equations (1) and (2) in this post, with (1) in Latex but (2) in plain text.

How many images are allowed per post? Is there any way round this? We'll never be able to have a proper technical discussion here if there's an artificially low limit on the number of equations you can post! I don't see why there is a limit as none of the images are being hosted on the AVEN server anyway so they're not taking up space.

EDIT^3: Problem solved thanks to the intervention of the Admod team and especially Kelly! The new limit is now 60 images per message. Previously it was 30. If you need yet more I suggest splitting the post into several pieces each of which has at most 60 equations. I have now texed all the equations in both messages.

[michaeld]

So Kelly's post pt 2. :)

Back to the Many Worlds Interpretation. Here, the kitty is not a superposition of a live and a dead cat, but it is either alive or dead in any given universe. Since it can be alive or dead, it is both, but in different universes. You, the observer, are in only one universe, so your kitty will be either alive or dead but not both. If the kitty is alive when you open the box and look, your doppelganger will observe a dead cat when he opens the box.

In fact, the final state is very much a superposition. The superposition is:

where a,b are coefficients that determine the amplitudes (and hence the probabilities) of the cat being dead or alive:

.

The first term of (*) corresponds to the first world in which everyone is weeping because of the loss of the cat. The second term is the second world in which the cat is alive and everyone (or almost everyone) is rejoicing. These two worlds both exist but can't see each other.

I don't really believe that, I tend to think that the cat is either alive or dead. True, we do not know which, but when there is an object (or particle) with possibilities that can be summed up in a wave function, I do not believe that universes are constantly splitting off. There are a lot of particles, and the creation of nearly an infinite number of universes, splitting off every time that there is a possibility to do so seems difficult. How many universes must there be by now?

Actually it's the easiest thing in the world! All one has to do is postulate the Schroedinger equation (which one has to do at all other times anyway). It's the non-many-worlds interpretations that are more complicated, despite initial appearances. All many worlders are saying is: well the Schroedinger equation works whenever else we tried it - why not postulate it for the observation process too! The many worlds interpretation then falls out naturally.

Regarding the particles and kitties as superpositions of eigenstates, I have a problem. The entangled photon pair is a good example. With particles, such as two photons that are made at the same time, and traveling out away from each other with their polarization states at 90 degrees from each other.

Since their electric fields must be 90 degrees apart, then if, say, a year later, when the two photons are two light-years apart, one photon is "observed", or its polarity measured, then if the other photon's polarity is measured just afterwards, then it will (it must) show a polarity 90 degrees apart from the first photon.

Conventional thinking is that the photons' polarities are a wave function with possibilities of being measured in one direction or the other, and that it does not have a definite direction until it is measured (observed) and then its wave function "collapses" and it falls into one eigenstate. And since the other photon must have a polarity 90 degrees from it, the first photon signals the second photon and tells it to collapse its wave function and in what state it should become. And it does so instantly—far faster than the speed of light.

I disagree! This is not conventional thinking within the Everettian framework at least (and arguably not even for other interpretations too, though that's more dubious). In particular, the MW theory simply postulates that

holds all the time. As the Hamiltonian is a local field operator, in relativistic quantum field theory, both sides of this equation - the Schroedinger equation - are 'local'. Therefore changes cannot and do not propagate faster than the speed of light. There are no faster than light signals.

What actually happens, from the Everettian point of view, is that when the second electron's state is observed, the universe splits at that point, but the split is not global in space. Rather the split starts at the observation, and travels at the speed of light (or possibly just under) until it reaches other points in the universe much later. It travels as fast as the information from the observation interacts with the environment.

Eventually however, by the time you could bring the electrons back together to make sure they really have compatible states, the split will have spread to the area of space containing both electrons. So if you bring them back together, you will indeed observe their states are compatible, as their entanglement implies. But there's no way to check this instantaneously and therefore no need for anything to travel faster than light. In one world, the electrons will have been found to be spin up + spin down and in the other they will have been found to be spin down + spin up. So both worlds are consistent, without any FTL signals.

I disagree.

Whereas I do agree that the photon may be thought of as having a possibility of having its polarity in one direction of the other, and that it is unknown until it is measured, I do not think that it did not have a definite polarity until it was measured, but instead, it had one to begin with, when the photon pair was first created. So, a year after the pair was created, and the two photons are measured one right after the other (say, with the first photon's polarity at 90 degrees and the second at 0) and the results are beamed to our experimenters on earth), the experimenters may say, See, that proves superluminal communication, because the first photon had to tell the second photon to collapse its wave function, and it did so in less than a second from two light years away!

