[Soul Surfer]

Yor on  the energy of a photon of a given frequency is always the same.  The best way to visualise it is to consider the response of a radio cavity resonator to an impulse  if the cavity has a high Q and is narrow band it rings for a long time before fading if it has a lower Q and a less precise frequency it decays much quicker  this is because for a high q cavity most of the energy is retained each cycle and more escapes from the lower Q cavity
This is analagous to the long transition time and the short transition time.  a narrowband photon consists of many cycles of the frequency of a lower amplitude and takes longer to detect.

Light arrow your experiment would only show that a large number of photons from this source possess a particular bandwidth which is no problem. you need to prove this property for one single photon so you would have to detect the full spectrum of a single photon using your detector and I am not sure if that is possible although i understand that it may now be possible to detect the passage of a photon without destroying it under certain special circumstances and this may be a route to an experiment.

[JP (OP)]

Isn't a single photon by definition a pure frequency? (E=hν)?  Therefore, aren't the finite bandwidth packets released by an atomic process a quantum superposition of photons of different frequencies?  If that's the case, the answer to the bandwidth problem would be that each photon has a well-defined frequency, but that most processes release a spectrum of possible photons (although upon detection you collapse the wavefunction to only measure one).

[yor_on]

Thank you Soul Surfer and JP. When it come so wavepackets the terminology is unfamiliar to me so anything that can clear that up is appreciated.  Looking I saw a lot of experiments using the term photon wavepacket which was a new experience for me I think I'm getting old fashioned, I've always differed between those two.

Never the less it becomes understandable if it, like JP suggests, have to do with 'superpositions' although that gives me another headache as I now start to wonder how and why a, or several', photons would 'join' up like that superimposed. It seems to imply, if so, that you have several processes taking place with the electron simultaneously, it also imply that the electron then is acting in a analogue way, being able to process them at the same time, sort of? Or maybe in a 'self like' way? A little like my thoughts about the 'Rindler observers' all describing different SpaceTimes 'simultaneously', as observed from my frame.

The other way that I like to look at photons is as 'probabilities' and doing so I presume that I might view those 'superpositions' as 'probabilities' instead. Does this make sense? For me personally it becomes easier to understand then, if we assume that it is in the interactions those 'probabilities' finds its expression. But I really have to give you both a lot of kudos for doing your best to 'boink' some sense into my head

It's rather hard (to do too), so it takes time.

Which reminds me. I'm still wondering if those orbitals transitions take time?
And if there is a state where they are gone /'superimposed'/not defined?
If there is shouldn't it be measurable?

And considering your question SoulSurfer, from my naive perspective, looking at it as 'probabilities' I would say that it will be the interaction that defines what you see. That some interactions are consistent over time is what we build on when we define the math regulating those probabilities. And the question that gives me is if 'interactions' live on a plane of itself We like to define it as 'forces' acting on each other creating those 'interactions' but, sh* I don't know ) I should have slept longer

And that makes me wonder another ting, if it was like this, then the relation would have to be the interaction observed between at least two proceedings/properties as observed in SpaceTime right? So for this to be right there can never be a proceeding initiated and concluded by a proceeding in itself, if I'm thinking right here? Or can there?

[JP (OP)]

Yor_on, when you're dealing with waves, you can choose a wave that has a certain value of some physical parameter you choose.  Let's choose sine waves for an example and define the frequency (i.e. how fast they oscillate).  It turns out that you can use combinations (or superpositions) of these sine waves to make a different type of wave, and conversely you can write a different type of wave in terms of a superposition of sine waves.  Why this is important is that in quantum mechanics, you choose what you want to measure, and then essentially "write" your wave in terms of other waves that have well-defined values of that quantity and then your measurement picks one wave from among these.  It can only pick one answer, so it picks among them randomly (with some rules giving the probabilities of picking each particular answer). 

Here's a short example.  Let's say I want quantum mechanically measure the sine wave frequency of a wave that looks like a sharp step.  To describe this mathematically, I first write it in terms of sine waves with known frequencies.  I can do so as shown in the figure (there are mathematical formulas that tell you how).  To get exactly to the answer, I need to add an infinite number of these, but they get smaller and smaller, so I only show it up to 50 terms here.  Since this is quantum mechanics and I'm measuring sine wave frequency, my measurement you can only get one answer, so my measurement would randomly pick from among the sine waves making it up (all the dashed blue lines in the figures).  (The probability of picking a given sine wave is related to how big [vertically] it is when I add it in the picture.)

