Sunday, June 11, 2017

The simple fact

If you could -- just for a millisecond -- notice the simple fact of consciousness (or rather, if consciousness were to notice itself -- because what, other than consciousness, notices?) without your mind subtly spewing out answers (and questions) about what it is (just an illusion!), where it comes from (just neurotransmitters!), whether or not it's anything special or remarkable (not particularly!), etc., you would be brought to your knees in a profound humility, reverence, awe, and gratitude that you could never have imagined possible.

Before wondering "why am I here?" or "what is the meaning of life?," perhaps spend more time looking (nonconceptually) into exactly what you mean by "I am here" or "I am alive." I guarantee you will be surprised and delighted -- and with enough luck (or really, enough sincerity, precision, simplicity, and directness), it will unequivocally resolve (if not exactly "answer") your first question.

So close you cannot see it
So deep you cannot fathom it
So simple you cannot believe it
So good you cannot accept it
-- Kalu Rinpoche

Wednesday, May 10, 2017

ACIM and Buddhism

It is remarkable how similar A Course In Miracles (or at least, this interpretation) is to the Mingyur Rinpoche quote:

The Course's assertion is that everything stems from the mind. The mind's thinking provides the basis for everything that it experiences. Whichever way the mind chooses to look at reality, it will find itself surrounded by and experiencing a "reality" that is the precise mirror of that. The mind's fundamental belief-system first manifests as inner feelings, emotions, interpretations and perceptions; and then manifests as the "outer" reality in which the mind seems to live.

Our healing, then, must be a healing of the mind, a healing of our fundamental perspective on reality. This is what the miracle does. It comes in a moment, a holy instant, when we decide to temporarily suspend our habitual perspective on things. As we momentarily loosen our grip on the ego, our minds are allowed to shift into a new way of seeing things. And since our thinking is the foundation for our entire experience, as our thinking shifts, so does everything else. Our whole experience of life is allowed to brighten from the bottom up, making this kind of healing more deeply liberating than being healed of even the most insidious and destructive physical disease.

Thursday, April 20, 2017

What do you really have?

What does it mean to be happy?

It means that for just a moment, you are not longing for something else. You are not craving or searching or yearning for things to be different in any way. What you have is truly enough.

That's it. That's a simple but complete description of the condition we spend lifetimes struggling and fighting and killing for. Of the one and only thing everybody fundamentally wants.

This may surprise you. It couldn't be that simple, could it? After all, most of the time you're not longing for something else, and yet you're not perfectly happy, right?

You may not have noticed that for the vast majority of your life, your mind is indeed preoccupied with scheming up ways for things to be different. It can take some practice to detect.

Or perhaps you are aware of this, but consider it perfectly reasonable. If you didn't seek ways for things to be different, you wouldn't accomplish very much, right? It's lazy to be content with what you have.

But have you noticed what you really have?

Suppose you say "I have a sports car!"

Concretely speaking, what you have then is not a sports car, but the thought "I have a sports car!"

Suppose you go to your garage and point at it, to prove it to me. Now what you have is a visual field that looks something like this:
(Yeah, right, you only wish you had a Lambo)

You can get it in and vroooom off into the distance, and you may have super-sweet vroooom sounds and wind in your hair, but you'll never have a Lamborghini.

What you will only, always, and ever have is this one moment and whatever it contains. Just one frame. You can save all you like, but you'll never have more.

Wouldn't it be a damn shame if you didn't want the one and only thing you had?

Wouldn't it be an incredible tragedy to discover at the end of your life that all you ever really had to do was appreciate the one thing you had?

Wouldn't it be unfortunate if the reason you failed to appreciate it was fear? Fear that if you enjoyed what you had, that you would turn into a lump of complacency?

Wouldn't it be amazing if the opposite turned out to be the case? That when you started enjoying what you had -- not what you thought you had, but what you actually had -- that things got better, not worse?

Wouldn't it be funny if teachers have come before to tell us of this, and we are just refusing to listen?