Not as far as I am concerned—I think that the reason why the second photon has its polarity at 0 degrees was not because it suddenly collapsed its wave function when the fist one did, but that its polarity already was at 0 degrees, and was ever since it was created.

I am sure that that is blasphemy, but there you have it.

*hides from the inquisitors*

Here comes the inquisition!!!

This is exactly the intuition Einstein and his collaborators had. They wrote a paper suggesting an experimental setup, now known as the EPR paradox, designed to show a flaw in QM. The experiment was eventually done and vindicated QM and not EPR. So you're in good company at least. But unfortunately it is also now known that this idea can't work!

What you're describing is a local, hidden variable alternative to standard quantum mechanics. The postulate that the electron's quantum state does not contain the whole story, and the electron starts out with an extra piece of information - a hidden variable - that determines its eventual spin measurement (or polarization or whatever else you want to measure). The idea is that both the electron and its partner have correlated hidden variables, which determine the eventual measurements.

The modern treatment was given by Bell - see Bell's theorem - and it was tested by Aspect. Basically Bell's inequality (or theorem) is a mathematical result that is obtained under the following assumptions.

(1) The entangled electron system is described by a local, hidden variable system. No FTL signalling! The measurement may though be determined by an extra hidden variable not seen in the wavefunction. (For example, the electron may really have had its spin or polarization all along, right from birth.)

(2) (often overlooked). Contra-factual definiteness. Every conceivable experiment has a definite single outcome.

(Note we do not assume determinism.)

Given these assumptions, an inequality can be derived between the spin correlations (or whatever) of the electron and the system. In practice Bell's original version is not used any more - instead the CHSH inequality is more convenient.

The results of the Aspect experiment?? Bell's inequality and the CHSH inequalities are violated! That means that one of the assumptions (1) and (2) are wrong. The electron cannot start with a definite spin that determines the (single) final outcome - at least if FTL signalling doesn't occur.

There have been various attempts to point out loopholes in the experiments over the years, but gradually they have all been closed. Quantum mechanics wins as usual, and local hidden variable theories with definitive single outcomes simply cannot work.

There are three big classes of solutions to this 'paradox' - the fact that (1) and (2) cannot both be true.

(a) Collapse theories. These circumvent the problem by violating (1) above. (Actually they often violate (2) as well.) The wavefunction collapse is non-local. But see my previous message for my problems with collapse theories.

(b) Bohmian mechanics. This also violates locality - assumption (1). This was Bell's preferred solution. Maybe later I'll talk about this later.

© Many Worlds. This violates assumption (2). There is no single outcome of these experiments. There are different outcomes in different worlds. Unlike (a) and (b), Many Worlds is a local theory. No FTL signals!

[< retired >]

I was browsing in the local farmer's market the other day, and came across my first Romanesco broccoli.

I was stunned - never before had I encountered such a perfect example of the 'fractal geometry of nature'. The veggie crouched in my frig for a few days before I finally mustered the courage to eat it. Very tasty!

I wondered how many levels of self-similarity were invisible to my eye (only about 4 or 5 were visible). Apparently quite a few: http://www.nature.com/emboj/journal/v29/n9/covers/index.html

Here's the wikipedia page for this wonderful veggie: http://en.wikipedia.org/wiki/Romanesco_broccoli

Bon appétit! :)

P.S.: if you count the number of bud whorls going clockwise and counter-clockwise, the two numbers may be adjacent numbers in the famous Fibonacci sequence. Another reason to admire this veggie! http://en.wikipedia.org/wiki/Fibonacci_number

[Inevitable]

I was browsing in the local farmer's market the other day, and came across my first Romanesco broccoli.

I don't know who you bought it from, but that's not broccoli.

Trust me, I've seen one of them before. They're alien space craft.

[Sally]

Comment from browsing non-scientist: Some of you use the term "kitty" instead of "cat". That is so AVEN! :)

Also, if you can imagine, 35 years ago when we actually used typewriters with balls (the metal kind), we had to take out the English/whatever ball and insert the symbol ball every time we typed an equation.

[michaeld]

Comment from browsing non-scientist: Some of you use the term "kitty" instead of "cat". That is so AVEN! :)

Also, if you can imagine, 35 years ago when we actually used typewriters with balls (the metal kind), we had to take out the English/whatever ball and insert the symbol ball every time we typed an equation.

