Real world Kraken Drives

[K^2]

Perhaps there are other ways of simulating the physics of our universe on a digital computer. If it were somehow possible that the laws of our universe could be simulated exactly, and not just approximated, then if it were being simulated on a computer we would never know.

However, with quantum mechanics, it would seem that our universe cannot be exactly simulated.

When dealing with any sort of numerical computation, the big question is always convergence. You can't, in general, get an exact result for any computation. But provided a "nice" dynamic, you can get as close as you need. If this is a simulation, there are three main possibilities. First, we might simply not have probed the universe with sufficient precision to matter. Second, it might actually be impossible to probe with sufficient precision because of how the dynamics workout. Plank scales come to mind. Finally, if simulation exists for our sake, precision could be adjusted on demand. The more sensitive the experiment, the more time the computer spends on making sure all the numbers match up. Attention-sensitive algorithm might sound contrived, but when you get right down to it, it's just like using multiple scales for turbulence simulation.

The fact that it's a quantum system only increases the size of the state space. It doesn't actually make the simulation harder. And if we are considering a computer that can run our entire universe, it's already something infinitely more complex, so it hardly makes a difference.

[78stonewobble]

Perhaps there are other ways of simulating the physics of our universe on a digital computer. If it were somehow possible that the laws of our universe could be simulated exactly, and not just approximated, then if it were being simulated on a computer we would never know. Furthermore, that computer could be anything from a Game Boy to a Matrioshka brain, because the speed of the simulation in the host computer's universe is not related to any information in our own universe.

However, with quantum mechanics, it would seem that our universe cannot be exactly simulated.

I don't think it's possible for us to simulate our universe perfectly due to quantum indeterminacy, but that doesn't necessarily preclude us, or something else (dun dun duuuuuuh), from simulating A universe "perfectly".

Interesting idea, but I don't really believe it, nor does it really matter anything.

[K^2]

quantum indeterminacy

There is nothing indeterminate about quantum mechanics.

[John FX]

You`re going to end up with a TARDIS you know...

[Sillychris]

There is nothing indeterminate about quantum mechanics.

If that's the case, I urge you to predict determinately where a single electron will end up after passing through a double slit setup.

[K^2]

If that's the case, I urge you to predict determinately where a single electron will end up after passing through a double slit setup.

I can write down a distribution function for it^*. You might be confused because you think that the electron is located at just one specific, randomly distributed place after passing through a double-slit. But it's not. It's actually physically located at all of these positions. Quantum mechanics is completely determinate, because the physical object is the wave function. Not a point particle in an everyday sense of such. Given an initial condition and the Hamiltonian describing the system, one can evaluate the exact state of the system at any later time. That's the very definition of determinism. The fact that you cannot possibly know the initial state exactly is a separate matter, which is true of real world classical problems as well.

^* The distribution as function of angle θ is proportional to sinc²(d₁À/λ sinθ)cos²(d₂À/λ sinθ). It needs to be normalized to unity to be the actual probability amplitude. The distance d₁ is width of the slits, and d₂ is separation between them. The wavelength λ is given by de Broglie equation, λ = h/p, where h is plank's constant, and p is electron's momentum. Naturally, this assumes normal incidence and initial conditions allowing us to treat incoming electron as a plain wave, which is typical for double-slit experiment.

[Javster]

My personal philosophical thought is that our entire universe is a pixel on someone's screen, and every pixel on our screen is an entire universe.

[The Jedi Master]

Let's hope the next update doesn't break saves.

On a more serious note, it is certainly an interesting and paranoia-inducing idea, but probably not one worth pursuing. However, the idea the the universe is a simulation has been discussed in the past by serious scientists. Look it up if you're interested.

[nhnifong]

Finally, if simulation exists for our sake, precision could be adjusted on demand. The more sensitive the experiment, the more time the computer spends on making sure all the numbers match up. Attention-sensitive algorithm might sound contrived, but when you get right down to it, it's just like using multiple scales for turbulence simulation.

That would suggest that the measurable properties of the universe had never been computed until we bothered to look. That would mean that our own evolution had not happened until we attempted to measure say, the mass of the earth, and its magnetic field strength, and other variables life is sensitive to. If our own history had never been computed, how did we come to exist to do the experiments that triggered the computations?

Do you think it is possible that something like this is happening even if the simulation is not created for our sake?

[Blue]

If there were bugs in the simulation of our observed reality, wouldn't it not break the hypothesis to also suppose that the maker of the simulation would also be able to correct bugs if they occurred, or that bugs regularly do occur but are not empirically reliable (i.e. miracles)?

