I'm going to assume that wave-functions are real things. It is a much more defensible position, more so than MWI. It's better than "I have no idea." As for epiphenomena having illusions creating consciousness, it all sounds pretty vague. It is more likely that ghosts and spirits do exist, but that the evidence is getting mixed in with other stuff.
Why Quantum?
jcr,
In order to avoid that our discussion peters out, I just clarify that Peter J. didn't at all deal with cosine transformation. Did Robert McEachern already utter himself to the question CT vs. FT?
You are right, my suspicion that, in contrast to Pauli's opinion, the complex representations are redundant not just in classical physics but also in quantum physics does not yet answer the question why quantum but possibly the question why Schroedinger introduced a complex wave function. He revealed his thoughts in his fourth communication in 1924. I see Heisenberg's equivalent musing based on the same fallacy.
Hegel denied the existence of atoms. Mach and Ostwald considered atoms for quite a while as mere imaginations without reality. I would like to cautiously answer the question why quantum by pointing to those few experimental results that don't rely on possibly questionable methods like careless application of Fourier transformation.
Eckard
If the wavefunction is ontological, which wavefunction is the real thing? The complex number wavefunction, or the quaternionic wavefunction? Both complex quantum mechanics and quanternionic quantum mechanics give the same predictions for the hydrogen atom. A pure state in complex quantum mechanics is defined up to a phase (a unit complex number) and a pure state in quaternionic quantum mechanics is defined up to a unit quaternion and so the two wavefunctions assign different values at the same space-time point. How can the wavefunction be ontological under this circumstance?
That is a very smart question, and the answer is: I don't know. I am a spiritualist, and so I am more comfortable with the existence of an aether if I can throw out the Michelson-Morley experiment, and replace it with some kind of wave-function aether filled with the Higgs field, virtual photon E&M field, etc. I think this interpretation of quantum mechanics makes more sense that the MWI interpretation, or just saying, "I don't know". If the aether is made out of ontological wave-functions, then how is that so different from quantum mechanics, quantum field theory and the Higgs field?
Eckard,
I'll not speak for Pete, but in earlier discussions Robert made the point that Fourier Transforms as commonly applied cannot extend naturally from the Bohr model Quantum Leap. I would encourage him to reiterate here from his own expertise in FT. To sum-up, his argument is that they are applied from an arbitrary start condition and only condense the observed variation of phase into a modulated waveform that doesn't extend as a continuous transformation from conditions inherent to the emission source, nor give any information as to what those conditions might be. I very much agree.
In case I'm anonymous (anon) some mass merchandiser bot tracking my usage (to better serve me) logs me out before I can submit a post. I have to log in to my IP and to FQXi ... and do it all over again. My guess is my purchase of a cheap Lenovo is tracked by Best Buy, NSA, and the Chinese People's Army. Hi Spooks! jrc
18% of Americans have seen ghosts.
http://www.pewresearch.org/fact-tank/2013/10/30/18-of-americans-say-theyve-seen-a-ghost/
If 18% of Americans are delusional, then why is our country so productive? So wealthy? So well off? Can someone explain that?
Florin,
It is nice to hear from you. It has unfortunately been a while since I went to your website. I had to reinstall browser and lost the bookmark.
The example with quaternionic QM is interesting. This is the quaternion Dirac equation and the model of the H-atom is a Euclidean form of gravitation. The complex wave function for a system is equivalent up to a phase, and for quaternions they are equivalent up to multiplication by any quaternion, not just the unit quaternion --- at least as I recall. We could write the quaternion wave function as
Ψ = c_1i + c_2j + c_3k + c_41
Expanded in the quaternion basis i, j, k, 1. This is equivalent under multiplication by a quaternion, just as the wave function gives equivalent physics when multiplied by a c-number or phase. So for simplicity multiply this by the quaternion i to get
iΨ = c_1i*i + c_2i*j + c_3i*k + c_4i
= -c_11 + c_2k - c_3j + c_4i
which is just an SO(4) rotation in the basis of elements. Of course QM and physics is invariant under changes of coordinates.
