# The Naked Scientists Forum

### Author Topic: How can photons be localised if the universe is expanding?  (Read 47258 times)

#### lightarrow

• Neilep Level Member
• Posts: 4586
• Thanked: 7 times
##### How can photons be localised if the universe is expanding?
« Reply #50 on: 05/02/2009 18:23:22 »
Ok another thought.
If we say that a photon if red shifted, that is, as seen from our frame of observation being of a lesser 'energy' content.
We also say that its wave is longer, right.
So in a BEC where we see photons as frozen/still that wave should be?
Infinite??

It's the opposite

λ = Vph

λ = wavelenght
Vph = phase velocity
ν = frequency

Since frequency doesn't vary for the wave entering the material, and phase velocity decreases, wavelenght decreases.

#### yor_on

• Naked Science Forum GOD!
• Posts: 11993
• Thanked: 4 times
• (Ah, yes:) *a table is always good to hide under*
##### How can photons be localised if the universe is expanding?
« Reply #51 on: 06/02/2009 09:19:43 »
If you look at the light as a wave, what is it that 'breaks it' in a BEC?

But if it is a wave it will have a 'frequency' until it 'disappear' Lightarrow.
There is no possibility of treating it as not having that to my eyes, as long as we have time.
A straight line is no wave.

There will be a wave stretching out into?
But it can't be seen as being 'everywhere'.
That seems a to far reaching conclusion to me.

The probability function here just state that 'it's gone out to lunch' and is not present.
But it will still be defined to the same location in spacetime.

--
(Thought of it as you describing 'waves height' here:)
((Yep, and a bad cold it is too::))
_______

Ok reading you once more, you're saying the opposite right.
That as the wave is slowed down its wavelength decreases?

--

But how is that possible?
When we talk about redshift we define it as being of lower 'energy' having a longer wavelength.
And this is what we do in a BEC? We 'steal' the waves energy, redshifting it until it 'disappears'.
So how can the wavelength decrease?

(got a cold, can I blame that:)
« Last Edit: 06/02/2009 10:06:43 by yor_on »

#### yor_on

• Naked Science Forum GOD!
• Posts: 11993
• Thanked: 4 times
• (Ah, yes:) *a table is always good to hide under*
##### How can photons be localised if the universe is expanding?
« Reply #52 on: 06/02/2009 10:33:44 »
Actually this gets me back to the question if photons inherently can be of different light quanta (energy).
If they as I believe only are of 'one' 'energy size' then what happens here?

When we 'steal' their energy?
We can't steal it 'gradually', not if it is a decided 'energy size'.

(It should be easy to test what is right here.
We just need to 'freeze' one photon:)
Ah, that was somewhat of a joke..

You see, we can say that we are 'slowing' photons down by taking away some of them (particle wise).
But that should then mean that all photons will be annihilated when we say they are 'standing still'.
doesn't make sense, does it:)

« Last Edit: 06/02/2009 10:51:29 by yor_on »

#### lyner

• Guest
##### How can photons be localised if the universe is expanding?
« Reply #53 on: 06/02/2009 11:33:48 »
Is there, in fact, a red shift? There doesn't appear to me to be any reason for a change in frequency under these circumstances. When going through any other transparent medium the frequency (colour) stays the same. In extreme cases, you wouldn't see any light if that happened.
Is that where your confusion arises?

#### yor_on

• Naked Science Forum GOD!
• Posts: 11993
• Thanked: 4 times
• (Ah, yes:) *a table is always good to hide under*
##### How can photons be localised if the universe is expanding?
« Reply #54 on: 06/02/2009 12:32:16 »
But doesn't it have to be treated as a red shift?
If we are discussing it from a wave perspective?

If I don't see it as a redshift of those waves, then how should I see it SC?
In what other way can one describe a wave losing its 'energy'?

Even if I looked on it in terms of 'reducing probabilities'?
And said that as the probability becomes 'zero' the waves can't be present any more.
But then we won't need suns either (sources), if this is correct.

Well, they will still be the greatest probability, but it wrecks havoc with a lot of processes we take for granted.

--------

There is an option where I don't look at a BEC as consisting of 'stopped waves' at all.
But just as consisting of stopped 'particles'?

But why should I need to do so?
Would that mean that only 'certain' manipulations are allowed in a BEC?
Those specifically 'wavelike' experiments might not work then?

And entanglement where you mix waves through a beamsplitter then?
Calling those entangled might work when dealing with waves.

