# What if spacetime were a kind of fluid? **URL:** \ **Category:** Great Debates\ **Created:** [April 23, 2014, 2:59pm UTC](https://boards.straightdope.com/t/what-if-spacetime-were-a-kind-of-fluid/686772 "2014-04-23T14:59:01Z")\ **Posts on this page:** 20\ **Page:** 9
**Author:** ![mpc755](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mpc755/32/7307_2.png) [@mpc755](https://boards.straightdope.com/u/mpc755)\ **Post date:** [April 28, 2014, 2:45am UTC](https://boards.straightdope.com/t/what-if-spacetime-were-a-kind-of-fluid/686772/161 "2014-04-28T02:45:13Z")
> [@Half\_Man\_Half\_Wit](#): > > So, you’re just going to flat-out deny what de Broglie says about his own theory? Not to mention what the equations defining it straightforwardly say. The quantum potential for any system of more than one particle is a function of the position of each of these particles; thus, in general, any change of any of these particle’s positions will have an instantaneous influence on all other particles, no matter their location. The only exception is if the wavefunction factorizes, i.e. if there’s no entanglement present (and in general, there will be entanglement between any two particles that have interacted in the past). That’s the nonlocality inherent in the theory. de Broglie’s pilot wave theory is a hidden variable theory. de Broglie himself realized his pilot-wave theory was incorrect. de Broglie’s wave mechanics and double solution theory is not a hidden variable theory. ---
**Author:** ![Half\_Man\_Half\_Wit](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/half_man_half_wit/32/21766_2.png) [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit)\ **Post date:** [April 28, 2014, 5:42am UTC](https://boards.straightdope.com/t/what-if-spacetime-were-a-kind-of-fluid/686772/162 "2014-04-28T05:42:44Z")
> [@mpc755](#): > > de Broglie’s pilot wave theory is a hidden variable theory. de Broglie himself realized his pilot-wave theory was incorrect. de Broglie’s wave mechanics and double solution theory is not a hidden variable theory. So the paper “Interpretation of quantum mechanics by the double solution theory” is not actually about the double solution theory? But [you yourself referred to it](http://boards.straightdope.com/sdmb/showpost.php?p=16944550&postcount=25) as an authoritative source for de Broglie’s wave mechanics. 😕 Or does de Broglie’s statement that the particle is precisely located at every instant somehow in fact mean that the particle is _not_ precisely located at every instant? Is his quantum potential only _mathematically_ identical to Bohm’s, and thus nonlocal, but in a way obvious only to your superior conceptual insight not _actually_ the same, depending on the locations of all particles but not actually depending on them? Honestly, how do you square the explicit statement by de Broglie that his theory is a hidden variable theory with your insistence that it’s not? ---
**Author:** ![mpc755](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mpc755/32/7307_2.png) [@mpc755](https://boards.straightdope.com/u/mpc755)\ **Post date:** [April 28, 2014, 3:37pm UTC](https://boards.straightdope.com/t/what-if-spacetime-were-a-kind-of-fluid/686772/163 "2014-04-28T15:37:54Z")
> [@Half\_Man\_Half\_Wit](#): > > So the paper “Interpretation of quantum mechanics by the double solution theory” is not actually about the double solution theory? But [you yourself referred to it](http://boards.straightdope.com/sdmb/showpost.php?p=16944550&postcount=25) as an authoritative source for de Broglie’s wave mechanics. 😕 > > Or does de Broglie’s statement that the particle is precisely located at every instant somehow in fact mean that the particle is _not_ precisely located at every instant? Is his quantum potential only _mathematically_ identical to Bohm’s, and thus nonlocal, but in a way obvious only to your superior conceptual insight not _actually_ the same, depending on the locations of all particles but not actually depending on them? > > Honestly, how do you square the explicit statement by de Broglie that his theory is a hidden variable theory with your insistence that it’s not? There are no such things as hidden variables. In de Broglie’s pilot-wave theory there is only the wave function. Pilot-wave theory is a hidden variable theory. de Broglie realized his pilot-wave theory is incorrect and went back to his original idea of his wave mechanics and double solution theory. In de Broglie’s wave mechanics and double solution theory there are two waves. There is the physical wave which guides the particle and the statistical wave function. The physical wave which guides the particle is local and not a hidden variable. The statistical wave function does not physically exist. The statistical wave function is used to determine the probabilistic results of experiments. As it does not physically exist it cannot be assumed to be part of a hidden variable. Watch the following video. In it there is a slide stating de Broglie’s wave mechanics is not a hidden variable theory and gives what is occurring physically in nature a different theoretical name. ‘The pilot-wave dynamics of walking droplets’ [![](https://i.ytimg.com/vi/nmC0ygr08tE/hqdefault.jpg "The pilot-wave dynamics of walking droplets") ](https://www.youtube.com/watch?v=nmC0ygr08tE) ---
