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#51493 - 03/31/14 01:42 AM Entanglement in 103 dimensions
Orac Offline
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Anton Zeilinger and his group have again pushed the quantum limits and managed to achieve a quantum entanglement with a minimum of 103 dimensions with only two particles

Full paper:
http://arxiv.org/ftp/arxiv/papers/1306/1306.0096.pdf

media reports:

https://www.uab.es/servlet/Satellite/lat...d=1345668721554

http://phys.org/news/2014-03-quantum-entanglement-multiple-dimensions.html

Note: I will give you something to look carefully at ... how they decide a dimension exists.


Edited by Orac (03/31/14 02:35 AM)
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#51494 - 03/31/14 02:59 AM Re: Entanglement in 103 dimensions [Re: Orac]
Bill S. Offline
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Impressive stuff, even with my limited understanding.

I'm a bit puzzled about exactly what doing something in 103 dimensions, or even 11 dimensions involves. Is it just a mathematical thing?
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#51495 - 03/31/14 07:37 AM Re: Entanglement in 103 dimensions [Re: Bill S.]
Orac Offline
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Entanglement occurs when you can bind two (or more) entities within a valid Schrödinger equation that is establish a valid collective coherent wave between the entities. So it is more about wave behaviour than actual mathematics, although obviously you can describe it with mathematics.

The nearest layman example I can think of that is close is music sampling where the human ear can easily distinguish the two sampled tracks. In entanglement the overlap is actually complete not in samples.

You therefor have to try and visualize the waveforms somehow occupying the same space at the same time or as we would say in our classic world a different dimension smile

This is sort of extension of the work taking two atoms splitting them apart and putting them back together that was done last year.

Media:
http://www.livescience.com/20926-quantum-physics-atoms-split.html

They will no doubt ultimately try and show that they have multiple physical copies as per the above work so the idea that this is some mathematical trick can be fully dispelled.
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#51504 - 03/31/14 03:57 PM Re: Entanglement in 103 dimensions [Re: Bill S.]
pokey Offline
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Registered: 08/22/07
Posts: 84
Bill S, previously in another thread you asked if a particle
could be in two places at once.

Does the following imply that they can?

"The states in which elementary particles, such as photons, can be found have properties which are beyond common sense. Superpositions are produced, such as the possibility of being in two places at once, which defies intuition."

http://phys.org/news/2014-03-quantum-entanglement-multiple-dimensions.html

Or is it bad writing?

Or is it me?

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#51506 - 03/31/14 06:38 PM Re: Entanglement in 103 dimensions [Re: pokey]
Orac Offline
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If you go back to last years work on splitting an atom into two places you will notice we have to be careful in our description

http://planetsave.com/2012/06/05/atom-sp...ntum-mechanics/

Quote:
In this experiment, the researchers succeeded in keeping a single atom in two places more than 10 micrometers apart, that’s a one-hundredth of a millimeter. That is an enormous distance for an atom.


Quote:
“The atom has kind of a split personality, half of it is to the right, and half to the left, and yet, it is still whole,”


Quote:
This isn’t visible directly, though. If you shine a light on the atom, the split will collapse.


So although you can measure and see interactions to infer the atom is in both places you can't directly observe it in both places at the same time ... it is very much like looking for the end of a rainbow.

So does it exist in two places depends directly on how you define "exist".

The result seems somewhat ridiculous in classic physics but it is not as strange as it appears if you think carefully about the nature of atoms. Try following the discussion link

http://sciencequestionswithchris.wordpress.com/2013/04/16/do-atoms-ever-actually-touch-each-other/

The waveform nature of the universe is very different to the solid classic physics world and trying to define a common state like "exist" can be very problematic.


Edited by Orac (03/31/14 06:43 PM)
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#51510 - 03/31/14 08:10 PM Re: Entanglement in 103 dimensions [Re: Orac]
Bill S. Offline
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I still don't see where the 103 dimensions enter the picture.
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#51512 - 03/31/14 08:33 PM Re: Entanglement in 103 dimensions [Re: Bill S.]
Bill Offline
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I think that they are talking about the various ways in which the particles could be interacting. You can count dimensions as the number of ways in which things interact. In this case I think they are saying that they have 103 different ways that the interactions could occur.

I think another way of saying it is that they have 103 degrees of freedom. In a strictly classical physics view that would mean that they could have 103 ways of moving. That would include right/left, up/down, forward/backward, rotating clockwise/counterclockwise, tumbling forward/backward, .... on and on.

Bill Gill
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#51516 - 04/01/14 02:16 AM Re: Entanglement in 103 dimensions [Re: Bill]
Orac Offline
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Absolutely spot on Bill.

It is very well covered in http://en.wikipedia.org/wiki/Dimension_(mathematics_and_physics)

You will find the key point

Quote:
The state-space of quantum mechanics is an infinite-dimensional function space.