But if seen as 'particles' instead, why do they get 'entangled' at all.
It is the spin we are discussing here.
« Last Edit: 06/02/2009 12:48:52 by yor_on »

#### lightarrow

• Neilep Level Member
• Posts: 4586
• Thanked: 7 times
##### How can photons be localised if the universe is expanding?
« Reply #55 on: 07/02/2009 07:18:36 »
But doesn't it have to be treated as a red shift?
Why?

Quote
If we are discussing it from a wave perspective?
If I don't see it as a redshift of those waves, then how should I see it SC?
In what other way can one describe a wave losing its 'energy'?
Photon's energy = hν and the frequency doesn't change...

Quote
There is an option where I don't look at a BEC as consisting of 'stopped waves' at all.
But just as consisting of stopped 'particles'?
There is no need. You have an electromagnetic field which varies in the time in every point of the BEC, but that doesn't propagate in space, as a stationary wave does. Where is the problem?

#### yor_on

• Naked Science Forum GOD!
• Posts: 11993
• Thanked: 4 times
• (Ah, yes:) *a table is always good to hide under*
##### How can photons be localised if the universe is expanding?
« Reply #56 on: 07/02/2009 13:41:56 »
Lightarrow If you look at light as waves and leave the duality aside for a moment.
What would you say is the properties of light getting slowed in a BEC?

The way I understand it, the only way we differ between the 'energy content' of waves.
Is that we say that the more 'red shifted' a wave is, the less 'energy' that wave will have relative us.

And 'energy' is a definition of the probable movement/fluctuations inside a observed object as well as its spatial acceleration or relative motion as observed from another frame of reference.

And if that is wrong I don't know how to see waves:)
And really would like to see how you see it.

Do you see another way of defining how waves lose their 'energy' in a BEC?
Or lose 'energy' generally as observed from our 'frame of reference'?
So what happens with that 'wave'?

That's where I get 'stuck'?
(for the moment:)

----------

Are you seeing it as a wave(s) inside a BEC contains its 'energy content' in some way?
Even though all 'motion' as seen from our frame of reference stops?

Won't I then need to question red shift as a definition of relative 'energy contents' if so?
Then red shift is an spatial effect, as when observed from 'another' frame, special for that part of 'spacetime' that we can observe.
And having nothing to do with its 'energy content'.
And the idea of 'frames of reference' then needs a clearer definition yet, as you can 'release' redshifted waves of light (flashlight) in your accelerating rocket as well as in any other 'frame' defined macroscopically seen?

Am I seeing waves wrong?
And red shift too perhaps?
And 'frames of reference?

No big surprise:)

----

If i extrapolate on that idea it seems to say that no matter how we define a wave, relative us observing, they have a 'gold standard' and are all 'the same', containing the same 'energy'.

And then frames becomes a very difficult concept to me.
Not that it wasn't before too.

And us saying that light should loose 'energy' by being 'stopped' is wrong.
Which should mean that what we call 'temperature' and 'energy' is two different concepts.
« Last Edit: 07/02/2009 14:37:33 by yor_on »

#### lightarrow

• Neilep Level Member
• Posts: 4586
• Thanked: 7 times
##### How can photons be localised if the universe is expanding?
« Reply #57 on: 07/02/2009 19:15:29 »
Lightarrow If you look at light as waves and leave the duality aside for a moment.
What would you say is the properties of light getting slowed in a BEC?
Phase velocity (as I had written).

Quote
The way I understand it, the only way we differ between the 'energy content' of waves.
Is that we say that the more 'red shifted' a wave is, the less 'energy' that wave will have relative us.
And what does "red shifted" means for you? If the medium is the same, then phase velocity is the same, then frequency is inversely proportional to wavelenght; but if you consider wavelenght and frequency in a medium, and then wavelenght and frequency in *another* medium, you can't say that the first wavelenght must be inversely proportional to the second frequency! It's meaningless. Equations says everything. λ = Vph/ν. What's the problem with it?

Quote
And 'energy' is a definition of the probable movement/fluctuations inside a observed object as well as its spatial acceleration or relative motion as observed from another frame of reference.

Quote
And if that is wrong I don't know how to see waves:)
And really would like to see how you see it.

Do you see another way of defining how waves lose their 'energy' in a BEC?
Why should they lose their energy? Does a light beam from the Sun lose its energy when it enters through your window (assuming no absorption from the glass)?

Quote
Or lose 'energy' generally as observed from our 'frame of reference'?
So what happens with that 'wave'?