**Author:** ![Czarcasm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/czarcasm/32/4050_2.png) [@Czarcasm](https://boards.straightdope.com/u/Czarcasm)\ **Post date:** [April 28, 2014, 3:39pm UTC](https://boards.straightdope.com/t/what-if-spacetime-were-a-kind-of-fluid/686772/164 "2014-04-28T15:39:43Z")
Cite for the existence of supersolids, please. ---
**Author:** ![mpc755](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mpc755/32/7307_2.png) [@mpc755](https://boards.straightdope.com/u/mpc755)\ **Post date:** [April 28, 2014, 3:41pm UTC](https://boards.straightdope.com/t/what-if-spacetime-were-a-kind-of-fluid/686772/165 "2014-04-28T15:41:48Z")
> [@Czarcasm](#): > > Cite for the existence of supersolids, please. The aether is the supersolid. See the behaviors in a double slit experiment. It is the aether which waves. ‘Offset between dark matter and ordinary matter: evidence from a sample of 38 lensing clusters of galaxies’ > **[Offset between dark matter and ordinary matter: evidence from a sample of 38...](http://arxiv.org/abs/1004.1475)** > > We compile a sample of 38 galaxy clusters which have both X-ray and strong lensing observations, and study for each cluster the projected offset between the dominant component of baryonic matter center (measured by X-rays) and the gravitational... _“Our data strongly support the idea that the gravitational potential in clusters is mainly due to a non-baryonic fluid, and any exotic field in gravitational theory must resemble that of CDM fields very closely.”_ The offset is due to the galaxy clusters moving through the aether. The analogy is a submarine moving through the water. You are under water. Two miles away from you are many lights. Moving between you and the lights one mile away is a submarine. The submarine displaces the water. The state of displacement of the water causes the center of the lensing of the light propagating through the water to be offset from the center of the submarine itself. The offset between the center of the lensing of the light propagating through the water displaced by the submarine and the center of the submarine itself is going to remain the same as the submarine moves through the water. The submarine continually displaces different regions of the water. The state of the water connected to and neighboring the submarine remains the same as the submarine moves through the water even though it is not the same water the submarine continually displaces. This is what is occurring as the galaxy clusters move through and displace the aether. ‘The Milky Way’s dark matter halo appears to be lopsided’ > **[The Milky Way's dark matter halo appears to be lopsided](http://arxiv.org/abs/0903.3802)** > > The atomic hydrogen gas (HI) disk in the outer region (beyond ~10 kpc from the centre) of Milky Way can provide valuable information about the structure of the dark matter halo. The recent 3-D thickness map of the outer HI disk from the all sky 21-cm... _“The emerging picture of the asymmetric dark matter halo is supported by the \Lambda CDM halos formed in the cosmological N-body simulation.”_ The Milky Way’s ‘dark matter halo’ is lopsided due to the matter in the Milky Way moving through and displacing the aether. _“The word ‘ether’ has extremely negative connotations in theoretical physics because of its past association with opposition to relativity. This is unfortunate because, stripped of these connotations, it rather nicely captures the way most physicists actually think about the vacuum. . . . Relativity actually says nothing about the existence or nonexistence of matter pervading the universe, only that any such matter must have relativistic symmetry. […] It turns out that such matter exists. About the time relativity was becoming accepted, studies of radioactivity began showing that the empty vacuum of space had spectroscopic structure similar to that of ordinary quantum solids and fluids. Subsequent studies with large particle accelerators have now led us to understand that space is more like a piece of window glass than ideal Newtonian emptiness. It is filled with ‘stuff’ that is normally transparent but can be made visible by hitting it sufficiently hard to knock out a part. The modern concept of the vacuum of space, confirmed every day by experiment, is a relativistic ether. But we do not call it this because it is taboo.”_ - Robert B. Laughlin, Nobel Laureate in Physics, endowed chair in physics, Stanford University The piece of window glass referred to by Laughlin is the supersolid nature of the aether. ---