And start a new page every time there was a typo... (unless it happened to be a special typewriter with an eraser function). Actually I've used a load of typewritten books and PhD theses from the 60s and 70s and quite often they'd just leave a space where there was to be an equation, write the thing in by hand and then photocopy! Well frankly I think I'd do the same thing...

Interestingly, TeX - the system I just used to write in the equations to the two posts, and the standard these days for all mathematics and scientific papers - was developed all the way back in the late 70s. But of course not that many people had access to it back then, at least at first...

[Sally]

And start a new page every time there was a typo... (unless it happened to be a special typewriter with an eraser function). Actually I've used a load of typewritten books and PhD theses from the 60s and 70s and quite often they'd just leave a space where there was to be an equation, write the thing in by hand and then photocopy! Well frankly I think I'd do the same thing...

The eraser function only worked when you noticed the mistake immediately and the guys I worked for (and they were all guys back then) did not send handwritten equations in to peer-reviewed journals. So, we used the balls, and white-out.

*non-scientist backs outof thread*

[Gatto]

I was browsing in the local farmer's market the other day, and came across my first Romanesco broccoli.

I was stunned - never before had I encountered such a perfect example of the 'fractal geometry of nature'. The veggie crouched in my frig for a few days before I finally mustered the courage to eat it. Very tasty!

I wondered how many levels of self-similarity were invisible to my eye (only about 4 or 5 were visible). Apparently quite a few: http://www.nature.com/emboj/journal/v29/n9/covers/index.html

Here's the wikipedia page for this wonderful veggie: http://en.wikipedia.org/wiki/Romanesco_broccoli

Bon appétit! :)

P.S.: if you count the number of bud whorls going clockwise and counter-clockwise, the two numbers may be adjacent numbers in the famous Fibonacci sequence. Another reason to admire this veggie! http://en.wikipedia.org/wiki/Fibonacci_number

Restate my assumptions: One: Mathematics is the language of nature. Two: Everything around us can be represented and understood through numbers. Three: If you graph the numbers of any system, patterns emerge. Therefore, there are patterns everywhere in nature. Evidence: The cycling of disease epidemics; the wax and wane of caribou populations; sun spot cycles; the rise and fall of the Nile. So, what about the stock market? The universe of numbers that represents the global economy. Millions of hands at work, billions of minds. A vast network, screaming with life. An organism. A natural organism. My hypothesis: Within the stock market, there is a pattern as well... Right in front of me... hiding behind the numbers. Always has been.

Personal note: When I was a little kid my mother told me not to stare into the sun. So once when I was six I did. The doctors didn't know if my eyes would ever heal. I was terrified, alone in that darkness. Slowly, daylight crept in through the bandages, and I could see. But something else had changed inside of me. That day I had my first headache.

Failed treatments to date: Beta blockers, calcium channel blockers, adrenalin injections, high dose ibuprofen, steroids, Trager Mentastics, violent exercise, cafergot suppositories, caffeine, acupuncture, marijuana, Percodan, Midrine, Tenormin, Sansert, homeopathics. No results. No results...

It's fair to say I'm stepping out on a limb, but I am on the edge and that's where it happens.

My new hypothesis: If we're built from Spirals while living in a giant Spiral, then is it possible that everything we put our hands to is infused with the Spiral?

Personal note: When I was a little kid my mother told me not to stare into the sun, so once when I was six, I did. At first the brightness was overwhelming, but I had seen that before. I kept looking, forcing myself not to blink, and then the brightness began to dissolve. My pupils shrunk to pinholes and everything came into focus and for a moment I understood.

[ChildOfTheLight]

The modern treatment was given by Bell - see Bell's theorem - and it was tested by Aspect. Basically Bell's inequality (or theorem) is a mathematical result that is obtained under the following assumptions.

(1) The entangled electron system is described by a local, hidden variable system. No FTL signalling! The measurement may though be determined by an extra hidden variable not seen in the wavefunction. (For example, the electron may really have had its spin or polarization all along, right from birth.)

(2) (often overlooked). Contra-factual definiteness. Every conceivable experiment has a definite single outcome.

(Note we do not assume determinism.)

I'm not a physicist, but I don't understand why (2) is not equivalent to determinism. Maybe I'm using informal definitions where physics ones subtly differ or something (I suspect there's a formalism of some sort corresponding to "experiment" here, for instance, but I don't know what it might be.)

