We have a gun that shoots electrons one
at a time due north. A little ahead of
the gun and in the path of the electrons
we have a beam splitter, that is,
a flat plate of material with horizontal
normal along the line from south
east to north west.
So, we fire the gun. The electron
hits the beam splitter. The wave
function splits with some going
east and the rest passing through
the beam splitter and going north.
One mile to the north of the beam
splitter and in the line of the path
of the wave function we have a
very good electron detector.
Similarly for one mile to the east.
So, we fire and some fraction of the
time we get a detection from the north
detector and the rest of the time,
from the east detector.
Now, let's move some of the mass of
the electron faster than the speed
of light: A little ahead of each
detector we have a very sensitive
detector of gravity (or, maybe charge).
So, as the two parts of the wave
function pass the gravity detectors,
we get a signal from both.
If the beam splitter sends 10%
of the wave function north and
the other 90% east, then
from the north gravity detector
we should get a signal
of 10% of an electron,
and from the east, 90% of
an electron.
Then, soon, one of the electron
detectors gives a signal,
of 100% of the mass (and charge)
of an electron. So, 90% or
10% of the mass (and charge)
of the electron moved
instantly,
faster than the speed of light.
along the line between the
two detectors.
Is this wrong? Why?
In more detail, what about the
electromagnetic field
from the moving parts of the
wave function? E.g., if the
electron is detected at the
east detector, is there
an electromagnetic field
still from the path of
part of the wave function to the
north?
My understanding is that the gravity detectors would not detect 10% or 90% of an electron. One would detect 0% and one would detect 100%. You cannot measure the wave function directly. Attempting to do so collapses it.
When that waveform collapse happens, everything about the quantum state collapses: electromagnetic field, gravity, etc.
Physics PhD here. You're correct. Any measurement of the electron state will affect the state.
Grandparent did an excellent job setting up the hypothetical scenario by the way. It just turns out QM is awesomely weird like that. It does mean a mass which was de-localized by miles can, theoretically, localize to a single point instantly. However, any information about that localization is restricted to moving at the speed of light.
Sounds like when the wave function of
the electron is moving, likely it
is following the local geometry
of space-time but otherwise is
essentially lost to the universe.
Then whenever we do detect a field,
gravity, electro-magnetic, strong, weak,
etc., necessarily we are detecting
just collapsing wave functions, each
of which happens at essentially just
a point in time. Then after the point
in time of the collapse, the electron
is just a wave function again off
on its way to another collapse.
E.g., when an electron accelerates
going around a circle and radiates
photons, each photon radiated
is from a collapse of the wave function
of the electron at which time
the electron creates a new wave function
and continues on? Sounds like that.
Hmm ... So, all we are seeing, feeling,
detecting, observing, measuring, etc.
are just high rate point processes
of collapsing wave functions? Gads.
Why didn't they tell me that back in
high school?
Regarding your electron-emitting-photons example: I would describe the photons being emitted as themselves in a quantum superposition of having been emitted/not emitted/emitted at different times, etc. It is when we detect or observe the photon that the state of the whole system collapses! The electron and the photon are entangled. Continue this line of thinking and you arrive at the famous Schrodinger's cat... it's a cascading entanglement of larger and larger groups of particles until you open the box and the waveform of every particle in the whole cat collapses to either alive or dead.
The waveform is not really a physical object; I think of it as a probability distribution about the state of the system when observed. These probabilities can be highly correlated; in this case, the probability of observing the electron at one energy level or another is 100% correlated to the probability of observing or not observing the photon at all - which is the definition of entanglement.
Yes, you are constantly observing collapsing wave functions. It might be some solace that most of said wave functions have highly-degenerate probability distributions. By this I mean that 99.999...% of the "mass" of the distribution lies in something reasonable happening. For example, each particle in a tennis ball is so highly entangled to every other particle, that when you throw it against a wall, it's exceedingly likely that the ball will bounce back. A single unentangled atom may have been able to pass right through the wall, but the tennis ball's "waveform" is much more stable and localized such that it's better approximated by classical mechanics.
I'm having trouble finding the reference right now, but if I remember correctly, an experiment similar to yours has actually already been tried. From my faulty memory, here's the experimental setup. I hope someone else who reads this can find the exact reference.
- There's a huge sphere of a dense metal (something like 20 feet in diameter).
- The sphere can be moved closer to or farther away from an incredibly precise accelerometer.
