Just to start this off, I thought I'd briefly give an account of the interpretations of Quantum Mechanics (hence forth QM) that are still valid. By "still valid" I mean that no research on QM has yet ruled them out. There were several early interpretations of QM that originally held promised, but have since been ruled out via a combination of mathematical and experimental work. I also don't want to over describe them, so I'm cutting out various "sub-interpretations" were people disagree on minor points.
There are really five interpretations. I'll illustrate them with an experiment to measure an electron's spin. The electrons are produced from superheating silver in an oven. They then stream out of the oven into the magnetic field between two powerful electromagnets. Spin up electrons will have their path curled upward, spin down electrons will have their path curled downward. Past the magnets lies a photographic plate which the electrons will strike, leaving a white mark. Spin-up electrons will strike the top of the plate, and spin-down electrons will strike the bottom.
(a) Modern Copenhagen: Microscopic particles do not intrinsically possess any properties independent of measurement. Everything we measure about them (aside from their mass, total spin and some other properties) is a property of the interaction between the particles and a large macroscopic classical object, not an intrinsic property of the particle itself.
In the experiment above, I have in fact simply generated the event of certain kind of mark appearing on the photographic plate in the presence of a magnet and silver oven, I cannot say anything about the electrons.
Further more, the event generated is random, i.e. has no underlying cause, but the distribution of the events is predictable, i.e. the mark will appear at a certain location on the plate ~35% of the time.
(b) Many-Worlds: Particles possess multiple values for their properties, e.g. they are spin up and down at the same time, or one could say that their properties are multi-valued. When a large object attempts to interact with them (in a measurement let's say), the large object becomes multi-valued. In the example above the photographic plate develops a mark on both the top and the bottom, in response to both values of the electrons spin.
At a deeper level, the photographic plate develops two completely different atomic structures, one corresponding to a mark at the top and one corresponding to a mark at the bottom. Initially these atomic states can interact and both states are influenced by both electron spins. Very rapidly however, each state of the plate becomes unable to interact with the "wrong" electron spin (i.e. the state with a bottom mark is no longer influenced by the spin-up value of the electron) and both become (almost) unable to interact with or influence each other.
If a camera then records the state of the plate, it develops two different atomic states that rapidly decouple, and so on in a sphere expanding close to the speed of light.
The world essentially gains two parallel states, one with a set of values attached to the electron having spin-up and the other spin-down.
These first two interpretations are, in a sense, the only interpretations of the mathematics of QM. The following three interpretations are actual alternate theories, that is they have different mathematics, that agree with QM as far as we have tested it. They're all similar in that the world is "set up" in some way to simulate QM.
(c) Non-local classical theories: This is really a whole class of theories. In these theories there is no randomness and no multiple-worlds. They're essentially classical theories in the sense of Newtonian Mechanics and Electromagnetism. They all have three common features:
(i) All particles in the theory can communicate with each other faster than light. (ii) All particles carry an infinite amount of information (this information supports the superluminal communication) (iii) The communication mechanism, and the information behind it, is completely inaccessible to measurement or outside detection.
These two features are necessary (due to a result known as Bell's theorem) for a classical theory to reproduce the features of QM.
There are several such theories, e.g. Bohmian Mechanics.
The reason this superluminal communication is necessary, is because QM would produce a different pattern depending on the set-up of the magnets prior to the plate (e.g. two versus one electromagnets, electromagnets parallel vs perpendicular) something which the oven has no knowledge of. So the atoms from the experimental apparatus in front of the oven communicate with the atoms of the oven faster than light in order to alter its thermal distribution to correctly reproduce the results of QM.
(d) Retrocausal theories: In these theories the future can communicate with and alter the past. So when the electrons stream out of the oven toward the plate, the atoms of the plate, together with the electrons, send signals back in time to oven, altering its heat distribution so that it fires out electrons to correctly replicate the QM pattern on the photographic plate.
Cramer's Transactional theory is one theory in this family.
Again this permits the oven to produce the correct pattern of electrons since the electrons can signal backward in time what set of circumstances they encountered after leaving the oven.
(e) Super-deterministic theories: If I perform the experiment with two sets of magnets, versus one set of magnets, QM will produce different patterns on the plate. In the theories above, the oven somehow becomes "aware" of the set-up and alters its thermal distribution accordingly.