That's where I get 'stuck'?
(for the moment:)

----------

Are you seeing it as a wave(s) inside a BEC contains its 'energy content' in some way?
Even though all 'motion' as seen from our frame of reference stops?

Won't I then need to question red shift as a definition of relative 'energy contents' if so?
Then red shift is an spatial effect, as when observed from 'another' frame, special for that part of 'spacetime' that we can observe.
And having nothing to do with its 'energy content'.
And the idea of 'frames of reference' then needs a clearer definition yet, as you can 'release' redshifted waves of light (flashlight) in your accelerating rocket as well as in any other 'frame' defined macroscopically seen?

Am I seeing waves wrong?
And red shift too perhaps?
And 'frames of reference?

No big surprise:)

----

If i extrapolate on that idea it seems to say that no matter how we define a wave, relative us observing, they have a 'gold standard' and are all 'the same', containing the same 'energy'.

And then frames becomes a very difficult concept to me.
Not that it wasn't before too.

And us saying that light should loose 'energy' by being 'stopped' is wrong.
Which should mean that what we call 'temperature' and 'energy' is two different concepts.
Light in a material medium behaves in a completely different way than light in the void, not only because the speed is different. Infact, saying "light moves in a material medium" is actually misleading. If physicists in the books, instead of talking of "light propagating inside the material", talked of "an electromagnetic field propagating inside the material", it would be less fascinating but probably less misleading. Inside a material, you just have many atoms, each of which oscillate electrically. That's all. You don't need anything else. Think about the OLA that you see in soccer stadiums made by people; there isn't conceptually any difference between the OLA and an EM wave travelling inside a material medium. What you see "propagating" in an OLA is nothing else than the phase of the oscillation; if people where not syncronized in that way, but in another, you wouldn't see anything propagating.
« Last Edit: 07/02/2009 19:17:35 by lightarrow »

#### yor_on

• Naked Science Forum GOD!
• Posts: 11993
• Thanked: 4 times
• (Ah, yes:) *a table is always good to hide under*
##### How can photons be localised if the universe is expanding?
« Reply #58 on: 07/02/2009 19:47:33 »
Lightarrow, thanks for answering, I'm just trying to see what you see.

I've always thought of red shift as a relation between two frames of reference.
Also that there exist a light quanta of a exact value.

Then those makes sense of the universe to me:)
Even though 'frames' is something I'm not sure of the definition of yet.

Also I've seen temperature as something having a direct relation to 'energy'.
And temperature being a description of 'movements' inside a molecule or a wave, and therefore of particles (photons) too.

So when photons is placed in a BEC their 'temperature' as well their internal 'movements' disappear I thought?

" phase velocity (physics) The velocity of a point that moves with a wave at constant phase. Also known as celerity; phase speed; wave celerity; wave speed; wave velocity. "

Where is the velocity of that waves 'point' in a BEC?

#### yor_on

• Naked Science Forum GOD!
• Posts: 11993
• Thanked: 4 times
• (Ah, yes:) *a table is always good to hide under*
##### How can photons be localised if the universe is expanding?
« Reply #59 on: 07/02/2009 21:26:40 »
Looking at the definitions of phase velocity I also found this.

"If we imagine the wave profile as a solid rigid entity sliding to the right, then obviously the phase velocity is the ordinary speed with which the actual physical parts are moving.

However, we could also imagine the quantity "A" as the position along a transverse space axis, and a sequence of tiny massive particles along the x axis, each oscillating vertically in accord with A0 cos(kx - wt). In this case the wave pattern propagates to the right with phase velocity vp, just as before, and yet no material particle has any lateral motion at all.

This illustrates that the phase of a traveling wave form may or may not correspond to a particular physical entity. It's entirely possible for a wave to "precess" through a sequence of material entities, none of which is moving in the direction of the wave. In a sense this is similar to the phenomenon of aliasing in signal processing.

What we perceive as a coherent wave may in fact be simply a sequence of causally disjoint processes (like the individual spring-mass systems) that happen to be aligned spatially and temporally, either by chance or design, so that their combined behavior exhibits a wavelike pattern, even though there is no actual propagation of energy or information along the sequence."

http://www.mathpages.com/HOME/kmath210/kmath210.htm
Is it this phenomena you are referring to Lightarrow.