[Sillychris]

I can write down a distribution function for it^*. You might be confused because you think that the electron is located at just one specific, randomly distributed place after passing through a double-slit. But it's not. It's actually physically located at all of these positions.

Yes, I am familiar with eigenstates simultaneously existing. I am also familiar with the notion that a wave/particle will collapse to one specific eigenstate when you decide to observe it. What we can't predict is which eigenstate it will collapse to, only the probabilities.

So you're telling me that if I send one electron through the double slit experiment into a phosphorescent screen it will light up the entire diffraction pattern at once?

Sadly, this is not the case. Low flux double slit experiments show an initial distribution pattern that is seemingly random. Only after a large number pass through does the distribution become apparent. You can predict fairly accurately the probability amplitudes of where the electron may end up and you can predict extremely accurately what the distribution of N electrons looks like. Predicting the precise fate of 1 electron is unfortunately impossible.

Here's a picture. Part a in that picture is what I'd like you to predict determinantly.

http://skullsinthestars.files.wordpress.com/2009/03/tonomuradoubleslit.jpg

Now let's talk about nuclei. How can you predict deteriminantly when a particular U235 atom will decay? And while you're at it, it would be nice if you can predict exactly what that atom will decay to. I'm not talking about N-atoms, I'm talking about 1 atom in 1 box. ie Schroedinger's cat.

What if we send two protons at eachother with insufficient energy to overcome coulomb repulsion? Can you predict whether fusion will occur or not?

What if we send two protons at eachother with way more than sufficient energy to overcome coulomb repulsion? Can you predict which particles will be created from the extra energy?

How about a hydrogen atom in an excited state? Can you predict determinantly which photon it will emit? I can only give you probabilities...

How about one excited nuclei in a metastable state? Can you predict determinantly when it will emit a photon? Can you predict determinantly whether this photon will be magnetic or electric in nature?

The list goes on. It's a long one. Probabilities and uncertainty are core to quantum mechanics. Einstein wouldn't accept QM because he believed so strongly in strictly deductive reasoning. "God does not play dice" he is supposed to have said to Bohr.

It is true that for very large N quantum mechanics becomes predictable. We take advantage of this a hell of a lot. I'm talking about n=1. Totally indeterminate.

[K^2]

Yes, I am familiar with eigenstates simultaneously existing. I am also familiar with the notion that a wave/particle will collapse to one specific eigenstate when you decide to observe it. What we can't predict is which eigenstate it will collapse to, only the probabilities.

You are mixing several different things into one. First, there is the fact that state of the particle is described by system's wave function. Second is the fact that superposition principle applies, meaning you can write that wave function as a sum of states. Eigen states are just a special case. Finally, you are throwing in Copenhagen collapse, which is interpretation-specific and isn't part of general Quantum Mechanics. Finally, Copenhagen Interpretation states that the system will collapse into an eigen state of the measurement operator. Why or how that happens is not touched in this interpretation, but is largely expanded on in more general theory. But lets tackle these things one at a time.

So you're telling me that if I send one electron through the double slit experiment into a phosphorescent screen it will light up the entire diffraction pattern at once?

Sadly, this is not the case.

It actually is. The entire phosphorescent screen transitions to the excited state. However, there is only energy for a single photon in the entire thing. When light is emitted, it is a superposition of all possible emissions. So as a point of fact, the whole thing does light up. But what you record on film is a little different.

Low flux double slit experiments show an initial distribution pattern that is seemingly random. Only after a large number pass through does the distribution become apparent.

This is where collapse happens. When you actually take the record of where the photons strike. A more modern experiment would have scintillators and sensors. But the idea is the same. The measurement operator is essentially that of position, so the collapse is to a photon detected at specific location. And yes, these appear to be random.

The question remains, however. Does the collapse happen because photons struck sensors? Turns out, it is not. Delayed Choice Quantum Eraser tells us that if we discard data from sensors, it's as if collapse did not happen. How is that possible?

Well, we've already covered the fact that the screen glows all at once, but you can't have a fraction of photons emitted. So instead, you have a superposition of photons being emitted from all possible locations at once. We can only measure one photon total, but we can measure any one of these with some probability. So what's to prevent sensors themselves from going into superposition? Turns out, absolutely nothing. For a short enough time. And for a short enough time, all of the sensors are in superposition of all possible combinations of just one of these sensors having been triggered. And we can write down the exact state of these sensors since we know the probability amplitudes. So no collapse took place yet and everything is fully deterministic. Lets keep going.

