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.....

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….

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:

Summary

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|b>

= <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 C2⊗C2). 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>

Whew.

Original ayahuasca piece

As mentioned in the previous post, this is in danger of disappearing from the web (though the wayback machine still has it). Another link. I think it's worth saving.

WHAT HAPPENS TO YOUR CONSCIOUSNESS WHEN YOU TAKE AYAHUASCA?

AUGUST 13, 2015 SUBMITTED BY YOU 131 COMMENTS

• 35.4k
  

Ayahuasca is a psychedelic brew mostly composed of Banisteriopsis caapi vine and can be combined with various other plants. The natural ingredients to prepare this medicine can only be found in the deepest jungles of South America; the amazons rain forest.

For hundreds of years, Indigenous tribes of South America have been using this ancient elixir to reconnect with the spiritual world and cleanse their bodies from all the negative energies they have collected through their long journeys. However, Ayahuasca serves a higher purpose; to help people reach enlightenment and a higher consciousness level. It is said that once you try this psychedelic brew, you’ll never look at life the same way.

This sacred elixir can help a person to awaken their intuition and reach consciousness by opening their mind to an experience out of the ordinary. This is why Shamans often say that this plant has its own soul. They call it “planta maestra” which means sacred plant. This sacred plant will take you into a journey to the world of the unkown, a world that very few people have had the chance to see.

The world of the spirits

After one hour, I started to think that maybe I was not worthy of having any visions. I felt sick and I was starting to feel disappointed. Suddenly, I began to see beautiful colors all around me. It felt like if I wasn’t in the same room anymore. The colors started to form shapes and faces.

They were not human faces and looked more like plants and leaves mixed with geometrical symbols. Is very hard to describe what the spirits looked like because there is nothing in this world that resembles them. Then, after a few minutes, I could see them clearly.

The room was full of spirits! I could see them everywhere. They were all dancing around and interacting with the humans. I noticed that people couldn’t see them. The spirits were next to them helping, talking, healing, playing and hugging them.
I noticed an old American man who was puking a lot. He looked very sick but he wasn’t alone. There were multiple spirits next to him, rubbing his back and holding him so he wouldn’t fall.

The ceremony felt as if we were in a big carnival, where spirits and humans joined together to celebrate. These beings were filled with love and concerns for people’s well being. They were flying around, helping people and having fun at the same time. They looked like little kids just enjoying life. The spirits were of all shapes;small ones, big ones and very big ones. Then suddenly, a spirit that was flying around saw me and said:

- Look, look! He has woken up! Look at him!

The spirit had a big smile on his face.  As he got closer to me, my first reaction was to try to touch him and to feel him but my hands would just go through him. More and more spirits approached me, one of them said laughing:

- He is a very curious one!

Then another spirit came next to me and offered me a fruit:

- Here, eat, eat!

Without thinking twice, I quickly grabbed the fruit and eat it. This fruit was like no fruit that exists in our world.  It was circular and was composed of beams of light from different colors that looked liked like crystals. It was tasteless to the tongue but I felt an ecstasy of energy going through my body. I was so fascinated by all of them that I quickly forgot about my physical discomfort. They were beautiful. I looked at them with amazement and asked:

- Who are you?

They replied at the same time:

- We are the spirits of the Ayahuasca.

One of them approach me and said; I feel that you feel alone, but don’t worry that won’t last for long; all you need is a little love. Then they all started hugging me and fixing my pillow to make me feel more comfortable. I could feel so much love in my heart that a tear fell off my cheek. I hadn’t feel that kind of love in years.

They were pure, strong, powerful, playful, wise, joyful and innocent. They loved shamanic music and would dance to it nonstop. It was like a big party for them.
One of them asked me with a big smile “why do you put mud on your hair?” He was clearly referring to the gel I had put on my hair that morning.  He even called other spirits to come look at my “muddy hair” and they all started poking it.

They were really curious, almost like children. They we were all laughing about it. The spirit insisted that I touched my hair and when I did, it felt like I was touching dry mud. I finally understood what the spirit was talking about – whatever I was putting on my hair was indeed a very strange human habit.

Seeing them all having fun and dancing was a majestic privilege. Then, I remembered the purpose of my trip. I had a lot of questions that needed answers. I focused and without wasting any time I said:

-I have so many questions to ask! I don’t know where to begin! What’s the purpose of life?! How do I reach happiness?

An older spirit approached me and just replied:

Just relax and enjoy the present moment, what you are experiencing now only comes once in a life time. Stop worrying, just enjoy the moment. Appreciate it. The answers to those questions will come at their right time.

I was a bit confused about what the spirit had told me. So I asked again:

- “Well can you at least tell me what I need to change in my life?

The spirit smiled at me and told me:

-“You don’t need to worry about that. You are on the right track. Just look at where you are right now! In the end everything will be okay, just enjoy the ride.”

