Wednesday, December 06, 2017

The cosmological constant is not the worst prediction ever. It’s not even a prediction.

Think fake news and echo chambers are a problem only in political discourse? Think again. You find many examples of myths and falsehoods on popular science pages. Most of them surround the hype of the day, but some of them have been repeated so often they now appear in papers, seminar slides, and textbooks. And many scientists, I have noticed with alarm, actually believe them.

I can’t say much about fields outside my specialty, but it’s obvious this happens in physics. The claim that the bullet cluster rules out modified gravity, for example, is a particularly pervasive myth. Another one is that inflation solves the flatness problem, or that there is a flatness problem to begin with.

I recently found another myth to add to my list: the assertion that the cosmological constant is “the worst prediction in the history of physics.” From RealClearScience I learned the other day that this catchy but wrong statement has even made it into textbooks.

Before I go and make my case, please ask yourself: If the cosmological constant was such a bad prediction, then what theory was ruled out by it? Nothing comes to mind? That’s because there never was such a prediction.

The myth has it that if you calculate the cosmological constant using the standard model of particle physics the result is 120 orders of magnitude larger than what is observed due to contributions from vacuum fluctuation. But this is wrong on at least 5 levels:

1. The standard model of particle physics doesn’t predict the cosmological constant, never did, and never will.

The cosmological constant is a free parameter in Einstein’s theory of general relativity. This means its value must be fixed by measurement. You can calculate a contribution to this constant from the standard model vacuum fluctuations. But you cannot measure this contribution by itself. So the result of the standard model calculation doesn’t matter because it doesn’t correspond to an observable. Regardless of what it is, there is always a value for the parameter in general relativity that will make the result fit with measurement.

(And if you still believe in naturalness arguments, buy my book.)

2. The calculation in the standard model cannot be trusted.

Many theoretical physicists think the standard model is not a fundamental theory but must be amended at high energies. If that is so, then any calculation of the contribution to the cosmological constant using the standard model is wrong anyway. If there are further particles, so heavy that we haven’t yet seen them, these will play a role for the result. And we don’t know if there are such particles.

3. It’s idiotic to quote ratios of energy densities.

The 120 orders of magnitude refers to a ratio of energy densities. But not only is the cosmological constant usually not quoted as an energy density (but as a square thereof), in no other situation do particle physicists quote energy densities. We usually speak about energies, in which case the ratio goes down to 30 orders of magnitude.

4. The 120 orders of magnitude are wrong to begin with.

The actual result from the standard model scales with the fourth power of the masses of particles, times an energy-dependent logarithm. At least that’s the best calculation I know of. You find the result in equation (515) in this (awesomely thorough) paper. If you put in the numbers, out comes a value that scales with the masses of the heaviest known particles (not with the Planck mass, as you may have been told). That’s currently 13 orders of magnitude larger than the measured value, or 52 orders larger in energy density.

5. No one in their right mind ever quantifies the goodness of a prediction by taking ratios.

There’s a reason physicists usually talk a about uncertainty, statistical significance, and standard deviations. That’s because these are known to be useful to quantify the match of a theory with data. If you’d bother writing down the theoretical uncertainties of the calculation for the cosmological constant, the result would be compatible with the measured value even if you’d set the additional contribution from general relativity to zero.

In summary: No prediction, no problem.

Why does it matter? Because this wrong narrative has prompted physicists to aim at the wrong target.

The real problem with the cosmological constant is not the average value of the standard model contribution but – as Niayesh Afshordi elucidated better than I ever managed to – that the vacuum fluctuations, well, fluctuate. It’s these fluctuations that you should worry about. Because these you cannot get rid of by subtracting a constant.

But of course I know the actual reason you came here is that you want to know what is “the worst prediction in the history of physics” if not the cosmological constant...

I’m not much of a historian, so don’t take my word for it, but I’d guess it’s the prediction you get for the size of the universe if you assume the universe was born by a vacuum fluctuation out of equilibrium.

In this case, you can calculate the likelihood for observing a universe like our own. But the larger and the less noisy the observed universe, the less likely it is to originate from a fluctuation. Hence, the mere fact that you have a fairly ordered memory of the past and a sense of a reasonably functioning reality would be exceedingly tiny in such a case. So tiny, I’m not interested enough to even put in the numbers. (Maybe ask Sean Carroll.)

I certainly wish I’d never have to see the cosmological constant myth again. I’m not yet deluded enough to believe it will go away, but at least I now have this blogpost to refer to when I encounter it the next time.

234 comments:

  1. JimV

    I never said that you can use QM to signal: you can't. That's the famous no-Bell-telephone theorem. But QM does require superluminal information transmission. That's what Bell showed. And information transmission does not require energy transmission. That's what my little example illustrates.

    All of the claims I just made are true. When I use the word "information" I mean Shannon information (which needs no adjustment at all to cover the pebble case). By a "signal" I mean a Shannon set-up that transmits information such that the transmitter state can be controlled by a person.

    You write "I don't go into Shannon Information Theory for the same reason I don't go into Sturm-Louiville Eigenfunction Theory: they are irrelevant to my argument, and red herrings." But as far as I recall, it was *my* claim that information transmission does not require energy transmission that set all this off. And what *I* claimed is using "information" in the way Shannon defined (and is perfectly intuitive as well.). So maybe all of this is just your insisting to misinterpret my terms. Rather willfully at this point.

    Shannon's definition, by the way, does not even require an agreement. Just the right counterfactual-supporting correlations.

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  2. Dan,

    I gave an example. It is decisive. There is a reason you keep changing it: namely because it is decisive. I'm not going to even bother with your modifications any more.

    I designed a signaling system that transmits one bit of information every 5 minutes. It transmits no information in the intervening time. When the information is "Bad Guy has not arrived" there is energy transmission between the transmitter and the receiver. When the information is "Bad Guy has arrived" there in no energy transmission.

    If Bad Guy arrives in the first 5 minutes then no pebble is ever thrown, no energy is ever transmitted, and a fortiori no energy transmission is ever modulated. But the signal is sent. This has become really pointless. I have no intention of worrying about Fourier transforms since they have nothing to do with my example. Your whole analytical apparatus has nothing to do with my example. It is just a counter-example to your claim. Unless you assert that no signal is sent in this last case (which is absurd) or that some energy is sent (which is absurd) you can't maintain that signals require energy. If you want to make one of the absurd assertions about my example, make it.

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  3. TM, if it was your claim that Shannon Theory does not disprove the possibility of energy-less signal transmission but does not prove it exists, then we are in agreement! Of course, I have not denied this. My claim has been that a simple model without any energy-less transmission covers all the same cases. (See previous comments for details.)

