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originally posted by: greenreflections
a reply to: joelr
Interestingly, at the largest scale, your question about the edges of the universe has a similar problem. Spacetime expands slowly on a local scale, like for galaxies and local clusters of galaxies. But galaxies really far away are moving away from us much faster..
But why do you think is that? Space-time expansion should not be different from where we are compare to the most outskirts of cosmos if we assume space-time expands equally from every point of it, imo.
Why space-time locally expands slower than we clock expanding distant galaxies especially when it is thought that expansion must be faster than light by now to accommodate calculations? The Moon should be getting further away from the Earth). Or, are there special areas of space-time where expansion more preferable?
thanks)
Reason: correction/ the Moon IS getting further away from the Earth/
Yes, because of tidal interaction, not because of the metric expansion of space.
the Moon IS getting further away from the Earth
The Earth and the moon are close enough together so that gravity dominates. Actually even at 2 million light years away, gravity seems to dominate the movement of the Andromeda Galaxy and other galaxies in the local group, which is why we don't really observe Hubble's law applying at distances less than about 30 million light years; Our "local group" of galaxies has a fair amount of gravity and are not that far apart as cosmic distance scales go.
whether the pull of gravity, or the push of dark energy dominates over a given region of the universe, depends on how much mass is there, and how widely separated it is. If they're far apart, the push of the dark energy wins, but if they're close together, gravity is going to dominate.
originally posted by: delbertlarson
a reply to: mbkennel
Thanks so much for your reply.
I am not sure what "emergent phenomenon in the limit of large particle number" means.
I do think I can be a bit more clear myself though on what I mean by discussing this topic in terms of my favorite example - the two slit experiment.
In the two slit experiment, light is impinged upon a barrier containing two slits. If a quanta of light interacts with the solid part of that barrier,
it shows a small speck of a dot as that portion of the light is scattered from its point of interaction. My view is that the wave function for that particular photon that hit the barrier is collapsed to a size of dx = hbar/dp, where dp is the momentum exchanged when the photon hit the solid barrier.
But for other photons that instead penetrate the slits, since there is no momentum transferred at all, and the wave function is then able to occupy both slits, but only the slits. (It can't exist at the solid part of the barrier or it would interact there.) After the slits the two portions of the photon travel to the distant wall. At the distant wall there are no open spaces and so an interaction is demanded. And the probability of the interaction happening at any point on the distant wall is determined by the square of the wave function there. This indeed is the interference pattern observed when many such photons are allowed to go through the two slits. But when any one photon hits the wall, it again shows the same speck of light that has a size of dx = hbar/dp.
I retain my belief that this interpretation of things is the simplest one we can have, and it doesn't have any of the hocus-pocus associated with competing quantum mechanics interpretations.
The above does however have a problem with relativity. The collapse of the wave function at that distant wall must happen in such a way that distant parts know that it is collapsing, or else it could begin to collapse in two places. And this action-at-a-distance is something relativity doesn't allow.
Then again, tests of Bell's theorem have also shown actions at a distance contrary to the special theory.
originally posted by: delbertlarson
a reply to: mbkennel
You mentioned a lot in your last reply, and it got me thinking. Thanks. I will try to clarify my position a bit more here. This reply will touch upon many of the topics of your last reply, but not all of them, as I don't want to try to have too large a scope in this single post.
I retain my belief that the essence of the quantum mechanical mystery is found in the simple two slit experiment, and I also retain my belief that my earlier post helps to understand that mystery in a way that can be grasped by the human mind. I will try to reformulate my view into a few postulates:
Postulate 1 - Any interaction between entities causes the original participating quantum states to collapse into one of the possible resultant quantum states available to them at the time of the interaction.
Postulate 2 - The probability of a collapse into any particular resultant quantum state is the square of the original wave function's normalized magnitude appropriately integrated over that particular resultant quantum state.
Postulate 3 - When momentum is transferred in a collapse, the quantum state will collapse to a size dx=hbar/dp, where dp is the momentum transferred.
For the photon impingent upon the two slits in the two slit experiment, the resultant possibilities include collapsing to the entirety of the two slits, or collapsing to any single spot on the barrier. This is different from the Copenhagen interpretation in that no sentient observer is needed.
The collapse does not occur because of an observation as in Copenhagen; instead it occurs because a choice is forced upon the original quantum state to become one of several possible resultant quantum states. This choice is forced by the existence of the barrier and walls and has nothing to do with an "observation".
In your reply you bring up the wave function of the barrier. In my simple view, the wave function of the barrier isn't all that important. That is because I believe that each particle in the barrier primarily has its own wave function, largely uncoupled from the other particles constituting the barrier. But more importantly, I believe the impinging photon is, for all practical purposes, totally uncoupled from the particles of the barrier until the collision occurs. This allows us to confine our focus to the photon wave function alone, along with what happens to it, and not be concerned about other wave functions.
If we instead attempt to concern ourselves with the wave function of the entire universe I believe things get so complex that we will never make any progress at all.
And that is why my focus has always been on the wave function of the single photon, and why I choose to treat the barrier and ultimate wall as separate entities here.
Within my view the photon consists of electric and magnetic fields which obey Maxwell's equations.
Maxwell's equations are linear equations that lead to the wave equation for the substituent magnetic and electric fields. That simple wave underpinning leads to a density at the distant wall that is in complete agreement with experiment for the many particle result of two slit experiment. I know of no experiment that shows anything incorrect about Maxwell's equations, so I don't see how any nonlinearity will enter in to them.
