Dubbelosix

However, it should be noted, that Nicolas Cerf and Chris Adami has shown conditional entropy can violate the entropy thermodynamic law, allowing entropy to have a negative solution. This used the conditional density operator [math]\rho_{A|B}[/math] which we have featured before. Though forbidden, what was shown that the negative entropy allowed the framework for quantum non-separability.

Somehow I had three typo's in the Bure's metric, quite a few posts back, just giving the careful version now. [math]F(\sigma, \rho) = \min_{A^{*}_{i}A_i} \sum_i \sqrt{Tr(\sigma A^{*}_{i} A_i)}\sqrt{Tr(\rho A^{*}_{i}A_{i})}[/math] As shown from the Venn diagrams, it is possible to show a distinct difference between the classical and quantum entropy by noting that inequalities arise relating that entropies are weaker in a quantum case. The inequality is in classical theory [math]S(A:B) \leq min[S(A), S(B)][/math] In quantum theory it is [math] S(A:B) \leq 2 min[S(A), S(B)][/math] You may interpret this in this form as meaning that entropy can reach twice the classical upper bound. The factor of 2 can also be thought of as qubits. This is the same kind of situation in the von Neumann entropy, in which the base log of 2 in information entropy is almost always calculated using base 2 log. You can also write this information theory in terms of energy (which may have implication for the difference of energies related to superpositioned geometry). [math]E = k_BT \ln(2)Nh[/math] (In conventional notation). The ln(2) is the conversion factor from base 2 of the log of Shannon entropy, to the natural base of e. [math]Nh[/math] is the amount of information in bits needed to describe the given system. Again, because we hypothesize that the gravitational superpositioning is not in equilibrium, entropy will not be zero. I've imagined, even in absence of a second particle, a single particle state could collapse if it has a centre of mass that fluctuates around the absolute square of its wave function (causing an instability, small, but gradual one). Keep in mind, that pure state symbol is a useful symbol to describe whether the state is separable. That means, if a mixed bipartite system descrived by a density matrix acting on [math]S_1 \otimes S_2[/math] and [math]\rho[/math] is separable iff [math]\rho \geq 0[/math] (which also preserves that entropy is never negative according to the thermodynamic laws), where I define [math](S_1,S_2)[/math] as quantum entropy phase spaces.

Thanks, feel free to add anything if you have a brain storm moment, I keep getting physics block lol There is such a thing as a conditional Neumann entropy, where we consider the bipartite quantum system [math](A,B)[/math]. A quantum generalisation of this two particle system from information-theory gives [math]S(A|B) = -Tr_{AB}[\rho_{AB}\log_b \rho_{A|B}][/math] This is known as the Von Neumann 'conditional entropy.' [math]\rho_{A|B}[/math] is a semi-def Hermitian matric in the joint Hilbert space. A joint state is stil [math]\rho_{AB} \rightarrow \sum_i A_i \otimes B_i \rho_{AB}A^{*}_{i} \otimes B^{*}_{i}[/math] and again, trace preserved through [math]A^{*}_{i}A_i \otimes B^{*}_{i}B_i = \mathbf{I}[/math] The entanglement is given as [math]E(\rho) = min \sum_i p_i S(\rho^i_A)[/math] With [math]S(\rho^i_A)[/math] as the Shannon entropy. The Shannon entropy therefore, must also be understood in the bipartite ensemble to ensure that we restore a quantum definition. This prompted me to investigate more into a quantum Shannon entropy, if such a thing existed in literature and I have provided a reference to such historical attempts to find a quantum information theory in terms of Shannon entropy. It is somewhat related to the notation we have been using above as well as you will notice when you read through it. I made it clear though, as instructed by hindsight from Mordred, that there would be complications to look out for one was stated by me in the previous post: ''Quantum mechanical density matrices in general though, have off-diagonal terms, which for pure states, reflect the quantum phases in superpositions.'' The interesting thing, is that in our model, the density matrices governing the curvature tensor relies on off-diagonal components - in specific, all diagonal components are zero; and that is just by the definition, but an important one to remember for antisymmetric matrices. So is there a hint here that there could be unification within the two? Being a collapse model, we must also remain vigilant over the use of the Hermitian matrix - which would be a post phenomenon to the superpositioned phase and the use of those off-diagonal terms in the curvature tensor. Seems almost impossible to do. Remember, the physical kind of picture we have in mind, is a superpositioned set of particles, which become entangled from the collapse of the systems by a gravitational interaction between the two systems, such as a non-equilibrium arising in the binding energy between the two states. This is by no means, an easy task, but with my investigations, I think I've narrowed the possibilities to some good ones - at least in theory. Yet to see it in practice, I'll try, no promises. ref. https://en.wikipedia.org/wiki/Quantum_relative_entropy The joint state evolution will also follow a unitary operation, and has almost identical structure to the the density joint state above, that's because each unitary operator is acting per each state denoted by [math]A[/math] and [math]B[/math]. [math]E(\sigma) = E(U_A \otimes U_B \sigma U^{*}_{A} \otimes U^{*}_{B})[/math] And so, if this is imposed, it removes a question of whether gravity in my theory follows unitarity - this also imposes that entropy is invariant always in the system. The symbol [math]\sigma[/math] just denoted a pure state.

