In this post I’m going to attempt the impossible: I’m going to explain (at a high level) Quantum Physics *using math* while trying to keep it interesting. I’m basically going to use a dumbed down and somewhat modified example I’ve taken from Roger Penrose’s book called *Shadows of the Mind: A Search for the Missing Science of Consciousness.*

I believe people willing to persevere through this post will find themselves surprised by the end by the rather starling philosophical implications of quantum physics. I also believe that, if you take it slowly, the math is understandable to any high school graduate. I am personally very bad at math and can only handle this example because the math is so easy. If you don’t assume you can’t understand it, you’ll find that you can.

**Forget What You Think You Know**

Unless you are a physicist, start by emptying your mind of what you think you know about quantum physics through popular books because there is a substantial gap between what people say about Quantum Physics and the real theory. It seems to me that Quantum Physics currently gets used as the new ‘magic’. It’s become common for the fad magical (or sometimes even religious) worldview of the moment to slap a ‘quantum’ label in there somewhere to add a scientific veneer. [1] The reason this happens is because quantum physics has a deserved reputation for being really ‘weird’. But keep in mind what ‘weird’ means. It only means “something I’m not familiar with.” Claiming something is ‘weird’ says nothing ontological about the object/idea in question and actually serves as a statement about the speaker’s state of ignorance of the subject. (A point I often bring up when we talk about Mormons or other religions being “weird.”)

Contrary to popular belief, it is not entirely true that quantum physics allows for an object to be in two places at once. This is only true in a very limited sense which I’ll explain as part of this post. It is also not true that quantum physics necessarily enshrines human consciousness as the center of reality. Amit Goswami’s popular science books aside (i.e.* The Self-Aware Universe*), once you understand how Quantum Physics really works I suspect you’ll agree that the case for the centrality of consciousness in Quantum Physics is lacking.

**The Dud Bomb Problem**

I’m going to use the “Elitzur-Vaidman Bomb Tester Problem” to teach the basics of quantum physics. I also choose it because it’s implications are startling.

Pretend that there is a group of bombs that are triggered by a single photon bouncing off a small mirror at the nose of the bomb. If the bomb is not a dud, the bomb explodes when the photon hits its trigger mirror. See illustration below.

So the problem to be solved is this: come up with a way to prove that a bomb is not a dud without causing it to explode?

This reminds me of the old Bugs Bunny cartoon where Bugs is on an assembly line and is hitting each bomb and, if it doesn’t explode, he writes “dud” on it. In classical physics, this problem is as unsolvable as it was for Bugs. But we live in a quantum world not a classical one, so *classic physics isn’t reality*. In *reality*, it * is *possible to test these bombs in such a way so that we can collect together a group of bombs that we

*know*are not duds yet haven’t, as yet, been exploded.

How? It’s impossible, right? That’s what makes quantum physics so dang strange. It’s utterly at odds with our intuitions about reality.

By the way, according to Wikipedia, this experiment (or a version of it) has been tested in reality.

**Part 1: Quantum Phenomenon and Half Silvered Mirrors**

Now start by looking at the illustration below.

In this illustration we have a photon source that emits a single photon that shoots out and hits a half-silvered mirror. A photon is a single ‘particle’ of light. It’s the smallest amount of light that can be emitted. It turns out that light is ‘lumpy’ because there are minimum quantities that can be emitted. That is to say, light is discrete, not continuous. It’s like pixels on a computer screen: it comes in a minimum size.

A half-silvered mirror is a mirror that has just enough ‘silvering’ on it such that there is a 50/50 chance that the photon will bound off of it vs. pass through it.

Now pretend like we add a photon detector at points |C> and |B>. What would you intuitively expect to happen? You’d expect to either detect a photon at point |C> or at point |B> right?

In this case, your intuition is correct. But I want you to mathematically understand why this is true using the quantum formalism.

Mathematically we’d write it like this:

|A> |B> + i|C>

Or, at least that is the closest I can get to the right symbols on a web page. Even using Microsoft’s “Math Input Panel” wasn’t enough to get it perfectly right.

But what does that funny looking equation mean?

**Explaining the Math**

The first thing to know is that the symbol “” is the one I’m not quite drawing right because I can’t get math panel to do it right. It basically means something like “evolves into.” The idea is that we start out in state |A> and as the photon shoots out it “evolves into” the state |B> + i|C> — whatever the heck that means.

Because it’s so difficult to write this all out for a web page, I’m going to simplify it further. For the example I’m using, I don’t really need the “|” and “>” so I’m going to drop it from here on in. So our formula now reads:

A B + iC

Now that you know that “” means “evolves into”, the only real mystery left is what “i” means.

**Imaginary Numbers**

Here, you’ll need to harken back to your junior high school days when they taught you about something called “imaginary numbers” and you scratched your head and wondered why they were teaching you this when it was clearly useless and you’d never use it again. Or at least that is what ** I** remember thinking about imaginary numbers.

What is an “imaginary number”? It’s essentially a number that contains a negative square root.

Yup, you heard me right. “Imaginary” numbers consist of numbers like and . The brainy mathematicians who came up with these seemingly useless numbers even went on to formulize how to write down imaginary numbers. Essentially they noticed that all you really need to write down to do imaginary numbers is . Why? Because if you have a way to write you already have a way to write and , don’t you? Consider that is the same as . (Remember from high school algebra that is just a quick way of writing “ X ”.)

So the brainy mathematicians realized that to work with imaginary numbers you really only need to add a symbol for “” to regular old numbers we already know and love and you could represent any negative square root you wished. So they decided to abbreviate as “i” instead. (Probably ‘i’ for ‘imaginary’.) So any time you see “i” just remember that it’s equivalent to writing .

So what, exactly, is equal to? Well, the whole point is that it’s equal to itself. It doesn’t matter if can’t picture it in your mind or not. If this answer doesn’t satisfy you, then bear in mind that once upon a time mathematicians were convinced that there was no such thing as just plain old -1 for precisely that reason: they couldn’t envision what -1 looked like in their mind.

But as it turns out, it doesn’t actually matter if you can envision -1 in your mind or not. All you really need to know is how to do mathematical functions with it like add, subtract, multiply, and divide with it. The same is true for . The bottom line is that if you decide to multiply two ’s together, you end up with “-1” as your answer for the same reason why if you multiply two s together you end up with “2” as your answer.

**Back At Our Formula**

So getting back to our formula now, the photon at state A has now evolved into state B + iC when it hit the half silvered mirror. This B + iC is typical of how brainy mathematicians write down imaginary numbers. They split them up into a normal number part (in this case “B”) and an imaginary part (in this case “C”). The end result is B + iC.

Frankly, I’m a bit unclear why we let “B” be the normal part of the formula and “iC” the imaginary part of the formula. This is really just something that is inherent to the nature of quantum physics. Apparently the path of the photon reflecting ends up being the “imaginary” part of the formula. Really, this won’t matter so much as I’m copying this out of a book from a brainy physicist, so we can trust he’s got it right and move on.