- When the sphere is close to the accelerometer, the accelerometer's reading change very slightly due to the gravitational attraction of the massive sphere. (The change in acceleration was just barely detectable given the technology.)
- A radioactive isotope has a 50-50 chance of decaying or not in a particular time period. Under the Many Worlds Interpretation, the experimenter is in a superposition of having seen the decay and not.
- If the isotope decays, the experimenter pushes the sphere close to the accelerometer. Otherwise the experimenter pushes the sphere away. Now the sphere is in a superposition of affecting the accelerometer and not.
- The experimenter reads the accelerometer.
The point of the experiment was to see if the accelerometer would detect the deformation in spacetime caused by the superposition of the massive ball in parallel universes. The result of the experiment is that no acceleration was ever detected by other worlds' balls.
>While it is easy to understand and agree with this on the epistemological level, the answer that I and many others would give is that we expect a physical theory to do more than merely predict experimental results in the manner of an empirical equation; we want to come down to Einstein's ontological level and understand what is happening when an atom emits light, when a spin enters a Stern-Gerlach magnet, etc. The Copenhagen theory, having no answer to any question of the form: What is really happening when - - - ?", forbids us to ask such questions and tries to persuade us that it is philosophically naive to want to know what is happening. But I do want to know, and I do not think this is naive; and so for me QM is not a physical theory at all, only an empty mathematical shell in which a future theory may, perhaps, be built.
...and maybe chapter 10 of his book, "Probability Theory: The Logic of Science".
>We are fortunate that the principles of Newtonian mechanics could be developed and verified to great accuracy by studying astronomical phenomena, where friction and turbulence do not complicate what we see. But suppose the Earth were, like Venus, enclosed perpetually in thick clouds. The very existence of an external universe would be unknown for a long time, and to develop the laws of mechanics we would be dependent on the observations we could make locally.
>Since tossing of small objects is nearly the first activity of every child, it would be observed very early that they do not always fall with the same side up, and that all one’s efforts to control the outcome are in vain. The natural hypothesis would be that it is the volition of the object tossed, not the volition of the tosser, that determines the outcome; indeed, that is the hypothesis that small children make when questioned about this. Then it would be a major discovery, once coins had been fabricated, that they tend to show both sides about equally often; and the equality appears to get better as the number of tosses increases. The equality of heads and tails would be seen as a fundamental law of physics; symmetric objects have a symmetric volition in falling.
>With this beginning, we could develop the mathematical theory of object tossing, discovering the binomial distribution, the absence of time correlations, the limit theorems, the combinatorial frequency laws for tossing of several coins at once, the extension to more complicated symmetric objects like dice, etc. All the experimental confirmations of the theory would consist of more and more tossing experiments, measuring the frequencies in more and more elaborate scenarios. From such experiments, nothing would ever be found that called into question the existence of that volition of the object tossed; they only enable one to confirm that volition and measure it more and more accurately...
>Biologists have a mechanistic picture of the world because, being trained to believe in causes, they continue to search for them and find them. Quantum physicists have only probability laws because for two generations we have been indoctrinated not to believe in causes - and so we have stopped looking for them. Indeed, any attempt to search for the causes of microphenomena is met with scorn and a charge of professional incompetence and "obsolete mechanistic materialism." Therefore, to explain the indeterminacy in current quantum theory we need not suppose there is any indeterminacy in Nature; the mental attitude of quantum physicists is already sufficient to guarantee it.
For being the top purveyor of maximum-entropy methods, Jaynes really should have been more willing to accept a probabilistic theory of fundamental physics.
Jaynes believed that the only kind of probability was that caused by uncertainty about the true state of the world. So he was advocating MAXENT as a way to summarise one's (lack of) knowledge about some system.
In fact, this point of view probably made him less likely to accept a probabilistic theory of fundamental physics. If you've discovered how a deterministic universe can appear random, and how probabilities can still be useful for measuring one's ignorance, then it's reasonable to suspect that these are the only kinds of probabilities and that the universe really is deterministic.
Determinism is dead. Long live an in-deterministic (and free) universe!
But seriously, why many scientists are so attached to wanting a deterministic universe is beyond me. Even at the highest levels, I'm amazed that physicists have an near moral repugnance to the idea that there's randomness inherent in the universe. They even go through such lengths as inventing the many worlds theories to try and recapture determinism.
If you accept that all effects have causes, you accept determinism.