With the past post help from Mordred, I believe I can sum this up in the following: von Neumann introduced [math]S = -Tr(\rho \log_b \rho)[/math] where we have used the base power of the logarithm. The Shannon entropy has a relationship to this [math]H = -\sum_i (p_i \log_b p_i)[/math] Which works, when we consider a mixture of orthogonal states. In this case, the density matrix does contain classical probabilities on the diagonal. Quantum mechanical density matrices in general though, have off-diagonal terms, which for pure states, reflect the quantum phases in superpositions. So... we know where we want to go with this. A useful equation I came across in information theory was the Shannon entropy in terms of correlation: [math]H(A) = H(A|B) + H(A:B)[/math] How do you read this strange equation? Well, the [math]H(A|B)[/math] is the entropy of [math]A[/math] after having measured the systems that become correlated in [math]B[/math]. And [math]H(A:B)[/math] is the information gained about [math]A[/math] through measuring the system [math]B[/math]. (Apparently), as is well known, these two quantities complement each other such that [math]H(A)[/math] will remain unchanged to satisfy the conservation of the second law. While this was interesting, I realised my understanding of the context of which I wanted to construct this theory relies on an interpretation of information theory that can contain an uncertainty principle - since my investigations have been primarily involved in understanding a possible non-trivial spacetime relationship, this shouldn't be too suprising. A paper by I. Białynicki-Birula, J. Mycielski, on ''Uncertainty relations for information entropy in wave mechanics'' (Comm. Math. Phys. 1975) contains a derivation of an uncertainty principle based on an information entropy and features here as [math]- \int |\psi|^2 ln[|\psi(q)|^2]\ dq - \int |\hat{\psi}|^2 \ln[|\hat{\psi}(p)|^2]\ dp \geq 1 + \ln \pi[/math] Where [math]|\psi(q)|^2 = \int W(q,p)\ dp[/math] using generalized coordinates just in case anyone wonders what [math]p[/math] and [math]q[/math] is. And, [math]|\hat{\psi}(p)|^2 = \int W(q,p)\ dq[/math] I have a bit of interest in this method, I generally get a feeling if I know I can do something with something else, like this above. It seems to have all the physics I need to try and piece this puzzle together. I do seem to be getting the impression that if the system is in equilibrium, it calculates as [math]S = - \sum_i \frac{1}{N} \ln(\frac{1}{N})[/math] [math]=-N \frac{1}{N} \ln(\frac{1}{N})[/math] [math]= ln(N)[/math] Which just looks like the Boltzmann entropy. While this last bit wasn't pertinent to the work, it is interesting for educational purposes. ref: http://www.cft.edu.pl/~birula/publ/Uncertainty.pdf The paper by I. Białynicki-Birula, J. Mycielski shows that there are ways to describe my model with gravitational logarithmic nonlinear wave equations. More* In particular, I want to see if these two equations can be merged into some unified definition, by merging the physics somehow to make sense of each other in context of my investigation. [math]- \int |\psi|^2 ln[|\psi(q)|^2]\ dq - \int |\hat{\psi}|^2 \ln[|\hat{\psi}(p)|^2]\ dp \geq 1 + \ln \pi[/math] Which is the equation we just featured, and an equation I derived was: [math]\Delta E = \frac{c^4}{8 \pi G} \int <\Delta R_{ij}>\ dV = \frac{c^4}{8 \pi G} \int <\psi|R_{ij} - <\psi|R_{ij}|\psi>)|\psi>\ dV[/math] [math]=\frac{c^4}{8 \pi G} \int (<\psi|R_{ij}\psi> - <\psi|R_{ij}|\psi>)\ dV[/math] Which was the difference in quantum geometries which as was already established, related to the uncertainty principle in the antisymmetric indices of the curvature tensor [math]R_{ij}[/math]. We never proved by any means, that this is how an uncertainty principle should be interpreted with gravity - that is a hard thing to do without a full understanding of gravity as it is. There are disagreements on how to approach a quantum theory, right down to vital questions about whether gravity is even the same as the other fundamental forces in nature. If it lacks a graviton, then you can count large portions of gauge theory will become questionable.