    (I have alluded to this before, so I still owe and will pay the 10 euros:) If the second party in the phone scenario has a heart attack and can not call when he should have, the first party will have thought there was a channel (under your model) when there was not, and that a signal was transmitted through that channel (under your model) which was not. I must admit (since I am assured that Shannon Theory covers every aspect of your scenario precisely) that I am impressed that Shannon considered and analysed such phantom signals.

    As I have also mentioned previously, my model or interpretation also works for quantum entanglement. Again it is a combination of previous information (quantum experiments) and locally-received information, without any actual transmitted signal from one entangled particle to the other. Physical confirmation of entanglement must be transmitted in the ordinary ways, as it is done in every experiment to conclude the experiment. Prior to that one assumes the entanglement (again, with the possibility of experimental error) based on previous results. (See previous comments for details.) (This does not deny that quantum entanglements are non-separable, with the resulting correlations.)

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  4. JimV

    No, it is not that Shannon merely *allows for* energyless information transmission and signaling, it is that by Shannon definitions is it trivial to construct energyless information transmission and signaling. My example is a trivial example, and your inability or unwillingness to acknowledge it is some glitch in you mind that you need to debug.

    Since you don't seem to know anything about Shannon, here is a little tutorial, although you should just learn it on your own. Shannon has three parts to an information transmission system: a transmitter, a receiver and a channel. All three are characterized by certain physical structure, and the analysis is carried out—how else could it be?—under the requirement that the structure remain intact. In my case, a heart attack would take the transmitter (me) out of the design specifications, so you need to redo the analysis. Not surprisingly, once you do the correct analysis for the new case, no information is sent.

    The "how do you know X hasn't gone wrong" question—how do you know that there has not been a heart attack, or someone built a wall between the buildings, or some third party has started throwing pebbles or whatever—just raises a skeptical regress that no theory of any sort can solve. The only way to get information about whether these sorts of things have happened is—surprise!—to use some information channel, which itself can be subject to further skeptical questions. That is as true of your type of signal analysis as of any other. That's called skepticism. If you want to start discussing skepticism, fine. But the most illegitimate way to critique any theory is to raise skeptical objections to it, while keeping your own pet theory insulated from even asking them. So here is a little exercise: take all of these skeptical questions you have raised about Shannon and apply them to your own approach. I guarantee you cannot solve them. This response to a criticism, by the way, goes by the name 'tu quoque".

    In any case, I am not really interested in "your model" model whatever it is. I was making the trivial point that sending information and sending energy are different things, and you can have one without the other. All of this is actually just a prelude to the really interesting question which has to do with *superluminal* transmission. My trivial example is obviously not superluminal, but that was not its intent. QM requires superluminal information transmission to violate Bell's inequalities at spacelike separation. It does not require the possibility of superluminal signaling. And it never even comes close to the neighborhood of superluminal energy transmission.

    The point about energyless information transmission and signaling was just a trivial point to make a clear conceptual distinction. The analysis of superluminal information transmission and superluminal signaling is rather subtle, and requires particular care about concepts and definitions. But superluminal energy transmission does not come into it at all: there is no reason in the world to think that is possible. So if you haven't clearly distinguished these three things in your mind you are bound to get confused. And if you refuse to acknowledge the first, trivial, example then there is no prospect of getting any of this sorted out.

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  5. Unless you assert that no signal is sent in this last case (which is absurd) or that some energy is sent (which is absurd) you can't maintain that signals require energy.

    Again, what I claim is that the signals are conveyed by the pulses (pebbles), and prior protocol agreement, and when an expected pulse fails to arrive, the receiver infers, based on all the previously received information and the reading on his own clock that the pulses have stopped some time between the last pulse and now. The receiver does not receive a new signal at this instant, he makes an inference. In effect, every time he receives a pebble, he re-sets a timer to ring a bell at 5 minutes and one second. If and when that bell ever rings, he knows the bad guy arrived at some time in the interval beginning with the last received pebble. But that bell isn’t an external signal, it is his own timer, initialized by an external signal and pre-agreed protocol.

    I gave an example. It is decisive.

    But your example is fallacious, as has been explained in detail. Again, you’re just transmitting a trailing-edge step function on a low frequency discrete carrier wave. This is a very well-known and thoroughly studied type of signaling, and it is not an example of energyless signaling. It is simply modulating the carrier wave (energy), with the understanding that the receiver requires some time after the last pulse of the carrier wave to infer that the modulation has definitely been applied, by pre-agreed protocol and his own clock. From this he can infer (with some imperfect degree of confidence) that the bad guy arrived (with transmission delay) some time between the last energetic pulse and the last pulse plus the pre-agreed interval.

    I designed a signaling system that transmits one bit of information every 5 minutes.

    This is a low frequency discrete carrier wave. You did not invent this. Such signals have been used and analyzed thoroughly for decades. Your innovation is just to mistakenly imagine that this represents energyless information transfer.

    If Bad Guy arrives in the first 5 minutes then no pebble is ever thrown, no energy is ever transmitted, and a fortiori no energy transmission is ever modulated. But the signal is sent.

    That reasoning isn’t valid. Without an agreed initialization, the receiver would strictly have to conclude that the bad guy arrived 18 billion years ago, because no pulse was ever received. Obviously by prior communication the bad guy has not arrived at “time zero”, so strictly there must be a pulse or some other communication to initialize the protocol. You could even post-initialize. For example, you might say “At noon on Jan 1, 2040, I will commence sending a pebble once every five minutes until bad guy arrives”, and so, one second past noon on Jan 1, 2040, having heard nothing from you in the intervening years and receiving no pebble, your friend calls the police. This is not an example of energyless signaling. (This is the same as your Hawaii trip.)

    I have no intention of worrying about Fourier transforms since they have nothing to do with my example.

    But they do. Energy corresponds to frequency, and the carrier wave has a different frequency than the signal wave, which in this case is a step function, which has its own non-trivial frequency characteristics. Look at the frequency spectral density and antocorrelation functions for simple step functions in the reference I cited.

    Failing that, it would be very helpful if you at least say whether you think that simply turning off the porch light when the bad guy arrives is an example of energyless information transfer.

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  6. All of this posturing, and parsing of terms, and slicing and dicing of concepts only underscores the fact that 83 years on, modern science still has no plausible physical explanation for the entanglement phenomenon. Except, of course, for Bohmian mechanics which, unfortunately, is generally disfavored, perhaps because it is physically plausible. That a plurality of 'scientists' prefer the scientifically vapid Many Worlds fantasy should be scandalous in its own right.