--------

So the 'wave' becomes an infinitesimal line of 'dots', each 'dot' representing a 'crest' of that wave, and the group velocity disappears?
« Last Edit: 07/02/2009 21:34:26 by yor_on »

#### lightarrow

• Neilep Level Member
• Posts: 4586
• Thanked: 7 times
##### How can photons be localised if the universe is expanding?
« Reply #60 on: 08/02/2009 16:25:46 »
Looking at the definitions of phase velocity I also found this.

"If we imagine the wave profile as a solid rigid entity sliding to the right, then obviously the phase velocity is the ordinary speed with which the actual physical parts are moving.

However, we could also imagine the quantity "A" as the position along a transverse space axis, and a sequence of tiny massive particles along the x axis, each oscillating vertically in accord with A0 cos(kx - wt). In this case the wave pattern propagates to the right with phase velocity vp, just as before, and yet no material particle has any lateral motion at all.

This illustrates that the phase of a traveling wave form may or may not correspond to a particular physical entity. It's entirely possible for a wave to "precess" through a sequence of material entities, none of which is moving in the direction of the wave. In a sense this is similar to the phenomenon of aliasing in signal processing.

What we perceive as a coherent wave may in fact be simply a sequence of causally disjoint processes (like the individual spring-mass systems) that happen to be aligned spatially and temporally, either by chance or design, so that their combined behavior exhibits a wavelike pattern, even though there is no actual propagation of energy or information along the sequence."

http://www.mathpages.com/HOME/kmath210/kmath210.htm
Is it this phenomena you are referring to Lightarrow.
Exactly. Phase velocity could be just "an artefact". Another example: do you know those yellow lamps which sometimes they have put on the border of a dangerous bent in a road? They are syncronized to switch on in a sequence: first the lamp n.1, then the n.2, immediately close to the first, and so on; in this way you have the sensation that a light is moving along the border of the bend; of course, nothing is *physically* moving, do you agree with it? What problem in imagine to syncronize those lamps so that at t=0 the first lamp switches on and then at t=1 second, the last lamp, 1 million of km away switches on? No problem at all. The flash of light has travelled for 1 million km in 1 second. Do something physical propagated at that speed? No. That's the same with phase velocity.

For a long time physicists believed that group velocity, that is the velocity of a group of waves taken as a single entity, would represent the "real" physical parameter. Then it was discovered that even group velocity can be > c!

What instead really counts is what is called "signal velocity" which however could be very difficult to compute or even to identify. Anyway, signal velocity is always < c.

Don't believe that the subject of waves is an easy one. (Maybe this is the main reason some people prefer to think of light only in terms of particles  ).
« Last Edit: 08/02/2009 16:30:46 by lightarrow »

#### lightarrow

• Neilep Level Member
• Posts: 4586
• Thanked: 7 times
##### How can photons be localised if the universe is expanding?
« Reply #61 on: 08/02/2009 16:43:03 »
Lightarrow, thanks for answering, I'm just trying to see what you see.

I've always thought of red shift as a relation between two frames of reference.
Also that there exist a light quanta of a exact value.
Ok but you don't have to change the medium: if you change frame of reference you have to stay in the void (or in another medium, but fixed); then you can relate wavelenght with light's frequency, with photon's energy and with the relative speed of the two frames.

Quote
So when photons is placed in a BEC their 'temperature' as well their internal 'movements' disappear I thought?
It's impossible to localize a photon, in the void or (as far as I know) in a BEC. About the photon temperature it's a meaningles concept in physics.

Quote
" phase velocity (physics) The velocity of a point that moves with a wave at constant phase. Also known as celerity; phase speed; wave celerity; wave speed; wave velocity. "
Where is the velocity of that waves 'point' in a BEC?
Imagine that at t=0 the electric field of the wave is maximum for atoms n. 1, 101, 201, 301, ecc.
Then you can identify the crests of the wave at t=0. Snap another picture at t=1. The atoms at which the electric field is maximum are the same as before or not? If not, the crests has moved, so the phase has moved, so phase velocity is ≠ 0; if they are, phase velocity = 0.
Don't know where is the photon, or if it still exist or not.

#### yor_on

• Naked Science Forum GOD!
• Posts: 11993
• Thanked: 4 times
• (Ah, yes:) *a table is always good to hide under*
##### How can photons be localised if the universe is expanding?
« Reply #62 on: 09/02/2009 18:07:09 »
Lightarrow, I will need to give this a lot more thought before I try to have a own 'view' on it, as this need a proper understanding, and, as I'm sloow:)

But in the meantime, :) I would appreciate a explanation of what you see as the difference between group and signal velocity.
To me it seems like a change of names? As I understand them both to describe the process by which no 'information' can propagate faster than 'c' in space?