**Probability Waves**

But what does that formula even mean? Well, that’s the other thing you need to know to understand quantum physics. Quantum physics is actually built up out of probabilities. When the photon hits the half silvered mirror we said there was a 50/50 chance as to which point it would go to. What did we mean by this? It’s not quite what you’d imagine.

What we actually do is we then take the state of the formula (i.e. in this case B + iC) that we’ve ‘evolved’ to and when we take a measurement (i.e. see if the photon reached point B or C) we take the ratio of the two states to determine the ‘probability’ of the chances we’ll detect the photon at either point B or C.

So, for our current state of B + iC the ratio is, of course, 1:1. So there is a 50% chance we’ll detect the photon at point B and 50% at point C – exactly as our intuitions would lead us to believe.

Wow, what was an awful lot of work for what ultimately was an intuitive answer, wasn’t it? But hold on to the seat of your pants because your intuition is about to go out the window.

**Part 2: Add Another Half Silvered Mirror and 2 Full Silvered Mirrors**

Okay, let’s now imagine that we’ve decided to add to the experiment so that it now looks like this:

Basically we’re going to reflect the photon off one of the two full silvered mirrors (i.e. it’s got 100% chance of bouncing and 0% chance of passing through) and finally both paths will converge on a final half-silvered mirror (i.e. 50/50 chance of bouncing or passing through.)

What does your intuition tell you is going to happen now?

Mine tells me that there is now a 50/50 chance that the photon will be at either point G or F, right? If you agreed, go to the back of the room and put on the dunce cap! Because your wrong! To see why this isn’t the case, we have to do that quantum math.

We were previously in state: B + iC. Now, based our experiment, we should expect that B iD and C iE because the photon has to bounce off one of the full silvered mirrors. So far so good. So here is our current “state” of the experiment (We call this a “wave state” by the way):

B + iC iD + i(iE)

Oh, that’s a bit harder to look at, isn’t it? What the heck does i(iE) mean?

But it looks scarier than it is. Remember that multiplication is transitive which means you can do it in any order. So i(iE) just means which, as we already know, is the same as –1E or just -E. So our final state is simply:

iD – E

What’s next? Well, it’s exactly what you’d guess. E evolves to be F + iG and D evolves to be G + iF. So let’s plug that into the formula and see what we get:

iD – E i(G + iF) – (F + iG)

Now simplify it down, first by spreading the first “i” over the (G + iF). That would be the same as iG + iiF which we know is the same as iG – 1F or in other words:

iG – F

Now add in the other part of the equation:

iG – F – (F + iG)

Finally, simplify:

= iG – F –F – iG

= iG – iG – F – F

= -F – F

= -2F

So our final state is “-2F”.

Wait! The G is gone!

It just so happens that the way this experiment is setup, the G ceases to exist due to the way imaginary number math works. Because there is no G, the ‘ratio’ between G and F is essentially 0:1. Or in other words, there is now – according to quantum theory – a 100% chance that the photon will show up at point F and 0% chance it will show up at point G! And this is precisely what happens in real life via experiment.

**Quantum Weirdness**

Now that is counter intuitive isn’t it? Why in the world does setting up an experiment with two paths like this happen to cause the photon to always come out at point F and never at point G? This counter intuitive phenomenon is what is known as “quantum interference.” The idea is that both paths for the photon actually, somehow, interfere with each other.

Okay, okay, let’s head off any objections. It’s just a theory right? Yeah! One that has been replicated countless times. If you actually try this in a laboratory, this is the result you get! The photon always comes out at point F!

**Let’s Add a Rock**

Now suppose you decide to change the experiment around by placing a rock in place of the full silvered mirror between B and D. Like this:

What happens now? You can work the math out if you wish. The bottom line is that there is now a 50% chance the photon will hit the rock (as per part 1 above) and a 50% chance that it will hit the full-silvered mirror between points C and E. If it does hit the full-silvered mirror between C and E, then, of course, there is a 50/50 chance it will come out at either point G or point F. So the odds are these then:

50%: hits the rock and we don’t detect anything

25%: hits point G

25%: hits point F

Stop and let that sink in for a moment. *Why is it that having the rock not blocking one of the paths changes things to cause it to always hit point F*! Why doesn’t it do the intuitive thing and just work out to be 50/50 of being G vs. F?

The answer to that question is stunning: somehow *the photon knows whether or not the path through B and D is open or not*!

**In Two Places At Once?**

This is the limited sense in which quantum physics says that the photon is in two places at once.

Quantum physics never allows for you to *actually* see the photon in two places. The real truth is that it just somehow *knows* that the other path (the one it didn’t take) was open to it. It is *influenced* by that other path that it didn’t take. I can see why some scientists refer to this as the photon being in two places at once, but I’m uncomfortable with this interpretation because I feel it intuitively leaves a false impression about what really happens. To me, if the photon is “in two places at once” then the wave function collapse – as I’ll explain in the next section – shouldn’t happen. Yet it does.

**Wave Function Collapse: Quantum Physics and “Observation”**

Now let’s change the experiment just a bit. Let’s put back the mirror between points B and D, but let’s add a little detector to the mirror so that we can see if the photon hit that mirror or not before bouncing along the path. So it now looks like this:

This setup is identical to the one above (before we added the rock) isn’t it? The photon again has both paths open to it. So what would be the outcome?

If you’re like me, you probably guessed that again we end up with the photon only exiting at F, just like before. In other words, you’re predicting that the interference of the second path starts to happen again because the path is open again. But this isn’t what happens!

The mere act of *adding the detector* cause the interference pattern to disappear – just like if there was a rock there! So the photon starts to exist at G half the time and at F half the time, just like our original intuitions thought it should.

To understand why this happens, you have to know one more thing about quantum physics: the act of observing causes the whole quantum evolution process to start over again. What this means mathematically is that once the photon hits the mirror between B and D (and is detected) the evolution of the path through C and E ceases to exist! This phenomenon is known as the ‘wave function collapse.”

Strangely, if the photon does take the C and E path the very fact that the B and D path *would have detected it* causes that path to cease to exist also.

As before, our evolution starts out looking like this:

A B + iC

But once the photon reaches either of the full-silvered mirrors we, in theory, can know which mirror the photon bounced off of. If the detector between B and D registers a photon, then we know that is the path the photon took. But if the detector does not register the photon, then we can be sure that the photon took the C and E path. Either way, we know (after reviewing the detector data) for sure which path the photon took. The very fact that we know have this data available causes the evolution of the equations to start over.

What this means mathematically is that if the photon hit the mirror between B and D, that becomes the start of a new evolution process. Likewise for if the photon bounced between the C and E mirror. So we’ll *either* end up with B iD *or** *we’ll end up with iC i(iE) *but we no longer add both together!*

Because the evolution of the quantum equations starts over, the interference pattern also disappears now. To demonstrate why this is, do the math. Where we left things was that we either had B iD or iC i(iE) but not both.

You can work out the math from here now:

Either:

iD G + iF OR iiE – F – iG

For both of these possible evolutions, the ratio between F and G is again 1:1. So we’re back to having a 50/50 chance of getting either F or G. The interference pattern is gone!