At that moment, I felt like he didn’t give me the answer I was looking for. It wasn’t until many years later that I realized that in fact the spirit had answered my question but I wasn’t ready to understand it.I still had a lot to learn from the spiritual world.

He was trying to tell me that the key to happiness is to appreciate the present moment and not worrying about the future or past. I was thinking about my questions so much that even when I was in a beautiful world with the spirits, I wasn’t appreciating that experience because I was thinking too much. The key to happiness is to enjoy every second of the present moment.

Being in the world of the spirit was amazing. That’s when I realized that the physical world wasn’t the only world. There’s a lot more than we do not know about. I was feeling so much bliss and love that I told them:

-“This is so amazing. How come people don’t know about this?! We should tell everyone about this and help them wake up! we should help the whole world.”

One of the spirits replied with a soft smile:

- “Listen, instead of worrying about changing the world, you should start by helping yourself first. That’s the first step for change. You can’t give what you dont have, so you must create happiness in your life first to be able to give to others”.

I asked the spirits how come they never tried helping humans. They reply with a little  laugh:

- In fact, we are always with the humans every single second of their lives. It’s just that humans choose not to see us.

After some time, I started to see less and less of the spirits. I realized I was coming back to reality. I felt sad and scared that I might never see them again. Then one of the spirit said “We are always there. Even when you can’t see us with your eyes, we are always there.”

Ayahuasca was one of the experiences that made me feel sure that there’s more in life than just the physical world we live in. It opened my mind; I realized anything is possible in this universe. There is magic in life, we just have to look a little bit closer.  I also learned about the main goal in life is to follow your heart and be happy.
Don’t take life too seriously, because like Shakespeare said: “Life is but a dream”. Life is a dream and when we die we awake to another world.

By: Raphael Echeverri

Ayahuasca: just look

This is taken from: http://www.abzu2.com/2015/08/15/what-happens-to-your-consciousness-when-you-take-ayahuasca/

I first found it here but it disappeared: http://thespiritscience.net/2015/08/13/what-happens-to-your-consciousness-when-you-take-ayahuasca/

It's only in one place on the web, so I have to reproduce my favorite parts here:

The ceremony felt as if we were in a big carnival, where spirits and humans joined together to celebrate. These beings were filled with love and concerns for people’s well being. ...

- We are the spirits of the Ayahuasca.

One of them approach me and said; I feel that you feel alone, but don’t worry that won’t last for long; all you need is a little love. Then they all started hugging me and fixing my pillow to make me feel more comfortable. I could feel so much love in my heart that a tear fell off my cheek. I hadn’t feel that kind of love in years.

They were pure, strong, powerful, playful, wise, joyful and innocent. They loved shamanic music and would dance to it nonstop. It was like a big party for them.

One of them asked me with a big smile “why do you put mud on your hair?” He was clearly referring to the gel I had put on my hair that morning.  He even called other spirits to come look at my “muddy hair” and they all started poking it.

They were really curious, almost like children. They we were all laughing about it. The spirit insisted that I touched my hair and when I did, it felt like I was touching dry mud. I finally understood what the spirit was talking about – whatever I was putting on my hair was indeed a very strange human habit.

Seeing them all having fun and dancing was a majestic privilege. Then, I remembered the purpose of my trip. I had a lot of questions that needed answers. I focused and without wasting any time I said:

-I have so many questions to ask! I don’t know where to begin! What’s the purpose of life?! How do I reach happiness?

An older spirit approached me and just replied:

Just relax and enjoy the present moment, what you are experiencing now only comes once in a life time. Stop worrying, just enjoy the moment. Appreciate it. The answers to those questions will come at their right time.

I was a bit confused about what the spirit had told me. So I asked again:

- “Well can you at least tell me what I need to change in my life?

The spirit smiled at me and told me:

-“You don’t need to worry about that. You are on the right track. Just look at where you are right now! In the end everything will be okay, just enjoy the ride.”

At that moment, I felt like he didn’t give me the answer I was looking for. It wasn’t until many years later that I realized that in fact the spirit had answered my question but I wasn’t ready to understand it.I still had a lot to learn from the spiritual world.

He was trying to tell me that the key to happiness is to appreciate the present moment and not worrying about the future or past. I was thinking about my questions so much that even when I was in a beautiful world with the spirits, I wasn’t appreciating that experience because I was thinking too much. The key to happiness is to enjoy every second of the present moment.

Being in the world of the spirit was amazing. That’s when I realized that the physical world wasn’t the only world. There’s a lot more than we do not know about. I was feeling so much bliss and love that I told them:

-“This is so amazing. How come people don’t know about this?! We should tell everyone about this and help them wake up! we should help the whole world.”

One of the spirits replied with a soft smile:

- “Listen, instead of worrying about changing the world, you should start by helping yourself first. That’s the first step for change. You can’t give what you don't have, so you must create happiness in your life first to be able to give to others”.

I asked the spirits how come they never tried helping humans. They reply with a little  laugh:

- In fact, we are always with the humans every single second of their lives. It’s just that humans choose not to see us.