Any help?

[Gatto]

The modern treatment was given by Bell - see Bell's theorem - and it was tested by Aspect. Basically Bell's inequality (or theorem) is a mathematical result that is obtained under the following assumptions.

(1) The entangled electron system is described by a local, hidden variable system. No FTL signalling! The measurement may though be determined by an extra hidden variable not seen in the wavefunction. (For example, the electron may really have had its spin or polarization all along, right from birth.)

(2) (often overlooked). Contra-factual definiteness. Every conceivable experiment has a definite single outcome.

(Note we do not assume determinism.)

I'm not a physicist, but I don't understand why (2) is not equivalent to determinism. Maybe I'm using informal definitions where physics ones subtly differ or something (I suspect there's a formalism of some sort corresponding to "experiment" here, for instance, but I don't know what it might be.)

Any help?

If you flip a coin it will be either heads or tails; not both. This is the case whether or not it is deterministic.

[LonePiper]

I was browsing in the local farmer's market the other day, and came across my first Romanesco broccoli.

I was stunned - never before had I encountered such a perfect example of the 'fractal geometry of nature'.

Wow, that is the most awesome looking food I have ever seen!

(Although whether it's really "natural" is debatable, since broccoli is a domesticated vegetable. I'm not saying it's wrong, it's just debatable! :P)

Anyway,

I hope this gives you as much of a nerdgasm as it did me!

[ChildOfTheLight]

The modern treatment was given by Bell - see Bell's theorem - and it was tested by Aspect. Basically Bell's inequality (or theorem) is a mathematical result that is obtained under the following assumptions.

(1) The entangled electron system is described by a local, hidden variable system. No FTL signalling! The measurement may though be determined by an extra hidden variable not seen in the wavefunction. (For example, the electron may really have had its spin or polarization all along, right from birth.)

(2) (often overlooked). Contra-factual definiteness. Every conceivable experiment has a definite single outcome.

(Note we do not assume determinism.)

I'm not a physicist, but I don't understand why (2) is not equivalent to determinism. Maybe I'm using informal definitions where physics ones subtly differ or something (I suspect there's a formalism of some sort corresponding to "experiment" here, for instance, but I don't know what it might be.)

Any help?

If you flip a coin it will be either heads or tails; not both. This is the case whether or not it is deterministic.

OK, I see. So it was "definite outcome" I was confused about.

[michaeld]

OK, I see. So it was "definite outcome" I was confused about.

Yes sorry if that was confusing. I just meant "single, well-defined" by definite. I did not mean that the outcome was definite before doing the experiment.

The condition of contrafactual definiteness (or as wikipedia calls it counterfactual definiteness) actually says a little more than every experiment has a single outcome. It implies that it is meaningful to talk of the outcome of any conceivable experiment, even those that you don't end up doing in practice. More precisely, it implies that the outcome of the experiment is given by the value of a function

F(A,H,R)

depending on three things, which I've called A,H,R.

Here A is a set of parameters determined by the experimental set up, H is a set of local hidden variables and R is a collection of local random variables. For example R could be the roll of a die. The allowed dependence of the results on a random R implies we do not assume determinism.

Kelly's theory clearly satisfies this contrafactual definiteness property in a very straightforward manner; according to her theory there is a single hidden variable H that determines the measurement.

F(A,H,R) = H.

This hidden variable H is simply the polarity/spin state/whatever we're measuring that the particle had ever since emission:

Not as far as I am concerned—I think that the reason why the second photon has its polarity at 0 degrees was not because it suddenly collapsed its wave function when the fist one did, but that its polarity already was at 0 degrees, and was ever since it was created.

So no need even for any dependence on a local random variable R.

Sadly, as this theory is also supposed to be local (no super-luminal communications) it means that it satisfies both hypotheses of Bell's theorem, and hence is ruled out by Aspect's experiment.

On the other hand, the Many Worlds theory violates the contrafactual definiteness property in a very strong sense. Not only is MWT not contrafactually definite; it is not even factually definite. Single experiments, involving spin measurements say, do not have a single outcome - even the experiments that you actually end up doing rather than just ones that you can conceive. They have one outcome in one "world" and another in another "world".

[NigelFt]

Can we do some real physics?

Y'know, macro scale stuff?