Notice something else here: *the photon detector* was the ‘observer’ here, not a human being. “Observation” in quantum physics is never specifically a conscious being observing something, as Amit Goswami (and others) might have you believe. Quantum physics does not appear to put human consciousness at the center of reality. Any sort of detector (or as we saw, even a rock) will do.

This is also why I’m hesitant to say that in quantum physics a photon or particle can be in two places at once. The fact is that the photon only takes one of the two paths. It is (as we’re about to see) really just the fact that the photon *could* have taken the other path *but we don’t know which path it took* that causes the existence of an interference pattern. Once you throw a detector on there, there is never ever a case where you can detect the photon taking both paths at once.

**Testing For a Dud**

I have now given you all that you need to solve the test bomb problem. Simply take the bomb, with its little mirror on the front, and make it the full silvered mirror between B and D. Like this:

Now, according to quantum theory, what happens? Feel free to do the math for if the bomb is a dud vs if the bomb is not a dud. I would appear something amazing happens.

In the case where the bomb is a dud, our experiment is exactly like not having a detector, for the bomb does not explode when the photon hits its mirror because it’s a dud. But if the bomb is not a dud, the bomb functions as a detector and the interference pattern vanishes!

So here is the key now: what does it mean if you shot a photon at the above experiment and you get a detection at point G?

It means you know for sure the bomb is not a dud *even though the bomb did not explode*!

**The Truth about Reality: Counterfactuals vs. Many Worlds**

Roger Penrose suggests that the best way to think of Quantum Physics is as somehow dealing with counterfactuals. A counterfactual is actually a familiar concept. It is not uncommon to say something like “had Romney not been a Mormon, John McCain would not have received the Republican nomination in the 2008 election.” What does a statement like this really mean? From a classical physics point of view, it means very little. Since Romney is a Mormon the statement is (logically speaking) factually false at the outset. [2] Its meaningless. Or is it?

Intuitively, we ‘get it’ that a counterfactual statement is not meaningless, though trying to explain what we really mean by it is a bit difficult to explain. We just mean that, had there been some other reality the same as ours save only that Romney was not a Mormon, the outcome of the 2008 primary election would have been different. (Did that explain it any better? Not really.)

What quantum physics is telling us, according to Roger Penrose, is that if the photon comes out at G, we know for certain that counterfactually, had the photon taken the B to D path, the bomb would have exploded. Thus we know it is not a dud. In short, counterfactuals somehow ‘physically exist’ in reality, at least in a case like this.

David Deutsch, on the other hand, would say that we live in a multiverse of many realities and that what actually happened is that in 50% of the alternate realities out there, the bomb did explode. That reality then decohered from ours and could no longer communicate with us and that is why we got the photon at point G. (i.e. that is why the exploding bomb acted more like the rock. It caused that reality and ours to stop communicating.)

It’s not hard to see that no matter which of these is the truth, there are significant philosophical ramifications.

The simple truth is that: quantum physics says something about reality that is wholly counter intuitive and simply fantastical. It is either saying something about counterfactuals being (in some sense) physically real or its saying we live in a multiverse of realities. Either way, if you are like me, your mind is probably blown out of your head and lying on the floor behind you. Excuse me while I pick mine up again and shove it back into my head.

**P.S.** Doing a post like this is quite difficult. So anyone that reads this that understood it even partially and enjoyed it and wants to see more such posts (and I’m assuming we’re not talking about a very large crowd) please be sure to put a comment if only “read and enjoyed by no comment”. This will give me an indication that there are a few people out there that really like this stuff as much as I do I’ll do more in the future. If you are a regular lurker, this might be a good time to make a comment for the first time in your life.

**Notes**

[1] *The Secret *is the prime abuse of quantum physics here. But also Barbara Hagerty, author of *Fingerprints of God: What Science is Learning About the Brain and Spiritual Experiences* wanted to use quantum entanglement to explain how a mother knows her child is in danger, etc. She suggests the entire universe is quantum entangled, etc. It makes one wonder why observing your child every day since birth didn’t collapse the wave function and end the entanglement.

[2] Well, actually, that’s not really true. The real truth is that if you make a statement “if X is true, then Y is true” and X is not true, then the whole statement is actually considered logically true. So that means the statement is factually true, not factually false. Just not in the way I meant it in that context.

THIS IS WHY I WANTED TO BE A PHYSICIST!!! =D I love this stuff.

So it works with a photon, why won’t it work with a tennis ball?

My head hurts.

Pretty amazing. So what ARE the philosophical and religious implications in your opinion?

Stan,

Tennis balls decoher too easily.

Geoff,

You and me both.

Jeff T,

Yes, I wish I had been a physics major in college.

Nate,

Do you mean beyond the point I made at the end?… well… no way I can get into all the possibilites in one post or comment.

Okay, Nate, let me give you one wild possible implication: If counter factuals are true (either by many-worlds or some other unspecified means) then the old argument about God existing of necessity — which is classically speaking a lame argument to the point of making me cry that humans are so stupid — might turn out to be correct after all for non-classic quantum reality! i.e. God exists because there counter factually exists a greater intellgence then all others.

Except that if God has free will and evil exists as a real option then there must be some world in which he is evil. I think MWI has lots and lots of problems for Mormon theology. Of course I think it has lots of lots of problems period.

I agree MWI has lots or problems for Mormon theology and probably even problems period.

The many worlds interpretation is hands down the most ridiculous physical theory I have ever come across. It has about as much merit as the proposition that Maxwellian anti-demons are causing entropy to increase by robbing the universe of information.

In addition, the only reason to credit it at all appears to be demonstrably false.

http://www.nature.com/news/quantum-theorem-shakes-foundations-1.9392

Physicists should get with the program. The world is real, the quantum wavefunction is real, the Bohr interpretation is ridiculous, the world is non-local, and relativity is on very thin ice.

“read and enjoyed”

“read and enjoyed” it, even though I surely didn’t grasp everything.. especially the final conclusion.

When you’re testing for a dud (and use the bomb as a detector), what are the probabilities for an actual explosion and what the probablities for each outcome?

Solon,

For the way I have this setup, the %s are this for a non-dud bomb:

50% chance it will explode

25% chance we get an F – and thus don’t know if its a dud or not

25% chance we know it’s not a dud because it comes out at G

However, it is possible to setup this experiment using the quantum math any way you like. It’s possible to get it to the point where we know with something just shy of certainty that the bomb is a dud or not without exploding. But that would be truly complicate, I’d imagine.

I’ve always had trouble dealing with a branch of math/science that relies on a number that isnt possible to create. The reason sqrt -1 is imaginary is that you cant square any number to get it. How do you build in reality with something that doesn’t in reality exist?

Excellent post, btw. Oh, and do you have any links to documentation of the experiment succeeding in reality? I’m having trouble with the detector allowing the experiment to continue, since the detector would consume the particle, thus not allowing it to reflect.

Pardon me while I hook up my finite improbability drive and cause the hostesses undergarments to move three feet to the left.

Note that imaginary is just a somewhat arbitrary term. Imaginary numbers when applied to physical systems can mean different things depending upon ones model. So in A/C circuits it turns out they are a great way to deal with the phase of the wave of electricity voltage. It’s amazingly useful in a surprising number of places but we have to be careful not to see it as too mysterious.