**Author:** ![Czarcasm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/czarcasm/32/4050_2.png) [@Czarcasm](https://boards.straightdope.com/u/Czarcasm)\ **Post date:** [April 28, 2014, 3:46pm UTC](https://boards.straightdope.com/t/what-if-spacetime-were-a-kind-of-fluid/686772/166 "2014-04-28T15:46:46Z")
> [@mpc755](#): > > The aether is the supersolid. Show me evidence that supersolids exist _at all_, don’t just repeat back one of your “Liza Program” responses. ---
**Author:** ![QuickSilver](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/quicksilver/32/7832_2.png) [@QuickSilver](https://boards.straightdope.com/u/QuickSilver)\ **Post date:** [April 28, 2014, 3:50pm UTC](https://boards.straightdope.com/t/what-if-spacetime-were-a-kind-of-fluid/686772/167 "2014-04-28T15:50:06Z")
> [@Czarcasm](#): > > Cite for the existence of supersolids, please. > [@mpc755](#): > > The aether is the supersolid. He’s got you there. ---
**Author:** ![Telemark](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/telemark/32/372_2.png) [@Telemark](https://boards.straightdope.com/u/Telemark)\ **Post date:** [April 28, 2014, 3:59pm UTC](https://boards.straightdope.com/t/what-if-spacetime-were-a-kind-of-fluid/686772/168 "2014-04-28T15:59:40Z")
> [@mpc755](#): > > The aether is the supersolid. “Well, Art is Art, isn’t it? Still, on the other hand, water is water. And east is east and west is west and if you take cranberries and stew them like applesauce they taste much more like prunes than rhubarb does. Now you tell me what you know.” – Groucho Marx ---
**Author:** ![Czarcasm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/czarcasm/32/4050_2.png) [@Czarcasm](https://boards.straightdope.com/u/Czarcasm)\ **Post date:** [April 28, 2014, 4:02pm UTC](https://boards.straightdope.com/t/what-if-spacetime-were-a-kind-of-fluid/686772/169 "2014-04-28T16:02:53Z")
[quote=“QuickSilver, post:167, topic:686772”] He’s got you there. > [@](#): > > From [the Wiki article about supersolids:](http://en.wikipedia.org/wiki/Supersolid#Experiments)Prior to 2007, many theorists performed calculations indicating that vacancies cannot exist at zero temperature in solid helium-4. While there is some debate, it seems more doubtful that what the experiments observed was the supersolid state. Indeed, further experimentation, including that by Kim and Chan, has also cast some doubt on the existence of a true supersolid. One experiment found that repeated warming followed by slow cooling of the sample causes the effect to disappear. This annealing process removes flaws in the crystal structure. Furthermore, most samples of helium-4 contain a small amount of helium-3. When some of this helium-4 is removed, the superfluid transition occurs at a lower temperature, which suggests that the superflow is involved with actual fluid moving along imperfections in the crystal rather than a property of the perfect crystal. and > [@](#): > > In 2012, Chan repeated his original experiments with a new apparatus that was designed to eliminate any contribution from elasticity of the helium. In this experiment, Chan and his coauthors found no evidence of supersolidity. Researchers are continuing to search for conclusive evidence of supersolidity. I have searched for any experiments done after Chan’s most recent, and have yet to find any that contradict it. ---
**Author:** ![Half\_Man\_Half\_Wit](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/half_man_half_wit/32/21766_2.png) [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit)\ **Post date:** [April 28, 2014, 4:13pm UTC](https://boards.straightdope.com/t/what-if-spacetime-were-a-kind-of-fluid/686772/170 "2014-04-28T16:13:07Z")
> [@mpc755](#): > > There are no such things as hidden variables. In de Broglie’s pilot-wave theory there is only the wave function. Pilot-wave theory is a hidden variable theory. de Broglie realized his pilot-wave theory is incorrect and went back to his original idea of his wave mechanics and double solution theory. > > In de Broglie’s wave mechanics and double solution theory there are two waves. There is the physical wave which guides the particle and the statistical wave function. And the position of that particle, always definite according to de Broglie, is a hidden variable—hidden because typically, you can know it only up to the limits dictated by the uncertainty