Here is something:

Red giant star Betelgeuse is mysteriously shrinking

The red supergiant star Betelgeuse, the bright reddish star in the constellation Orion, has steadily shrunk over the past 15 years, according to University of California, Berkeley, researchers.

Long-term monitoring by UC Berkeley's Infrared Spatial Interferometer (ISI) on the top of Mt. Wilson in Southern California shows that Betelgeuse (bet' el juz), which is so big that in our solar system it would reach to the orbit of Jupiter, has shrunk in diameter by more than 15 percent since 1993.

Since Betelgeuse's radius is about five astronomical units, or five times the radius of Earth's orbit, that means the star's radius has shrunk by a distance equal to the orbit of Venus.

"To see this change is very striking," said Charles Townes, a UC Berkeley professor emeritus of physics who won the 1964 Nobel Prize in Physics for inventing the laser and the maser, a microwave laser. "We will be watching it carefully over the next few years to see if it will keep contracting or will go back up in size."

Townes and his colleague, Edward Wishnow, a research physicist at UC Berkeley's Space Sciences Laboratory, will discuss their findings at a 12:40 p.m. PDT press conference on Tuesday, June 9, during the Pasadena meeting of the American Astronomical Society (AAS). The results were published June 1 in The Astrophysical Journal Letters.

Despite Betelgeuse's diminished size, Wishnow pointed out that its visible brightness, or magnitude, which is monitored regularly by members of the American Association of Variable Star Observers, has shown no significant dimming over the past 15 years.

The ISI has been focusing on Betelgeuse for more than 15 years in an attempt to learn more about these giant massive stars and to discern features on the star's surface, Wishnow said. He speculated that the measurements may be affected by giant convection cells on the star's surface that are like convection granules on the sun, but so large that they bulge out of the surface. Townes and former graduate student Ken Tatebe observed a bright spot on the surface of Betelgeuse in recent years, although at the moment, the star appears spherically symmetrical.

"But we do not know why the star is shrinking," Wishnow said. "Considering all that we know about galaxies and the distant universe, there are still lots of things we don't know about stars, including what happens as red giants near the ends of their lives."

Many people think that Betelgeuse will nova, or even supernova, likely within a million years. It would be an interesting sight.

Betelgeuse is the bright red star in the upper left of the consetellation Orion:

On the bottom right is the even brighter star Rigel.

Here is an infrared pic of Betelgeuse posted recently in Scientific American. Note the interesting bright spots:

Now that is interesting. I could speculate on why Betelgeuse is losing mass, but that would only be a guess. Speaking of super massive stars, one of my favourites has always been Eta Carinae, in the constellation Carina:

Interestingly enough, it is at least binary system, with the main star (I think the small white blob in the picture) of the system is more than 100 solar masses. They're are more massive stars, and more luminous ones, but with the twin gas globules, and the surrounding nebulae, it is one of the more photogenic.

Another favourite is Vega, in the constellation of Lyra:

Fifth brightest star in the night sky, and second brightest in the northern hemisphere.

(and at the risk of being mushy in a deeply scientific thread, a star that has certainly lit up my life ...)

I was browsing in the local farmer's market the other day, and came across my first Romanesco broccoli.

I was stunned - never before had I encountered such a perfect example of the 'fractal geometry of nature'. The veggie crouched in my frig for a few days before I finally mustered the courage to eat it. Very tasty!

I wondered how many levels of self-similarity were invisible to my eye (only about 4 or 5 were visible). Apparently quite a few: http://www.nature.com/emboj/journal/v29/n9/covers/index.html

Here's the wikipedia page for this wonderful veggie: http://en.wikipedia.org/wiki/Romanesco_broccoli

Bon appétit! :)

P.S.: if you count the number of bud whorls going clockwise and counter-clockwise, the two numbers may be adjacent numbers in the famous Fibonacci sequence. Another reason to admire this veggie! http://en.wikipedia.org/wiki/Fibonacci_number

Wow ... just ...wow.

Yet another excuse for my love of fractals. And I quite like steamed broccoli too

[LonePiper]

Another favourite is Vega, in the constellation of Lyra:

Fifth brightest star in the night sky, and second brightest in the northern hemisphere.

Also central to the plot of Carl Sagan's book "Contact", one of the most beautiful, inspirational and scientifically motivational books I've ever read. Shame they never made a movie about it.

"But they did make..."

I SAID shame they never made a movie about it!