Thank you, very fascinating. Will definitely keep reading.

This was very beneficial because I learned that the “detector” is never human consciousness. I was unclear on that for some reason. I’ve got the book “Quantum Theory for Poets” and have been through the book twice, and still find myself only absorbing maybe 35% of it. I love the subject though, as it is the underlying of Newtonian Physics, and despite quantum strangeness of atoms, as they begin to behave in similar fashion that averages past 50% we start to see the beginnings of predictable behaviors that build bridges and airplanes….or do I understand that correctly?

Bruce:

Loved this. I think you’re right that quantum mechanics causes some real problems for CONVENTIONAL interpretations of Mormon theology. But I think that’s because JS and successors kept trying to interpret the revelations from a CLASSICAL mind frame; they were trying to understand things they didn’t yet have the background to grasp what they were really being shown.

At least Mormons have the Book of Moses. Try rethinking those “worlds without number” that are all called “earth” from the kind of perspective your post suggests. It leads to a lot of potential answers to explore to the Mormon theology problems, which, by the way, are answers to questions with which mainstream Christianity will also have to deal.

http://thefirestillburning.wordpress.com/2009/06/03/youve-read-this-post-before/

My nonsense theory about the Final Judgment is that God can measure the decisions I made in my life against all of the possible decisions I could have made in any of my lives and somehow come up with a final number of all of the good effects I created in this life vs. all of my other possible lives. In one of the multi-verses, I stepped off of the curb into traffic and died at the age of 4; in another life, I married my high school sweetheart who was not a member of the Church and didn’t serve a mission as a result and never married in the temple; and so on, and so forth. In one of my lives, I obtained a “perfect” score, but, unfortunately, it wasn’t this one.

The more we look at the world, the stranger it gets.

A couple of examples are given in which microscopic quantum effects lead to macroscopic results.

It gets even weirder.

European Robins, and perhaps other birds, use a pigment aptly named cryptochrome to quantum-entangle and disentangle electrons, giving the “Quantum Magno-Vision”, the ability to see magnetic fields.

By examining the birds, we are able to infer that they see magnetic fields as indigo in color, and that they are unable to see magnetic fields in the dark.

Chloroplasts, in the process of photosynthesis, use a “quantum cheat” by allowing incoming photons to follow every possible path in the reaction, then somehow “choosing” the most efficient one, converting light into glucose with almost 100% efficency.

And the Photosynthesic Reaction underlies the entire existence of life on Earth.

John,

I’d like references please. This is exactly the type of stuff I’ve been seeking. Book? Articles? Web Pages?

This all sounds supiciously Penrosian to me.

Mark N: Like

FireTag: I’m glad you found my post. I asked Hawk to put up a link as a light for you. I noticed that refernece in the Book of Moses too. However, I’m not yet convinced MWI is correct. But I’m also not convinced it’s not correct.

Rude Dog: “This was very beneficial because I learned that the “detector” is never human consciousness.”

I should clarify. For an experiment with a photon, how could it ever be a human?

However, when you star at your cat, I suppose there is a sense in which it is human consciousness ‘making the observation.’ (Or at least it’s the photons of light bouncing off of the cat and going to your eyes that are making the observation, depending on how you choose to view it.)

Frank: “Oh, and do you have any links to documentation of the experiment succeeding in reality? I’m having trouble with the detector allowing the experiment to continue, since the detector would consume the particle, thus not allowing it to reflect.”

The only link I have is the one I gave. I.e. I specified “wikipedia” claims equivalent experiences have been done. As for the detector consuming the particle. If the detector is a photoplate, then you’d be correct. But this experiment is based on a hypothesized mirror detector that is so sensitive that it can detect the mere reflection of a photon. (Or this is how Penrose explains it on page 266.) I have no idea how the ‘equivalent’ experiment in real life was setup. The key point here is that quantum theory, as we currently understand it, does not require any specific sort of observation. *Any* observation of any sort will do to ruin the interference. (Penrose suggests that maybe the mirror with the detector is ‘wobbly’ and this is what ruins the interference. However, there is nothing in the formalism that suggests this has to be the case.)

Clark: “It’s amazingly useful in a surprising number of places but we have to be careful not to see it as too mysterious.”

I should probably note here that I’m not sure this isn’t mysterious, though maybe not in the way Frank was suggesting. I guess to me the ‘mystery’ is why the heck does reality happen to have so many things that imaginary numbers happen to describe so well? Isn’t this in and of itself an even greater mystery about the nature of reality.

Frank said: “The reason sqrt -1 is imaginary is that you cant square any number to get it.”

Did you mean you can’t square any number to get -1? Or did you literally mean you can’t square any number to get the square root of -1?

Mark D says: “The many worlds interpretation is hands down the most ridiculous physical theory I have ever come across. It has about as much merit as the proposition that Maxwellian anti-demons are causing entropy to increase by robbing the universe of information. In addition, the only reason to credit it at all appears to be demonstrably false. [article link]”

Mark D,

I finally read the article and I can’t for the life of me figure out how it relates to your comment on MWI. If anything it’s an article that MWI fans will be dancing in the streets over. They’ve been claiming the wave function was real and not a probability since Everett came up with MWI. They’ve even specified *in what sense its real.* This new theorem undermines Copenhagen (as the article itself says) not MWI.

I realize the article suggests non-locality as an alternative possiblity and perhaps this is what you are refering to. But it does not sound like the theorem itself suggests non-locality over MWI. That’s just the science writer adding that.

But truth be told, my post above proved that quantum physics wave function was real and not a simple probability. We’ve known that quantum physics isn’t just about simple probabilities for years and years now. If it were, the bomb example above would not work according to theory.

Just for the record, one of the main reasons Penrose wrote about the example in my post was to disprove the idea that the wave function was about probabilities and to prove that it was physically real.

I guess the next question people will ask is: if we already knew it was physically real, why is the article Mark D linked to so ground breaking.

Answer: its not.

You have to understand that many scientists do not accept that the wave function is real even though the formalism insists on it. Face it, it’s difficult to believe.

But look at the example above. Do the math for yourself. Tell me there is a way to look at a counter factual bomb detector as a wave of probabilities that isn’t physically real. In short, it doesn’t matter what most scientists think if you can understand the formalism for yourself and see that they are wrong.

(Incidently, the vast majority of physicists aren’t cosmologists. I.e. it’s not their job to care what is or isn’t real. They can afford to be positivists and ignore that it all means. But most cosmologists [like Deutsch and Penrose] all accept that the wave function is physically real although they have different idea as to what sense it is real.)

“The real truth is that it just somehow knows that the other path (the one it didn’t take) was open to it…It is influenced by that other path that it didn’t take.”

“This is the limited sense in which quantum physics says that the photon is in two places at once.”

I wouldn’t say it that way – this language sounds unnecessarily like a violation of causality. If both paths are open to the photon’s wave function, then the photon will exist as superposition of both states – both paths in this case.