Now let's talk about nuclei. How can you predict deteriminantly when a particular U235 atom will decay? And while you're at it, it would be nice if you can predict exactly what that atom will decay to. I'm not talking about N-atoms, I'm talking about 1 atom in 1 box. ie Schroedinger's cat.

Good. Lets talk about Shroedinger's cat. One atom, one detector, and we set it up to be triggered with a 50% chance. Cat is killed if detector is tripped within the mean life of the atom. Or it is not killed if the atom did not decay within the time window. But the whole point of the experiment is that the cat in the box is in superposition of dead and alive. Why hasn't cat's observation of the result collapsed the system?

Well, let us look at this whole experiment formally. Let me call |a> the cat alive state and |d> the cat dead, or dying, state. The atom is going to be |1> for its initial state, and |0> when it decayed. We start out with the |a1> state, and after the mean time elapses, the system turns into a (|a1> + |d0>)/Sqrt(2) state. Do you recognize it? This is an entangled state. This is actually the real outcome of a Quantum Mechanics measurement. Before we start talking about collapse and interpretations, a measurement actually takes a superposition state and creates a superposition entangled state of the measuring device and the system being measured. So what's going on from perspective of the cat?

Well, this is where superposition principle kicks in again. It tells us that every state in superposition can be considered separately. We don't need to talk about the entire (|a1> + |d0>)/Sqrt(2) state. We can talk about each of the possibilities |a1> and |d0> separately. Specifically, given some time evolution operator U(t), we can say that U(t)(|a1> + |d0>) = U(t)|a1> + U|d0>. In other words, each state evolves in time as if the other states don't exist. The dying cat sees the broken poison vial and if it could, it would conclude that the atom has decayed. It's not aware that it's in the superposition state. From its perspective, the atom's state, and its own, has collapsed. The cat which is alive also sees the intact vial and from its perspective, decay did not happen. It would, however, also conclude that the state has collapsed.

Are cats special? Of course not. Any observer, be it human, animal, or machine. Anything capable of recording a state, in fact, is going to become entangled with the state being measured, and from its perspective, observe collapse. The main alternative to Copenhagen Interpretation is the Many Worlds Interpretation, and it takes precisely that stance. That no real collapse ever happens, and the only thing that's going on is things becoming more and more entangled, leading us to a number of "alternate time lines", which are really just series of states within the grand total superposition which we consider separately.

What if we send two protons at eachother with insufficient energy to overcome coulomb repulsion? Can you predict whether fusion will occur or not?

What if we send two protons at eachother with way more than sufficient energy to overcome coulomb repulsion? Can you predict which particles will be created from the extra energy?

How about a hydrogen atom in an excited state? Can you predict determinantly which photon it will emit? I can only give you probabilities...

How about one excited nuclei in a metastable state? Can you predict determinantly when it will emit a photon? Can you predict determinantly whether this photon will be magnetic or electric in nature?

And these are all the same. I can write down the outcome state for each of these. For some, rather approximately. Being a particle physicist, I can tell you not from second hand knowledge that the process of fusion is actually an extremely complicated one, despite the choice of final states being fairly straight forward. For hydrogen atom, though, with a bit of work, I can write a simulation that produces the exact state of the electromagnetic field "after the decay". It will contain a suitable superposition of photons.

What you are still being stuck on is the actual collapse, and that is just one of possible interpretations. Copenhagen Interpretation, does, indeed, rely on random chance, but that's just one of the reasons why it's rapidly falling out of favor. In Many Worlds Interpretation, there is no chance at all. Everything is fully determined. Some of the more down-to-earth interpretations recognize that there are limits to how far superposition principle can be pushed. At some point, density of state turns energy spectrum practically into continuum, and then what you have is decoherence, which, from observer's perspective, again, looks just like collapse of the system. But it's not a true collapse either, but rather a state where a lot of information has been lost to chaos.

And that brings us to the ultimate point. There are things in Quantum Mechanics which we cannot predict. But it is not because the dynamic is unpredictable. The underlying "randomness" is very similar to what you see in Thermodynamics. There are just too many interacting states, with energy being transitioned back and forward, so it is impossible to know the initial state perfectly. But if you do know initial state and the Hamiltonian, you can evolve it to final state in a completely deterministic way.

Einstein wouldn't accept QM because he believed so strongly in strictly deductive reasoning. "God does not play dice" he is supposed to have said to Bohr.

And so far as we know, he was right. It is a shame that Many Worlds Interpretation was developed a few years after his death. He would have liked it.