    Ultimately, entanglement of the Alice-Bob sort is a scale dependent, highly constrained laboratory experiment that tells us something very interesting about how matter and energy interact on quantum scales. It can even be said that it tells us something fundamental about matter-energy interactions, but only on that scale. The experiment does not tell us something metaphysically fundamental about the nature of physical reality - that reality is inherently indeterminate. Physical reality has both determinate and indeterminate aspects, the relative mix of the two effects varying with scale.

    What Bohmian mechanics gets right about this is the interplay between determinism and indeterminism at the quantum scale, where the electron always has a definite position but its position at some future time cannot be predicted except as a probability distribution. This is because the electron's interaction with the chaotic sub-quantum field, that produces the associated pilot wave, cannot be fully specified over time.

    Entanglement is then consequent on two electrons sharing a common source pilot wave, giving them a light-like, time-independent connection via the pilot wave, even as their paths diverge. This phenomenon does not scale.

    It follows therefore, that quantum behavior is fundamental only to the quantum scale but not to the classical or cosmological scale, each of which has its own behavioral characteristics, even though all three scales are interrelated. In the aggregate they constitute physical reality.

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  7. "Dan",

    So I admit to being naive, and having thought that you were actually posting under a real name, and were a real person. It is a pity to have to go through life on guard all the time. Especially when your only motivation is to try to clear up some of the manifold confusions that are preventing progress in physics. But "Dan Couriann" is just a phony name made up for this occasion, and you are just a troll. I guess that is better then your actually being as dim or as willfully stubborn as you made out.I guess.

    The interesting question is what your motivation is. I have some conjectures, but will keep them to myself. Communication ended.

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  8. After reflecting on what Tim has said and reading the back-and-forth, it looks like Tim and other participants may be talking past each other. So I decided to jump into the discussion another time after being "scolded" by Tim for mangling/muddying his clean examples with a different measuring system involving a calorimeter...

    After thinking about Tim's comments in a different light, I've decided that he is quite correct about energyless information transfer, and that his examples of this are indeed valid. JimV and Dan, see if you agree with my thinking; and Tim, please correct me if I'm misrepresenting the situation.

    It seems there are two forms of information under discussion here, where Tim is talking about one and those who disagree with Tim (including me, until I thought about it differently) are talking about another. I'll call the first form "information in general" and call the second "information we care about."

    I think those who disagree with Tim are assuming the second kind. Here, we're waiting for the Bad Guy to arrive or some other event of interest; that's the information we care about. We expend energy either continuously or at discrete times to indicate "all is normal" and then turn of the signal when the event has occurred. Clearly the signal we care about can never occur without an expenditure of energy, either when telling the receiver to start waiting for a signal or while sending a stream of "all is normal" indicators. I proposed the calorimeter detector as a way to make this idea more transparent.

    However, I don't think Tim is talking only about "information we care about." Looking at the signalling system differently, it seems clear that both in Tim's examples and Dan's "carrier signal" we can't disregard the fact that information is being transmitted (using energy!) each time a pebble is thrown or while a light beam is being emitted. Namely, "all is normal" is information too, even though it may not be "information we care about." Thus, a bit of information is transmitted every time a pebble is thrown, but a bit of information is also transmitted when a pebble isn't thrown as expected. Clearly the pebble throwing involves energy transfer, and equally clearly it doesn't require energy to not throw a pebble. So Tim's claim is valid in that regard, as long as we include "all is normal" as information too.

    Again after thinking about it, it seems clear that invoking prior agreements, algorithms, etc. (which surely require energy to create) is beside the point, as Tim has argued. In effect the algorithms and agreements are nothing more than "maps," i.e. they map bits of information (e.g. pebble thrown or not thrown) to "information we care about." Once in effect, the maps merely take a binary input (thrown/not-thrown or on/off) and translate it to an output that is more useful to the information consumer. If they are regarded as maps in a mathematical sense (i.e., abstract objects rather than energy-consuming devices that perform the task), then clearly they only change the input from one form to another without creating or destroying information.

    So, Tim and others, do you agree? Have we actually been talking about the same view of information, or only thinking we have (and arguing accordingly)?

    If we can get on the same page about this, I'm hoping Tim will move the discussion forward to entanglement, etc.

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  9. And Tim, I don't know whether "Dan Couriann" is the actual name of the commenter, but I doubt that he is merely a troll. He seems sincere in his arguments, and is trying to illustrate his point in different ways. But like I suggested in my previous comment, I don't think you are arguing about the same notion of information as he is; there may have been a basic breakdown in communication.

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  10. Tim,

    “Let me repeat one more time...correlations are only defined between *sequences* not between individual states. Put it this way: think of the Game of Life CA. if you just pick two cells at some time and ask "are they correlated?", you have not even asked a question with any content. At any given time either they are in the same state (both on or both off) or in different states (one on and one off). Neither of these possibilities is more "correlated" than the other. But if we track the state of the two cells over some period of time and get a sequence for each—off, on, on ,on, off, off, on, etc. for one and another sequence for the other—then we can sensibly ask whether the sequences display any correlations. That is a well-defined mathematical question. It can be asked of any pair of sequences, irrespective of the causal structure of the CA. “

    You can know if two cells (or two groups of cells) are correlated in two ways:
    1. Register a long sequence of states and apply some statistical tests to see if some correlation exists. You need to do this when you either don’t know the rules or, even in case you know them, if you don’t know the large distance consequences of those rules.
    2. Look at the math.

    Now, I specified that the CA I am interested in is a CA where the laws of classical electromagnetism are implemented. So, we know both the rules and the large distance consequences of those rules. For example, we know how the electric field parameter of one cell depends on the charge parameter of another cell (Coulomb’s law). So, there is no point in providing a long sequence of states. We are in the option “2”.

    “Now I claim that in the Game of Life, as long as there are a lot of cells active and no large scale exact symmetries, both the states of individual cells that are far apart and the parities of groups of cells that are far apart will almost always be statistically independent of each other.”

    Game of life is not the kind of automaton I am arguing for. It is a “billiard-ball” type of CA, not a “field-like” CA. And I have already agreed that such a CA allows for statistical independence (except for the case of fine-tuning). So, again, think of a CA simulation of classical electromagnetism, not of a CA simulation of bullets or billiard balls. You cannot explain E-M induction using billiard-balls so why in the world would you even consider such a model to explain QM? It only makes sense to start from the most advanced classical model, and that is a field model.