You could imagine each path as a channel of water, and the electron as a water wave. When it encounters the first mirror, the wave is split into two waves, one which continues straight down channel B, and one that is bounced up channel C. When a wave is reflected (or bounced) off a rigid surface, its phase is reversed (inverted). That is, /\/\/\ turns into \/\/\/. This is true for waves in general – you can see it by wiggling a jumprope or slinky on the floor. You can think of the mysterious “i” as simply tracking this change. When the two waves reach the second half-silvered mirror, each undergoes the same split, just as you have said, and the wave components interfere with one another. What comes out at F is /\/\/\ + /\/\/\ = /\/\/\, ie something that looks like the original wave. What comes out G, on the other hand, is /\/\/\ + \/\/\/ = ——, ie a flat water surface, also known as no wave at all. The two wave components emerging at G have canceled each other out, just like (ambient airplane sound waves, ie noise) + (your active noise canceling headphones) = (no sound wave going into your ear at G). Note that this is a conceptual model – you can’t do classical simple wave reflections and get this result.

If you block the lower channel (or fail to turn on you noise activating headphones), then the \/\/\/ component shown above never makes it to G, so that wave is not cancelled out (or you still hear how to use your seat as a flotation device). Saying that the photon “somehow knows that the path it didn’t take was open to it” sounds like it had to take either one path or the other. But it didn’t, any more than the original water waver had to travel down either one channel or the other. At intermediate times, the photon is “in two places at once” in a manner similar to how the original water wave is “in both channels at once”.

It seems to me that the conceptual challenge here is not “under what conditions can we find out which path the photon took” or “if the photon takes the upper path, then what does it know about the other path”, but rather “what is a particle”. And the short and, admittedly, wholly unsatisfactory (counterfactual?) answer is “It’s not a tiny little billiard ball”.

Here is an abstract of the original paper on quantum photosynthesis:

http://www.ncbi.nlm.nih.gov/pubmed/11933253

This is the original paper on what has come to be called “avian quantum magno-vision” by Rodgers & Hore at Oxford. There has been substantial additional work on this since then.

http://www.pnas.org/content/106/2/353.full.pdf

I am no physicist, but quantum photosynthesis seems to me to be an argument against the many-worlds interpretation. Photosynthetic efficiency is high since the photons “choose” the most efficient path; are there “junk worlds” where photosynthesis is less efficient, because the photons took different paths? Why do we live in the most efficient of all possible worlds?

Bruce N, congratulations. If you had bet me $10,000 that we would get this much discussion on quantum physics I would have taken the bet and you would be $10,000 richer. That is what happens when you make $10,000 bets, you lose.

It’s been said that the reason it is so hard to comprehend is because of the language barrier in trying to explain it. As it is far more comprehensible through mathematics, quantum physics is still a strange and weird world, but not quite as strange as when we say “the electron knows which path”, or “the electron knows when it is observed”. Both statements are poorly constructed to explain, and assumed not improvable with our limited language. These concepts are hard to explain, yet so precise, predictable, and constant in experiment after experiment. It is relying on quantum strangeness and even quantum entanglement that allows us to do things like type this message on our computers to MRI machines. It may not fulfill our philosophical tastes, but quantum mechanics is used everyday under our noses, and it is powerful indeed. I don’t think it fair to bash Bohr when Bohr’s uncertainty principle has furthered the cause so brilliantly. See John Bell’s experiments, and Bell’s Theorem and thought experiments.

This brings me to another point. I think it unwise we somehow interpret quantum strangeness into our existing doctrine. Someone mentioned the Book of Moses, and truth be told, the only sure thing quantum mechanics has given us is the surety that the Sun definitely does not get its light from Kolob. Spiritualists, Prophets, Imams, and Shamans have been trying to hitch their stars to this powerful theory. It doesn’t work as they claim, and Physicists are frustrated by attempts to shoe horn it into personal philosophies. I think it unwise we try to do the same. The attempts in the Pearl of Great Price to explain the cosmos are exactly what we’d expect from 19th century understandings, and should be seen at best, as speculative writings.

John:

“are there “junk worlds” where photosynthesis is less efficient, because the photons took different paths?”

Yeah. In worlds in which photosynthesis is less efficient, the birds die out, just as in the worlds where birds where cells don’t evolve very efficient means to avoid getting cancers from stray cosmic rays.

MW is not counter to evolution, but works with it.

Rude Dog,

The comment on the Book of Moses came from a CoC member (i.e. not LDS.) Given the CoC’s approach to theology, there is really nothing inconsisent for him in the same way it is for us LDS.

John,

I’ll take a look.

When I said this sounds “Penrosian” I would point out that Penrose is against MWI. So you might well be right here. More research needed.

Aaron,

I basically agree with everything you said except your conclusion. To be speicific I can’t agree with “the photon is “in two places at once” in a manner similar to how the original water wave is “in both channels at once”.”

The example I gave above proves there is no real ‘similarity’ between the wave function taking both channels at once (true) and the *photon* taking both channels at once (false).

For that analogy to be apt — even if photons aren’t little billard balls — then the bomb would explode when the photon takes both paths and hits the detector. But this is precisely what *doesn’t* happen.

In short, the math insists that there is some sort of difference between the wave function and the photon itself. It’s just not clear what that difference is under the current theory.

I will, however, agree with you that my wording is somewhat inaccurate. But so is yours. I sort of doubt that there is a way to accurately word this right now other than through MWI style explanations. (Note: this doesn’t mean I accept MWI, it just means I accept that MWI does in some legtimate sense ‘explain’ more than alternative explanations given your current state of knowledge.)

(For those that don’t know what MWI is: it’s Many-world interpretations. In MWI the wave function is a description of the photon across the so-called ‘many worlds’ so there is somewhat of a distintion between the wave function and the photon. Though it’s more complicated then I’m making it sound.)

FireTag,

I think John’s question can be rephrased to be stronger. Or at least this rephrasing is what is on my mind personally:

Why is it that we only see nearly 100% proficient photosynthesis? Why wouldn’t our world get a mix as would all worlds? What makes our world special in that it gets the 100% ones?

Geoff, you mean you don’t remember that we *did* make that bet?

Wait, isn’t that some of the strangeness, that indeed photons are “little billiard balls” or little packages of quanta that behave as both wave and quanta?

Also, how does MWI and entangled states relate, or do they?

Bruce (21). I suppose I can agree imaginary numbers are mysterious in that way. Although by that line of reasoning all math is mysterious and imaginary numbers no more so that addition. It’s the old question of why reality is so mathematical. As for why imaginary numbers

in particularare useful it goes to the isomorphism between imaginary numbers and position on a circle. So the group (in the technical sense) that imaginary math fits in with is useful for anything that fits that group: i.e. wave mechanics. That doesn’t explain why arithmetic, algebra and calculus are so useful though. (Well perhaps arithmetic makes more sense if reality is can be modeled as made up of individual things)Bruce (23), I’m not so sure this does invalidate the cophenhagen interpretation which as I read it is just an empiricist approach focused on epistemology rather than questions of realism. That interpretation arose back when neo-Kantianism was dominate in science and after the big battles between the realists and idealists in philosophy. (Which actually continued in US colleges up through WWII)

Now ignoring the fact that how many physicists take the copenhagen interpretation might not line up with what Bohr and company meant, I do think that everything hinges upon an equivocation over “real” when we talk about whether the wave function is real. Empiricists who don’t worry about “reality” in an ontological sense have no trouble saying there are real tables, chairs, and wave functions. They just don’t mean by real something mind-independent. Thus the wave function is just as real as anything else they worry about.