In point of fact the Dirac operator and the quaternion function are both the same thing --- quaternions. The action of the Dirac operator on the quantum field quaternion is equivalent to the cohomology condition ψψ = 0. This is known as the Pauli exclusion principle.
The statement that the wave function is real does have this odd implication that all complex numbers are equal to a quaternion. Mathematically this is strange, and even without quaternions the wave function being real means complex numbers are all real. Physically the nonlocal properties of QM simply can't be reduced to a classical realization. We might even go so far as to say that classical physics is an illusion. We know it is an illusion because it is falsified outside of certain domains of applicability, such as atomic physics.
Cheers LC
Jason,
The Higgs field is a quantum field, and it fits very well within the quantum paradigm of physics. The Higgs field though has a quartic potential which makes it different from a scalar field with just quadratic potential. For the quadratic potential the potential function has a single minimum point, which means that to get a particle orbiting around it requires the input of energy. The quantization of the field means these orbits come in discrete steps. For the quartic function there is a circle as the minimum of the potential, what might be thought of as the trough of the Mexican hat. This means under tiny amounts of energy you can set up an orbit. There is then a vast degeneracy of quantum states here that fill up a condensate. This condensate can couple in with certain particles, such as the W and Z particles of the weak interactions. This coupling might be thought of as the Whiggs and the Zhiggs (sounds like the British party of old and the Zh has a Russian sound). This gives the Z and W its mass.
Something happens when this happens. Gauge fields with a massless gauge boson have transverse degrees of freedom, two degrees per particle. A massive particle has a longitudinal degree of freedom. The coupling with the Higgs field gives the W and Z particles this extra degree of freedom.
This was proposed because a quantum field with mass has this longitudinal degree of freeom, and at very high energy this field effect has anomalous propagations --- it propagates faster than light. So Higgs, Englert, Kibble and others proposed this mechanism so that massive bosons of the weak interaction could be massless at high energy. This prevents the quantum field theory from becoming sick.
Cheers LC
Jason,
I think to be honest the United State of America would not have become the dominant world power without World War II. I honestly think this country would have become a somewhat better off English speaking form of a nation similar to those seen in Latin America in the 20th century. WWII caused many scientists to leave Germany and Europe to the United States of America, and remember Enrico Fermi got the first sustained chain reaction. Also the war demolished the economies of every developed nation except the United States. Highly advanced nations, in particular Germany, but also France, Italy and others were economically ruined with the war. Even Britain remained on war rations for almost 10 years after the war. The Soviet Union was brutally ruined, and barely made it through the midpoint of the war. The US economy surged forwards with no competition.
Since the reconstruction of Europe and East Asia, ending around 1970 or so, the US has been declining consistently, and with virtually all metrics from educational levels, to productivity per capita to internet connectivity relative to the rest of the world. The following little clip from the program "The Newsroom" sort of captures the nature of the problem
https://www.youtube.com/watch?v=1zqOYBabXmA
Americans are behind on metrics such as education and we are a people that have traditionally been low on the educational and intellectual scale. There is a long tradition of know-nothingness in this nation, and this has been hobbling the country. Of late this stuff has been politically popular. We also have trends of xenophobia, and now the right winged panic-mongerers are screaming about a wave of immigrants --- who happen to be children. They are kids for ^&%*#$@ sake, not terrorists! There are these sick trends in this country, they have been with us for quite a while and are now very rampant, similar to the early 1950s with greater durability.
Are we really that great?
LC
jrc,
Robert is right: Application of FT requires an arbitrarily chosen "starting" point t=0 of reference to which phase refers too. This is the primary deviation from reality. While time spans between two points, between an event-related starting point (1), and an observer-related current endpoint (2), the direction of view for FT is opposite to that for an observer. FT refers to (1) and looks from there ahead toward (2). The ear is the observer and obeys causality. Therefore it refers to point (2) of observation and looks from this current moment, the now, backward to what already happened, i.e. to point (1).
This logically compelling in common sense physiology is not agreeable with the idea that all time, i.e. the entity of all events, a priori exists and extends bilaterally between infinitely far past and infinitely far future.