It is true that people have tied uncertainty or indeterminism with the a matter of intrinsic randomness - I do not share this view. I am Einsteinian Deterministic, I believe the universe follows (complete) deterministic laws. I do not believe that the uncertainty principle is a measure of our inability to know the underlying structure that creates reality because of randomness, but rather a restriction on how much information we can obtain from a system. I meant intrinsic randomness, I have correct that.

Actually, Einstein himself had something different to say on the matter. In relativity, he says the past and future are stubborn illusions. Yes, past memories exists in our minds, but we don't literally ''jump into the past'' when we think about a memory - you remember events always in the present moment. Except, not everyone can agree when events happen. That's the mind boggling nature of relativity, but makes perfect sense if you have took the time to study why these things happen. When Einstein said the past and future where stubborn illusions, he meant the distinction between them are illusions - simply because the relativity of simultaneity.

Well, you did say before, if I needed any help with the math, I may take you up on that offer. Any suggestions how to create the Bure metric in terms of the Cauchy Schwarz space inequality? I've been looking into it and while I had confidence (and yes there is literature out there talking about the two subjects as being related) I lost this confidence and realized the terms wa sas you said, something where care was needed. I am a bit stuck at the moment.

But our minds are not the only relative systems, everything is relative. If this is some kind of argument that you need consciousness to explain relativity, you actually don't. Particles act according to rules of time dilation and their interactions are completely perfect substitutes for ''conscious observation.''

try this link: Tell me what you think https://www-thphys.physics.ox.ac.uk/people/JohnCardy/seminars/Cambridge2013.pdf Bure's metric as I have written has a typo, an extra sigma when there should just be a rho term, which isn't actually density, sigma and rho are the fidelity of quantum states.

It has been argued by many authors, Einstein's equations with the antisymmetric components that describe the torsion as being set to zero, is only the most boring case - torsion and rotation are part of the full Poincare group of spatial translations, it certainly should be expected to be non.zero in many circumstances. There have been active attempts to solve these issues, I'd rather say issues than problems. https://arxiv.org/abs/1101.2791 It's a good paper and will offer a valid solution to your question. And yes me and Matti have even speculated the black holes may have been more massive than what theory predicts. Corrections to binding energy also from other black holes expected within the theory.

I have an equation wrong above, it should be [math]S_A \equiv - \sum_i |c_i|^2 \log |c_i|^2 = S_B[/math] Whereas, last night, I was writing it out differently as was working from memory, the rest is fine though. I am just working on it right now to try and find a model that makes sense. So this must be corrected before we continue. Also, you can see the above in another form - [math]S_A \equiv - \sum_i |c_i|^2 \log |c_i|^2 = \sum_i |c_i|^2 \log (\frac{1}{ |c_i|^2})[/math] where once again you can define [math]|c_i|^2[/math] as [math]|\psi|^2[/math] from the Shannon entropy. Just a further look into some standard operations. Joint state is [math]\rho_{AB} \rightarrow \sum_i \otimes B_i \rho_{AB} A^{*}_{i} \otimes B^{*}_{i}[/math] These states are correlated. And it preserves the trac through [math]\sum_i A^{*}_{i}A_i \otimes B^{*}_{i}B_{i} = \mathbf{I}[/math] Disentanglement is found normally through [math]\sum_i p_i(\rho^i_A \otimes \rho^i_B)[/math] Entangelment is defined as [math]E(\rho) = min\sum_i p_i S(\rho^i_A)[/math] Where [math]S(\rho^i_A)[/math] can be seen as the Shannon entropy. For a simple case of disentangelment, the shannon entropy will become zero - and for maximally entangled state, it gives [math]ln2[/math]. For any pure entangled state with coefficients [math](\alpha |00> + \beta |11>)[/math] the measure should reduce to the Von Neumann or Shannon Entropy form for [math]-|\alpha|^2 ln|\alpha|^2 - |\beta|^2 ln|\beta|^2[/math] Because my model is about the collapse of a wave function due to gravity and in extended model, about entanglement between two states in some superpositioned geometry, I may find myself coming to find the Bure's metric valuable. [math]E(\sigma, \rho) = mim_{A^{*}_{i}A_i} \sum_i \sqrt{Tr(\sigma A^{*}_i A_i)} \sqrt{Tr(\rho\sigma A^{*}_i A_i)}[/math] This seemed natural since the Bure's metric has implication for quantum geometric information theory.