In super-deterministic theories however, a set of gamma rays arrive from the M31 galaxy, let's say, just in time to alter the electron beam, in such a manner as to replicate the appropriate pattern. In this case, the oven does not gain knowledge of it's surroundings, rather the electron beam is altered mid-flight by something from outside the experiment, always in such a way as to reproduce the predictions of QM.
A set of such coincidences must occur for all experiments at all times. Basically, something always "messes up" the experiment in a way that looks like QM.
't Hooft's cellular automata theory is one such theory.
Edited by Son Goku, : Proofreading, slight expansion on (c)
The book has very little in the way of solid content, I've read it before, and starts by challenging the view that time isn't real, even though modern physics doesn't state this.
The process formulation is basically the old fashioned Copenhagen interpretation conveyed reasonably well in English, it's not a new interpretation.
The amount of American slang I've learned on EVC, I've never heard this expression.
What if the Multiverse is like a tube of toothpaste?
Just to be clear, when you say Multiverse, do you mean "loads of different universes, with different properties" or do you mean the QM version, that is multiple timelines of the same universe.
In essence though, yes, what you describe is a resolution to the quantum interpretation problem. A world with no probabilities, but with objects which possess infinite possible states and which are all intrinsically connected.
Such models have not been developed in as much detail as ones obeying the many-worlds or Copenhagen interpretations (standard QM), they can currently only replicate non-relativistic particle physics, but there is no theorem blocking their development.
Note though, that none of the modern interpretations really have an "observer" as part of the theory, that's a confusion from older QM, i.e. pre-1980s
Sorry for the delay, busy with the family at Christmas.
Explain to me in a nutshell the prevailing theories on the concept of multiverses.
So in a nutshell, there's really only two. They're not competing in any way, both could be true, as they deal with separate issues.
The First: In Quantum Mechanics we have the Many-Worlds interpretation. In brief, unlike most theories of physics, the maths of quantum mechanics doesn't come with a clear mental picture of what is going on. So there are several "narratives" people use to picture the maths mentally. Many-Worlds is one such.
It basically says the universe has several parallel timelines. In one timeline an atom decayed, in another it didn't. Two separate histories. Now in science fiction this is usually presented as "every possibility" occurs, but that isn't true, only a small range of histories are possible and most don't differ all that much. I can say more about this, but it becomes a bit technical, keeping in mind having a nutshell answer.
The Second: Genuinely different universes with totally different laws. Maybe a world with ten dimensions and nine forces, rather than four dimensions and four forces like ours. Worlds where gravity works differently so that things spin when they fall. Places where relativity isn't true. Totally different worlds. Some theories of particle physics suggest this. In most models of this conjecture there are a lot of such different universes.
Again, both could be true. Our universe might have several timelines and there could be separate universes as well.
Are they realistically plausible?
The first type (multiple timelines) has no evidence against it yet, despite some attempts to falsify it. However all the evidence can still be explained by orthodox versions of Quantum Mechanics, so the jury is out. In other words, it makes predictions we can verify and those predictions hold up, but other ways of looking at Quantum Mechanics also make those predictions, so hard to know.
The second type has no strong evidence in its favour, but we're not advanced enough to perform the necessary experiments. It's the kind of thing that may need to wait until we colonise space.
Could we hypothetically exist in multiple dimensions?
I'm taking this to mean "does the universe we live in possibly have more than four dimensions?" So far the evidence is strongly against this, we seem to exist in a four dimensional reality. Predictions of theories with more than four dimensions have been shown to be wrong.
How does a mathematician connect the hypothetical to reality?
For the different universes or multiple dimensions theories the connection takes one of two forms.
They predict something about particles, e.g. an extra species or maybe a change in how they collide with each other. For example if we live in four dimensions photons flying toward each other bounce off each other 0.00012% of the time, but if there is a hidden fifth dimension they bounce off each other 0.00027% of the time.
Or they predict something about the heat signature of the big bang, e.g. if there are other universes out there, the should have affected the big bang and the cold patches in the big bangs after glow should be 0.0045% cooler than they would be otherwise.
For the multiple timeline theories, going into the way you connect it to reality would go outside the nutshell scope, it's a technical enough topic.