In order to restrict the analysis to already existing data, avoid the necessity to arbitrarily choose a reference point, and therewith create unnecessary redundancy, FT can equivalently be replaced by the CT, which unilaterally extends to the endpoint (2), the now. Robert might not yet trust in this implication because it is not yet generally accepted, not even among the experts of signal processing. Of course, CT does not allow phase shift, and it fails in the unrealistic case of a sin function.
Eckard
Eckard
Yes, the start-point vs end-point measurement is what makes the seemingly paradoxical nature of SR so frustrating. My answer has been to postulate that energy density varies in direct proportion to true velocity across the wave length as an acceleration/deceleration event. I don't want to abuse the forum in self-promotion, but would argue that the constancy of light velocity is properly measured relative to the waveform itself rather that in relation only from the start or end point of observation. Then SR is both demystified and generally co-variant in terms of energy density. jrc
Lawrence,
I think that both our world views are pretty fixed. You're an atheist down the core who doesn't believe in an afterlife. I am a Spiritualist who believes in the existence of spirits, an afterlife, and God. Neither of our world views are going to change. For my part, one of the problems I have with atheism is that it is so entrenched in cynisism. I don't even think that atheists believe that there exists physics beyond GR and QM, other than some quantum gravity theory. Some of the things I liked about Spiritualism was their positivity, their sense of hope, as well as the countless uncanny evidences from psychic readings, and the entities that I've personally witnessed, and my fiance who was assaulted by a ghost (shoved down the stairs), and this nagging feeling that wave-functions mathematics is describing an all pervasive spirit.
Now, I agree with you that there are people who claim paranormal phenomena who are just painful to watch. They take pictures of dust particles and bugs and call them spaceships. So I totally agree with you that there is a lot of crap in the paranormal literature. But on the other hand, there are a few really good jewels in there as well. It warms my heart when a skeptic is confronted by a ghost, an entity, grey aliens, or some psychic who is so talented that they make it look like something impossible is going on. I've listened to cold readers and they sound like crap; they sound all intellectual, like their guessing, it sounds forced, it doesn't flow. My break is over, but I just wanted you to know that my philosophical beliefs are based in impressive evidence, not junk, not hooey.
I don't see any evidence that the physics community is able to detect ghosts. There could be shadow figures flying around people's living rooms or evil entities with glowing red eyes haunting families and physically attacking peopple, and the physics community would have no ability to confirm this. All these ghosts really need is some ability to manipulate virtual photons to create potential energies.
jcr,
If something happens at a moment (1) then a belonging signal arrives at an observer at a later moment (2). (1) and (2) are not points in space but points of time. Moment (2), the now, is the natural zero of always positive elapsed time. You wrote "true velocity across the wavelength". Perhaps you referred to the propagation of light in empty space. Michelson's 1881/87 experiments led to the unexpected result that light does not propagate like sound relative to the wavelength along a medium. In case point (P1) of emission is moving relative to point (P2) of arrival, (P2-P1 at 1) differs from (P2-P1 at 2). The velocity of light relates then to the distance (P2 at 2) - (P1 at 1). This easily explains Michelson's null result without invoking mystical length contraction and also without SR.
Please don't shy back from convincingly offering something else. Your hint to energy density worries me. Doesn't it decrease with growing radius in case of a radiating sphere? Also, I wonder if SR needs considering acceleration/deceleration.
The question "why quantum" sound to me a bit like an unnecessary attempt to resolve the discrepancy between Einstein's relativity and quantum theory by questioning the latter. That's why I dislike your just "seemingly paradoxical nature of SR".
Eckard
I did not indicate anything about what I believe with regards to metaphysical ideas and so forth. I do though think one needs to keep ideas about spiritualism independent of scientific thought. The idea that the Higgs field is somehow related to ghosts or spirits running around is pure buncomb.
LC
Jason, being so knowledgeable about ghosts, I would like to know:
1. Does time flow for ghosts OR do they have different ages?
2. Are there female and male ghosts, and if there are can they copulate to give birth to more ghosts?
Thanks,
Akinbo
Lawrence, the address is: http://fmoldove.blogspot.com/. I am doing a series on differential and algebraic geometry to introduce the tools needed to discuss gauge theory and the standard model. It's all very good stuff explained intuitively: homotopy, homology, cohomology, de Rham, Hodge. Then I want to explain fiber bundels, Yang-Mills and the relationship with general relativity. Last I'll explain non-commutative geometry.