Gravity isn't acting differently, gravity is a long ranged force. Torsion could play the role of black holes dragging systems around with them. Black holes are like sink holes, they tend to eat not only matter and energy but also spacetime as well. Also, it is not that our understanding of gravity is wrong, but rather our understanding of black holes and their role in galaxy evolution and maintenance.

You need to read the OP, the bulge is affected in some cases.

Using the Schmidt decomposition, we have [math]|\psi > = \sum_i c_i|\psi_i>_A \otimes |\psi_i>_B[/math] We can recognize that [math]\sum_i c^2_i = 1[/math]. You can quantify the amount of entanglement in the system from the entropy: [math]\frac{S_A}{S_B} \equiv -\sum_i |c_i|^2 \log |c_i|^2[/math] This is equivalent to looking at the density matrix in terms of the Von Neumann entropy [math]\rho_A \equiv Tr_B |\psi><\psi|[/math] [math]\frac{S_A}{S_B} = -Tr_A \rho_A \log \rho_A[/math] The entropy of entanglement is actually just [math]E(|\psi><\psi|)[/math] and it measures the entropy of the pure state [math]|\psi_i>[/math]. Because our gravity theory is a theory about gravitional induced collapse by possibly a collection of particles in a superposition, and is not a true static configuration, then there will be a non-zero entropy associated to the system similar to how we viewed this equation: [math]\frac{S_A}{S_B} \equiv -\sum_i |c_i|^2 \log |c_i|^2[/math] This was an important realization because this will tie my entire model together like I wanted - I wanted a theory of spacetime itself, which incorporated the Cauchy Schwarz inequality which is basically a geometric interpretation of the uncertainty principle. I wanted this as a natural mechanism for fluctuations in spacetime, something which is treated in some literature as lacking. My final hope was to incorporate entanglement and thus have some kind of gravity-entanglement as well. Looks like I can do it this way. http://research.physics.illinois.edu/QI/Photonics/papers/My Collection.Data/PDF/Maximal entanglement versus entropy for mixed quantum states.pdf Entanglement entropy in QFT would require a definition of the ground state [math]<0|R_{ij}|0>[/math] but I much prefer to stay away from this and concentrate on the formalism above which can incorporate a collapse model. That requires perhaps the Shannon entropy [math]-Tr|\psi|^2\log|\psi|^2[/math].