So superposition is basically the way you write a complicated wave in terms of waves with well-defined measurable values, and it's important in quantum mechanics because you randomly pick one of the measurable waves when you actually do a measurement.

 [ Invalid Attachment ]

[yor_on]

JP you make sense
In a slightly weird way )

But as I'm, ah, ever so slightly weird myself I think I get it, a very nice explanation. In that motto a superposition will be how you define a given wave by using approximations to narrow it down to a 'best answer'?

But can there be a definite answer to such a procedure, doesn't it just goes on and on?
But very very good explanation of the mathematic principle for it. Sweet one JP.

And a 'wavepacket', if you tried to define it like this, or could I see this as a 'reversed wavepacket procedure' sort of? You should be able to do this both ways mathematically, shouldn't you? I think of a wave packet as what it seems to say, like a 'packet of waves' together.
===

This one though, could you expand on how you mean here?

"Why this is important is that in quantum mechanics, you choose what you want to measure, and then essentially "write" your wave in terms of other waves that have well-defined values of that quantity and then your measurement picks one wave from among these.  It can only pick one answer, so it picks among them randomly (with some rules giving the probabilities of picking each particular answer)."

I'm sort of losing myself in it
==

Hey, I know what it reminded me of now A analogue signal to digital, right? And that makes sense, it's 'cut outs' right? A way to treat the universe as 'quanta' so to get a 'over see able' system?

Or am I bicycling in the blue younder again? And the 'digitalized' concept here, could that be a conceptual idea of 'photons' from a wave perspective then? I need to get a time machine Or find that well of youth.. So I can start all over again :))

[JP (OP)]

But as I'm, ah, ever so slightly weird myself I think I get it, a very nice explanation. In that motto a superposition will be how you define a given wave by using approximations to narrow it down to a 'best answer'?

But can there be a definite answer to such a procedure, doesn't it just goes on and on?
But very very good explanation of the mathematic principle for it. Sweet one JP.

In many cases, it does go on and on, like in the case above.  This is one of the cases where physicists can use infinities to do some useful stuff, like keep track of the infinite number of sine waves in my above example.

And a 'wavepacket', if you tried to define it like this, or could I see this as a 'reversed wavepacket procedure' sort of? You should be able to do this both ways mathematically, shouldn't you? I think of a wave packet as what it seems to say, like a 'packet of waves' together.

A wavepacket is also like what I showed above.  It's a wave of short length that you can break into a superposition of waves just like how I did it above.  You just change the step function I showed to a packet of your choice.  Of course, the recipe for how to add sine functions to get the wave packet changes, depending on the packet. 

This one though, could you expand on how you mean here?

"Why this is important is that in quantum mechanics, you choose what you want to measure, and then essentially "write" your wave in terms of other waves that have well-defined values of that quantity and then your measurement picks one wave from among these.  It can only pick one answer, so it picks among them randomly (with some rules giving the probabilities of picking each particular answer)."

Quantum mechanics is all about measurements.  It gives you recipes to predict the probabilities of getting different measurements.  Let's say you have a wave function (like the step function I showed above), and you want to predict the probability of measuring a certain value X of some measurable quantity.  Your original wave function usually doesn't have an exact value of your measurable quantity: for example, the step function above doesn't have an exact value of sine-wave frequency since it's not a sine wave, but in quantum mechanics you can still make a measurement of sine-wave frequency and get a single answer.  So how do you make predictions about the answer that you get?

The rule for making that prediction is to write your wave function as a superposition of simpler waves, where each simpler wave has an exact value of the thing you're trying to measure, which is exactly what I did above by writing that step function in terms of sine waves.  Then the probability of making each measurement is the amplitude (in other words "how much") of that particular simpler wave.  So in the example above, the amplitude of the sine waves would correspond to the probability of measuring that sine-wave frequency in an experiment.

By the way, the collapse of the wave function just says that after you make the measurement, your original wave function becomes the one you measured.  So if I measured one particular sine wave, from that point on, my wave function would actually be that sine wave, and the step would have ceased to exist.

Hey, I know what it reminded me of now A analogue signal to digital, right? And that makes sense, it's 'cut outs' right? A way to treat the universe as 'quanta' so to get a 'over see able' system?

Or am I bicycling in the blue younder again?

I think that's a bit of a stretch, since it loses the idea that each simple wave has an exact value of something you're trying to measure.

[JP (OP)]

By the way, I'm happy to go on about superpositions and quantum mechanics (I find this stuff really cool), but maybe we should start a new thread if you have more questions, since it's a bit off topic?