By the way, I did obtained QM from physical principles. I have a preprint in alpha release and by the end of next month will be in beta release (the archive). I am searching now for a suitable journal (Reviews in Mathematical Physics, Advances in Mathematical Physics, Journal of Physics A: Mathematical and Theoretical, Journal of Mathematical Physics). I have to decide before the archive upload because they all have different styles you need to follow. Here is the abstract:
"Quantum and classical mechanics are derived using four natural physical principles: (1) the laws of nature are invariant under time evolution, (2) the laws of nature are invariant under tensor composition, (3) the laws
of nature are relational, and (4) positivity (the ability to define a physical state). Quantum mechanics is singled out by a fifth experimentally justified postulate: nature violates Bell's inequalities."
I derive the Poisson algebra for classical mechanics and the phase and Hilbert space formulation for QM all in a constructive fashion.
[deleted]
Lawrence,
I think you're getting the idea of number confused with the idea of function. It cannot be true that "... the wave function being real means complex numbers are all real." Complex numbers have no preference for the real line; only when the imaginary part is zero, do complex numbers behave as real numbers. Therefore, it also does not follow that "Physically the nonlocal properties of QM simply can't be reduced to a classical realization."
Nonlocality is a necessary assumption of applying the n-dimension Hilbert space formalism to quantum mechanical phenomena; it is not a result.
Only were the wave function equal to zero, and therefore not continuous, would it be both necessary and sufficient to frame physics in a completely probabilistic measure schema. Every physical result would have a definite probability -- a quantum number -- on the closed interval [0,1]. However, because we know that the wave function evolves deterministically, we also know that this is not true. Numerical discreteness does not determine a continuous function; it's the other way around.
Attached is a piece I am working on at the moment, to help frame the problem of continuous functions vs. quantum numbers.
Best,
[deleted]
Eckard
Thank-you for your willingness to discuss alternative ideas. While I am in general agreement with you as to the time parameter, what I stress is that the single wavelength can be described as a closed system with a start point and end point in space. It creates a finite volume which is constant for any wavelength but which is protracted as a partition of the Planck Quantum between an electrodynamic charge coupled with an accelerating charge which propels the rest moment quantity to peak periodic velocity at mid point of wavelength. The model I developed needs further refinement but results in a spectrum of continuous transform from a prolate spheroid to oblate spheroid of energy volume. Where the Second Law is violated in this closed quantum system is in the collapse of the volume in the second half of the wavelength, recovering the accelerating charge at end point of wavelength. Again, I don't want to get on my own soapbox and shout, but the volumetric transformation is rigorously precise and the rationalization of the volume of the rest moment electrodynamic charge at peak velocity expands laterally and contracts longitudinally which together with a reduction of density in that peak velocity cylindrical disc by a value of 1 magnitude of light velocity is consistent with the difference of electric field strength and magnetic field strength. This computed out as consistent with the observed upper and lower bounds of the EM spectrum based on a qualitative property of density which assigns requisite densities to produce response as kinetic (inelastic), electrostatic (elastic), magnetic (fluid), and gravitational (ethereal) physical properties of energy.
This is admittedly a naïve model, but the point to be made is that ANY model that provides the mechanics which allows velocity to be measured from the waveform itself rather than an observer position can explain the constancy of light velocity and the null result of Michelson-Morely.
By the way, I'm from Ohio. The collaboration of Michelson and Morely led to the consoldation of Case University and Western Reserve into the esteemed Case Western Reserve University of today. The CRC Dictionary of Scientific and Technical Terms was originally a publication of the Cleveland Rubber Company. These days we have the Rock and Roll Hall of Fame. Not that in not an old Rolling Stones fan, it's just a bit of a come-down. jrc
Hi Lawrence,
Why would anomalous faster than light propagations make QM sick? Wouldn't FTL be a threat to GR? Not QM?