The real debate is not over reality but whether the wave function is a useful fiction as are notions like its collapse. But that is, at least in my mind, a bit independent of the copenhagen interpretation. Rather it’s a question of whether the wave function just describes probabilities where we measure something. Maybe I’m misinterpreting all this. (Always a possibility – it’s been years since I last studied philosophy of quantum mechanics) It really does seem like a lot of the discussion hinges upon various equivocations over “real.” It seems at best an attack on certain realist interpretations of statistical mechanics in quantum mechanics which is something quite different from copenhagen (and honestly never a very well thought out position at the best of times)

It is true it might affect the debate over whether Von Neuman screwed everything up by making us think in terms of a

collapse of the wave function. I don’t know enough on its implications to speak to that. (After all one can talk about a wave function independent of a collapse)Bruce:

As you phrase the question, it looks like I will have to look into the paper more closely, despite my allergy to the biological sciences.

“To be speicific I can’t agree with “the photon is “in two places at once” in a manner similar to how the original water wave is “in both channels at once”.”

The example I gave above proves there is no real ‘similarity’ between the wave function taking both channels at once (true) and the *photon* taking both channels at once (false).

For that analogy to be apt — even if photons aren’t little billard balls — then the bomb would explode when the photon takes both paths and hits the detector.

In short, the math insists that there is some sort of difference between the wave function and the photon itself. It’s just not clear what that difference is under the current theory.”

Actually, I don’t think there is any sense in which the wave function *is* is the photon. The wave function is a mathematical description of the probability of localizing the photon as a function of space and time. To say that the wave function is nonzero at (for example) both fully reflecting mirrors is not to say that the little light particle has flown down path #1 and the same little light particle has also flown down path #2. Rather it is the wave function that has propagated like a water wave down both channels simultaneously. That doesn’t mean that the bomb has to explode, because its not triggered by a wave function. It’s triggered by a small transfer of momentum and/or energy, and probability functions aren’t known to push on things very hard. You can ask whether or not the wave function is then “real”, but I don’t know what that question means. Does it mean that it is made out of smaller subentities? Or that it contains energy independent of the photon? To me, it sounds like asking “Is energy real?” We use conservation and exchange of energy to mathematically describe all sorts of processes, and with astounding precision, but is it a real thing? In a sense, the only way we interact with and experience the universe is through mathematics (typically unintentionally), and the fundamental mathematical description of a quantum particle (for now at least) is a nonlocalized probability function. So lacking a better or more fundamental model, I can only treat the photon itself as often similarly nonlocalized. Not “in two places at once” but “everywhere”.

Regarding your wording, I don’t have any problem with phrases like “the photon knows…” (I’ve often used the same language), only the mental picture of one little photon traveling along as two little photons. And you are right that my conceptual example is, well, just that (just count the number of phase inversions down each leg and watch it fall apart at the end).

Finally, I certainly hope my argument doesn’t require something like a MWI. Those seem to me like a departure from physics to philosophy, since I’ve never understood how even in principle they could be tested.

By the way, what I should have started with is “Thanks for a great post!” There should be way more of this in public in general.

Bruce and John:

Based on a review in New Scientist back in November, I ordered a book by Terrence Deacon called “Incomplete Nature: How Mind Emerged from Matter” which seems, now that I’ve got it in front of me, to provide an underpinning for the kind of bird/photosynthesis phenomena John’s point addresses:

From the cover jacket blurb, with my comment added:

“…although mental processes do indeed lack…material-energetic properties, they are still entirely products of physical processes and have an unprecedented kind of causal [self-evolving?] power that is unlike anything that physics and chemistry alone have so far explained. Paradoxically, it is the intrinsic incompleteness of these semiotic and teleological phenomena that is the source of their unique form of physical influence in the world… Specific absences (or constraints) play the critical causal role in the organization of physical processes that generate these properties.”

Deacon is the Chairman of the Anthropology Department at UC-Berkley as well as a Professor of Neuroscience there.

I’ll tell you what I think after I wade through it (its about 550 pages before the footnotes, so it won’t be tomorrow. :D)

Bruce – “Did you mean you can’t square any number to get -1? Or did you literally mean you can’t square any number to get the square root of -1?”

The first, with the caveat that you can’t square any

realnumber to get -1. Squaring i to prove the existance of i is circular.My bad for not putting enough words in for clarity.

Bruce N, A couple of comments. First, MWI is not a scientific theory, in the sense that it no empirical evidence can ever be brought to bear in favor of its primary contention.

Reality of the wavefunction, of course, does not invalidate MWI. A non-statistical wave function, however, completely invalidates the only argument supplied in favor of MWI, and that is the primary result described in the article I referred to.

Mark D.:

Not at all. The article itself points out that the theorem depends on a critical assumption that it is always possible to prepare totally uncorrelated states by multiple methods and then bring them together in a measurement, and that there are interpretations (other than MWI) in which that assumption is just wrong. The paper itself notes that this assumption is NOT true for entangled states, where a measurement on particle X can guarantee what a similar measurement on particle Y will show.

For an example of one of these alternative approaches, a couple of months ago, New Scientist reported on a new idea of “spontaneous localized wave function collapse” which says that ANY two particles anywhere in the universe have some non-zero probability of interacting so that their wave functions entangle. Macro-measurements then are simply the macro-representation of the same phenomenon, with the probabilities magnified by orders of magnitudes because of the macroscopic number of particles “rolling the dice”. They even propose experimental tests of the idea. And a universe in which there is a minimum probability of entanglement is no more weird than a universe in which there is a minimum constant (Planck’s constant) that describes the non-commutative nature of making measurements in opposing orders (i.e., AB – BA is NOT equal to zero.)

Wave functions are real, but they naturally live in Hilbert space, not conventional space-time, and there is no a priori reason to think space-time is more fundamental to quantum behavior than the Hilbert space. The motivation for MWI was that, in general, the wave function can have an infinite number of pure state solutions, and wave function collapse was a patch to rationalize the observation that an observer saw only one solution in general at random.

It’s all about where you wish to assign the weirdness.

Frank says:

“The first, with the caveat that you can’t square any real number to get -1. Squaring i to prove the existance of i is circular”

Yes, but it’s also true that you can’t squre any real number to get 1 except 1 and that therefore squaring 1 to prove the existence of 1 is circular. Instead, think of i as an number that is added to the number line by adding a new dimension to it.

Mark D:

I don’t really understand what you are saying. In what sense does “non-statistical wave function, however, completely invalidates the only argument supplied in favor of MWI.” I confess I’ve never in my life heard anyone cite ‘statistical wave function’ as a basis for belief in MWI. I can’t even guess how they’d be related.

FireTag,

I’ll be buying that book too, I think. But you will be required to do a guest post when you finally read it and have an answer to my question.

Aaron,

I think we are basically agreeing.