“Accept — then act. Whatever the present moment contains, accept it as if you had chosen it. Always work with it, not against it.This will miraculously transform your whole life.” -- Eckhart Tolle

Tuesday, April 11, 2017

Abstractions, gratitude, and god

Consider how life goes.

You are presented with a bewildering array of colors, sounds, and textures. From their behavior, you infer the existence of abstractions called matter, time, space, etc. to explain them. Next, you take these abstractions to be the (only) "real things," and the experiences from which you inferred them to be secondary. The things you have merely inferred become certainties, and the things you can actually be certain of (experiences) become curiosities at best.

It's a marvelous sleight of hand that is remarkably hard to detect, but the payoff is worth it. It is possible (indeed overwhelmingly common) to spend a whole lifetime missing out on connecting with the Sure Thing in favor of abstractions.

One remarkable place we do this is in expressing gratitude. We suspect there's something profoundly amazing about just being alive. To objectify this sense, we have to make use of abstractions. What is life? A combination of amino acids. How did they come about? From fusion and other processes. So we become grateful for amino acids, fusion, evolution, etc. Those are all fascinating things to be grateful for, but again there's a sleight of hand: the realization that sparked the gratitude was the sense of being alive, not any of the abstractions that we suspect caused that miracle.

It is actually possible (and incredibly worthwhile) to allow the gratitude to remain precisely on the alive-ness itself, and not on any of the abstractions (such as our calculation of the remarkably low odds that we should be alive). I hesitate to proffer my own take, but here goes: if you manage to be genuinely grateful for the Real Thing for even a moment, you may catch a glimpse of what sages across time have been calling Enlightenment or God. (Yes, those too are abstractions, so don't chase them either.)

How do you get to the Real Thing?

One possibility is to deepen your felt sense of gratitude, but don't be grateful for anything in particular, or because of any particular reason. Don't let your gratitude "land" anywhere. Be grateful for "what is," without in any way identifying what it is or why it is.

Another technique commonly offered is meditation. It certainly can work, but there's a common trap you can fall into: abandoning some of the abstractions, but solidifying deeper ones. For example, it's easy to sit and meditate with a clear mind, while maintaining (and even deepening) the sense that you are an individual meditating within a real world. You will know you are making progress when your gut-felt certainty about your abstractions called time, space, self, objective reality, etc. begin to loosen. What arises in their stead? I will leave that for you to discover.

Friday, March 24, 2017

Does QM imply that reality is a simulation?

From a response to someone who asked me whether QM proves that we're in a simulation:

It's logically impossible to prove that you're not living in a simulation (since the evidence against it could all be fabricated), but that's not exactly what QM is showing. Instead, it is starting to show is that there is may be no way things "actually are." For example, a particle may not even have a well-defined spin before being measured. Not only that, but other features of what we normally call "reality" are getting harder and harder to support with each successively more clever experiment. In other words, it's getting harder to support the idea of objective reality.

But even if objective qualities do not really exist, it does not necessarily mean that they are simulated, either. It might mean, for example, that they're not objective at all. Perhaps they are entirely subjective. This would fit nicely with the von Neumann - Wigner interpretation, which roughly says that "consciousness causes collapse" (i.e., that it causes one of many possible realities to become real reality). There are many reasons physicists don't like that interpretation, but even your average Joe might not like it, because it seems to indicate that you are creating reality. That would be ludicrous (and scary).

But there's a neat way out of this. Experientially speaking, what is this consciousness? It's the thing that's aware of the world, as opposed to being a part of the world. But similarly, it is aware of your body, and so cannot be your body. It is not your thoughts, memory, or personality. In brief, it cannot be "you" in the normal sense. And yet, it is "what is looking." Which takes us into the mystical traditions, which are more or less saying that you are, indeed that which creates.

Of course, they also say that the safest and best way to discover this is by practicing meditation (and related things) with discipline. That way, instead of merely believing any of those stories, your mind settles to the point where you can investigate them for yourself. What is this thing that wants to know whether this is a simulation? Find the answer to that question, and don't do it by filling your mind with more thoughts.....