I still enjoy the way you methodically explain your point(s), but, does this mean that phase velocity soon will be 'gone' from physics?

-----
Does this make better sense?
I've changed my questions to stop 'chopping it up'?
« Last Edit: 09/02/2009 18:44:41 by yor_on »

#### JP

• Neilep Level Member
• Posts: 3366
• Thanked: 2 times
##### How can photons be localised if the universe is expanding?
« Reply #63 on: 09/02/2009 19:56:29 »
I can take a shot at this since I've done a bit of reading up on these different velocities.

The signals you're worrying about here are what are called "analytic."  This means that all the information about the entire signal is contained in every tiny bit of the signal.  If you had perfect instruments, you could measure an infinitely small chunk of the signal and immediately know the entire analytic signal.  What this means is that (theoretically) you have all the information in the signal as soon as its tip reaches you.  The signal velocity is therefore the time it takes this tip of the signal to reach you.  This can never exceed the speed of light or information could move faster than light.

Group velocity is essentially the speed at which the "shape" of the pulse travels.  If you choose your pulse's shape right and pick the proper medium to send it through, you can make the peak of the pulse travel ahead faster than c, but you can never make the very tip of the pulse move ahead faster than c.  It's fairly tough to do this, which is why people thought for a long time that the group velocity was the signal velocity.

The poorly-drawn diagram should illustrate this.  The tip of the pulse is the red bit at the start.  You can change the shape of the pulse behind so that the peak comes sooner or later by adjusting the group velocity.

Finally, there's good evidence to suggest that for (classical) light signals, the signal velocity is always c.  However, the tip of the signal is usually so small that you can't actually measure it with any real-world detectors, so the practical signal velocity ≤ c.

#### Vern

• Neilep Level Member
• Posts: 2072
##### How can photons be localised if the universe is expanding?
« Reply #64 on: 09/02/2009 20:30:10 »
I've seen studies where pulses of light tunneling through a barrier seemed to move faster than light. But what was actually happening was that the light pulse position was measured from the centre of the pulse. The input pulse was wider than the output pulse. The centre of the shorter pulse exited the barrier before the centre of the input pulse arrived at the barrier.

So to me it seemed no mystery at all.

#### yor_on

• Naked Science Forum GOD!
• Posts: 11993
• Thanked: 4 times
• (Ah, yes:) *a table is always good to hide under*
##### How can photons be localised if the universe is expanding?
« Reply #65 on: 09/02/2009 23:10:34 »

Although I need more (always:)
The idea that every 'bit' of that wave would contain the information about the whole wave sounds very holographic to me?
I presume we are talking about a analog waveform here, so 'bit' could as easily be exchanged for 'slice', right?

But what about the phase velocity then?
It seems to be seen as a specific 'wave crest', undulating up and down, of a larger sets of connective wave, as we follow it in time.
That then describes that one 'wave crest' inside this larger system of waves. And the group velocity then will be an 'average' description of the waves propagation.
And as that also could break 'c' in 'materials' we have defined a new definition called 'signal velocity' to keep the theory intact?

Am I correct here?

#### yor_on

• Naked Science Forum GOD!
• Posts: 11993
• Thanked: 4 times
• (Ah, yes:) *a table is always good to hide under*
##### How can photons be localised if the universe is expanding?
« Reply #66 on: 09/02/2009 23:35:10 »
Reading that alternative point of view from 'mathpages' I find that easier to encompass.
If one allow a wave to be seen as series of changes in different substances/materials as we are used to measure them, then their 'absence' in 'space' (vacuum/absence of matter)  just becomes another part of its geometry, just like its 'inherent energy', 'virtual particles' 'photons' and 'spontaneous particle creation'.

Then the question seems to be not what we measure, but more what we are 'missing' if you see my drift.
Aether presumed some sort of 'substance' with some sort of 'density/resistance' if I understood it right? But this phenomena we are discussing here seems more to have with 'limitations of observing' combined with 'times arrow'?

Although, if this was correct it should imply either that there is an 'arrow' even for subatomic processes or that spacetime itself force some 'causality flow' to a larger system (spacetime) that we won't notice when studying 'delimited' versions of subatomic systems?