principle. There’s only two options: either the particle’s position is always definite, in which case it’s a hidden variable, or it’s not, in which case you’re not talking about the double solution theory. So, what is it? Do you believe the particle always has a definite position, or not? > [@](#): > > The physical wave which guides the particle is local and not a hidden variable. This is patently false, as well. The wave is a solution of the Schrödinger equation, and like all solutions of the Schrödinger equation is a function of the positions of all the particles considered; thus, it is nonlocal, as the position of some particle 1 instantaneously influences the value of the guiding wave at the position of particle 2 and vice versa. The only case in which that’s not obvious is that in which we limit our attention to a single particle. But in the general case, the velocity of the _i_th particle will, via the guidance equation, depend explicitly on the positions of all other particles. This is, again, just a simple fact of the mathematical formulation of the theory. I mean, once again, you of course always have the possibility of convincing me of the opposite, by writing down the wave function for many particles and show that it always factorizes—if it were possible, it would be simple math. But of course, if it were possible, it would also mean that the theory is wrong, because it could not account for nonlocal quantum effects. > [@](#): > > As it does not physically exist it cannot be assumed to be part of a hidden variable. Nobody talks about the statistical wave as being a hidden variable; it’s the position of the particle that is the hidden variable. > [@](#): > > Watch the following video. In it there is a slide stating de Broglie’s wave mechanics is not a hidden variable theory No. They call _their model_ an ‘exposed variable theory’, because you can see explicitly where the particle is at all times. But in a fully quantum theory, the particle’s position is subject to uncertainty, and can’t in general always be fully known. This ‘hides’ the variable that is explicit in their model. ---
**Author:** ![QuickSilver](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/quicksilver/32/7832_2.png) [@QuickSilver](https://boards.straightdope.com/u/QuickSilver)\ **Post date:** [April 28, 2014, 4:14pm UTC](https://boards.straightdope.com/t/what-if-spacetime-were-a-kind-of-fluid/686772/171 "2014-04-28T16:14:28Z")
> [@Czarcasm](#): > > I have searched for any experiments done after Chan’s most recent, and have yet to find any that contradict it. Of all the posters on this board to be whooshed by sarcasm, why’d it have to be you? 😉 ---
**Author:** ![Czarcasm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/czarcasm/32/4050_2.png) [@Czarcasm](https://boards.straightdope.com/u/Czarcasm)\ **Post date:** [April 28, 2014, 4:17pm UTC](https://boards.straightdope.com/t/what-if-spacetime-were-a-kind-of-fluid/686772/172 "2014-04-28T16:17:31Z")
> [@QuickSilver](#): > > Of all the posters on this board to be whooshed by sarcasm, why’d have to be you? 😉 Naw-I saw _that_ one-I just quoted the wrong post. :smack: ---
**Author:** ![Jonathan\_Chance](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jonathan_chance/32/701_2.png) [@Jonathan\_Chance](https://boards.straightdope.com/u/Jonathan_Chance)\ **Post date:** [April 28, 2014, 4:22pm UTC](https://boards.straightdope.com/t/what-if-spacetime-were-a-kind-of-fluid/686772/173 "2014-04-28T16:22:17Z")
> [@mpc755](#): > > _“The word ‘ether’ has extremely negative connotations in theoretical physics because of its past association with opposition to relativity. This is unfortunate because, stripped of these connotations, it rather nicely captures the way most physicists actually think about the vacuum. . . . Relativity actually says nothing about the existence or nonexistence of matter pervading the universe, only that any such matter must have relativistic symmetry. […] It turns out that such matter exists. About the time relativity was becoming accepted, studies of radioactivity began showing that the empty vacuum of space had spectroscopic structure similar to that of ordinary quantum solids and fluids. Subsequent studies with large particle accelerators have now led us to understand that space is more like a piece of window glass than ideal Newtonian emptiness. It is filled with ‘stuff’ that is normally transparent but can be made visible by hitting it sufficiently hard to knock out a part. The modern concept of the vacuum of space, confirmed every day by experiment, is a relativistic ether. But we do not call it this because it is taboo.”_ - Robert B. Laughlin, Nobel Laureate in Physics, endowed chair in physics, Stanford University > > The piece of window glass referred to by Laughlin is the supersolid nature of the aether. mpc755, I told you on page two that endlessly quoting this would earn you a warning. You have now done so and this is an official warning. I am electing to leave this thread open in the short-term but may decide - in things don’t improve - to close it forthwith. ---