[yor_on]

It's okay JP, i see your point there. Why we started it was when I asked about how to see those wave packets, and I think I've gotten a very good explanation to that

And that helps me see how the idea is mathematically. And yes, I agree, QM is really cool but (as you said) we might need to steer this back to electrons. So I'm still wondering if those orbitals transitions take time? And if there is a state where they are gone /'superimposed'/not defined? And if there is, shouldn't it be measurable?
===

Why I'm asking it is because I need to know

It's about how I should look at electrons in general. As entities or as probability functions (wavepackets). You can look at it this way too. When a electron is alone orbitaling the nucleus its energy is well defined as I understands it? But when together with other electrons their energies seems to become a function of them all? Very confusing

And then my question is, can we say that those 'jumps' take a measurable time inside our arrow? Or how should I look at it? As wave functions subtly changing depending on interactions but without any defineable 'transition times'. Don't know if this makes sense at all, but I'm interested in your views.

[Soul Surfer]

JP  you already appear to understand Fourier transforms so it is perfectly obvious to you that any wave that starts and stops CANNOT BE A SINGLE FREQUENCY so why are you worried about this?  A single photon cannot possibly be a pure sine wave of a single frequency because such a sine wave goes on (and has gone on)for ever with a constant amplitude and no one ever said it was.  The wave packet has its maximum energy at a particular frequency and tails off  at frequencies on either side of this according to its line width.  (this is a property of a spectrum line that can be predicted from quantum mechanics and measured to show that the prediction is accurate).  You are taking simple descriptions that are approximations used to describe things to scientists who are starting to learn and applying them absolutely.  As you and everyone else should realise.  EVERYTHING IN PHYSICS IS AN APPROXIMATION there are absolutely no absolutes.  These absolutes only exist in mathematics  which is NOT physics.

Nearly all the arguments in these pages are caused by people realising that all approximations fail under certain limiting  conditions and then either trying to apply them beyond their limits of suitability or finding alternative hypotheses to get round the "problem" suggesting that the main core of scientific opinion does not really know what it is talking about.

[yor_on]

No disrespect meant here Soul Surfer, but I hope you don't mean me now? I'm fully in agreement with your definition of approximations and the need for understanding why they exist, and as far as I know I'm not trying to go around anything? I just want to see them better, to do that I ask

And JP gave me a tool to understand your thoughts better here. I think that he too is aware of that it's only an approximation, but for me and as I guess, for some others his description gave me an idea of how they are thought to work.

As for a sine wave not having an end? It will have in its interaction, won't it? As a mathematical concept it won't as it is an idealization of a smooth repetitive oscillation, with the weight put upon 'repetitive'. But what you seem to say here is that a wavepackets then have limits, which they need if they ever will have a resemblance to what we call photons, but it's  mathematically I presume? In which way do those waves in wavepackets then differ from sine waves?

After reading your thoughts I went up to look some more on waves and superpositions . And there they had this definition of a wavepacket?

--Quote--

The regions of large wave amplitude are called wave packets. Wave packets will play a central role in what is to follow, so it is important that we acquire a good understanding of them. The wave packets produced by only two sine waves are not well separated along the x-axis. However, if we superimpose many waves, we can produce an isolated wave packet. For example, figure 1.9 shows the results of superimposing 20 sine waves with wavenumbers k = 0.4m, m = 1,2, \ldots , 20, where the amplitudes of the waves are largest for wavenumbers near k = 4.

--End of quote--

As I said Soul Surfer, I'm not trying to rewrite QM, just trying to see where the ideas stands today.

[Soul Surfer]

No I was referring to jPs  apparent insistence that photon wave packets only included a single frequency pure sinusoid.  Note they could contain a single frequency gaussian amplitude modulated sinusoid.  This would produce the normal line widths observed in spectrum lines.  This is probably the best way to imagine what the waveform of a photon is like.

My definition of a photon wave packet is a burst of energy of a specific frequency that starts small builds to a peak and falls away to zero over a specific time period longer than a single wave. This is not like a bell which starts with an impulse and then dies away.  mind you some of the more extreme pulse modulators nowadays can produce light waveforms that are just about a single wave.

[yor_on]

Soul Surfer I got to admit that I fail to see what a 'single frequency gaussian amplitude modulated sinusoid.' might look like? Can you simplify your description somewhat so I might get an idea

If I look at a single photon I would say that it has an energy but no waves. and for it to get a wavelike property you will have to superimpose them in 'place' and possibly 'arrange' them so that they will differ in energy over times arrow?