---

Or that there is a 'arrow' to something that then will be one 'step' further down.
Passing both particles and photons, a coherence to 'spacetime' itself, not even noticing our differentiation.
Yep, a damned mystic, that's what I am:)
« Last Edit: 10/02/2009 00:33:49 by yor_on »

#### JP

• Neilep Level Member
• Posts: 3366
• Thanked: 2 times
##### How can photons be localised if the universe is expanding?
« Reply #67 on: 10/02/2009 02:56:45 »
The idea that every 'bit' of that wave would contain the information about the whole wave sounds very holographic to me?
Do you mean holomorphic?  If so, they're quite similar.  Holomorphic generally means that the function is defined over a region in the complex plane, and that knowing the complex derivative at a point is enough to reconstruct the function anywhere in that region.  More often a signal is defined over some real variables, but you can relate it by extending those variables to the complex plane.

Quote
I presume we are talking about a analog waveform here, so 'bit' could as easily be exchanged for 'slice', right?
I don't think so.  A bit is usually represented by a wave being in one of two states, being "on" and "off" respectively.  Think for a moment of going from "off" to "on", i.e. sending a 01 signal.  Your wave goes from 0 amplitude to 1 amplitude, which is a discontinuous jump--or a non-analytic point.  This jump contains the information about your signal and it's the thing that propagates at the signal velocity.  In reality things can get more complicated if you want to determine on/off by sampling your signal at even time intervals.  Then you could send "0000..." by just an unchanging wave of amplitude 0.  Still, the signal velocity would be limited by c.

Quote
But what about the phase velocity then?
It seems to be seen as a specific 'wave crest', undulating up and down, of a larger sets of connective wave, as we follow it in time.
That then describes that one 'wave crest' inside this larger system of waves. And the group velocity then will be an 'average' description of the waves propagation.
And as that also could break 'c' in 'materials' we have defined a new definition called 'signal velocity' to keep the theory intact?
Phase velocity is the speed of a single frequency of the signal.  For light, this is a plane-wave component of the field, which exists over all space at all time.  So these plane waves themselves can't send information--they already exist everywhere.  An arbitrary pulse can be written in terms of these plane waves by using Fourier transforms.  If you put a non-analytic point in your pulse to send information with it, you end up needing a whole bunch of plane waves to describe it (I'm pretty sure you need infinitely many of them, but I'd have to double check the math).  In that case, the non-analytic point, which is composed of a bunch of single-frequency plane waves, travels at the signal velocity.  The phase velocity isn't terribly meaningful in this case, since you don't really end up caring about the single-frequency plane waves.

Signal velocity: the speed the signal transmits information.  For light, this is generally the speed at which "kinks" in the signal propagate.

Group velocity: the speed at which the bulk of the "pulse" appears to propagate.  This can be greater than c, but the "kink" at the start of the pulse is still limited by c, and doesn't have to move with the group velocity.

Phase velocity: the speed at which a single frequency component of a signal propagates.  This is useful when decomposing signals into plane waves, but I don't think it has much application in analyzing the propagation of information via a pulse.

#### yor_on

• Naked Science Forum GOD!
• Posts: 11993
• Thanked: 4 times
• (Ah, yes:) *a table is always good to hide under*
##### How can photons be localised if the universe is expanding?
« Reply #68 on: 10/02/2009 11:53:03 »
Quote
I presume we are talking about a analog waveform here, so 'bit' could as easily be exchanged for 'slice', right?
Quote
I don't think so.  A bit is usually represented by a wave being in one of two states, being "on" and "off" respectively.  Think for a moment of going from "off" to "on", i.e. sending a 01 signal.  Your wave goes from 0 amplitude to 1 amplitude, which is a discontinuous jump--or a non-analytic point.  This jump contains the information about your signal and it's the thing that propagates at the signal velocity.  In reality things can get more complicated if you want to determine on/off by sampling your signal at even time intervals.  Then you could send "0000..." by just an unchanging wave of amplitude 0.  Still, the signal velocity would be limited by c.

Now you're giving me problems Mr jpetruccelli:)
But you have written a very clear description all the same.
And that takes some work to do, so thanks for it.
Now, on to my questions.

If you treat a analogue signal bit wise you will take away 'information' from it, won't you?
So by doing so you transform it into a 'simpler' solution?

I know that there are ideas of our universe where one treat it as a 'bit' or as some say 'pixel' universe representing 1:s or 0:s  from the 'bottom up" and sees it all as 'information'.
Is this what this idea represents?