Also, determinism will be resurrected. Look at Pilot Wave theory. It explains quantum weirdness with a deterministic worldview, but everyone would prefer to hype voodoo theories.
"But pilot wave theory could still be important, because it has a different conceptual formulation, so if you set out to modify the theory, you get different modifications. In that sense, it is a good new idea. I personally think that you can produce a truncation of pilot-wave which doesn't coincide with ordinary quantum mechanics, but which is mostly the same as quantum mechanics when you are dealing with only a few particles only slightly entangled. In this case, you need the wavefunction to be a complicated function of the hidden-variables (the particle positions) which only obeys the Schrodinger equation approximately. This type of thing is a true modification of quantum mechanics, but I was never 100% sure that it works. I described the idea roughly in my answer to one of 'tHoofts questions on physics stackexchange."
Wild guessing from someone who has no background in physics:
1. Simulating QM-level events is NP-complete.
2.Assuming P=/=NP, a machine that simulates a volume of size X in QM-correct terms must be exponentially larger than X.
3. This includes X itself.
4. Therefore, the universe is taking sweeping shortcuts that look like classical mechanics at large scale. These are not 'our' computational shortcuts, they're actually how things work at a fundamental level.
5. ...maybe if we build a big enough quantum computer we can overflow the universe's buffer.
You're missing step 0, which is assuming that our universe is a simulation. Also, you're making a lot of assumptions about the laws of physics and what is computationally feasible in the universe that that computer is running in.
I'm not assuming simulation. It's more of "if the universe can pack something that can predict the outcome of an NP-complete system (that is, the universe itself) in real-time into a relatively very tiny space, then either it's cheating or P=NP."
As for the assumptions, I agree. Hence it's wild guessing.
If you're not assuming the universe is simulated and is instead "fundamental" (whatever that means), then who are you to put limits on its processing power?'
I think you have a level-confusion here - the universe isn't packing computational machinery into itself. Remember that space-time is a part of this universe. If something is computing our universe, it has to hold the representation of space-time, too. The computation machinery isn't in here with us.
If 'fundamental' stuff gets to break P=/= NP, then I don't see why we can't do it in a computer, if only by aping the design. But then P=NP and things get weird.
I'm not sure why you keep mentioning NP and P. A problem being exponential doesn't mean it can't be computed. Maybe the universe does the calculations the hard way.
Einstein had amazingly good intuition for the character of physical laws, i.e. what shape the laws of physics must necessarily take. And in this case he was right, too. God doesn't play dice; the universe is deterministic. Unfortunately, he didn't stumble upon the right answer, Many Worlds. I sometimes wonder how much longer it will take popular science writers to stumble upon it, too.
The popsci version of Many Worlds is terrible, because it implies that some sort of meta-conservation laws are violated in the creation of all of these universes. (where do all the universes come from?)
This is simply just bad explanation of perfectly reasonable math. This happens all the time with fundamental physics. Unfortunately the bad explanations persist, because coming up with good nuanced metaphors is hard, and they tend to be harder to communicate.
I have known about MW for 25 years or more, thanks to popular science writers. I don't see it getting more traction than it already has absent some way to falsify it. It's stylish from a distance, but like imaginary numbers, you should tidy up your multiverse when you are done playing with it.
That's a common criticism, but many-worlds is a consequence of a theory, not a theory itself. Plus all the other candidates are worse. (And Copenhagen isn't really a theory at all since it never gets around to defining what a 'measurement' is.)
Many worlds requires postulates (Everett's word!) that are not a consequence of theory, in particular that the wavefunction is an objective property of a particle. This is very much in dispute, and is rejected by the ensemble interpretation, consistent histories, etc.
I don't agree that those interpretations are inferior to MWI. In particular those theories postulate that the world is essentially probabilistic, and so do not have MWI's trouble with predicting probabilities.
>Many worlds is by far the best hypothesis to date.
well, to me it actually works in the opposite direction, like prove by contradiction - if the Many Worlds is the best/logical/natural consequence of the indeterministic view of QM than the indeterministic view is definitely have to be overturned.