    “Now to appeal to a common cause explanation here, it is not enough just that the two sequences have *some* common causes in the overlap of the past light cone. Those common causes must, all by themselves, *determine the states that display the correlations*, e.g. determine the state of the individual cell or the parity of the group of cells.”

    The common cause is the global state of the system in the past. That state is special because it has to obey the constraints imposed by EM laws. And we know that such a state will evolve into another state that also satisfies those constraints (otherwise the theory of EM would not be consistent). So, if we agree that in the past the field is related to the charge distribution it remains so in the future.

    -will continue

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  11. -continuation

    “And then add on top of all that the example I have gone back to over and over: setting the apparatus by the parity of the digits of pi. In that case, the "common cause" can do no work at all: the sequence of apparatus settings is determined by the parity of the digits of pi, and nothing in the past light-cone of the computer can influence that at all. So there can be no common cause.”

    Before the experiment begins the detector (that is coupled to the computer) has to be in state that will necessarily evolve in a future state that describes a computer calculating Pi. This is a consequence of determinism. That state is unique. If you want your computer to calculate sqrt (2) instead of Pi you need a different past state for that. If you want to replace the computer with some other “device” to control the settings (like a radioactive source connected to a counter or a monkey trained to press buttons) you need again a different initial state. Each of those states will determine a different field configuration at the location of the source. So, the source “knows” that you are going to calculate Pi, or sqrt (2) or if there is a monkey there and what the monkey will do, and so on. Of course, this is metaphoric, the source only knows the position/momenta of the electrons and quarks in those devices but this is enough to determine their behavior.
    OK, so in the past the detector is in the state like:

    “I am ready to start calculating Pi and rotate the polarizer following algorithm A”

    And the source is in a state like:

    “I know from the local electric and magnetic fields that there is a detector over there that is going to calculate Pi and rotate the polarizer following algorithm A”

    When the experiment starts the detector unsurprisingly starts rotating according to algorithm A using the digits of Pi and the source feeds it with specially designed particles that will give results in agreement with QM.

    “the sequence of apparatus settings is determined by the parity of the digits of pi, and nothing in the past light-cone of the computer can influence that at all”

    This is a denial of determinism. Not only that the past state of the CA in the region the computer is located “influences” the computer’s behavior, but it uniquely determines it. The fact that you are calculating Pi now implies that the past state was as such that calculating Pi was inevitable.

    “I think you are getting stuck on two points. One is that you are thinking about individual pairs of states rather than sequences of states and the other is that your simple example of the single charged particle is too simple.”

    I have addressed that above.

    “There my be correlations in distant sequences in such a simple world exactly because there is a common cause that *alone determines* the states of the distant cells. But in a complex world this just isn't the case, and your example does not hold up.”

    An increased complexity (more charges) does not get you independence. The fields are still related to the particle distribution in an exact way. For the electric field you need to apply the (classical) superposition principle, just add the fields originating from each source.

    Andrei

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  12. Marty, thanks for your participation. The issue I have is not that person B (when person A is calling or not calling person B) doesn't learn anything (or think he or she does) by the lack of a scheduled call, but that this "information" is not a solidly-transmitted fact but a conjecture (which could easily be mistaken), or inference. We learn things (or think we do) by inference all the time. When nothing has been physically transmitted to us, nothing has been transmitted. If we start calling a non-transmission a transmission, where does this end?

    TM's logic seems to be, I can represent this as a transmission using SIT, so therefore it must exist and be a transmission. My reasoning is, I can represent it as a non-transmitted inference and my system works equally (if not more simply) well. I am not arguing that he can't represent it as a transmission in SIT, but I prefer my interpretation, in which transmissions are physical things that can be detected by third parties and therefore proven to exist, and things that form in our minds due to previously-transmitted information and local information are inferences.

    He seems to think I am missing or refusing to acknowledge the beauty of SIT. For my part, I think he is missing the point that if there are two models for a process (say phlogiston or oxidation), one gets to pick which one is more convincing in explaining the evidence.

    This is what I have been saying all along, so I feel I owe the site another 10 euros. I encourage all other participants to consider whether they too are saying the same things and if so, pay the same toll. (Non-donations are not the same thing as donations; although I am sure they are in some model.)

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  13. TM, so when person A keels over, and person B thinks he has received a signal but hasn't, you agree that he did not receive a transmission. Yet he thinks he knows something as a result of not receiving a signal. He thinks he has information. Has he not then made an inference? If he can do so legally then, why not in all cases? (Sometimes a correct inference, sometimes a mistaken inference.)

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  14. Marty

    Everything you said is perfectly accurate. The only quibble is that it is not my theory of information but Shannon's, which is just the standard theory to use, especially if you want to quantify information. And another is that, as I have mentioned, Shannon's definitions do not even require that there be anyone to set a protocol or "interpret" a signal: I just added that to make the situation more vivd. All Shannon cares about, once you have defined the physical parameters of the transmitter, reliever and channel, is the counterfactuals (or subjunctive conditionals) between states of the transmitter and states of the receiver. If the transmitter should be in State A1, what are the probabilities (given the physics of the channel and the receiver) that the receiver will be in each of its possible states. Same if transmitter should be in State A2, etc, through all the possible transmitter states. From these conditional probabilities, Shannon can quantify how much information about transmitter is transmitted to receiver. If the transmission channel is cut, so there is no dependence of the state of receiver on the state of transmitter, then zero information is sent. In this sense, trees rings record information about rainfall: had the rainfall been different, so would the size of the rings. No one settled any protocols for this to be the case.

    Shannon was working at Bell, and cared about real information transmission over phone lines, including noisy lines where the connection between the state of the transmitter does not alone determine the state of the receiver. I have been discussing a noiseless channel, because it is simple and makes the points more clearly. All that is important are the subjunctive connections (the conditional probabilities) between the states of receiver and transmitter. Whether, in any particular instance, any energy is transmitted from transmitter to receiver (which is the only question I have been interested in) is nether here nor there as far as Shannon is concerned. And these absolutely trivial examples were just meant to illustrate that.

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  15. Andrei

    I have been talking about a CA with local dynamical rules (i.e. the next state of a cell is a function of only its present state and the states of adjacent cells) because that's what 't Hooft has in mind, and because locality is the central issue at the end of the day. I don't know what you have in mind by a "field-like" system, but if it is not local, i.e. is the dynamics requires that you specify the state of *all* of the cells in order to determine the next state of *any* of the cells, then we are not talking about a local physics at all. If you are thinking of Coulomb's Law as an instantaneous action-at-a-distance law, then you are not implementing classical EM. Of course Gauss's law holds, but you can't use that to transmit any information because you can't vary the net charge of a system at all.