Holomorphic?
Nice word:)

To me, if you say that you by analyzing one part of a system can get information about the whole system, then that seems a holographic principle.
I will have learn what differs them, could you describe it so that I could get a inkling to the difference between those descriptions?
That as holography is easily proved by verifiable experiments,  even though every 'slice' will have lost some information it still will give us a visual representation of a 'whole' system/image.
On the other hand, 'slices' in holographic 'representations' will be non linear descriptions, and therefore not 'limited' into bits if I'm correct.
I like the way you explain phase velocity, and I'm sure it makes a lot of sense mathematically.

To summarize I get an impression that you are telling me that to get a 'linear solution' (1+1=2) of waves, we will need to break them down into bits. And as I think you say, the sampling frequency is what will define the precision then.

But how one expect a 'bit' to be a holographic representation of a whole system is harder for me to understand?
A bit is one isolated state of a binary system and as you say it represents either 'on' or 'off'?

I'm learning.
Slowly:)
« Last Edit: 10/02/2009 12:11:25 by yor_on »

#### JP

• Neilep Level Member
• Posts: 3366
• Thanked: 2 times
##### How can photons be localised if the universe is expanding?
« Reply #69 on: 10/02/2009 16:56:42 »
If you treat a analogue signal bit wise you will take away 'information' from it, won't you?
So by doing so you transform it into a 'simpler' solution?
I think this is quickly going far from the original question, so if anyone wants to split this thread, it's probably a good idea.

I'm not a signals expert, but the point is that both the digital and analog signals I'm talking about are waves.  A simple representation of a digital signal is just an wave that can only be amplitude 0 or amplitude 1.  An analog signal has a continuous range of amplitudes it can take on.  But if you send either signal as a wave waves the basic ideas of waves should apply.

As to holographic.  I believe I misinterpreted what you were asking about before.  Holographic has to do with encoding information from somewhere such that every point of your recording receives information from every point in your original image.

The analytic/holomorphic concept I'm talking about is a particularly nice behavior of "smooth" functions such that you need only see a small piece of a function to know its broader behavior. If you have an analytic function, then you need only see a piece of it to get the entire thing, which means if someone is sending an analytic signal at you, you (theoretically) get all your information along with the tip of it.  I'm not concerned with how much information each function carries, just that all of that information resides at the tip.

Assuming you're dealing with waves that can be pieced together from analytic functions (and this is the case for classical electromagnetic fields, but I assume it holds for waves in general), each section carries its information in its tip (and at every other point in the section).  That's why it makes sense to define the signal speed to be the speed at which the tip of a signal travels.

I've completely swept under the rug all considerations about information content as well as practical considerations of how to physically send/detect signals.  In practice, your information content is going to be limited by how you encode and send your waves.  Plus, measuring the very tip of a wave with infinite accuracy is impossible, so you'll be limited in how much information you can get from it.

#### yor_on

• Naked Science Forum GOD!
• Posts: 11993
• Thanked: 4 times
• (Ah, yes:) *a table is always good to hide under*
##### How can photons be localised if the universe is expanding?
« Reply #70 on: 10/02/2009 18:08:28 »
Nice explanation again friend.
As you said we seem to move a little apart from the original question though.
We'll let it rest for a while then?

I'm sure it will come up again though:)

---------

Just one more Q.
I see holographic information as a non linear description/system.
Even though they make it by rotational linear polarization the result, as it is caught as 3D-image, will  be non linear.
Would you say that 'Holomorphic functions ' describes a linearly or non linearly system?

But suddenly I'm not so sure about holographic images?
It's defined by the way waves reflects and diffracts, so can one say that such a image is 'indefinable' or should one say that the information density contained is 'finite' and therefore a solvable problem, that is linear?

But that is wrongly thought of me, right:)
Non linearity isn't about the amount of information in that 3D-image.
It's about if the solution of it mathematically is possible as a finite description?
finite here is should be a single clear answer, not indefineable.

I think? :)
---

You're right.
« Last Edit: 10/02/2009 19:25:07 by yor_on »

#### JP

• Neilep Level Member
• Posts: 3366
• Thanked: 2 times
##### How can photons be localised if the universe is expanding?
« Reply #71 on: 10/02/2009 21:37:48 »
This might be another question of the kind of language we're using to describe things.  When I think of linear problems, it has to do with how the mathematics treats your input variables.  If you have a linear operation, L, acting on some system, S1 and some system S2, then L(S1+S2)=L(S1)+L(S2).  In other words, L acting on the sum of the systems equals the sum of L acting on each system independently.  Additionally, if you multiply a system by a certain number, c, then L(cS)=cL(s).