**Author:** ![mpc755](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mpc755/32/7307_2.png) [@mpc755](https://boards.straightdope.com/u/mpc755)\ **Post date:** [April 28, 2014, 5:34pm UTC](https://boards.straightdope.com/t/what-if-spacetime-were-a-kind-of-fluid/686772/174 "2014-04-28T17:34:23Z")
> [@Jonathan\_Chance](#): > > mpc755, I told you on page two that endlessly quoting this would earn you a warning. You have now done so and this is an official warning. > > I am electing to leave this thread open in the short-term but may decide - in things don’t improve - to close it forthwith. That quote was relevant to the specific question. The question was, “Cite for the existence of supersolids, please.” Robert Laughlin describing the aether as a piece of window glass is evidence the aether is a supersolid as that is how a piece of window glass particles of matter can move through and displace would behave. Please make the effort to understand the context of why I have repeated text from a previous post before banning. ---
**Author:** ![mpc755](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mpc755/32/7307_2.png) [@mpc755](https://boards.straightdope.com/u/mpc755)\ **Post date:** [April 28, 2014, 5:37pm UTC](https://boards.straightdope.com/t/what-if-spacetime-were-a-kind-of-fluid/686772/175 "2014-04-28T17:37:15Z")
> [@Czarcasm](#): > > Show me evidence that supersolids exist _at all_, don’t just repeat back one of your “Liza Program” responses. The observed behaviors of particles of matter and the aether is evidence supersolids exist _at all_ as that is what the aether behaves as. ---
**Author:** ![Czarcasm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/czarcasm/32/4050_2.png) [@Czarcasm](https://boards.straightdope.com/u/Czarcasm)\ **Post date:** [April 28, 2014, 5:40pm UTC](https://boards.straightdope.com/t/what-if-spacetime-were-a-kind-of-fluid/686772/176 "2014-04-28T17:40:53Z")
> [@mpc755](#): > > That quote was relevant to the specific question. The question was, “Cite for the existence of supersolids, please.” > > Robert Laughlin describing the aether as a piece of window glass is evidence the aether is a supersolid as that is how a piece of window glass particles of matter can move through and displace would behave. That is not evidence for the existence of supersolids-that is Robert Laughlin claiming that aether _is_ a supersolid…which(until supersolids are proven to exist at all) is about as valid as me saying that aether is unicorn breath. ---
**Author:** ![mpc755](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mpc755/32/7307_2.png) [@mpc755](https://boards.straightdope.com/u/mpc755)\ **Post date:** [April 28, 2014, 5:44pm UTC](https://boards.straightdope.com/t/what-if-spacetime-were-a-kind-of-fluid/686772/177 "2014-04-28T17:44:20Z")
> [@Telemark](#): > > “Now you tell me what you know.” Aether has mass which physically occupies three dimensional space and is physically displaced by the particles of matter which exist in it and move through it. There is no such thing as non-baryonic dark matter anchored to matter. Matter moves through and displaces the aether. The Milky Way’s halo is the state of displacement of the aether. The Milky Way’s halo is curved spacetime. What is referred to geometrically as curved spacetime physically exists in nature as the state of displacement of the aether. The state of displacement of the aether_is_ gravity. A moving particle has an associated aether displacement wave. In a double slit experiment the particle travels through a single slit and the associated wave in the aether passes through both. In a double slit experiment it is the aether which waves. ---
**Author:** ![Jonathan\_Chance](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jonathan_chance/32/701_2.png) [@Jonathan\_Chance](https://boards.straightdope.com/u/Jonathan_Chance)\ **Post date:** [April 28, 2014, 5:46pm UTC](https://boards.straightdope.com/t/what-if-spacetime-were-a-kind-of-fluid/686772/178 "2014-04-28T17:46:17Z")
> [@mpc755](#): > > That quote was relevant to the specific question. The question was, “Cite for the existence of supersolids, please.” > > Robert Laughlin describing the aether as a piece of window glass is evidence the aether is a supersolid as that is how a piece of window glass particles of matter can move through and displace would behave. > > Please make the effort to understand the context of why I have repeated text from a previous post before banning. All of that is irrelevant. I’m not moderating you for content but for debate tactics. Your repeated use of the same quote shows a certain amount of either debating in bad faith or an inability to debate at all. Neither is welcome in Great Debates though - for the second - we encourage poster to learn to do so. ---