    Here is a key sentence: "Each of those states will determine a different field configuration at the location of the source". Not in a CA it won't! think about what you are claiming. You are claiming that each individual cell of the CA contains complete information about the global state of the entire universe! Unless each cell has a monstrous number of states available, that can't possibly be correct. And the more monstrous the number of possibilities for each individual cell, the huger the space of possible global states, and so the more monstrous each set of individual cell possibilities would have to be. At the end, you need not a CA but Leibniz's theory of Monads, where the state of each Monad reflects, in perfect detail, the state of all the rest. This is not physically possible or even mathematically possible for a CA. How many distinct states are you thinking are available for each cell in your CA anyway?

    Here is another key passage "Each of those states will determine a different field configuration at the location of the source. So, the source “knows” that you are going to calculate Pi, or sqrt (2) or if there is a monkey there and what the monkey will do, and so on. Of course, this is metaphoric, the source only knows the position/momenta of the electrons and quarks in those devices but this is enough to determine their behavior." Again, you are assuming that each location has full information about all other locations at that time, which is impossible, but you are assuming even more. Suppose you know that I am about to calculate the digits of pi. Suppose you even know the algorithm I will use to do it. And suppose you want to set the value of some parameter of a particle so it reflects the parity of the digit of pi that will be being computed when the particle reaches the detector. Well, even with the information you have, your work is not done. What you still have to do is *calculate the digit yourself and figure out its parity*. And you have to do all this before you can pre-set the particle to the appropriate state. But how in the world is the source going to manage that trick! It doesn't have a computer to use to do the calculation.

    You are not thinking physically or clearly here. Classical EM does not imply that the state of every small region encodes the complete global state: it can't. Nor can any CA.

    A simple example may help. In a vacuum, the total EM field is everywhere zero. In the interior of a charged sphere, is it also zero, So the local state does not determine the global state. And all the laws of EM are satisfied.

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  16. JimV

    There are not competing theories here. Shannon information is Shannon information: it is what Shannon defines it to be, and in any physical situation where the operating parameters of the transmitter, receiver and channel are satisfied the Shannon information is transmitted. The existence of any other way to conceptualize or quantify information and information transmission is not relevant. I am using Shannon's definitions to analyze the situation.

    In my scenario, having a heart attack was not within the proper operating parameters of the transmitter. If you want it to be, fine: then the state of the room across the street at a certain time contains information that either Bad Guy arrived within the last 5 minutes or there was a heart attack in the last five minutes. And similarly for any other eventuality you want to contemplate. But the same holds for any definition. A pebble hits the window. You want to think of that as a "real" transmission. But it may be a pebble from across the street or from some third party. If you want to take account of that new possibility then things get more complicated. The case with the heart attack and no-pebble is exactly like the case of the third party and pebble. In each case you might make an inference and be mistaken. Your making the inference was just a device to make things vivid: Shannon does not rely on anyone making an inference for there to be information transmission. All that is required is that the state of the receiver depend on the state of the transmitter in a certain way. As I said, tree rings contain Shannon information about earlier rainfall, no matter whether anyone ever infers anything from the tree rings or not.

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  17. TM, you seem to have a Shannon hammer and think all information is obtained from Shannon-nailing. I think there are various ways of obtaining information, which includes inference.

    If information is only obtained via Shannon transmission, then it would seem that there is no new, original information, since all of it must have been transmitted from somewhere else.

    So far your definition has expanded from imaginary channels to phantom transmissions to transmissions which contain all possible information at once, whether the recipient realizes it or not. If you prefer that model, that is your privilege. I prefer mine, which has not had to be expanded.

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  18. TM, I should have responded to your point that a fake call (or pebble) can be transmitted.

    There is the difference however, that there are ways to authenticate physical transmissions, and a careful person will make use of them for important communications. How is this to be done for non-transmissions where there is nothing to authenticate? Does Shannon cover this?

    It is not so much that I want physical transmissions "to be real" (I think they are, although they may be misleading) but that you want non-transmissions to be transmissions. I see no problem with thinking things that can be physically-detected are real. I do with thinking that things that can't be physically-detected (such as spirits) are real. Perhaps our notions of reality are different. (And there goes another 10 euros.)

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  19. JImV,

    I really don't know how to end this. I am using standard information theoretic definitions to analyze an information-theoretic problem. Our interest in this case requires information transmission from one location (Room A) to another (Room B) because our question is whether information about one room is available at the other. We are treating the presence or absence of Bad Guy in Room A during a 5-minute window as a free one-bit variable. The person in Room B simply cannot get information about the value of that variable—a variable that pertains to the physical state of Room A—by inference from the information they have initially. That is clearly impossible. That would be precognition. In order to be in a position to infer that Bad Guy is in Room A, the person in Room B must acquire some new information about Room A. He does. I have explained, in painful detail, how and when the the information gets to Room B, and how the person in Room B thereby comes to be able to make the critical inference. Further, the presence or absence of anyone in Room B is neither here nor there. That is just an extra detail to make the facts vivid. Even if Room B is empty, and no one makes any inferences, the information from Room A arrives at the moment and in the way that I have described. It is only with the arrival of that information that there is enough information in Room B to make the inference possible. And that information from Room A and about Room A arrives in Room B without being accompanied by a speck of energy from Room A.

    These are just simple, straightforward facts. At a certain time, there is more information about Room A available in Room B than before that time. If you want to try to construct an alternative to Shannon's theory, that is your privilege, but you'd better construct it to get this result, or else it is just wrong by any standard. Meanwhile, if you want to be able to tackle the very tricky problem of superluminal information transfer and superluminal signaling, you need an actual, correct theory of information and information transfer. If yours does not get the simple room-and-pebble case right, then it will be of no use at all for the interesting and difficult case. Because it is trivial that nothing to do with entanglement transmits any energy. So long as you remain wrongly convinced that energy transmission is a prerequisite for information transmission or for signaling, you won't have a chance to understand what is going on in Quantum theory, or the significance of violations of Bell's inequality.

    Long story short: to reliably violate Bell's inequality for experiments done at space-like separation there has to be superluminal information transmission between the sides. But there is zero energy transmission between the sides. So if you insist that information transmission requires energy transmission you must conclude that QM cannot predict violations of Bell's inequality in this setting. But it does. So your assumption is just flat wrong.

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  20. Marty says "A bit of information is transmitted every time a pebble is thrown, but a bit of information is also transmitted when a pebble isn't thrown as expected."