I've been thinking over the past few months how to express the essential mystery of quantum mechanics. As a result here is the briefest simplest version I can give. I've decided to cut all technical minutia and focus on the core issues in three short posts. This one is about the main issue with understanding Quantum Mechanics.
The Main Issue: The basic problem with Quantum Mechanics is that it doesn't really seem to be "about" anything.
In the mathematics of Newtonian Physics you can point to terms in the equations and say, oh that's a force, that's momentum, that's the position of the particle, etc Even the solutions of equations have an obvious meaning, i.e. this is the path the object will take.
In General Relativity it's the same. Yes it might discuss spacetime and four-dimensional curvature, these are abstract and strange. However it is still a narrative about entities changing and developing, they just happen to be very abstract entities.
Quantum Mechanics on the other hand is only "about" probabilities to see results. It just says "in such and such a circumstance when you have equipment set up in a particular way, you have the following chance of seeing this value for that quantity". However it doesn't say how things get those values. It's sometimes not even clear that the values are really a property of the object in question, an atom let's say, or just something you get when your equipment interacts with an atom.
It's not even really clear if an electron is actually an object in quantum mechanics, or just a bunch of probabilities arranged in a certain way, i.e. in certain experiments with equipment arranged a certain way you have a high chance of detecting charge concentrated around a point. However it's not clear that's actually due to you finding a small object with a charge, or is it just something that happens to your equipment in those situations.
This is not just philosophical musing, quantum mechanics itself is genuinely unclear about which is the case.
The following is additional and provided because I have noticed it helps some, but others find it confusing. If it is the latter for you, just ignore: Julian Schwinger in his book "The symbolism of atomic measurement" and Giacomo Mauro D’Ariano in "Quantum Theory from First Principles: An Informational Approach" both derive Quantum Mechanics from first principles as a theory of how a rational agent might assign chances to experimental outcomes, without basically any insight from physics. D'Ariano in particular essentially derives it as the most general mathematical theory of "learning", i.e. updating your knowledge of the world. This provides a clearer picture of the problem to some. What are you learning about? Just experimental results and how "bet on them", or something genuine about the world?
So continuing on, what is difficult when you try to make sense of QM? What aspects make it difficult to see what QM is about?
I realised three posts wasn't going to cut it, but I'm still trying to keep things brief! Apologies!
A brief sketch of QM mathematically will help.
Quantum Mechanics describes the current state of the world as a set of amplitudes. Amplitudes are numbers that when you square them, they give the probability of some event occurring. Right now, since I'm not giving anything an interpretation, that's all they are.
So there's an amplitude for anything of the form: Amplitude to see quantity A in region R have value V at time period T .
A concrete case would be: Amplitude to see the Voltage in this wire be 4.5V between 10:40 and 10:50.
QM might give this an amplitude of -0.2, squaring makes it 0.04. So that's a 4% chance of this happening.
Just note that the amplitudes can be negative, however since we square them to get the probabilities, the probabilities won't be.
The final component is the uncertainty principle. Most quantities come in pairs, like position and moment, voltage and electric potential. When the amplitudes for one are concentrated around one value, meaning that outcome is very likely, the probabilities for the other become more spread out and uniform. Or put another way, as one element of the pair becomes more certain, the other becomes more random. Such pairs are called conjugate variables.
With this in place, I'll begin a list of problems, spread over some posts, before ending with interpretations.
1. What's a particle?
So QM presents a very detached and almost totally observation based picture of a particle. It is simply the case that there are certain "states of the world", that is lists of amplitudes, where a set of quantities co-occur (abstract, but just wait).
So an electron is just a case where the amplitudes say certain equipment will always detect a bit of spin with a bit of electric charge. To then conclude that there is an object, like a little ball, that travels around holding those properties is a mental picture that QM doesn't give any particular support to. This will get more extreme in the two cases below.
The silver oven: Let's say I've set up an oven that burns silver and I build a piece of equipment that can detect spin and charge. I then notice the oven makes the detector click every 30 seconds. So I say I have detected an electron, which the oven produces at a rate of one every 30 seconds. My detector is sensitive enough to narrow the location of the clicks down to the nanometer.
Now, without touching the oven, I go off and get a new detector that can narrow the clicks down to the femtometer and position it outside the oven. So I will continue to get clicks every thirty seconds, but sometimes it will be three clicks. Two with negative electric charge and one with positive. In a particle based view, I have seen two electrons and one positron.
