the L, on 15 October 2012 - 07:01 PM, said:
What you trying to tell when you said that we cant project 3D crystal momentum on 2D surface without loosing info and that experiments shows info about electrons in crystal lattice? I think I didnt conclude well...
I was trying to break down some of the issues I have with the Holographic Universe idea in terms of simple physical systems.
So consider a perfect diamond: I think we can all agree it has a well-defined surface. Is all of the information about the diamond contained on the surface? Certainly the surface helps define the diamond (mathematically, it is obviously provides the ``boundary conditions''). But from an experimental perspective there is more to it. I can probe the behaviour of electrons
inside the diamond, and I will find that distinct electronic states are partially defined by
three components of crystal momentum; because the electronic states are in 3D space. If one of those components turned out to be random, or defined entirely by the other two, then the information of each electronic state could be contained - somehow - on the 2D surface of the diamond. But in general all three components are independent: choose any three
arbitrary values for these components and you will be able to find
some electronic state with that momentum.
In a non-magnetic system (like diamond) each electronic state has 4 components: three components of crystal momentum (usually denoted as
kx,
ky,
kz) and an energy (usually denoted
E). However you only need to know
three of these numbers to determine the 4th. In other words, you can arbitrarily choose
any values for
kx,
ky,
kz and expect to find an electronic state with a particular energy
E (or possibly a few states with different energies). You can't arbitrarily choose any value for all four components and expect an electronic state to exist.
This makes sense if you consider that a
free parameter is the same as a
dimension, and the diamond is ``really'' in 3D space. If the diamond were ``really'' just a 2D surface, then you would expect only
two of
kx,
ky,
kz, and
E to be arbitrary.
the L, on 15 October 2012 - 07:01 PM, said:
Why wouldnt my sponge skin be also projection?
Could we all be like Star Trek Hologram?
My argument here is just ``what is the surface a macroscopic object (like a person) is projected on''? A black hole has a very distinct surface (the event horizon). A human being does not. What is the difference between the 2D surface of an incredibly fine sponge and an actual 3D object?
the L, on 15 October 2012 - 07:40 PM, said:
Seupul about your fraction link...isnt that search to grasp infinty?
Not really, I was just trying to address what I mention above in a different manner. On a molecular level, your body is a sponge; it is full of holes. On an atomic level, a molecule is mostly empty. On a subatomic particle level, an atom is mostly empty. But for your body to be a projection, it needs to have a surface - where is this surface?
You could argue that each subatomic particle is itself a 2D projection, and we are just composed of these projections, but in the Standard Model a subatomic particle (electron, quark, etc.) is a ``true point particle'', i.e. a 0D object. Elevating this object to 2D is... unnecessary.
the L, on 15 October 2012 - 07:52 PM, said:
Sepul can you explain me so that I could even understand Double-slit experiment. I read it twice and dont get it.

A bit off topic, but I will try.
A
wave is a periodic travelling fluctuation of
something. A water wave is a good example: a periodic travelling fluctuation of the surface of a body of water. All waves have parts that are higher than average (i.e. the crests of water waves), parts that are lower than average (i.e. the troughs of water waves), and parts that are exactly average (called nodes).
Two waves can pass through each other. When they do, they create
interference. This interference can be
constructive when two crests or two troughs meet in the same place and make the
thing (i.e. the surface of the water, the electromagnetic field, etc.) at that location higher than it would be from only one wave alone, or the interference can be
destructive when a crest meets a trough and the two (partially) cancel each other out.
If the two waves are
coherent, that is they have the same frequency, then the interference pattern is constant. You can easily see this in a
ripple tank (here they have two small paddles going up an down in synch to create the waves); note in the video there are straight lines where the water is basically flat; these are locations of destructive interference.
The
double slit is just a technique for making light waves
coherent. How can you tell if two lamps, lasers, or whatever are emitting light in synch? Basically you can't, so the trick is to take
one lamp or laser and shine the light through two small slits. Each slit is effectively acting as a ``source'' of light, so you end up with two ``sources'' radiating light in synch, and the light waves can create constructive and destructive interference, just like the water in the ripple tank video mentioned above.
So
IF light is a wave, then you should see an interference pattern on the other side of a double slit. (And you do! And you can do it yourself at home with a few easy-to-obtain items, see
here. Note: the author of the video seems confused about what he calls ``single slit interference''; what he actually sees is called
Fraunhofer diffraction - not interference.)
BUT, as quantum mechanics rather conclusively has shown, light comes in discrete packets called ``photons''. What happens if we use a very precise light source that only sends
one photon at a time through the slits? (Unfortunately, this is NOT an experiment you can easily do at home.) Well, when they do that experiment the interference pattern still shows up! So clearly each photon is acting as a ``little wave'' and going through both slits at once, then interfering with itself on the other side. No problems so far!
BUT a photon is supposed to be an indivisible packet of energy, so what if we put energy detectors on
each slit? Will we detect a ``half photon'' going through each slit?
The answer is
NO. We only detect
one photon going through a particular slit (and
zero photons going through the other slit) at any given time. And suddenly, when we use this detector, the
interference pattern vanishes! The photons are
no longer acting like waves.
This is often described as ``observation changes reality'', which appears to be true (in many cases, not just the double slit).
However people often make the
false assumption that ``observation'' implies ``a human mind'' or an otherwise ``conscious observer''. It is the
detector that is doing the ``observation'',
not the scientist. If the scientist turned the detector on, but put some tape over the detector display so he/she couldn't see which slit the photon went through, the interference pattern
would still be gone. Unfortunately there is a lot of pseudo-scientific nonsense on the internet (not in the least from those ``Doc Quantum'' videos on Youtube) that perpetuate this concept.
The double-slit experiment is an example of
wave-particle duality, a still-somewhat-unresolved branch of the philosophy of quantum mechanics, on which I can give more details if you want.
But in a nutshell, the double-slit experiment is as follows:
- When a single photon is sent towards a double slit without a detector to measure the photon at the slit, the photon behaves as a wave after passing through the slit.
- When a single photon is sent towards a double slit with a detector measuring the photon at the slit, the photon behaves as a [b]particle[/i] after passing through the slit.