Edited April 3, 2014 by K^2

[Sillychris]

I'm still waiting for my deterministic prediction of observed behaviour.

So there is a theory that tells us the whole screen lit up and the superposition is then transferred to the sensors. I accept that idea, it's neat. But like you said, we can only measure one photon for one electron... well, in this universe anyway. Problem is, I'm stuck in this universe and I can only observe effects here. I'd like to limit the discussion to predicitions in our own universe. I am open and hopeful for multiverses, but how my own universe unfolds is what I am most interested in.

Let's Gedanken. I have a classic electron double slit setup with a phosphorescent screen. Only one electron passed through, and the results recorded in a standard way. I am using this as what I view as a truly random method to flip a coin.

If the light is recorded as emitting from the left side of the screen, I go to grad school.

If the light is recorded as emitting from the right side of the screen, I go to Nepal

If the light is near enough the center that it is hard to say which side, I send another electron through and try again.

The effects of this one electron have immense effects on my life, and potentially on human civilization.

What is it? Does sillychris go to Grad School or Nepal?

I also have another question for you, K^2. Do you believe the universe is deterministic? I'm not looking to unhinge the discussion, I'm just curious.

[K^2]

Of course, the universe is deterministic. It's more than that. It's already determined. I'm sure you are aware of problems of simultaneity in relativity. What's future to you is present to someone from a moving coordinate system. If your future hasn't happened yet, then how can that even be?

Time is just a direction. It's a weird one, and thanks to Statistical Mechanics making it even weirder, we perceive it as time flow, but ultimately, it's still just a direction. Saying that future is undetermined until you get to it is like saying that what's in the next room is undetermined until you walk in. It just doesn't work that way. Not even in Quantum Mechanics. Superpositions? Sure. Undetermined? Never.

I'm still waiting for my deterministic prediction of observed behaviour.

The observed behavior is a superposition. The fact that you are part of superposition is your problem. If I leave a red ball or a blue ball in the next room, and don't tell you which, from your perspective, the "observed behavior" is a ball of random color when you open the door. But you aren't going to tell me that it's an undetermined system, are you? That's just absurd. You lacking full knowledge of the system doesn't make it random or undetermined.

Let's Gedanken.

[...]

What is it? Does sillychris go to Grad School or Nepal?

As an external observer, knowing full setup of the system, I know exactly what the outcome is going to be. A superposition of you going to Nepal and you going to Grad School. The fact that your observations differ, again, stems only from the fact that you are part of the system, and you have limited information about the outcome.

This is a "more random" sort of situation, because being part of the system, there is no way to obtain full information, but it doesn't make it undetermined.

More importantly, as an external observer, I can verify my prediction.

Lets step away from superpositions of major historical events, because divergent histories are very difficult to collect back together, (Statistical Mechaaaaaaaanics!) but we can do the same experiment with particles. Lets simplify the experiment. We really just need a yes/no system, not something with slits and screens, etc. I'm sure you agree that it's not the point. So lets take a particle in a superposition of up and down spins. I can determine which it is using Stern Gerlach experiment. But I can also make a more direct measurement using NMR. Using quantum amplification algorithm, I can take the initial state of two particles |00> + |10> (one particle in superposition, second is in "down" state) and convert it to a maximally entangled state |00>+|11>. As I have explained earlier, this is a real measurement. If I decide to run the second particle through Stern Gerlach, I can use the result to determine spin of first particle. Naturally, the only outcomes possible here is that I either end up measuring both particles spin down or both particles spin up.

But I'm going to be much trickier. I'm going to run another state transformation. Note that the final state is one of the Bell States. It's the + state. So lets transform the state so that Bell+ state goes to singlet, Bell- goes to superposition triplet, and the remaining two states, are mapped to the remaining triplet states. This transformation is Hermitian, so I can carry it out using NMR. What I'm going to end up with is a pair of particles which can have either a total spin 0 (singlet state) or total spin 1 (triplet states). And the way the experiment is set up, I should only get the singlet state. So I can measure total spin and confirm that it always comes out to be 0 in this experiment.

As such, while the result of measurements were in superposition, and if I were to try and do a Stern Gerlach, I'd get "random" results, if I do the experiment differently, I can verify that 100% of the time I confirm the deterministic predictions of Quantum Mechanics, because I eliminate possibility of losing information by becoming part of the experiment.

[Dodgey]

Say our universe is a simulation. How did you determine that the apparent laws in this universe apply to the universe in which our simulation is being run?

[cantab]

Assuming the universe is in fact a simulation would it be reasonable to assume there are physics bugs in the simulation E.G. floating point errors and that it would be at least in theory be possible to design a machine that is capable of exploiting these bugs for our own gains or is the simulation much like the kraken drive.