All the Bell experiments i read about so far have obvious gaps allowing for obvious explanations. And if you take the latest one, the heralded loop-free, then there is obvious question - why didn't they published the statistics of the unconnected, non-entangled runs? I mean it is obvious from current QM orthodoxy that non-entangled runs wouldn't produce S>2, yet from alternative, locally-realistic, experiment result explanations the S>2 would be produced in that case too (the S>2 isn't possible in the locally realistic world, yet it is possible to locally realistically explain S>2 in all the Bell experiments that so far i've seen)
Many worlds is not a logical consequence of the non-deterministic view of quantum mechanics. One of the reasons cited in favour of the MWI is that it is wholly deterministic. That is probability doesn't appear at all in it's framework. This is much more in keeping with previous physical theories (Newtonian mechanics and Maxwell's laws of electrodynamics for example) which were also wholly deterministic.
If you're interested other reasons the MWI is often considered "nice" is that it is: linear, local, causal, realist, entirely unitary and in some sense (this is often disputed) minimal. Other interpretations have to add mechanisms (for example wavefunction collapse) in a rather ad-hoc way in order to stop many worlds happening.
That is also one of the most common critiques: because MWI is wholly deterministic, there is no way for probability to arise in it, and therefore no way to derive probabilistic phenomena like the Born Rule.
Many worlds is a consequence of the idea that the laws of physics apply equally to physicists and experimental apparati as they do to the particles under study.
I think the trouble arises when you try to connect that to consciousness and human experience. From my perspective ("me" being the version in me in the "current" universe or whatever), I only experience one timeline, and so the universe appears totally nondeterministic. What use is this to science or even philosophy?
I disagree that Einstein's intuition carried him through quantum mechanics. I rather think that history shows him to be probably on the wrong side of the EPR/Copenhagen split. Not only did he cling to determinism (and I think he would have believed in something stronger than MW, which is a sort of very-weak determinism) but he also constantly objected to "spooky action at a distance" aka quantum entanglement which has now been very well observed.
It is true that Einstein was wrong about his insistence that there must be hidden variables, but I'm not so sure I would call him on the wrong side of the debate, as the correct hypothesis wasn't available during his lifetime. I wonder what he would have done with it had he heard about it.
Einstein's objection to spooky action at a distance and clinging to determinism is exactly the kind of thing to point to when trying to explain his amazingly good intuition for the character of physical law. He was 100% right about the action at a distance not being real and physics being deterministic. To be clear, entanglement is real, but there's no effect that happens at faster than lightspeed; the resolution to this is, of course, MWI.
As for what use there is - the primary use is that we can all stop being confused about this. And stop thinking that just because quantum physics is mysterious, it must necessarily be connected to other concepts that are mysterious too, like consciousness. And when else would we question the justification for learning the truth of what we all and the universe are made of?
(P.S. In what sense do you believe that MWI is very-weak determinism? It's deterministic through and through.)
Maybe we only experience one timeline, but we can imagine many. And maybe there's leakage among them at small scales. But I'm not a physicist. I just enjoy SF. Anyway, for those interested in such matters, I recommend Anathem by Neal Stephenson, and Diaspora by Greg Egan :)
Many Worlds? That just abstracts the probability one step further, ie why am I in THIS world and not the other one (or if you prefer, why did my universe experience the string of events A-C-C-A-B and not A-C-C-A-A)?
The deterministic solution to quantum mechanics is Pilot Wave theory. It can explain nearly all quantum weirdness. Spacetime vibrates.
We have a gun that shoots electrons one at a time due north. A little ahead of the gun and in the path of the electrons we have a beam splitter, that is, a flat plate of material with horizontal normal along the line from south east to north west.
So, we fire the gun. The electron hits the beam splitter. The wave function splits with some going east and the rest passing through the beam splitter and going north.
One mile to the north of the beam splitter and in the line of the path of the wave function we have a very good electron detector. Similarly for one mile to the east.
So, we fire and some fraction of the time we get a detection from the north detector and the rest of the time, from the east detector.
Now, let's move some of the mass of the electron faster than the speed of light: A little ahead of each detector we have a very sensitive detector of gravity (or, maybe charge).
So, as the two parts of the wave function pass the gravity detectors, we get a signal from both. If the beam splitter sends 10% of the wave function north and the other 90% east, then from the north gravity detector we should get a signal of 10% of an electron, and from the east, 90% of an electron.
Then, soon, one of the electron detectors gives a signal, of 100% of the mass (and charge) of an electron. So, 90% or 10% of the mass (and charge) of the electron moved instantly, faster than the speed of light. along the line between the two detectors.
Is this wrong? Why?
In more detail, what about the electromagnetic field from the moving parts of the wave function? E.g., if the electron is detected at the east detector, is there an electromagnetic field still from the path of part of the wave function to the north?