*Dares anyone to disagree*

[edit]And re: betelgeuse losing mass:

Someone explain this a bit more fully, please. Apparently this is considered a bit of a mystery, but I thought that Betelgeuse was close to going supernova, and stars close to going supernova regularly shed vast layers of matter into space. Why doesn't this simple answer explain why it's losing mass?[/edit]

[Næt.]

Also central to the plot of Carl Sagan's book "Contact", one of the most beautiful, inspirational and scientifically motivational books I've ever read. Shame they never made a movie about it.

"But they did make..."

I SAID shame they never made a movie about it!

*Dares anyone to disagree*

Yeah, real shame that. Would have made a good film.

[Gatto]

[edit]And re: betelgeuse losing mass:

Someone explain this a bit more fully, please. Apparently this is considered a bit of a mystery, but I thought that Betelgeuse was close to going supernova, and stars close to going supernova regularly shed vast layers of matter into space. Why doesn't this simple answer explain why it's losing mass?[/edit]

Shrinking and losing mass are 2 different things. Many stars (e.g., cepheid variables) change size. They also change in luminosity. Other types of stars can lose large amounts of mass.

[< retired >]

On the other hand, the Many Worlds theory violates the contrafactual definiteness property in a very strong sense. Not only is MWT not contrafactually definite; it is not even factually definite. Single experiments, involving spin measurements say, do not have a single outcome - even the experiments that you actually end up doing rather than just ones that you can conceive. They have one outcome in one "world" and another in another "world".

Has anyone working in quantum mechanics ever tried to express the various claims being made about the nature of the universe (or universes) in the language of modal logic? It seems a bit odd to develop a sophisticated mathematical model of reality (or realities) and then employ a rather messy informal 'natural' language like English to interpret and express the results. Modal logicians have been laboring for decades to formalize various modalities of truth such as possibility and necessity; it would be a shame for this work to be neglected if it might have some utility.

If you would like to tackle this project, I suggest pairing up with an expert in modal logic. The learning curve is rather steep. I've read several books in the subject, but still only have a rudimentary grasp of the field. I have yet to encounter a book on modal logic that I really like, but a bit dated book that concentrates nicely on the history and conceptual foundations is Introductory Modal Logic- Konyndyk.

Good luck! :)

[LonePiper]

[edit]And re: betelgeuse losing mass:

Someone explain this a bit more fully, please. Apparently this is considered a bit of a mystery, but I thought that Betelgeuse was close to going supernova, and stars close to going supernova regularly shed vast layers of matter into space. Why doesn't this simple answer explain why it's losing mass?[/edit]

Shrinking and losing mass are 2 different things. Many stars (e.g., cepheid variables) change size. They also change in luminosity. Other types of stars can lose large amounts of mass.

So the mystery is why Betelgeuse is shrinking, not why it is losing mass?

[Ged of Earthsea]

Has anyone working in quantum mechanics ever tried to express the various claims being made about the nature of the universe (or universes) in the language of modal logic? It seems a bit odd to develop a sophisticated mathematical model of reality (or realities) and then employ a rather messy informal 'natural' language like English to interpret and express the results. Modal logicians have been laboring for decades to formalize various modalities of truth such as possibility and necessity; it would be a shame for this work to be neglected if it might have some utility.

If you would like to tackle this project, I suggest pairing up with an expert in modal logic. The learning curve is rather steep. I've read several books in the subject, but still only have a rudimentary grasp of the field. I have yet to encounter a book on modal logic that I really like, but a bit dated book that concentrates nicely on the history and conceptual foundations is Introductory Modal Logic- Konyndyk.

Good luck! :)

This thread will never stop surprising me.

Modal logic is by no means neglected. Interaction with programming language theory, linguistics and algebra have driven it in directions that its founding fathers could not have imagined. A recent and comprehensive overview of (mathematical) modal logic is the book by Blackburn, de Rijke and Venema.

Many modal logicians have studied physics from a logical viewpoint. The master himself, Goedel, discovered non-standard solutions to the relativistic equations that would admit a universe with closed time-line curves. I don't know if it was due to his influence, but several logicians have studied the logical content of space-time geometries.

Modal logicians have been studying quantum logics and related ideas at least since the 70s. There are several non-trivial problems to be solved here. Possibility and necessity are not enough. The quantum world does not have the same observability properties as the logical world. Information behaves differently in a quantum setting: no complementation, distributivity is questionable, etc. The distressing problem for a logician is to identify the mathematical universe underlying a logic and it's axiomatics. There have been different proposals, digging away at the quantum universe in different ways, but none is there yet. There has been a great resurgence of this area in recent times because several new algebraic and topological structures have been identified for logics and these are more quantum friendly. The problem then becomes that these structures are extremely abstract and somewhat different from what physicists use and their contribution to mainstream physics is questionable. But that's always the case with foundational issues isn't it.