Thursday, March 23, 2017

QM for dummies

Sometimes I think my "QM for dummies" requires too much understanding of tensor products on Hilbert spaces.

In light of that, here's a non-mathy intro taken from my journal. More to come later. Some background: Einstein, Podolsky, and Rosen published a paper claiming that QM is incomplete, because otherwise it is absurd in a particular way. The experiment involves two particles, originally conjoined, and sent off in opposite directions. Each particle gets measured along one particular axis (x, y, or z), and each result can either be +1/2 or -1/2. ...

I think I explained the EPR experiment poorly the day before. Something about how you end up with measurements that cannot be explained classically. Because in the classical case, it is only possible to see certain distributions of outcomes, and they're violated in the actual experiment. And if I showed you the math, you'd understand….

But there's a much more simple way to explain it: the outcome of a measurement here can depend on the choice of what to measure there, even though light itself could not travel fast enough to tell the particle here "how to behave" (i.e., how it should be measured). To show this, you'd need to (a) demonstrate that the outcome of measurement here and the choice of measurement there are correlated, and (b) do it using an experiment where the two measurements happen almost simultaneously. You might be thinking: can't the correlation be explained by them having shared some information when they started out (together)? This is called a "hidden variable" (i.e., some influence that we just haven't discovered). The only other alternative is what they dubbed "spooky action at a distance." That was clearly wrong, so there must be hidden variables, they said.

What JS Bell showed was that even hidden variables have their limits: they could not produce the outcome that QM would predict, for his particular experiment. If it's not hidden variables, then it must be spooky action, right? Actually, no. The preferred interpretation is that there is no action. It's just that the joint state of the system is described by a mathematical entity that doesn't have well-defined values on both sub-systems (the spin of the particles). In other words, it's simply meaningless to say that a particle even has a well-defined spin (either plus or minus ½) in a given direction, assuming it was last measured along some other direction (called a "non-commuting" direction). This is the famous Heisenberg Uncertainty Principle. It also is the wave-particle duality: if you know where the light "is," it cannot behave like a wave. And when it acts like a wave, you cannot know where it is -- because it is not in any particular place. It's not just that we don't know where it is.

It's like the EPR pair above: the second particle does not have a well-defined spin in the chosen direction. If it did, its result wouldn't depend on the choice of measurement of the first particle. If it has a well-defined spin now, it can only be because the other one "gave" it one now, after having been measured.

So the natural question is: what constitutes a measurement? Because whatever it is "prevents" particles from acting like waves. And this is where the story really starts to get fun….

Saturday, March 18, 2017

The two-slit experiment: putting together the pieces

Apologies if this is not the clearest post ever. It's just that I finally put together a few loose ends that were bothering me about the two-slit experiment, and I want to record them.

First, some "basic" QM, from Richard Feynman:

1. The probability of an event is given by the square of the absolute value of a complex number φ which is called the probability amplitude:

P = Probability
φ = probability amplitude
P = |φ|2

2. When an event can occur in several alternative ways, the probability amplitude for the event is the sum of the probability amplitudes for each way considered separately. There is interference:

φ = φ1 + φ2
P = |φ1 + φ2|2

3. If an experiment is performed which is capable of determining whether one or another alternative is actually taken, the probability of the event is the sum of the probabilities of each alternative. The interference is lost:

P = P1 + P2

A simple example will help here.

Consider vectors in C2
Consider a basis {x, y} and alternate basis {a, b} where:
a = 1/√2(x + iy)
b = 1/√2(x - iy)

Now we want to know: what is the probability of a particle in state |a> being measured in state |b>?

Classical method

If we assume the particle must have gone either through |x> or through |y> on its way to |b>, we sum P(a ⇒ x ⇒ b) + P(a ⇒ y ⇒ b) like bullet 3 above.

= P(a ⇒ x & x ⇒ b) + P(a ⇒ y & y ⇒ b)
= P(a⇒x)P(x⇒b) + P(a⇒y)P(y⇒b)
= 0.5*0.5 + 0.5*0.5
= 0.5

This is just classical probability theory. It turns out that if we do try to detect which way the particle went (i.e., measure it in the x-y basis, followed by the a-b basis), we find it ends up in |b> half the time.