As per Bill's post our "classic" world has a small set of dimensions of freedom being 3+1 ... those degrees of freedom are 3 of space and 1 of time.

If you think about electromagnetism it clearly shows this problem in that it is definitely 4 dimensional. Almost all humans are also well versed in turning 3D images into 2D pictures and drawings and we can even do 4D. When we draw the classic electromagnetic wave we are actually bringing a 4D waveform back to a 2D drawing and we usually draw it like this



Try drawing the above image moving in 3D space ... see the problem time is already occupying the 3rd dimension and you can't. The dimensionality issue is not just restricted to QM even a basic EM wave has the problem smile

So extra dimensions don't have to be real to us and whether we can represent them depends on our imagination rather that any physical reality.

Quote:
In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it.


So perhaps the real issue is in classic physics we tend to think of dimensions in a certain physical way because of the way we are taught and experience the world via our eyes and so the dimensions in the two discussions don't really refer to the same thing .... dimensional space versus abstract dimension.


Edited by Orac (04/01/14 03:53 AM)
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#51519 - 04/01/14 03:59 PM Re: Entanglement in 103 dimensions [Re: Orac]
pokey Offline
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Registered: 08/22/07
Posts: 84
Orac,

Thanks for the information and links.

The following one sure had a lot of answers to various questions.
http://sciencequestionswithchris.wordpress.com

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#51527 - 04/02/14 08:50 AM Re: Entanglement in 103 dimensions [Re: newton]
Orac Offline
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Marosz you are a day late for April fool's day and completely off topic to this post you stupid troll frown


Edited by Orac (04/02/14 09:13 AM)
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#51530 - 04/02/14 03:04 PM Re: Entanglement in 103 dimensions [Re: Orac]
paul Offline
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could you point out the 4 dimensions in the above image?

or did you already point them out.

Quote:
So extra dimensions don't have to be real to us and whether we can represent them depends on our imagination rather than any physical reality.


I only see 3 dimensions in the image.

the electric field and the magnetic field occupy the same
space , the only other dimension is the time dimension which
is simply the direction of the emitted photons involved and their spacing or their cycle which is simply the frequency or the rate at which the photons are emitted in a time frame.

I dont see a fourth dimension.






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#51532 - 04/02/14 07:16 PM Re: Entanglement in 103 dimensions [Re: paul]
Orac Offline
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Think about it carefully Paul smile

At the moment the E & B fields are going into what would be the width and height the time field is what would be the Z movement so what is drawn is linear polarized. I guess what you could do to try and make it more generic to many cases by corkscrewing it but it still doesn't really work but that would at least cover angular momentum (http://en.wikipedia.org/wiki/Angular_momentum_of_light)



The image sort of gives an impression of width to the light is the width of the E & B fields as well which is interesting. Google width or diameter of a photon and tell me how wide or what diameter a photon is and that is the problem with the above image smile

The real problem is this (http://en.wikipedia.org/wiki/4-potential) which brings in time.

Quote:
An electromagnetic four-potential is a relativistic vector function from which the electromagnetic field can be derived. It combines both an electric scalar potential and a magnetic vector potential into a single four-vector.


http://en.wikipedia.org/wiki/Four-vector

So the 3D representation above is probably about as good as you can get as a visual in our heads for a school level and I don't mind it but you need to remember it is a simplification. It is useful to bring in the concept of perpendicular E & B fields but it is still a long way from a realistic complex real world EM wave.

I am going to have a crack at drawing the above with phase and group velocities which I think I can squeeze into the 3D and that would probably take us to about a realistic light image we can draw if we ignore relativity.


Edited by Orac (04/02/14 09:36 PM)
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#51535 - 04/03/14 01:54 AM Re: Entanglement in 103 dimensions [Re: Orac]
paul Offline
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ok, I thought about it.

I still only see 3 dimentions not 4.




1 the B dimension
2 the E dimension
3 the k dimension

123

the cycle or frequency is not a dimension.

so where is the 4th dimension?


to me a electromagnetic wave should look more like this.



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#51536 - 04/03/14 02:23 AM Re: Entanglement in 103 dimensions [Re: paul]
Orac Offline
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I agree the drawing is 3D (you can't really draw 4D) that isn't the problem the problem is it really doesn't represent the reality.

See those E and B fields they are not widths they are strength vectors I think you are treating them as a physical dimension

So here are my questions:

1) How far do those E & B fields go. Most students and I suspect you are thinking they are just the width or height shown, hint not even close they are a representation of a changing strength. As I said what is the width or diameter of a light wave or photon please look it up.

2) To show you the time problem imagine I sent your waveform past a very large sun so now your drawing has to bend or gravity lense around the sun the only way you could bend you waveform would be to change the shape of the lobes of those field sinewaves but that would change the properties of the EM wave.

3) At the moment we haven't got the group and phase properties of the wave in I am doing that now I have a bit of time.