[michaeld]

Yet another excuse for my love of fractals. And I quite like steamed broccoli too

Anyone else here spent hours and hours playing with FRACTINT on the old DOS machines? Well I found out just recently that it's still going and works just as well on newer computers. Here it is!

[michaeld]

Modal logic is by no means neglected. Interaction with programming language theory, linguistics and algebra have driven it in directions that its founding fathers could not have imagined. A recent and comprehensive overview of (mathematical) modal logic is the book by Blackburn, de Rijke and Venema.

Indeed.

Many modal logicians have studied physics from a logical viewpoint. The master himself, Goedel, discovered non-standard solutions to the relativistic equations that would admit a universe with closed time-line curves. I don't know if it was due to his influence, but several logicians have studied the logical content of space-time geometries.

"time-like" I think you mean. As Ged knows, but others may not, what the existence of a closed time-like curve impliies is that time travel is possible, at least in Goedel's universe! This doesn't necessarily imply that our universe has time machines in it, but it shows that general relativity alone cannot rule it out.

Anyway: yes that's true, but as far as I'm aware the only connection with formal logic per se is that these solutions were first discovered by Goedel. Goedel was actually interested in a lot of things, and he was good friends with Einstein when they were both at Princeton so it's not surprising he did some decent work on GR as well as his better known work in logic.

The problem then becomes that these structures are extremely abstract and somewhat different from what physicists use and their contribution to mainstream physics is questionable. But that's always the case with foundational issues isn't it.

I think this is fair. I personally think it's unlikely that quantum logic or modal logic will provide a critical insight, solving the foundational problems of physics. Natural language (especially technical scientific language) does surprisingly well, and I don't think its imprecision is the limiting factor, for the most part, in the study of these fields at a deep level.

Of course that's not to say that quantum and modal logic aren't very interesting and shouldn't be studied but I see their relation to modern physics as roughly the same as the relation of formal classical logic to classical physics and mathematics. An indispensable tool but not a replacement for natural language for the most part, in the everyday working of scientists.

[daveb]

Yet another excuse for my love of fractals. And I quite like steamed broccoli too

Anyone else here spent hours and hours playing with FRACTINT on the old DOS machines? Well I found out just recently that it's still going and works just as well on newer computers. Here it is!

No, but I did play around quite a bit with "The Game of Life" and some program from one of Dawkins' books for creating and evolving "creatures" (sort of stick figures that could end up looking like bugs, trees, and many other things).

[Elliekat]

I stumbled into this thread and all the quantum physics is utterly confusing me. I'll stick with my ecology, thank you very much :>

[cosmicbimbo]

I stumbled into this thread and all the quantum physics is utterly confusing me. I'll stick with my ecology, thank you very much :>

Yeah, I was hoping I would learn something but, all that math makes my eyes glaze over.

[Ged of Earthsea]

It's not over yet. Kelly already gave a lot of general overviews earlier. Mathematical nitty gritties details only kicked in later.

Here's a very very quick and dirty summary of all that modern physics (please don't beat me, real physicists). If you move ultra-super-mega-duper fast, crazy stuff happens. If you get itsy-bitsy-teenie-weenie small, crazy stuff happens. If you get humongously, ginormously heavy, crazy stuff happens. The theory of fast is special relativity. Theory of small is quantum theory. Theory of heavy is gravitation.

(0,0,0) is before mechanics. The three directions you can go from there are to develop the theories of gravitation, special relativity and quantum mechanics. Classical gravitation came from Newton. Special relativity is associated with Einstein though several people were thinking along those lines. General relativity combines moving really fast around massively heavy objects that are super-far. It was the brainchild of a relatively small number of people and is beautiful, elegant and concise. Quantum physics was developed over a longer period of time with important pieces of the puzzle contributed by a large number of prominent physicists. While equally fascinating, the mathematical models and physical laws involved are less concise. The big question in fundamental, theoretical physics is to unify these three theories. Kelly has described a few proposals in some posts.