And for a photon to exist you will need an interaction right? And then an EM field is needed, am I correct? And when you have an EM field and a atom interacting you can't really define it as only a single photon, or can you? Is there any way to guarantee that your wavepacket only will represent a discrete energy level?

(Hey, soon I will decide that there can be no single photons:)
==

As I understand it a photon has no magnetic field (it's zero) and without that how can there be any EM fluctuations? If I want one photon to be representative of waves, won't I need those fluctuations present in times arrow intrinsic to that photon?
==
Awh, this is really confusing. I'm trying to see how a photon can be seen as a wavepacket, and mathematically it seems to work, but only when choosing appropriate 'cutoff's'. Or am I loosing it again )

[JP (OP)]

No I was referring to jPs  apparent insistence that photon wave packets only included a single frequency pure sinusoid.  Note they could contain a single frequency gaussian amplitude modulated sinusoid.  This would produce the normal line widths observed in spectrum lines.  This is probably the best way to imagine what the waveform of a photon is like.

Soul Surfer, I agree with you completely, but I think you've misinterpreted what I said.  A photon doesn't have a well-defined spatial representation by its nature, so it can't be a sinusoid.  However, it does have a precise frequency, which has to do with its energy, and is modeled as an excitation of a harmonic oscillator.  (If you've dealt with quantum harmonic oscillators, you know that the frequency of the oscillator isn't sinusoidal.)  You can check a textbook like Mandel and Wolf for details, and some of it is online here.

Is it worth starting a new post about the bandwidth of photons or the photon model?  I don't want to drag this any more off topic.  Soul Surfer, since you had the original question on photons and bandwidth, do you want to do so?

[yor_on]

E = h nu?
But how? Is a relationship the same as saying that "as it exist it must be, at all times"?
Or does it speak about interactions, as that's where we draw those conclusions from as I see it. And from there my next question must become. Can we speak with surety of anything while it's not interacting?

Yeah, I know

sleep, right?
==

"higher frequencies mean shorter wavelengths"
So what is the energy of virtual photons in that motto?
Or their frequency?
==

So, if I accept that, photons must have a frequency, right?
And then I will have to state that a single photon oscillates too
And from there?

So from being a particle of no geometric size and with a EM field of zero, to a oscillating particle of an extremely short wavelength(?) being well defined in space; And also simultaneously defined to an extremely long(?) wavelength and therefore diffused geometrically. But now definitely of some defined placement in SpaceTime depending on frequency aka energy, even as a photon. My headache is now astronomical

And you're right JP, in a way, but it's difficult to discuss electrons without interactions in time
==

As if I assume that even if a photon of high energy would be better defined in SpaceTime it would still matter which way I was traveling, and what speed I had relative it, right? And the same goes for its energy. And it can do this without any magnetic field whatsoever. And it won't emit any radiation.
==

Sorry, saw that it wasn't that clear what I meant
Hope its reads better now

[yor_on]

And there's one more thing that disturbs me. As I understands it we say that virtual photons are under Planck time right? And we use this phenomena for describing a lot of strange possibilities, like being able to get out from a Black Hole. Maybe I'm thinking wrong here but to me there are major differences between macroscopic SpaceTime and what we have under Planck time.

But reading about 'Rindler Observers' and the way their observations will differ from a observer being at rest with f.ex. Earth they , if i got it right, will see virtual particles as being real. That opens major questions for me. For one I can't help wondering about the arrow of time, if I assume that this phenomena now have passed some sort of threshold as it exists continuously in the observations by those Rindler observers? And what should  the definition of inside versus outside our arrow of time be. Why should 'virtual particles' become real particles due to a uniform acceleration. It's like SpaceTime exist on a sliding scale of 'reality'?

But I'm neither doubting photons as particles or as waves. When it comes to wavepackets I've tried to avoid them as I have enough troubles trying to understand photons as particles:) But as wave packets are able to predict a lot of behaviors they are working, right? But I'm still wondering what a photon is? and 'times arrow' too.

When it comes to wave packets I understands that your starting presumptions and definitions are of the utmost importance when it comes to the decide the outcome of a experiment?

--Quote--

Wave packet propagation is a useful technique for solving quantum mechanical problems over a wide range of applications. Since very few quantum mechanical problems can be solved exactly, each propagation technique can only provide an estimate to the actual solution. For a propagation algorithm to be useful it must be fast in addition to being accurate. With most algorithms a high accuracy can be reached by taking a small time step between propagation calculations. However, if the time step is too small too much time is needed to reach a final answer, so a balance between speed and accuracy is needed for each algorithm. In addition, the parameters of the energy spectrum I am interested in calculating must be taken into account, since the energy range of the spectrum determines the maximum time step that can be taken, and the energy resolution of the spectrum determines the length of time that the wave packet must be propagated.