Why though? The oven creating the particles hasn't changed, I've just made the equipment finer in resolution. Now the normal intuitive explanation is that the equipment, by probing so deeply, provided the energy to create the particles, but QM is silent on this. In fact it always presents there being a nonzero amplitude to detect three clicks in a femtometer sized region. The previous equipment just didn't have access to regions of that size, but QM always said the possibility was there.
So what is the oven actually emitting. It's hard not to conclude that its just "some charge and some spin" which will be packaged as single or multiple clicks depending on your equipment.
The beam of light: Take a beam of light. The conjugate variables in the case of light is colour(frequency) and photon number. Hence the higher the probability for the light to be a single colour, the more spread out its probabilities are for photon number. This can be tested with Laser light. Lasers are states of the electromagnetic field that are highly likely to be observed having only one consistent colour. Consequently when you place a photon detector in front of them they have an equal likelihood of producing several values. The exact same beam of laser light could be measured as containing 10 photons one minute and 1000 the next.
Again how many particles are there? Is the possible conclusion that there is no such thing, simply probabilities for clicks?
Similar "uncertain particle count" occurs in all quantum mechanical system of sufficient complexity, for example most atomic nuclei have an indeterminate number of pions inside them. So to what extend can we say what anything is "made of", if particle count isn't fixed?
Ending on a brief point, even Hydrogen in QM is just a state with a set of amplitudes that "often" act like those of a proton combined with those of an electron. However some of the amplitudes for hydrogen events can't be parsed as a combination of those for a proton or an electron. So to what extend is it made of a proton and electron?
2. Interference:
In Quantum Mechanics possibilities can interfere. (If the mathematics below is tedious, skip to the bolded point)
Consider betting on a horse to come in various positions in a race, say 1st, 2nd, 3rd in a three horse race. The horse can be fed either Smithson horse food or Johnson horse food.
In the first case his chances of coming in the various positions are: (0.1,0.4,0.5)
i.e. 10% chance of coming first.
In the second case: (0.2,0.4,0.4)
If you don't know which of the brands of food the horse takes, you can combine the above to get: (0.15,0.4,0.45)
So a 15% chance of winning when you aren't sure of which brand he took.
However in the QM case, since amplitudes can be negative, we could have for the first case: (0.316,-0.632,0.707)
and for the second: (0.447,0.632,0.632)
I won't go into how these are combined when the horse could eat either brand of food, but the main point is that the second possibility would cancel out due to the minus signs.
Hence a quantum horse has a chance of coming second if he eats one brand, a different chance of coming second when he eats another brand, but if he could eat either brand he has no chance of coming second at all. It is possible for an outcome to cancel out from two different sets of possibilities,even though it is possible in each of them alone.
This is why the double slit experiment is confusing. There are points on the detection screen that have a chance of being lit up when either slit is open, but not when both are open, because the two events of "particle goes through right slit and hits point A" and "particle goes through left slit and hits point A" have their probabilities cancel out.
If you see the probabilities as purely a reflection of your knowledge, it is very hard to see how this is possible. How by not knowing a binary outcome (Horse food A or B) do I remove something that can happen under either outcome?
I've nothing profound to offer on that point unfortunately. I'm motivated to study it the same way I'm motivated to play sports, swim or read fantasy. I just like it. When I hear something from it I just want to know more.
Like many modified gravity theories, recent observations of galaxies like NGC1052-DF2, which obeys General Relativity without Dark Matter, make them less likely to be true.
It's easier to explain them as the presence or absence of Dark Matter, rather than some Galaxies obey General Relativity and others don't.
The theory also has internal problems related to energy-momentum conservation and how realistic it is that quantum systems would have the properties it requires.
EDIT: I should add that there are hints gravity and thermodynamics are related in some way, which this theory is attempting to use. However in its particular case there are the problems I mentioned above.
Okay back to the short posts, since the grunt work was done in the last.
3. Superposition:
Superposition is just when more than one of the probabilities is non-zero.
So let's say there is a particle that could be spin up or down. Definitely up is (1,0), definitely down is (0,1), a superposition is then something where the amplitudes are like:
(0.707,0.707)
If you square the amplitudes you get the chance of each (1/2 for both). So superposition is a case where various outcomes might be measured, i.e. If A,B,C,etc are outcomes it's just the case where the possibilities are
A or B or C or....