Time-travel got mentioned so let me say something about that. One way to think (abstractly) about time is that there is a future and a past and the two are distinct and only connected by the present. Such a model of time is the one intuitively used in physics. However, you can view the issue from the other side. Rather than asking for equations that model our universe, you can say, assuming the equations of (relativity, quantum mechanics etc) model the universe, what kind of universe is it. This is how you try to make predictions about nature. We can say, suppose we view time as always moving in the same direction but allow it to loop back. So, time always progresses, but the future and the past (at the scale of the universe) don't quite behave as we assume. Here's what I find fascinating: this view of time does not contradict the equations of general relativity!

Time could potentially move in a loop and in such a universe, some form of time travel would be conceivable. Please don't quote me on the next bit - I'm not sure the physicists would like my telling of it. It seems that time-travel (in some sophisticated form) may be admissible in general relativity. But, general relativity does not tell the entire story of the universe. There's also this quantum stuff and how it interacts with relativity. To find out if time in our universe doesn't flow around in a loop, we need to know what this model looks like. In a nutshell then, all this business of unifying quantum theory and gravity is really about finding out if Dr. Who might drop by for a visit.

[michaeld]

Here's a very very quick and dirty summary of all that modern physics (please don't beat me, real physicists). If you move ultra-super-mega-duper fast, crazy stuff happens. If you get itsy-bitsy-teenie-weenie small, crazy stuff happens. If you get humongously, ginormously heavy, crazy stuff happens. The theory of fast is special relativity. Theory of small is quantum theory. Theory of heavy is gravitation.

I like it. Of course it's oversimplified but that's entirely expected and appropriate. My only quibble is that some of the vertices and arrows seem to be mislabelled. "Quantum gravitation" is non-relativistic??? I've never heard the term be used that way. It's very unlikely that relativity can be added to a quantized theory of gravity as an afterthought. Nearly all approaches to quantized gravity are relativistic from the outset. The only exception I can think of in recent years is an interesting proposal by Horava (who is incidentally a very well respected physicist, who's written highly influential papers with the great Ed Witten among others).

http://arxiv.org/abs/0901.3775

The term "classical physics" at (0,0,0) is very strange. The term "classical" in modern physics essentially just means "not quantum". Newtonian mechanics is certainly regarded as classical - but so even are Einstein's special and general theories of relativity.

The arrow labelled "action" is also a little odd. What would fit better there is "Planck's constant". The only connection with action is that Planck's constant has the dimensions of action.

Time could potentially move in a loop and in such a universe, some form of time travel would be conceivable. Please don't quote me on the next bit - I'm not sure the physicists would like my telling of it. It seems that time-travel (in some sophisticated form) may be admissible in general relativity.

Er, well it is. As you pointed out yourself earlier, Goedel constructed a solution to GR with a closed timelike curve, aka a time machine. On the other hand, such solutions are generally thought to be highly pathological, for various reasons. A better question might be whether any solution with similar properties could plausibly describe the universe we happen to live in.

In a nutshell then, all this business of unifying quantum theory and gravity is really about finding out if Dr. Who might drop by for a visit.

That's one possible question it may shed light on but by no means the only or main one.

[Bobandirus]

So heres another question for you physics people. And I do apologize if its a bad question do to a shoddy knowledge of the relevant physics.

As far as I understand, the current theory is that there are patches of the universe which are more dense than others, affecting many things (quite what, I'm not sure). These are spread throughout the universe, and can be many sizes. In that case, is is possible that we are in one ourself, and the time is sped up in them. With this effect its not actually that long after the big bang. Or possibly the other way, time goes really slowly in here, its ages after the big bang and things are slowing down, hence why expansion is at the wrong rate, and hence the need for dark matter? Does that make any sense, and is it accurate at all?

[< retired >]

Many modal logicians have studied physics from a logical viewpoint.

I googled ["quantum mechanics" "modal logic"] and got a nice hit: Conceptual Foundations of Quantum Mechanics:. the Role of Evidence Theory, Quantum Sets, and Modal Logic

This is exactly what I was proposing. I didn't read the paper (I'll leave that for folks who want to delve deeper), but the title and abstract look promising. I'm not embarrassed for asking my original question, because none of the (introductory) books I've read in modal logic have mentioned applications in quantum mechanics.

BTW, George J. Klir (a coauthor of the above paper) published a good book in 2005 on uncertainty and information theory: Uncertainty and Information: Foundations of Generalized Information Theory. This book is on my Amazon 'wish list' - when I feel like forking over $100 I'll add it to my library. :)