But QM predicts that |a> should never be measured as |b>, because they're orthogonal. What went wrong is that we cannot assume that it went through either |x> or |y>. 

Quantum method

Instead, we should simply take the inner product of |a> and |b>, i.e. <a|b>. We know it's zero (they're orthogonal), but we can calculate this explicitly in the x-y basis:

|a> =  1/√2(1, i)

|b> =  1/√2(1, -i)
<a|b> = 1/√2 (1 * 1 + -i * -i ) = 1/√2 (1 - 1) = 0

The terms in the above sum are the terms in Feynman's (2). We could have also written this as

= <a|x><x|b> + <a|y><y|b>
= (1/√2)(1/√2) + (-i/√2)(-i/√2)
= ½ + -½

= 0

(Because <x|a> is just the x-component of |a>, and <a|x> is its conjugate). Sometimes you see this written:

Where i takes on the basis vectors under consideration (in this case, x and y), and:
ψ*i = <ψ|i>
φi = <i|φ>

If you compare the two calculations (for the classical, or "which-way" case, vs the quantum case), you'll notice that they differ by some terms that we can call "interference terms." There's nothing really interfering here, unless we force ourselves to think of |a> and |b> in terms of the x-y basis, in which case we can understand this as the |x> and |y> components interfering.

Elsewhere I've demonstrated why entangling a state |x> + |y> (so that it results in |x>|0> + |y>|1>), results in a similar loss of interference (and I give a quick rehash at the bottom).

Anyway, that was all a prelude to the main course: what's happening in the two-slit experiment?

Mapping back onto the two-slit experiment

The solution to the Schrodinger equation for a plane wave is 

Ignoring the time component, we see that it's basically a complex number whose phase is proportional to r, which is the distance from the source. In our case we're actually close to the source, and the light's strength will be proportional to the inverse of the distance squared.

(One super confusing thing is that in some contexts, the whole Ae^(i*t) is called the "complex amplitude," but in other contexts, we call just A the amplitude. Let's not do the second. Another super confusing thing is that often when referring to the "phase" of a photon, we're talking about the relative phase of the polarization components.)

For any given point on the screen, we will have one such complex amplitude for each slit. Per Feynman's (2), we can just sum these to get the overall amplitude that will give us the probability of finding a photon at that point.

It's hard to get an intuition for what this sum looks like without pictures, but basically you're getting two complex numbers that are sometimes "in phase" (i.e., sum to a number whose modulus is bigger) and sometimes "out of phase" (mostly or entirely cancel). The overall pattern is the one you've seen before:

If we know which way the particle went, we use (3). It's hard to say the "reason" that we use that formula, but again, if we look at knowing which-way as just an entanglement rather than a "collapse" (thereby preserving the quantum nature), it turns out that equation (2) does just reduce to equation (3).

Why does entanglement cause decoherence, i.e., kill interference?

In brief, it works like this. Let's rewrite:
|a> = |x> + |y>
|b> = |x> - |y>

Suppose Pb is the projector onto state |b>, which gives us the probability that some state is measured as |b>. Notice that Pb(|a>) = 0-vector. But now let's entangle it:

|a'> = |x>|x> + |y>|y>

To find the probability that |a'> ends up in |b>, we can't use Pb (since it operates on C2, whereas we now need a projector on C2C2). Instead, we use Pb' = Pb ⊗ I

If you look at the action of Pb' on |a'>, you will discover that it is not the zero-vector, but instead

√2/4 (|x> - |y>)⊗(|x> - |y>)

whose norm-squared is 0.5, just like we saw in the classical case above. 

Another way of seeing this is simply writing |a'> in the a-b basis, and noticing that half of it is in |a> and the other half in |b>:

|a'> = (|a> + |b>)(|x>) + (|a> - |b>)(|y>)
= (|a>)(|x> + |y>) + (|b>)(|x> - |y>)
= |a>|a> + |b>|b>