The problems about trying to find a description of a pre-big bang phase is going to be difficult, even with a Friedmann equation, because you can argue the kind of Friedmann equation we deal with, isn't actually an accurate representation of our universe as it really is... too simple. There are also other hints of breakdown with a consistency with reality: The density parameter from the Friedmann equations measures the ratio of the observed vacuum density to the critical density. Only when these two quantities are [exactly] the same does the Friedmann equation allow a geometry which would fit Euclidean flat spacetime. This exact parameter when both terms are equal, would serve what we see in the vast cosmos, since the universe appears to be spatially flat and homogeneous. Or does it? There is an inconsistency which may hint that the large scale homogeneity could be an illusion. It turns out afterall, that the observed being equal to the critical density doesn't match observation at all. The critical energy (a tool used to explain possible collapse models) is worked out to be five atoms of hydrogen per cubic metre of space. The actual observed density of the matter in the universe, is somewhere between 0.2-0.25 atoms per cubic metre.Something isn't consistent here. For flat space truly to exist, requires the observed and the critical densities to be exactly equal, but calculation of the actual density of the vacuum is no where near the estimate required to satisfy a flat spacetime model. You can argue dark matter could correct the discrepancy, but I don't hold faith in dark matter theory. Let me give you something we might expect: A modified Friedmann equation to take in all reasonable density parameters a universe like ours may or would require. We write it in the form of the Raychauduri equation and we feature six density parameters: [math]\dot{H}\Theta + H^2\Theta + \frac{kc^2}{a^2}\Theta = \frac{8 \pi G}{3c^2}(\rho_{on} + \rho_{off} + \rho_{pressure} + \rho_{vel} + \rho_G + \rho_{EM} - \rho_{\sigma})\Theta + \omega^2\Theta[/math] [math]\rho_{on}[/math] - density due to on-shell particles (ordinary matter or observable matter) [math]\rho_{off}[/math] - density due to off shell dynamics (the world of the fluctuation which may have to be set to zero over cosmological flat space, but maybe not curved space as the fourth power over their momenta may be non-zero) [math]\rho_{pressure}[/math] - the density due to pressure, however, keep in mind there are different kinds of pressures. There is a radiation pressure and then there is a pressure that can be associated to particle velocity, also called the velocity pressure. Density and pressure have the same dimensions. [math]\rho_G[/math] - the density due to gravitational force [math]\rho_{EM}[/math] - the density due to electromagnetic force [math]\rho_{\sigma}[/math] - the density due to a torsion field I could write the whole terms out in their full form, but its a long equation and pretty late here. Seeing the universe in light of these reasonable energy density parameters, just shows us how complicated the universe may actually be, the effective density part now consists of density due to on-shell particles, density due to off-shell particles, density due to pressure, density due to gravitational binding, density due to primordial electromagnetic fields and the density due to torsion. I haven't spoke about primordial magnetic fields or electric fields in the universe - but its a very important question for the unification theories, in which some investigations have shown that gravity and electric fields may have a complimentary existence, ie. charge vanishes from the early universe as the strength of gravity increases! Here is a link that highlights the unification problem better, in the Wilczek picture https://www.newscientist.com/article/mg20827853.600-why-the-early-universe-was-free-of-charge/

Now this is more interesting - it looks like people are working with their good ol' brain boxes. I actually like your solution as well to my problem. If the solution holds, alas, you do not win a prize.

I know. I was just adding some things.

Well you can argue gravity is never absent in the universe. So special relativity isn't fundamentally correct at the core ''We have all seen footage of astronauts floating freely in space, performing twists and turns that seem to defy gravity. As a result of these portrayals, many people believe that there is zero gravity in space. However, this statement could not be further from the truth. Gravity exists everywhere in the universe and is the most important force affecting all matter in space. In fact, without gravity, all matter would fly apart and everything would cease to exist.'' http://www.yalescientific.org/2010/10/mythbusters-does-zero-gravity-exist-in-space/ But yeah, think about when protons get flattened in high energy scattering as an example of fundamentally flat systems, at least by all practicality.

Oh yes, it is possible, for at least gravitational waves (as a warping of spacetime) could be permanentl http://www.pbs.org/wgbh/nova/next/physics/gravitational-wave-memory/ Though this is about damaging spacetime, but in some treatments it is hard to separate a notion of matter from spacetime. So unclear.

Special relativity is indeed flat because it is a theory of moving systems in the absence of gravity. What may help is looking into flat land and then investigate the implications of higher dimensions - you might find a gem of knowledge in it.