Edited by Orac (04/03/14 02:25 AM)
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#51537 - 04/03/14 02:34 AM Re: Entanglement in 103 dimensions [Re: paul]
Orac Offline
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Originally Posted By: Paul

to me a electromagnetic wave should look more like this.





Absolutely spot on .... you absolutely have got it .. I am very impressed.

So now lets add the phase and group properties in the waveform is not uniform over time the other obvious problem with the original 3D drawing.

What we are trying to represent is this



So that ring changes intensity or diameter over time and can spin for the angular momentum.

This is the sort of best animation of a photon I can find sort of looking at it in 3D and even it has issues




Edited by Orac (04/03/14 02:41 AM)
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#51538 - 04/03/14 02:52 AM Re: Entanglement in 103 dimensions [Re: Orac]
paul Offline
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Quote:
See those E and B fields they are not widths they are strength vectors I think you are treating them as a physical dimension


they are a physical dimention.

when you are building a digital tv antenna you look up
the frequency of the tv station you want to pick up.
then from that frequency you determine the length of your
pick up wire or material that you are building the antenna from.

the rf wave length never changes its length because the station
is licensed to broadcast on that particular frequency which includes the B , E , and Time dimensions.

the amplitude of the signal is what determines the E and B fields height or width as you call it.

the signal never changes shape or amplitude , it only becomes weak with distance from the broadcasting station due to obstructions or the curvature of the earth.

rf waves are focused or changed by tv antennas by design.
all waves tend to fill in the shadow that an obstruction presents to the wave.



in the above image the rf waves are directed onto the the
pick up wires , notice the pick up wires are of same lehgth.

Please look it up.




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#51539 - 04/03/14 03:14 AM Re: Entanglement in 103 dimensions [Re: paul]
Orac Offline
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yes to all that but its a little more complex because of the intensity problem.

Actually that gives me a way to explain it

When you look at a normal bitmap you have two dimensions but you also have a color at each pixel location.

So to describe a bitmap pixel by pixel you need

X location, Y location and Color of pixel

Now lets imagine we had a 3D TV or Hologram lets take the classic stars wars one



Ok to describe Leia as a 3D we need 4 numbers

X location, Y location, Z location and color of pixel

So to make a colored 3D image you need 4 dimensions in that case 3 are physical and 1 is a color or intensity if in greyscale.

So if you want to call it 3D + color that is the same as we call it 3D + time so we avoid calling it 4D to stop this problem smile

That is as near as I am probably going to get you to understanding why you will need 4 dimensions and I don't mind if you object to calling the last one a dimension so 3D + something is fine to me.


Edited by Orac (04/03/14 03:20 AM)
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#51540 - 04/03/14 03:17 AM Re: Entanglement in 103 dimensions [Re: Orac]
paul Offline
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Quote:
This is the sort of best animation of a photon I can find sort of looking at it in 3D and even it has issues


I dont like that one either , were looking for a single
emitted photon or a line of emitted photons.

my problem is still the 4th dimension you spoke of , Im not saying that there is no 4th dimension , that would be pure
speculation.

I do like the phase and group velocity gif images you posted
but a 3d view would be better.

using circles instead of a line.

to me that would be a more accurate representation of the wave a photon would generate.


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#51541 - 04/03/14 03:37 AM Re: Entanglement in 103 dimensions [Re: paul]
Orac Offline
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Originally Posted By: paul
I dont like that one either , were looking for a single emitted photon or a line of emitted photons.


There really is no such thing as a solid line of emitted photons what process is ever going to do that ... you have to create the photons and that process is not instant I know you have looked at this smile

Light bulb, LED or laser there is a time and rate they can fire out photons because of the creation process do a read up on it again. In general you have to excite an atoms electron, it emits the photon and then drops back down and that all takes time there is a finite rate a chain of photons could be put out of the same atom.

That is what makes lights different intensity which is how fast they can spit out photons and how close together they are it's that whole particle nature behaviour of light thing you need how many photons per second thru a cross sectional area.

You can actually calculate how far apart each photon must be for a given light intensity see if you can work out the calculation. Google will help its a standard problem the sun for example emits 1E45 photons every second.

If you want to do an additional exercise look up the surface area of the sun and then work out on average how far apart are photons that are ejected per second on the suns surface.

Originally Posted By: Paul
I do like the phase and group velocity gif images you posted
but a 3d view would be better.

using circles instead of a line.


That is exactly what I am working on drawing and if that is as far as we can get you to that 3D point it is fine it is a lot closer to reality.


Edited by Orac (04/03/14 04:25 AM)
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#51545 - 04/03/14 09:04 AM Re: Entanglement in 103 dimensions [Re: newton]
Orac Offline
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Rose care to deal with our pollack troll ... it just breaks up actual discussion as it isn't related to what is being discussed ... it's clearly aimed just to disrupt discussion.


Edited by Orac (04/03/14 09:31 AM)
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