    There isn't a transmission of information when a pebble isn't thrown. Remember, the detection system consists of a pebble detector and a clock, which is initially set to zero and rings the alarm bell if it reaches 5 minutes plus (say) one second. Each time a signal (pebble) is received, the clock is reset to zero, so the bell never rings until a pebble has not been received for over 5 minutes. The only signals transmitted from house to house are the pebbles. The expiration of the timer and ringing the alarm bell does not coincide with reception of a mythical "energyless signal" (which would violate a basic principle of physics), it is simply a deduction that can be reached, from the agreed protocol, using the pebble signals and the internal timer at the receiver.

    Hopefully it's clear that if a continuous signal was turned OFF when the bad guy arrives (turning off the porch light), it would not be an energless signal. This is a simple step function on a continuous carrier that looks like this

    ----------------_________________________

    But we can just as well impose a step function on a discrete pulse carrier, so it looks like this

    --__--__--__--__--_________________________

    Because of the crude carrier wave, the receiver needs to wait a certain amount of time to verify that the step function has been applied, using an internal timer, but this obviously does not represent energyless transfer of information.

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  21. TM, as I dimly understand it, Shannon was interested in transmitted information and how to distinguish it from random noise. The fact that he defined that sort of information in a certain way does not prove that all information is obtained by transmission and reception. Can you prove all information is obtained that way? You have not done so thus far (nor answered my previous objection to it), you have merely assumed it. You have not proved that inferences do not exist. If they exist, and I think they do, I have a viable model.

    The plain fact from my point of view is that non-transmitted messages are not transmitted. Since no transmission was involved, information gleaned from them, when it is, is gleaned by inference (causing some energy to be expended by the brain cells involved).

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  22. Hi JimV,

    You said:
    The issue I have is not that person B (when person A is calling or not calling person B) doesn't learn anything (or think he or she does) by the lack of a scheduled call, but that this "information" is not a solidly-transmitted fact but a conjecture (which could easily be mistaken), or inference. We learn things (or think we do) by inference all the time. When nothing has been physically transmitted to us, nothing has been transmitted. If we start calling a non-transmission a transmission, where does this end?

    Tim may have already addressed this satisfactorily for you, but I'll say something anyway. I agree with you that the lack of positive indication (involving energy transfer) for both "not yet" and "it happened" means that you can't have full confidence in your inference about whether an event of interest has occurred. Two comments about this:

    1. Even if you set up the protocol to give a positive indication of whether the event has occurred, you necessarily rely on inference to some extent in drawing conclusions. For example, let one pebble thrown every five minutes mean "not yet" and two pebbles thrown in rapid succession mean "it happened." If you only hear one pebble can you positively say that the event hasn't happened yet, or must you allow that the thrower didn't have a heart attack right after throwing the first pebble? Or can you say positively that a squirrel didn't kick a nut against the window immediately after a pebble was thrown, giving a false signal? Presumably you never assign probability P(event)=1, but assign different probabilities (usually very low) to different kinds of channel/transmitter/receiver interference.

    2. If you look at Tim's example, then the same reasoning applies. If you hear a pebble thrown every five minutes, you can't completely discount the possibility that a squirrel kicked a nut at just the right moment or an accomplice spoofed you by throwing a pebble at the right time (both are sources of "channel noise"), but presumably you assign correspondingly low probabilities to those alternative scenarios. Likewise, if you don't hear the pebble hit the window when expected (no energy received) then you can't completely discount the possibility that the sender had a heart attack, or the pebble hit a bird that randomly flew in front of it -- you would assign relative probabilities to each alternative, presumably.

    Thus, in a realistic situation the best one can do is assign conditional probabilities to each outcome: given that you heard a pebble hit (or not hit), what is the probability that the received signal gives information about the actual state of interest rather than just being noise? (Here, the received signal contains energy if the pebble hit the window, and has no energy if no pebble hit when expected.) If the conditional probability is nonzero that the received signal is uncorrupted by noise, then it seems necessary to conclude that some information has been passed, regardless of whether the inferred signal contains energy or not.

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  23. JimV

    I don't think you have bad intentions, but if you can't get even the basic question here then there is just no point of going on. The issue is whether a signal can be sent from Room A, carrying information about Room A, to Room B without there being any energy transmission *from Room A to Room B*. The fact that energy might be used inside the brain of someone in either room is completely irrelevant to the question.

    Inferences do not produce new information. That is actually the point of a deductive inference: the content of the conclusion is already contained in the premises. The person in Room B does not arrive at their knowledge that Bad Guy has arrived in Room A by inferences *from the information that they had when they entered Room B*. If they did, then they could have arrived at that conclusion immediately. The fact that later they can conclude that Bad Guy has arrived means that they have in the mean time received fresh information, information about the goings-on in Room A. Shannon explains how that information got there and when. You seem to want to deny that the information about Room A ever got to Room B at all, which is obviously false. That is all there is to say. I'm done.

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  24. Marty,

    Thanks, that is exactly right. The way Shannon would put this is that the physics of the transmitter and the information channel are idealized in some way (no heart attacks, no squirrels, etc.). If you come to worry about the ideaization, you can make the model more complicated. You would need some statistics on how often heart attacks occur, and squirrels kick nuts....that would be more noise in the channel. No matter what you do, you will never be certain that something you didn't think of hasn't happened, but that's just life.

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  25. JimV says "We learn things (or think we do) by inference all the time. When nothing has been physically transmitted to us, nothing has been transmitted."

    Right. The receiver in this scenario can't just listen for pebbles (or non pebbles), he must also have a clock. The correct description is that he can infer the arrival of bad guy if/when more than five minutes has passed since the reception of the last pebble. No "energyless signal" is transmitted.

    To really understand this in detail, it's necessary to distinguish between the carrier wave (represented by the pebbles) and the signal wave (corresponding to the step function modulating the carrier to zero when the bad guy arrives). A perfectly uniform carrier wave conveys no information. Only by modulating the carrier wave do we create a signal with information. For example, if the porch light (continuous carrier wave) is ON until the bad guy arrives, and then we turn it OFF, the signal is neither the ON state nor the OFF state, it is the edge from ON to OFF. But this obviously is not an energyless signal, and the same applies with a discrete carrier wave (like pebbles), which just provide poorer resolution of precisely when the transition occurs. Again, there is no energyless transfer of information.

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  26. Tim,

    I just sent you an email about violations of Bell's inequalities to your nyu.edu address. Am "warning" you here in case you have a spam filter that routes emails from a .org address to a spam folder. You'll recognize my first name.

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  27. Tim says Inferences do not produce new information. That is actually the point of a deductive inference: the content of the conclusion is already contained in the premises."