However the problem is that unlike "or" in normal probability, the separate outcomes can affect each other (interference above) or create new behaviour not possible in either.
For example in some atoms, there is a special frequency of light that when the outer shell of electrons has spin up the light is passes through, when it is spin down the light the light passes through, but when it is spin up or spin down the light is reflected. So "or" can create totally new behaviour.
Think about this if it were applied to everyday objects. Drug A doesn't cure a certain disease, Drug B doesn't cure it either. However if the drug was put in a box where nobody knew which one it was, i.e. it was "Drug A or Drug B", that did cure the disease.
It would mean double blind studies couldn't be done, because they'd create new effects (and indeed you can't do the equivalent of double blind tests on quantum objects)
If you combine 2. and 3. together, we can see that although QM describes things probabilistically, it is very hard to attribute this probability purely to lack of knowledge, since altering probabilities can destroy behaviour present in two of the outcomes, or create behvaiour present in neither.
4. Entanglement:
And here ends the difficulties, probably the major one. It is really just superposition applied to states of more than one object.
If I have two electrons, I can have four possible states for their spin:
Up, Up Up, Down Down, Up Down, Down
An entangled state is one like (using the order above):
(0.707, 0, 0, 0.707)
A half chance for both to be up and a half for both to be down.
States like this are a complex subject, but the essential point about them is that they are highly correlated. Many explanations of these types of states assume an interpretation, so I am going to give a completely interpretation neutral description.
Imagine a pair of gloves are made in a machine. One is the left hand glove, one is the right hand glove and one is red and one is green. They are each locked in a box and shipped to China and Chile. A scientist in Chile lowers a spectroscopy unit into the box and discovers his glove is red. Obviously he knows the one in China is green. However it's still 50:50 as to whether the Chinese glove is left or right handed.
Pairs of quantum particles are more strongly correlated than this. In the "Quantum Glove" case learning your glove is red not only tells you the other is green, but gives you a 75:25 chance that the other is left vs right handed, i.e. you learn a little about the properties you didn't measure.
The really confusing thing is that this only works for two gloves, not one on its own. If you had just made one quantum glove, finding out that it was red would still leave handedness 50:50
So learning one of a set of 50:50 binary options for one of the objects actually improves the odds for an unmeasured aspect of the other object. It is very difficult to understand how this could be the case. How do I affect and improve the probabilities for something I didn't even measure? In QM two objects can be so correlated that separate properties get linked. Learning about one means you learn a bit about the other, but only when you have two objects.
With this done, there is one more post. The interpretations.
Adán Cabello of the Universidad de Sevilla has shown that Quantum Mechanics can be explained if one assumes subatomic phenomena have no mathematical laws controlling them.
This would imply quantum randomness is more indeterminism, the actions of subatomic stuff cannot be predicted because no mathematical laws exist constraining its behaviour.
This is just the latest in a series of results showing issues present with all realist mathematical accounts of QM, i.e. explanations which explain QM via new underlying physics.
A picture is emerging that QM is simply a theory of knowledge or credence bookkeeping that agents must use for aspects of the world with no laws.
This no laws view is quite old, going back to Bohr and promoted by Wheeler.
What no laws means could be either that the fundamental stuff of reality is ineffable/indescribable or that quantum events reach into the same creative force behind the Big Bang and thus the events don't follow from any event currently existent in spacetime.
Well basically entanglement is a coincidence/correlation in the values measured for two particles that cannot be explained in the normal manner such correlations are normally explained in physics. Normal explanation are that two particles have related values because they:
(a) Are interacting now (b) Interacted with each other or a common third system at some point in the past
In entanglement with can rule out (b) experimentally via the Bell Inequalities and (a) seems to be ruled out by imposing relativity and separating the systems by a large distance (so that they can't interact due to the speed of light restriction).
If you want a simply picture of it. Imagine two photons and you can measure their Vertical and Diagonal polarizations. It doesn't matter if you don't know what exactly these are, just that they are two quantities X and Z. Something can either be polarized Vertically or not (X = 1 or X = 0). Same thing for diagonal polarization (Z = 1 or Z = 0).
