This is an interesting article.
My essay :"Rethinking the Double Slit Experiment" have discussed the three slits experiment. The cross-link angle establish the magic connection between two slit
[math]T_{{\color{red}1}}=T_{c}\cos(\theta_{{\color{red}2}})[/math]
http://fqxi.org/community/forum/topic/1452?search=1
One slit, two slit, three slit, more slit
OK -
I apologize - I'll try and be more professional
If one assumes a theory in which a micro particle becomes spatially macro in size once it leaves the source, then it can go through one, two, three, or even more slits. If this same theory assumes that the particle re-convenes to a single agreed upon non-time-dilated-micro-entity when it reaches the screen, then it can produce a single point again. Such is CIG Theory, whereby a moving particle becomes spatial. The faster the moving particle, the more the particle manifests into its spatial equivalent. This is exactly where the space comes from for there to be an "expanding universe". And, it explains the double, triple, quadruple slit experiment as well. I haven't yet followed the Delayed Choice Quantum Eraser, but if you want to try my theory to explain the delayed choice, please be my guest.
I'll try to be more professional.
THX
doug www.CIGTheory.com
The prospect exists that quantum mechanics and relativity are really two aspects of the same thing. Both of these domains of physical observation rely upon a constant which defines a projective bundle. In a categorical sense we may find that quantum physics and relativity are equivalent, and further they embed within a larger system.
Relativity has a projective subspace defined by null rays. A projective space is constructed from a space by looking at all lines through a point and considering them as equivalent element under all rescalings. Lorentz spacetime contains this in a set of light rays which pass through a point. The distance along a null ray is zero, no matter how much one rescales coordinates x or t. This then constructs the projective Lorentz group, where the Lorentz group has a projective fibre or line bundle over this projective variety.
Physically the speed of light is just a conversion factor which converts between distance and time. The constancy of light speed means this factor defines the projective subspace in spacetime.
Quantum mechanics has a similar structure. The Planck constant ħ is a conversion factor between the variance in position and momentum with the Heisenberg uncertainty principle ΔpΔx ~ ħ. In addition there is a projective variety. To show this we can start with the Schrodinger equation:
iħ|∂ψ)/∂t = H|ψ)
I have to use parentheses for bra-ket notation on this blog. We look at the overlap between the state |ψ(t)) and |ψ(tδt)) and Taylor expand it
(ψ(t)|ψ(tδt)) = (ψ(t)|ψ(t)) δt(ψ(t)|∂ψ(t)/∂t) (δt^2/2)(ψ(t)|∂^2ψ(t)/∂t^2) ...
Now use the Schrodinger equation to get
(ψ(t)|ψ(tδt)) = (ψ(t)|ψ(t)) - (i/ħ)δt(ψ(t)|H|ψ(t)) - (1/ħ^2)(δt^2/2)(ψ(t)|H^2|ψ(t)) ...
We now evaluate the modulus square of this to get
|(ψ(t)|ψ(tδt))^2 = 1 (δt/ħ)^2 [(ψ(t)|H^2|ψ(t)) - (ψ(t)|H|ψ(t))^2] ...
This term O(δt^2) can be written as (δt/ħ)^2 ΔH^2, which recovers the Heisenberg uncertainty principle. The overlap is determined by a phase term e^[(δt/ħ)^2 ΔH^2], which is the line bundle or projective bundle.
The only known intertwining relationship between ħ and c is the Planck length, or other Planck scales
L_p = sqrt{Għ/c^3}
This may be written as ħ/c = (L_pc)^2/G, which can be expressed according to the Planck mass m_p = sqrt{ħc/G} as
ħc = Gm_p^2 = 3.16x10^{-26)kg m^3/s^2.
This is then a constant, which is in naturalized units "one."
Cheers LC
Hello everyone in FQXi world -
"applicable to 3 or more slits" = "light related"
Light is finite because at its maximum value of "c", all the mass of any given traveling particle has turned entirely to its spatial equivalent (Space), and so there is nothing else left to travel. With nothing left to travel, there is nothing left to go faster.
Are the electric/magnetic fields simply very heavy Dark Matter (HDM)? Spatially manifested (i.e. new space) entities based on the motion of the given particle under way (i.e. electricity). Essentially, this would be the CIG Theory interpretation. Wherever matter travels, space will be created.
[Dark Matter Electric Field Proposal] = please evaluate
But why would the balloon hold the space in (see my balloon questions posted elsewhere), but not the wire/cable insulation jacket? Perhaps the cable is not flexible enough?
see CIG Theory - www.CIGTheory.com
Does anyone understand CIG Theory?
thx
doug
Hello,
Do Not Erase = light related = ten even twenty slit experiment!
I was just watching Fay Dowker talk Spacetime Atoms and the Unity of Physics (Perimeter), and the section on Lambda.
Just a thought:Where Lambda = Ten to minus 120 (10 to the - 120), and we are talking about the Cosmological Constant here, and vaccuum energy, and CIG of course!
Perhaps this is the value of the Cosmological Non-constant at full "c" value.
The quantum theorists value of Lambda = 1 may be mass traveling at zero % "c"
Remember, CIG Theory offers a varying cosmological constant.
Black Hole value = 1 = full spacetime curvature
Dark Energy = Ten to minus 120 (10 to the - 120) = no curvature = pure space
Just a thought. Perhaps everyone is right!
Now, back to our show.
THX
doug
It would be really interesting to see the results of this three slit experiment, and the interference pattern that is generated.
The experiment may help to verify the Spacetime Wave theory which is covered in:
In the terminology of the Spacetime Wave theory the wave quantum (photon) passes through all paths of the interferometer as a spacetime wave and the interference pattern would reflect the wave magnitude at the detection screen. With more than two slits (paths) this would depend on the precise alignment of the different interferometers which might mean that there is no point in the plane of the detector screen where all three wave maxima coincide.
It would also mean that the form of the pattern would depend on the precise distance from the interferometers to the detection screen.
One would expect that because of the lask of coincidence of the three waves that the pattern would be less distinct than for two paths.
Richard
What if...
Quantization appears when the freedom of the quantum object is squeezed, constrained
Light has speed and direction. The light beam direction is squeezed by the slits. 'direction' becomes a quantum number for the object and will now assume discrete values.
Direction is quantized and you get discrete directions on the screen ... a pattern.
Whenever we observe-interact with a quantum object we somehow contrains its freedom and cause the temporary quantization of the property being observed... (That's quantum mechanics)
Marcel, (crazy enough?)
For each quantum object in the universe, there exists both an inner as well as an outer solution to the Schrodinger equation. Light represents the outer solution and each photon of light complements an inner binding solution for microscopic matter.
When we confine light, we create a hohlraum whose modes define the light that leaks out of any aperture. For a coherent hohlraum, a single photon as a wave leaks simultaneously out of any number of apertures onto separate world lines and yet we detect that photon along only one world line.
The photon will interfere with itself if the apertures reconverge. It is not necessary to use slit diffraction, which really just unnecessarily complicates the analysis. All that is needed is a mode-locked laser cavity with apertures on TEM11 instead of a single aperture on TEM00.
For a mode-locked laser, each time packet represents a superposition of identical coherent photons. All that is necessary to measure one photon at a time is attenuation. It is a complete mystery why people seem to make such a big deal out of photons that interfere with their other possibilities. Since this is what makes laser work, single photon coherence manifests itself in any number of different ways.