The cold fusion bug. It got patched though.

[Guest]

What is this "real world" you people keep mentioning?

[Sillychris]

What is this "real world" you people keep mentioning?

It's this weird place outside the Kerbal system where you have limited resources to build spacecraft with.

[Sillychris]

As an external observer, knowing full setup of the system, I know exactly what the outcome is going to be. A superposition of you going to Nepal and you going to Grad School.

How awesome would that be!

[The Error]

I feel like I should point out the good ol' theory here:

"How do you know it's impossible until you've tried?"

So I propose we use the fastest, most powerful computer we can find to run experiments. These experiments would be very small, and theoretically impossible. After you try it once? Turns out it's impossible. But you get that first try in.

So do millions of tiny experiments, all theoretically impossible, all slightly different - thus, you'll bug out the simulation we call "real life" and find loopholes to exploit.

And from there, we escalate to reactionless drives. Booyah.

[NERVAfan]

I've never gotten Many-Worlds. Assuming a near infinite number of unobservable universes seems way counter-Occamian.

Sure Copenhagen interpretation is weird, but so what? The universe isn't bound to follow our common sense (though it does seem to be mathematically comprehensible).

I'm not at all convinced that the universe is really deterministic either -- that strikes me as a philosophical question rather than a scientific one. (EDIT: largely due to the fact that you can never make initial measurements with sufficient precision to predict a deterministic universe deterministically, so whether it actually is deterministic or not is forever untestable...)

[K^2]

I've never gotten Many-Worlds. Assuming a near infinite number of unobservable universes seems way counter-Occamian.

Sure Copenhagen interpretation is weird, but so what? The universe isn't bound to follow our common sense (though it does seem to be mathematically comprehensible).

Thing is, from perspective of observer, the two are indistinguishable. There are theorems stating as much. Honestly, take your pick.

But I recommend everyone to understand both, and understand them well, because many things intuitive in one are completely counter-intuitive in the other. Having both interpretations at your disposal will let you sort through problems that much quicker.

[NERVAfan]

Thing is, from perspective of observer, the two are indistinguishable. There are theorems stating as much. Honestly, take your pick.

Yeah. SO there is by that fact no evidence favoring the many-worlds interpretation, no possible observation of the other worlds. And Copenhagen (according to my admittedly limited understanding) works fine with one universe while many-worlds requires immense numbers of universes.

I think Occam's razor makes the choice obvious

[K^2]

There is only one universe in Many Worlds. They like to call observer/observed pairs "worlds" to help intuitive understanding, but there is just one wave function. Same as with Copenhagen. Except, Copenhagen adds a wave function collapse statement. Many Worlds does not. So if you want to go with Ocam's razor, MWI is a simpler interpretation of the two.

More importantly, as I've said, they are completely indistinguishable. It's not like Universe really works the way a) and not , but we don't know it yet. No. To say that, there has to be some way to distinguish the two, even if we can't carry out the experiment. There is no way. They are mathematically equivalent. So one cannot be right while the other is wrong.

And if it makes you feel better, both are almost certainly wrong. Starting with the fact that they are based on measurement axioms which don't play nice with the gauge freedoms of the Field Theory and just many-particle QM in general. And then there is the fact that superposition principle, which both take for granted, does not work on large scale. Meaning that "worlds" cannot be completely independent, and collapse just leads to contradictions outright.

Ultimately, you should view QM as a tool. It's not how the world actually works. QM is a tool that helps you interpret and work with the underlying field theory. But quantization of the field theory is not required. We make perfect use of Gravity without quantizing it, because it's a fairly straight forward field theory. Similarly, we can do full description of Electrodynamics without employing Quantum Mechanics, so long as particle fields are not involved. It's only when you introduce particle fields into both and try to look after all of the interactions, that the underlying field theory gets too complex to even interpret, let alone try and make computations with. That's where quantization comes in and saves the day. But it's just what we use to describe the system with much simpler algebra. Which is not the same thing as actual physics of the thing being that.

[Camacha]

Forget about it. I've had to argue with some aeronautical engineers about the topic for hours.

There seem to be these myths floating around when it comes to wings and lift, even when you talk to quite informed people. You get all sorts of explanations claiming that the airflow splits and has to neatly rejoin at the same point behind the wing and more nonsense like that. I do not pretend to have a comprehensive and detailed grasp of all the phenomena involved, but the ridiculous explanations people do give often have obvious (and massive) flaws.