Clark says:

“I suppose I can agree imaginary numbers are mysterious in that way. Although by that line of reasoning all math is mysterious and imaginary numbers no more so that addition”

Agreed!

Rude Dog (on billiard balls):

Actually, think uncertainty principle here. I’d actually say that photons are nothing like billiard balls.

“Also, how does MWI and entangled states relate, or do they?”

This is one I’m still trying to figure out.

FireTag, help please!!

Here is the question: how does one square quantum entanglement in it’s most extreme forms — specifically quantum teleportation — with MWI? I can’t seem to figure this out and David Deutsch never explains it.

The primary motivation for MWI is the criticism that quantum mechanics is intrinsically stochastic, which is a violation of causality, and the principle of sufficient reason.

So the claim is that no, QM is not stochastic at all, any observer is only on one branch of many. Since all possibilities are materialized, there is no causality problem.

If on the other hand, the QM wave function is not irreducibly stochastic, there is no reason for multiple worlds at all. Multiplying entities on a flimsy justification is bad enough, multiplying them with no justification is flat out pathetic.

A quick answer ’cause it’s late:

MWI says that the act of measurement entangles the wave function of the “observer” (which can be your rock or particle detector as well as a human being) with the wave function of what’s being measured. “Entanglement” is the name for the phenomena that shows the “spooky action at a distance” in quantum mechanics. If I know the state of an element of an entangled group, I also know with certainty the state of the other elements. I can never make a measurement of the other element that will show any other state until I disrupt the entanglement, even if there is no time for any information to pass between them.

So wave function entanglement replaces wave function collapse as the explanation of why we only observe a single state. The wave function is ALWAYS real and always evolves in a predictable, non-random way. Every solution to the wave equation before the measurement stays a solution after the measurement — but now they are coupled (entangled) to solutions of the wave functions of the “observers”.

And I’ll consider the guest post an opportunity when the book is read.

I guess Mark D. was writing at the same time I was, so I missed his last comment.

“The primary motivation for MWI is the criticism that quantum mechanics is intrinsically stochastic, which is a violation of causality, and the principle of sufficient reason.”

That may be the PHILOSOPHICAL motivation for MWI, but physicists’ motivations appeal more to the gut feeling of mathematical elegance. We only play philosophers on TV or in blogs. The elegance of many worlds was always that the wave function is ALWAYS real, it requires NO new entities, since the phenomena of entanglement and multiple solutions to the wave function are ALREADY there inherent in the math, and you don’t need a NEW, separate explanation (wave function collapse) to get rid of solutions.

Physicists have been making progress for more than a century by assuming solutions that pop out of the math are real and then finding evidence of them. We don’t need them to explain what we’ve seen, they just pop out for free and explain phenomenon we haven’t noticed yet.

Our rule of thumb is more “that which is not forbidden is required.” It’s how we found most of the sub-atomic particles in the standard model, the latest being the evidence this week that the last particle in the standard model, the Higgs boson, is making its appearance in the Large Hadron Collider experiments.

So Mark’s paper threatens the Copenhagen interpretation much more than it does MWI.

I should also add that every universe predicted in MWI is also identical to a universe elsewhere in space time that would occur under the standard model of COSMOLOGY, as well as the standard model of particle physics I mentioned above. Again, no NEW entities required.

FireTag, one problem for MWI is exactly why there are multiple universe of the type it posits. Where do they come from and why? They brush under the rug the conservation of energy arguments by arguing they just apply to a single universe and not the multiverse. They brush the Ockham’s razor complaint away by arguing they don’t create more

classesof entities (which was Ockham’s worry) but neglect that creating whole universes certainly gets at the issue of simplicity which is what most actually mean by an appeal to the razor.I think though that the proponents like the simplicity that arises out of taking mathematical entities as physical entities (or physical classes) but don’t feel inclined to deal with the ontological issues. I don’t think they realize that all they’ve done is create a more restrained modal realism from David Lewis. (Lewis’ realism is splitting universes based upon logic whereas QM puts much more limits on possibility – but beyond that it’s pretty similar)

The strongest argument (IMO) against modal realism as well as MWI is that the most fruitful avenue of discovery and knowledge has been the recognition that reality is

much more restrained than possibility suggests. Modal realist theories end up throwing out this most fruitfully productive approach to reality. (I’d add that to a certain extent this is a problem of string theory as well and constitutes the base of a lot of its critisms: it explains too much)Clark:

“Where do they come from and why?”

“…the most fruitful avenue of discovery and knowledge has been the recognition that reality is much more restrained than possibility suggests.”

These two statements get at the difference between how physicists and philosophers view reality.

The natural question for a physicist to ask would be “Why would these solutions (universes) go away?”

Similarly, to a physicist, the most fruitful avenue of knowledge and discovery has been the recognition that reality is AS UNRESTRAINED as possibility suggests.

The energy for the other universes came from the same place the energy from this universe came from. The other solutions were ALWAYS there occupying the same physical space and time our solution does. The energy embedded in them was ALWAYS there, but our measuring instruments for energy couldn’t interact with them anymore than any other of our measuring instruments can, so we missed the energy.

So let me reverse the question: during wave function collapse, where does the energy GO? For example, the hydrogen atom wave function has an infinite number of pure solutions, each of which has an associated energy and angular momentum. Under Copenhagen, they exist in a superposition until collapse, so their energy exists until collapse (or alternatively the state and the energy were “unreal”). What happened to their energy?

It’s the same degree of violation of our classical views of energy conservation under either Copenhagen or MWI. Nature doesn’t work according to our classical biases.

Firetag – “The energy for the other universes came from the same place the energy from this universe came from. The other solutions were ALWAYS there occupying the same physical space and time our solution does. The energy embedded in them was ALWAYS there, but our measuring instruments for energy couldn’t interact with them anymore than any other of our measuring instruments can, so we missed the energy.”

So does this mean its still possible for the Sun to be getting its energy from Kolob, just that we don’t yet have the tools for measuring said energy?

Firetag – I consider myself more of a physicist than a philosophy although of late I’ve read more philosophy than physics. However I don’t think I agree with you. Rather I think this is a divide within the physics community that in some ways maps onto the pro-string and anti-string divide. Both perceptions really map on to ways people think through physics. Philosophers typically think quite differently.

Regarding the collapse, I confess I’m one of those skeptical about the collapse and who thinks Von Neumann screwed things up a bit by casting QM in that form. In any case I can’t figure out what the collapse is and am sympathetic to the view there is no collapse. I think the wave function represents something real however I’m not sure it represents something actual. The mindset of MWI is to make that distinction non-existent. (In philosophy-speak it is the claim that MWI is based upon a nominalism drive)

Frank:

Kolob isn’t part of my canon, so I’ll leave speculation on that to LDS.

Clark: Fair points. I will simply note that physicists have made progress by making the leap from mathematical to real to actual since Maxwell’s equations told us to look for non-visible light and we found radio waves. I don’t think people should “shut up and calculate”, but I do think they should not STOP calculating until the philosophy is worked out.

Firetag – hmm. Perhaps then the existence of spirit matter? The idea that we are more than the sum of our known parts.