Hadn't heard of this either, but Born rigid has a long history - and a very interesting one. I've took the liberty of finding this history for you: ''1909: Max Born introduces a notion of rigid motion in special relativity.[6] 1909: After studying Born's notion of rigidity, Paul Ehrenfest demonstrated by means of a paradox about a cylinder that goes from rest to rotation, that most motions of extended bodies cannot be Born rigid.[1] 1910: Gustav Herglotz and Fritz Noether independently elaborated on Born's model and showed (Herglotz-Noether theorem) that Born rigidity only allows of three degrees of freedom for bodies in motion. For instance, it's possible that a rigid body is executing uniform rotation, yet accelerated rotation is impossible. So a Born rigid body cannot be brought from a state of rest into rotation, confirming Ehrenfest's result.[7][8] 1910: Max Planck calls attention to the fact that one should not confuse the problem of the contraction of a disc due to spinning it up, with that of what disk-riding observers will measure as compared to stationary observers. He suggests that resolving the first problem will require introducing some material model and employing the theory of elasticity.[9] 1910: Theodor Kaluza points out that there is nothing inherently paradoxical about the static and disk-riding observers obtaining different results for the circumference. This does however imply, Kaluza argues, that "the geometry of the rotating disk" is non-euclidean. He asserts without proof that this geometry is in fact essentially just the geometry of the hyperbolic plane.[10] 1911: Max von Laue shows, that an accelerated body has an infinite amount of degrees of freedom, thus no rigid bodies can exist in special relativity.[11] 1916: While writing up his new general theory of relativity, Albert Einstein notices that disk-riding observers measure a longer circumference, C′ = 2π r √(1−v2)−1. That is, because rulers moving parallel to their length axis appear shorter as measured by static observers, the disk-riding observers can fit more smaller rulers of a given length around the circumference than stationary observers could. 1922: In his seminal book "The Mathematical Theory of Relativity" (p. 113), A.S.Eddington calculates a contraction of the radius of the rotating disc (compared to stationary scales) of one quarter of the 'Lorentz contraction' factor applied to the circumference. 1935: Paul Langevin essentially introduces a moving frame (or frame field in modern language) corresponding to the family of disk-riding observers, now called Langevin observers. (See the figure.) He also shows that distances measured by nearby Langevin observers correspond to a certain Riemannian metric, now called the Langevin-Landau-Lifschitz metric. (See Born coordinates for details.)[12] 1937: Jan Weyssenhoff (now perhaps best known for his work on Cartan connections with zero curvature and nonzero torsion) notices that the Langevin observers are not hypersurface orthogonal. Therefore, the Langevin-Landau-Lifschitz metric is defined, not on some hyperslice of Minkowski spacetime, but on the quotient space obtained by replacing each world line with a point. This gives a three-dimensional smooth manifold which becomes a Riemannian manifold when we add the metric structure. 1946: Nathan Rosen shows that inertial observers instantaneously comoving with Langevin observers also measure small distances given by Langevin-Landau-Lifschitz metric. 1946: E. L. Hill analyzes relativistic stresses in a material in which (roughly speaking) the speed of sound equals the speed of light and shows these just cancel the radial expansion due to centrifugal force (in any physically realistic material, the relativistic effects lessen but do not cancel the radial expansion). Hill explains errors in earlier analyses by Arthur Eddington and others.[13] 1952: C. Møller attempts to study null geodesics from the point of view of rotating observers (but incorrectly tries to use slices rather than the appropriate quotient space) 1968: V. Cantoni provides a straightforward, purely kinematical explanation of the paradox. 1975: Øyvind Grøn writes a classic review paper about solutions of the "paradox" 1977: Grünbaum and Janis introduce a notion of physically realizable "non-rigidity" which can be applied to the spin-up of an initially non-rotating disk (this notion is not physically realistic for real materials from which one might make a disk, but it is useful for thought experiments).[14] 1981: Grøn notices that Hooke's law is not consistent with Lorentz transformations and introduces a relativistic generalization. 1997: T. A. Weber explicitly introduces the frame field associated with Langevin observers. 2000: Hrvoje Nikolić points out that the paradox disappears when (in accordance with general theory of relativity) each piece of the rotating disk is treated separately, as living in its own local non-inertial frame.'' This was extracted from the Ehrenfest problem of rotating bodies that should experience a length contraction. As Swansont has pointed out, and other posters have hinted at, there are no preferred frames in existence and asymptotic time is not a universal feature - that is we cannot always agree on what time it is, and for moving observers, this translates into we cannot always agree on when things happen!

You'll need to define these things carefully, for instance, particles experience time contraction as well. Does that make particles relative? Of course, everything is relative in the universe.

oops! Then yes should be dark matter ! Well spotted. As for the other questions, I must leave them till tomorrow... pretty tired and need my bed. Good night. You may need to clarify this bit for me tomorrow though. Black hole scale can be translated to spacetime curvature. Clearly larger black holes exert larger curvature (and therefore gravity) around spacetime.

Isn't what you are talking about called solipsism ? I don't believe it is solid at all as an argument, or philosophy. Things where happening in the universe long before any intelligent recording devices, like ourselves where around. At least, this is my opinion on the matter. The mind is not all there is - we are inside the universe, we are not so special that the universe be literally in us. The reality you experience arises from a complex series of complicated electro-biochemical interactions, which are then interpreted by your brain.

Yes.. but I would also like to add, that I don't personally believe that the collapse is random. Though a wave function may have a high probability of collapsing to the most likely outcome, but because this is not a set rule (ie. the wave function can collapse to lower probability states), then the wave function is considered (in this case) as not deterministic. I took the liberty to find you a paper, swansont. https://arxiv.org/pdf/1607.06438v1.pdf