    You're overlooking the crucial role of the receiver's clock. If the receiver had no sense of time, he could never conclude that the bad guy had arrived. This shows that there is no "energyless signal" at the 5 minute mark. It is the receiver' own internal clock, combined with the received pebbles and the agreed protocol, that enable the inference. So, there is no energyless signal.

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  28. Well, I am convinced that TM and Marty think a non-transmission can transmit information, and this does shake my confidence; but going down this road seems paradoxical to me, for the following reasons:

    From two previous comments:

    "The difference with your Andromeda case is easy: the state on the earth will be exactly the same whether or not your inference is correct. The state of the receiver (Earth) is not sensitive in this way to the state of Andromeda."

    "Yes, you are not getting phone calls all the time, and that does of course give you real, precise, definite information that you would not have if the phone were not present or were ringing. For example, from my not getting a phone call right now, I get the information that Donald Trump, whatever he is doing, is not calling my number right now."

    So under TM's model, I have not been getting calls from about 7 billion people for my whole life and these "transmissions of information" must have changed my state. Yet I never noticed it or thought about it. So far, Andromeda thoughts have had a bigger effect on me.

    That might be an exaggeration, though, because at another time it was stated that an active channel was necessary as part of the set-up. So people who don't know my phone number, are asleep, too busy doing something else, etc., shouldn't count? That leaves a much, much smaller number, so few in fact that there are probably times when I not getting any non-
    calls at all; and the next moment a friend wakes up, picks up a phone, and doesn't call me. I of course notice nothing different about this "change of state".

    It seems this is the sort of information transfer that cannot be detected unless you make an effort to think about it (which by the way takes energy - more energy than simply absorbing specific physical information without considering alternatives), and you are not apt to think about it without some previous cause, i.e., by previous information and inference.

    Further, it has been admitted that non-call information-transfer must contain all possible conditions that could have led to the non-call (heart attacks, etc.), which might include things that no human could conceive of in our present state of knowledge, as well as lots of things that individuals do not think of (as when they were not included in the
    original example). What changes in our physical state or surroundings as all this different information bombards us? How do we actually detect any of it? I think by going over a limited number of possibilities that are generated (if any) in our minds and trying to determine which of them is most likely - inference.

    Note also there is usually one and only one salient reason to not get a call from someone (e.g., usually not a heart attack) but this specific reason is not physically distinguishable - other than by inference. The rest is actually misinformation. So if a non-call is a real transfer of all this information from somewhere else and the information is not locally generated in a person's brain by inference from previous experience, it is mostly bad information and mostly not received (detected).

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  29. JimV and Dan

    You are getting hung up on the word "changed". Right now, if your phone is not ringing, then you a getting Shannon information about every person on the face of the earth with a working phone. You are getting the information than none of them are calling you.

    Does this information "change your state"? In the intuitive sense, of course not! But that is not the relevant question. The relevant question is: would your physical state *have been different from what it is* had any one of those billion of people been calling you? And that answer to that, supposing the phone system is working, is obviously "yes". If any of them had been calling your phone would have been ringing and the physical state of your eardrums would be different. Indeed, your presence or absence is irrelevant: the information is in the state of your phone, whether or not you are there to hear it. Information transmission does not require that anyone make any inferences, or "retrieve" the information at all. There was all sorts of information transmission in the world before there were any humans or any animals with brains. As I mentioned, the pattern of tree rings contains information about the amounts of rainfall in the area years earlier. They contain that information whether or not anyone ever bothers to examine and measure the rings, or make any inferences. The point is that *if by examining the rings one can find out about the rainfall, then information about the rainfall must be encoded in the rings*. The information is there. And Shannon's analysis says it is there. Any acceptable account of information must entail that it is there.

    This holds true as well in the pebble case. At a certain time, at five-minute intervals, the state of the window contains information about the state of Room A because the state of the window would have been different if the state of Room A had been different. It may be that an observer needs a clock to extract that information, but that is neither here nor there. The person with the clock can only extract the information because the information is in the state of the window. If the information were not there, then no amount of clocks or anything else will help. You can't get blood out of a stone no matter what you do, and you can't get information out of a window no matter what you do (using clocks, etc.) if the state of the window does not contain the information. The relevant information is evidently not in the clock!

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  30. Tim,

    “I have been talking about a CA with local dynamical rules (i.e. the next state of a cell is a function of only its present state and the states of adjacent cells) because that's what 't Hooft has in mind, and because locality is the central issue at the end of the day. I don't know what you have in mind by a "field-like" system, but if it is not local, i.e. is the dynamics requires that you specify the state of *all* of the cells in order to determine the next state of *any* of the cells, then we are not talking about a local physics at all. If you are thinking of Coulomb's Law as an instantaneous action-at-a-distance law, then you are not implementing classical EM. Of course Gauss's law holds, but you can't use that to transmit any information because you can't vary the net charge of a system at all.”

    I used Coulomb’s law (in fact only the inverse-square law describing the electric field, not the force itself) just as an approximation to the full theory because it is simpler and easier to visualize. I did not make any use of its non-local behavior (I have always referred to correlated past states evolving to future correlations). The only property I am interested in is that the fields in one region are correlated to charge distribution in another region. And this is true in the full, local theory of classical EM only that you have to make the appropriate Lorentz transformations.

    Before addressing your other objections I want to make a clear distinction between two different claims that I support here with different degrees of certainty.

    The first claim is that CA-superdeterministic theories are not ruled out by Bell even without using non-scientific assumptions like the fine-tuning of initial conditions. I think that my argument here is strong and it rests on:

    1. There is a natural way to select a special subset of possible initial states by requiring them to be compatible with the laws of electromagnetism (or GR, or some other field theory ).

    2. Statistical independence assumption does not hold in such a theory. This can be easily seen from the fact that there exist field states at the location of the source that are incompatible with some charge distributions of the detectors. Trivially, a null electric field at the source is not compatible with a net positive charge at the detectors. This is enough to falsify the statistical independence assumption. If you accept the Wikipedia definition:

    “ two events are independent, statistically independent, or stochastically independent[1] if the occurrence of one does not affect the probability of occurrence of the other”

    we have the case that the occurrence of one ( a detector state with a net positive charge) makes the probability of a null field at the source exactly 0 so the source would not be able to emit particles corresponding to such an environment. There is one assumption we need to make here, that the spins of the emitted particles depend on the field at the source, but this is hardly a controversial one.