Clark and FireTag,

I have a personal bias against MWI. But I also have no doubt that MWI explains aspects of quantum physics that can’t currently be explained by the more common interpretations. There is an undeniable power in this ‘additional explanatory power.’

When I read Penrose, one of the main reasons why I did was because I heard he was anti-MWI. But his ‘explanation’ against MWI was basically rejectionist. He said it didn’t answer anything and had more to explain (of course) and that he doesn’t really believe the current quantum physics is anything but a stop gap theory anyhow. I was sort of disappointed.

I can’t think of anything MWI explains better than the competing models. I believe all of them explain all the science. At best the only way to distinguish them is via ones biases or extremely weak arguments. Although I don’t have a problem with that. The advantage of thinking through the metaphysics is to continue inquiry since eventually it may move from metaphysics to physics. It also shows us our hidden assumptions (or hidden incoherencies in our thought)

Firetag – physics definitely has made progress by questioning whether elements of the math were physical. However you’ll note that the way it does this is through experimentation. My post (linked above) goes through a bit of this. I’m sympathetic to Quine’s approach here although often a physical theory don’t tell us what does or doesn’t exist. (i.e. virtual particles) So it’s a bit more complex. I’ve long thought that metaphysics has a significant place in physics despite what many physicists think. Einstein was arguably doing metaphysics initially. And I’d argue string theory is nothing but metaphysics.

Frank:

I don’t believe in spirit “matter”, but my interest in parallel universes (and MWI is only ONE way to generate parallel universes; they pop out of MOST of the major theories of cosmology) and action at a distance is because I think they provide an unexplored route to relate spirit to consciousness to matter.

The analogy I use is that spirit is to person as mind is to neuron. It takes the interaction of a lot of copies of neurons to house something as complex as a human mind, and I suspect it takes the interaction of a lot of copies of a human mind to house something as complex as a human spirit.

That’s a long research program, I know, but I find it the most promising avenue currently available to reconcile the testimony of the spiritual naturally to the scientific understandings of consciousness and matter.

Clark:

Obviously, from the above, I do believe theology/metaphysics/philosophy have something to offer each other, but I just have the talents to approach the problem from a preferred side.

Firetag, no one in his right mind believes in the Copenhagen interpretation either. Wavefunction collapses are a wart on the face of QM. Science fiction fodder, mostly.

Fortunately, they are entirely unnecessary, and this has been known for more than fifty years. The Bohmian formulation of QM is strictly deterministic, and has no wave function collapses.

That electron you speak of will remain in a superposition of states indefinitely until it loses or gains energy through some external interaction.

In addition, you are neglecting the main problem with MWI. In the general sense it is completely unfalsifiable. Scientifically speaking, it is useless. No experiment can be done to give any evidence in favor or against.

Mark D.:

Multiple interpretations have persisted because no one has figured out ways to falsify ANY of them, because they MAKE THE SAME EXPERIMENTAL PREDICTIONS. They, in other words, are discussions of meanings of mutually accepted data.

Bohmians aren’t necessarily wrong; they’re just heavily outnumbered.

Mark, technically the collapse was a theory of Von Neumann. I don’t think it’s technically part of the Copenhagen interpretation proper.

Thanks Bruce, really the best ‘readable’ explanation I’ve read about the point.

Doc

Clark, every source I am aware of considers wavefunction collapse to be one of the essential elements of the Copenhagen interpretation. Himmel, Quantum Physics and Observed Reality (1992) states that it is one of the Copenhagen interpretation’s five core rules, for example.

Firetag, Bohmian QM does have empirically different properties than other formulations. For example, in Bohmian QM there is no fundamental obstacle to transferring information faster than the speed of light (instantaneously actually).

In addition, the recent work I referred to above (if it holds up) invalidates the Copenhagen interpretation completely. That is the best news in physics in decades, in my opinion.

Mark, it depends upon what one means by the Copenhagen Interpretation. Some people use it fairly loosely. If one is going by what Bohr meant then there isn’t a collapse the way most talk about a collapse. Rather there’s simply a measurement and we have one result. However that’s not a collapse because Bohr’s anti-realist interpretation doesn’t make any claims about the reality of the wave function itself.

There are some variations that are sometimes cast under the rubric Copenhagen. Indeed Von Neumann’s own view which emphasizes the role of consciousness is sometimes called the Copenhagen Interpretation. I too have noticed that a lot of books aren’t careful in this regard although often you’ll find them making caveats in the small print. There are even ontological takes on the Copenhagen Interpretation (which is what sounds like what you mean by Copenhagen Interpretation) But these are quite different from Bohr’s more neo-Kantian views.

The “collapse” in the formal version of Copenhagen is just the removal of eigenvalues. If that’s what you mean by collapse I agree it’s part of Copenhagen but that’s certainly not what I mean by collapse in the above. Collapse in a philosophically relevant meaning seems to require more than just a change of equation but a claim about

howthe equations change. If the change is merely epistemological then I don’t think one is really making any claim beyond a change has happened.So I guess it really comes down to whether by Copenhagen you mean Bohr’s views or whether you mean something more akin to Heisenberg’s in the 1950′s. (Which was when I think the term became more popular) Most people I’ve spoken with tend to use the term to refer more to Bohr and the early views. However to be fair, as I said other people use it in a much more expansive way.

Read the post — and the comments!

Awesome.

I hope in some other world that I can understand this stuff better than I do here. ;>)

I’d like to hear some one talk about one’s continuity of memory and identity as zillions of worlds endlessly splinter off throughout the whole of one’s life.

Just to add to the above, here’s a relevant quote from the SEP on the Copenhagen Interpretation. Interestingly it has quite a different definition from the Wiki entry.

Jack:

The question of memory and identity — independent of any interpretation of QM — is a whole ‘nother question, indeed. It’s tied indelibly to the question of why are we conscious at all.

QM just makes the problem a bit more puzzling, when you realize that “measurements” and hence, collapse, splitting, and/or entanglement happen on Planck timescales, i.e., quadrillions of quadrillions of trillions of times per second in every one of our brains. Your states of consciousness is changing far faster than you can know you’re conscious.

Well I’d be careful with that. Exactly what the relationship of a state of consciousness is with a state of matter isn’t clear.

Getting in late to the game but I enjoyed your post and would like to see more of them. I have a good math background, but physics isn’t my field, so I enjoyed learning something new.

Imaginary numbers are just another axis. The use of the term “imaginary” to describe them was a misstep in many ways — though it kept the Soviets from being able to manufacture color televisions as the communist hierarchy insisted that imaginary numbers were a corrupt concept (color televisions, having three colors to make them work, need a three axis system, which requires positive, negative and imaginary numbers to calculate).

Sometimes I’m sad I moved away from physics in college, though I have to enjoy essays like this.

Nice job, Bruce. I read through it and could not quite follow the math, but I’m going to try again when I have more time to give it my full attention. The part I grasped was extremely interesting, though I’m not generally the math/science type.

This is so fascinating! I have been wanting to look into physics to see if I should take it at school next year. However, the teacher who teaches that class is not very good at explaining or class control, but maybe I’ll look into taking a course during the summer at my local college. Thanks so much for writing this post