The only issue is how can we understand the collapse, and I believe my postulates above allow for such an understanding. They do not allow for a prediction of where an individual collapse will occur however, and only result in allowing us to understand how such a thing could happen and what non-sentient causes there are for such a collapse.
originally posted by: mbkennel
Something deep in the wavefunction/functionalspace/matrix can happen non-locally, and we need to accept that as physical truth. And likewise, something in QM also seems to prevent nonlocal classical information transfer, so that we will not be able to exploit this nonlocality macroscopically for paradoxical and amazing purposes.
originally posted by: ImaFungi
originally posted by: mbkennel
Something deep in the wavefunction/functionalspace/matrix can happen non-locally, and we need to accept that as physical truth. And likewise, something in QM also seems to prevent nonlocal classical information transfer, so that we will not be able to exploit this nonlocality macroscopically for paradoxical and amazing purposes.
I believe the weirdness has to do with at least either hidden fields and/or Earths complex multiple movements;
Hidden fields; Imagine you were in a pool of crystal clear water and there was a camera above you that due to focus and/or aperture and/or resolution and/or other reasons could not detect the water at all, and there was a floating ball at some distance to you, and so the camera detects that you move your hands around (in the water) and the ball moves (spooky action at a distance).
And/or (combined) with Earths complex multiple movements (if the milky way is moving relative left or right or up or down from a real position it formally occupied; besides revolution of stars and planets around the center, but as a system, stars and planets and center moving relative etc.) Earth moving linearly through ultimate absolute space time via aforementioned milky way as a system moving (unless you believe the center remains absolutely fixed point still and ignoring all else beyond the milky way, the milky way is a fixed point carousal or fixed point whirlpool with a center which stars and planets revolve around); Earth revolving around central black hole; Earth revolving around Sun; Earth rotating;
From what I have seen on this thread of EM and photon, I have never seen anything that would suggest what has been explained and described as EM and photon physical mechanical nature, a single quanta of photon can be split into two.
A minimally nonlinear von Neumann equation for a Stern-Gerlach or Bell-type measuring apparatus, having a scalar product structure over the configuration space, i.e. a sum of locally acting terms, is shown to display a competition for survival between diagonal density matrix elements assigned to each detector combination, with a single winner randomly selected according to Born's rule and the rest collapsing to zero. Randomness is emerging from deterministic-chaotic dynamics of the detectors, their microscopic states acting as a nonlocal set of hidden parameters, controlling individual outcomes. The scheme works without any kind of action-at-a-distance; still it is fully reproducing quantum behavior, which warrants it is non-signaling.
originally posted by: mbkennel
A minimal physically realistic but potentially very small nonlinearity can make wavefunctions collapse and derive the Born rule as a phenomenon instead of an axiom.
I'm having fun reading the discussion. There is some confusion over the word "observer" and it's sometimes misunderstood to refer to consciousness in Copenhagen, but it doesn't require a sentient observer according to Heisenberg and I'm sure he's not the only one who would say so. In fact we have experiments to show the "collapse" doesn't require the information to be made available to a conscious observer, so if Copenhagen really inferred that we would have to stop teaching it and teach something else.
originally posted by: mbkennel
Does Copenhagen require this?
It is the `factual' character of an event describable in terms of the concepts of daily life which is not without further
comment contained in the mathematical formalism of quantum theory, and which appears in the Copenhagen interpretation by the introduction of the observer. Of course the introduction of the observer must not be misunderstood to imply that some kind of subjective features are to be brought into the description of nature. The observer has, rather, only the function of registering decisions, i.e., processes in space and time, and it does not matter whether the observer is an apparatus or a human being; but the registration, i.e., the transition from the `possible' to the `actual, ' is absolutely necessary here and cannot be omitted from the interpretation of quantum theory.
originally posted by: ImaFungi
originally posted by: mbkennel
A minimal physically realistic but potentially very small nonlinearity can make wavefunctions collapse and derive the Born rule as a phenomenon instead of an axiom.
What is the minimal definition/requirement of the term 'nonlinearity'? And can you provide a simple real or thought experimented example?
Otherwise, if they are both quantum particles, then this isn't true---an entangled state is exactly a mutually interacting one of profoundly quantum entities which haven't collapsed, and this phenomenon is experimentally real.
Seems reasonable, but do you believe collapse can happen only with transfer of momentum? What about a flavor changing weak interaction? (to pick up on something exotic at random).
Does Copenhagen require this?
Operationally of course, but the philosophical problem is there---if QM is fully linear then you get multiple universes in effect.
Here's my postulate and the one advocated by the paper I quoted
"God does not play dice with the universe"
As I said there's a lot of confusion on this issue, but I need to clarify further. Heisenberg not only feels there is a need for an observer in Copenhagen, he says it is absolutely essential. The confusion which ensues is a result of people inferring that "observer" implies a "conscious observer" and Heisenberg is very clear this is not the case when he says "it does not matter whether the observer is an apparatus or a human being" per the above citation.
originally posted by: delbertlarson
I don't know that Copenhagen requires an "observer". I do know that Bell spent a lot of time on that idea, and that it was flourishing for a while some decades ago. I felt it was one of those wild speculations I find unappealing. I note that Arbitrageur has pointed out that Heisenberg didn't feel the need for an "observer" so perhaps Copenhagen really doesn't need one.