    -to continue

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  31. -continuation

    Now let me respond to your other objections keeping in mind that those objections do not contradict the above weak claim but another, stronger one, that superdeterministic CA’s are actually true (not only they are not ruled out by Bell but they can actually reproduce QM). The evidence here is much weaker and what I am going to say is mostly speculation, but I will give it a try:

    “Here is a key sentence: "Each of those states will determine a different field configuration at the location of the source". Not in a CA it won't! think about what you are claiming. You are claiming that each individual cell of the CA contains complete information about the global state of the entire universe!”

    A single cell does not make a single atom, let alone a source. The states available for a cell are the electric and magnetic field vectors (magnitude and direction) and the charge. So it’s clear that the state of a single cell does not allow one to pinpoint the charge location even for a single charge (a charge two times closer and for times weaker would generate the same field at our cell). If you have however a group of several cells you can determine the location of the charge from the filed states of those cells. For a large number of charges you may need a larger number of cells, but how many are needed depends on the details of the implementation. A short search on Google shows an estimate of about 10^80 particles in the universe and about 10^73 Plank volumes in a hydrogen atom. So, with some simplifications, it is in fact conceivable that the required information might be available. Most cells will only have field states (null charge) and those states are redundant (they are determined by the charge distribution) so you only need the information about the cells with charges.

    “Again, you are assuming that each location has full information about all other locations at that time, which is impossible, but you are assuming even more. Suppose you know that I am about to calculate the digits of pi. Suppose you even know the algorithm I will use to do it. And suppose you want to set the value of some parameter of a particle so it reflects the parity of the digit of pi that will be being computed when the particle reaches the detector. Well, even with the information you have, your work is not done. What you still have to do is *calculate the digit yourself and figure out its parity*. And you have to do all this before you can pre-set the particle to the appropriate state. But how in the world is the source going to manage that trick! It doesn't have a computer to use to do the calculation.”

    Of course the source does not actually calculate anything, probably a better way to look at this is synchronized clocks. The field-charge distribution correlation that exists before the experiment would be analogous to the synchronization of two distant clocks. Then they will give the same reading not because they simulate what other clock is doing but because it is inevitable given their past state. So, the charge distribution corresponding to the computer calculating Pi would generate a field at the source that will determine it to produce particles with spin as predicted by QM. I hope that makes sense. Of course, I have no idea if such an arrangement is possible but it does not appear absurd to me. Unfortunately the complexity of the experiment would probably preclude a direct test using computer simulations so, the best hope would be to try reproducing some other, less demanding QM predictions like the energy level of hydrogen.

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  32. -continuation

    “Classical EM does not imply that the state of every small region encodes the complete global state: it can't. Nor can any CA.”

    I will look more into this but I think that each infinitesimal region should encode the complete state because of the continuous structure. The amount of information contained in that region is virtually infinite. I just cannot think of an example of different charge distributions generating identical fields in any point of such a region. The situation is a bit different in a CA because the information contained in a small region is finite. On the other hand the available states are also finite.

    “A simple example may help. In a vacuum, the total EM field is everywhere zero. In the interior of a charged sphere, is it also zero, So the local state does not determine the global state. And all the laws of EM are satisfied.”

    The problem is that a charged sphere is just a macroscopic approximation. Due to charge quantization it is not physically realizable. At microscopic level there is no sphere, just empty space with a few charges here and there. So an electron inside a metallic charged sphere would still detect a field which, averaged over a long enough time would approach zero.

    Andrei

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  33. Andrei,

    There is really too much for me to go through point by point. A few main points. You write "The first claim is that CA-superdeterministic theories are not ruled out by Bell even without using non-scientific assumptions like the fine-tuning of initial conditions"

    The issue about superdeterminsm has to do with treating certain variables—like the setting of the apparatus—as not statistically independent of other variables. Whatever classical EM illustrates it is not the failure of statistical independence of large-scale macroscopic variables like the position of a polarizer, from another macroscopic state or from microscopic variables like the initial state of a pair of photons. The large-scale variable has an incredible number of micro states compatible with it. I guess you want to say that every single one of those micro states is connected the same way to the state of a particle pair being created elsewhere. Good luck with that. We possess no theory with that character.

    Bell does not "rule out superdeterminism" in the sense of having a proof against its possibility. It just appears to him—and me—not a possibility to take seriously. Basically, we don't know how to design such a theory. Not a clue.

    The problem with your clock example is that the settings of the clocks exactly cannot be treated as free variables. You can't mess with the clocks or you break the correlation. You can mess with the setting of the apparatus.

    The CA clearly cannot store information about the states of all other cells in the state of a cell. That is mathematically impossible, unless you have restricted the initial conditions so that there are only as many possible initial conditions as states of a single cell. Hyper, hyper fine tuning.

    The point about the vacuum state in EM holds even if there are particles. Just arrange them symmetrically around a point

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  34. Tim,

    Sorry for my long posts, I know that you are a busy man so I’ll try to express myself in a more condensed matter.

    “The CA clearly cannot store information about the states of all other cells in the state of a cell. That is mathematically impossible, unless you have restricted the initial conditions so that there are only as many possible initial conditions as states of a single cell. Hyper, hyper fine tuning.”

    I have not claimed that a single cell contains the information about all other cells. I have claimed that a large, but finite group of cells can contain all relevant information about the state of CA, meaning position/momenta of charged particles. This is entirely possible as I will show you below:

    It is a mathematical fact that a system is completely determined if the number of equations equals the number of unknowns. The electric field in one cell gives you an equation, so the electric field in 3 cells gives you the exact location of a particle. In the same way the magnetic field in 3 cells gives you the momentum of that particle in 3D space. So, in order to store the state of the entire universe containing N particles (estimated to about 10^80) you need 3N cells. If you choose the size of a cell as Plank length that would require about 10^8 atoms, which is an acceptable size for a PDC source. Of course there is no reason to set the cell to be Planck length, you can take it to be smaller so that the fields in the volume of one atom could completely describe the known universe.

    “The point about the vacuum state in EM holds even if there are particles. Just arrange them symmetrically around a point”

    This cannot be true for a region containing at least 3N cells, because, as shown above, the fields in those 3N cells completely determine the position of those N particles (symmetrically distributed or not). But the interior of a sphere would always contain more cells than its surface so the fields inside of a sphere composed of point charges cannot ever be 0 everywhere. It will be 0 just in the middle of the sphere.

    “The large-scale variable has an incredible number of micro states compatible with it. I guess you want to say that every single one of those micro states is connected the same way to the state of a particle pair being created elsewhere. Good luck with that. We possess no theory with that character.”

    Yeah, I guess this is my idea. I know that I cannot prove it but I don’t see any reason to reject it as unscientific either. Only time will tell.

    Andrei

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