**Author:** ![Czarcasm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/czarcasm/32/4050_2.png) [@Czarcasm](https://boards.straightdope.com/u/Czarcasm)\ **Post date:** [April 28, 2014, 5:46pm UTC](https://boards.straightdope.com/t/what-if-spacetime-were-a-kind-of-fluid/686772/179 "2014-04-28T17:46:31Z")
> [@mpc755](#): > > Aether has mass which physically occupies three dimensional space and is physically displaced by the particles of matter which exist in it and move through it. > > There is no such thing as non-baryonic dark matter anchored to matter. Matter moves through and displaces the aether. > > The Milky Way’s halo is the state of displacement of the aether. > > The Milky Way’s halo is curved spacetime. > > What is referred to geometrically as curved spacetime physically exists in nature as the state of displacement of the aether. > > The state of displacement of the aether_is_ gravity. > > A moving particle has an associated aether displacement wave. In a double slit experiment the particle travels through a single slit and the associated wave in the aether passes through both. > > In a double slit experiment it is the aether which waves. Is this a computer program that just spits out random sentences from a select list? Say something new that pertains to what people are actually saying, please. ---
**Author:** ![mpc755](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mpc755/32/7307_2.png) [@mpc755](https://boards.straightdope.com/u/mpc755)\ **Post date:** [April 28, 2014, 5:48pm UTC](https://boards.straightdope.com/t/what-if-spacetime-were-a-kind-of-fluid/686772/180 "2014-04-28T17:48:23Z")
> [@Half\_Man\_Half\_Wit](#): > > And the position of that particle, always definite according to de Broglie, is a hidden variable—hidden because typically, you can know it only up to the limits dictated by the uncertainty principle. There’s only two options: either the particle’s position is always definite, in which case it’s a hidden variable, or it’s not, in which case you’re not talking about the double solution theory. > > So, what is it? Do you believe the particle always has a definite position, or not? > This is patently false, as well. The wave is a solution of the Schrödinger equation, and like all solutions of the Schrödinger equation is a function of the positions of all the particles considered; thus, it is nonlocal, as the position of some particle 1 instantaneously influences the value of the guiding wave at the position of particle 2 and vice versa. The only case in which that’s not obvious is that in which we limit our attention to a single particle. But in the general case, the velocity of the _i_th particle will, via the guidance equation, depend explicitly on the positions of all other particles. This is, again, just a simple fact of the mathematical formulation of the theory. > > I mean, once again, you of course always have the possibility of convincing me of the opposite, by writing down the wave function for many particles and show that it always factorizes—if it were possible, it would be simple math. But of course, if it were possible, it would also mean that the theory is wrong, because it could not account for nonlocal quantum effects. > Nobody talks about the statistical wave as being a hidden variable; it’s the position of the particle that is the hidden variable. > No. They call _their model_ an ‘exposed variable theory’, because you can see explicitly where the particle is at all times. But in a fully quantum theory, the particle’s position is subject to uncertainty, and can’t in general always be fully known. This ‘hides’ the variable that is explicit in their model. ‘Exposed’ variable means you can know the position and momentum of the particle without detecting it. Due to the downconverted photon pair traveling with opposite angular momentums each of the downconverted pair can determined the position and momentum of the other. Each of the pair can determine the state of the other. Even though the position and momentum is not known to us it is not hidden to each of the pair. Entanglement is defined as an ‘exposed variable theory’. [Previous page](https://boards.straightdope.com/t/what-if-spacetime-were-a-kind-of-fluid/686772.md?page=8) [Next page](https://boards.straightdope.com/t/what-if-spacetime-were-a-kind-of-fluid/686772.md?page=10)