Now when people measure the two photons they find the following:
Entanglement correlations
First Particle
X
Z
Second Particle
X
=
=
Z
=
≠
So if somebody measures X on the first particle and somebody else measures X on the second particle, they'll both get the same answer (both get 0 or both get 1). If one measures Z and the other X same thing. However if they both measure Z they'll get different results, i.e. one gets 0 and the other gets 1.
Try to think what possible values X and Z could have had that would obey this table. There are none.
So normal explanations are ruled out, because no matter how their X and Z values were set when they interacted with each other or some common third system, the values won't obey this table.
Now one possible way out is to say that when they get measured, one of them sends a signal/interacts with the other so that the others value gets altered to obey the table correctly. An example:
Let's say for the first particle (X = 0, Z = 0) and for the second (X = 0, Z = 0). This obeys all of the tables results except the ZZ combination. The idea would be that when the first particle has Z measured and found to be 0, then the first particle sends a message to the second changing its values to (X = 0, Z =1). Which will then obey the table correctly.
The problem is that the particles can be arbitrarily far apart, so this would require the signal to travel faster than light.
Okay fine you might say. However how come we never see these signals? If literally everything everywhere is sending them all the time (most objects in the world are entangled with something else). It turns out we should be able to see them. So you have to basically say that the signals work in a very fine-tuned precise way that evidence of them is always exactly washed out by the experimental noise of the equipment you use to detect them.
There are other explanations possible, they are: (a) Space is structured in such a way that the signal can pass without going faster than light, e.g. there are loads of mini-wormholes everywhere (b) The signal moves faster than light (discussed above) (c) Every time you make a measurement there are several worlds created (d) The particles send signals not faster than light, but back in time (e) There is no objective mechanical/mathematical/physical explanation of these coincidences between the particles values
For example in (d) when one particle gets measured with X and the other with Z, they send this back in time to their early versions so they can alter themselves in advance to obey the table.
The problem with (a)-(d) is that they all have to be fine tuned. We should have noticed the wormholes, faster-than-light signals, other worlds or retrocausal signals by now. You have to assume how each of these mechanisms work is precisely fine tuned to be washed out by experimental noise.
This has led most physicists to (e) (Cabello's work I mentioned above is just a strong case for (e)).
There are coincidences between the values of properties of different objects in the world that have no objective mechanical explanation. Literally why they coincide cannot be explained in mathematics or language, there is no mechanical account in terms of "objects X,Y,Z doing actions A,B,C" that can be encoded in any way. Beyond a certain level Nature has no "laws" as we conceive of them.
The best one can do is Quantum Mechanics, which provides a subjective first-person set of expectations for what quantum systems might do.
The options in the list to explain the phenomenon are difficult to quantify. Some of them honestly come across as science fantasy to some degree. I think option 'a' may seem to be the more viable of the options since space itself is not necessarily constrained by the speed of light threshold. At least, to my knowledge. I believe that's how mathematically they assert a warp drive could actually work.
To expand on this, and I am looking at this from my electrical engineering background. One of the things I often considered and I came across some videos discussing the topic as well is if it would be possible to create a communication device that could operate using entanglement. i.e. if you have a quantum radio and I have one as well which are both entangled with each other, could we actually use Morse code or some digital communication mechanism to communicate with each other instantaneously? Seems it would be a revolutionary concept from the standpoint of communication.
No, it is impossible to use entanglement to communicate faster-than-light. Provably so mathematically from Quantum Mechanics and experimentally verified not to be the case.
I can explain why if you wish, but it is a little technical.
This is the problem with options (a) and (b). They both should allow faster-than-light communication by default, however since we experimentally know that you can't use entanglement to do this, they all have to be precisely tuned to avoid it.
So the wormholes in option (a) by nature should allow you to transmit signals faster-than-light. Since you can't use entanglement this way, the wormholes have to have a specific structure that matches how our experimental devices work in such a way that signals never usefully get passed along them. The signal must get scrambled in such a way that it arrives as noise and not just noise, but noise that is indistinguishable from noise due to natural reception errors in the receiving device, otherwise we would have already noticed these signals. Same with the faster-then-light signals in (b).
This is the reason most physicists don't hold to these two views, they require ultra-precise fine tuning of the wormholes/faster-than-light signals. They require you to think that the faster-than-light signals get scrambled in a way that causes them to "sound" identical to the natural background hum of our equipment.
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