In this language, you need to specify the process and the system you're concerned.  The process of recording a hologram is generally nonlinear with respect to the input field, since its usually the square of the fields that gets recorded.  Playing back a hologram is usually linear with respect to the input field since you just multiply the hologram by the reference field.

Reconstructing function at any point from a given patch isn't linear in the function's variables.

Linear systems are usually desirable because solving them is usually much simpler, and asking a computer to crunch the numbers is often much faster.

#### lightarrow

• Neilep Level Member
• Posts: 4586
• Thanked: 7 times
##### How can photons be localised if the universe is expanding?
« Reply #72 on: 11/02/2009 07:43:16 »
Lightarrow, I will need to give this a lot more thought before I try to have a own 'view' on it, as this need a proper understanding, and, as I'm sloow:)

But in the meantime, :) I would appreciate a explanation of what you see as the difference between group and signal velocity.
To me it seems like a change of names? As I understand them both to describe the process by which no 'information' can propagate faster than 'c' in space?
A detailed explanation would require complicated drawings. Group velocity, in already existing EM waves, is an "artefact" just as phase velocity is. It is not only if you consider a so short pulse of light that you can be sure all of the EM perturbation can be identified with the very pulse; in that case group velocity is also signal velocity. Group velocity is an artefact because it represents the speed at which the "shape" of the wave packet travels; this shape moves just in virtue of phase shifting among the various pure components of the packet, so it's nothing physical who moves.

Quote
I still enjoy the way you methodically explain your point(s), but, does this mean that phase velocity soon will be 'gone' from physics?
What do you mean? Phase velocity is ω/k and both are important parameters and also phase speed is important because is directly related to index of refraction.

#### yor_on

• Naked Science Forum GOD!
• Posts: 11993
• Thanked: 4 times
• (Ah, yes:) *a table is always good to hide under*
##### How can photons be localised if the universe is expanding?
« Reply #73 on: 12/02/2009 12:59:36 »
I got the impression before that you meant that phase velocity was phased out :) in exchange for signal velocity Lightarrow?
That's why I asked. I haven't used that description 'signal velocity' before.

Btw: What do you mean by Phase speed being "directly related to the index of refraction."?

-----
Yes, JP (jpetruccelli) I knew that a linear equation is a solvable one :)

Are you saying that a holographic image is a 'solvable system' then?
I would have thought that it's not?
In a way it seems similar to the idea of 'synergy', that a 'whole' becomes more than its parts.
At least those that we are able to describe.

--------

But I liked that other description wherein a wave is just a representation of the 'time quality' of causality.
Then it is like those 'traces' you see inside that 'fog chamber' where particles gets observed.
image for image put together to make a description in time.
It's both easier to accept and much more complex as it is about all movements, not only waves.

But now people will tell me that time is 'events' again:)
Nope, it's not.

This phenomena, if seen like I do (for the moment:), is more about the qualities of space / vacuum.
Also it's about what we define as movement generally.

We do it using the arrow of time that we observe macroscopically.
That's what define us all here.

So you won't be able to define any movements without using time as a component.
I don't really care if you try to 'obscure' time by changing the name to 'events'.
If there is a 'time like' component then its name doesn't matter.

In fact the idea of time being 'events' seems to create more problems than solutions.
Like needing a 'time aether' binding those 'events' etc.

Then what we see as a wave demands a 'causality' at least macroscopically.
You could see it as a 'sea of happenings' in that vacuum wherein 'spacetime' just 'put forward' those happenings that fit our macroscopic reality / observations (arrow of time).
Or like there is a causality arrow hidden there inside 'spacetime' as a whole.

If I by 'spacetime' also define and take into consideration those processes that we don't really can quantify.
Like virtual particles operating outside HUP.
« Last Edit: 12/02/2009 13:44:44 by yor_on »

#### lightarrow

• Neilep Level Member
• Posts: 4586
• Thanked: 7 times
##### How can photons be localised if the universe is expanding?
« Reply #74 on: 12/02/2009 19:35:38 »
I got the impression before that you meant that phase velocity was phased out
What does it mean?

Quote
:) in exchange for signal velocity Lightarrow?
That's why I asked. I haven't used that description 'signal velocity' before.
So you can say you have learnt something new

Quote
Btw: What do you mean by Phase speed being "directly related to the index of refraction."?

Vph = c/n  where n = index of refraction.

#### The Naked Scientists Forum

##### How can photons be localised if the universe is expanding?
« Reply #74 on: 12/02/2009 19:35:38 »