The different propagation techniques I have studied include the Feit & Fleck split operator method, a time dependent modified Cayley method, a second-order differencing scheme, an iterative Lanczos reduction, and a Chebyshev polynomial expansion. Various coordinate systems have been used for the propagations, including normal coordinates, Jacobi coordinates and Radau coordinates. Finally, different methods for calculating the kinetic energy of the system have been explored, including FFT's and various finite-difference schemes.

When normal coordinates can be used, the Feit & Fleck split operator propagation technique, using FFT's to calculate the kinetic energy, is the most robust and fastest of the various combinations studied. However, normal coordinates do not preserve the symmetry of the OClO molecule and therefore cannot always be relied upon to produce accurate results. In such cases Radau coordinates must be used, and in order to reproduce the reflectional symmetry of the angle coordinate a finite-difference scheme must be used to find the kinetic energy, rather than an FFT. We use a 25-point finite difference method because we found it gave the best compromise between accuracy and speed. Since FFT's cannot be used with Radau coordinates the split operator propagation technique is no longer viable; a Chebyshev expansion is instead used to propagate the wave packet.

--End of Quote-- Wave packets

And perhaps?
Back to electrons:)

[Soul Surfer]

yor-on From your writings in the previous few replies (as opposed to your quotations) it is clear to me that your mental image of electromagnetic waves in general and photons in particular is extremely confused and inaccurate.  A lot of your quotations appear to be either from advanced texts or spoof garbage texts (there are a lot of fake pseudo scientific texts around on the web that look learned but are really just rubbish)  that are not relevant to the problems that you have with understanding. 

I would recommend that you read a good well established basic physics textbook on the topics and try to understand initially classical electromagnetic wave theory and then extend this to the most basic quantum theory.  To go back to square one and put it all in here is more work than I am prepared to do at the moment

[yor_on]

Well Soul Surfer, your opinion is your own of course. But all together with the way you reacted towards JP I can't say I'm surprised

Be cool.
==
Btw: What's so apparently wrong in my comments?
Never said I understood wave packet theory?
I said I tried to stay away from it, more or less

As you imply, that may make me a 'fossil' not understanding anything about waves.
Sh* never said I did, you do then
Come on Soul Surfer, give your solution to us mortals.

We need it...

[Soul Surfer]

Well lets have a go.  You appear to make a lot of categorical statements about electromagnetic waves and quanta please forget all these and we will start from the beginning.

A varying electrical field in space causes an electrical current to flow as space itself is charged up to crate the field.  An electrical current creates a magnetic field.  A varying magnetic field creates an electrical field as the magnetic polarisation of space itself changes.  This is a property of space in the same way as mass and gravitation.  This as Maxwell realised creates the possibility of waves (like waves in the sea) where energy is propagated by moving between electrical energy and magnetic energy within space even when nothing else was present.

The velocity of these waves is determined by the electrical permittivity and the magnetic permeability of free space and is equal to the well known velocity of light.  the wavelength of the waves is defined as in all wave motions by the equation wavelength times frequency equals velocity.  The velocity of the waves is constant for all frequencies in free space.

Wavelengths and frequencies of electromagnetic radiation can vary over a vast range from kilometres as in long waves  through meters and centimetres for TV, phones and microwave cookers  to nanometers for light and very much shorter for X-rays and Gamma rays (ionising radiation).

An electron is a single negative electrical charge  a proton is a single positive electrical charge but much heavier than an electron.

Let us consider (in a purely classical physics sense) what might happen as a single electron approaches a single proton to form a hydrogen atom if the electron has some angular momentum it could go into orbit around the proton like the earth around the sun and let us ignore any motion of the proton around the common centre of gravity.  This could in theory be a stable situation except that the electron as it orbits would create a varying electrical and magnetic field in space and would lose energy by radiating electromagnetic waves and the proton and electron would quickly fuse together but this does not happen.  For certain very specific orbits the electron it is found by experiment that it is stable for quite a long time before it decays and at one particular state the ground state it is permanently stable in the absence of major disturbances.

When the electron moves between  two of the metastable states it radiates a pulse of electromagnetic waves.  this consists of a wave of a particular frequency that starts builds up over a few cycles and then decays taking a time that is related to that particular change.  This pulse of electromagnetic waves which is in effect usually much larger that the atom that originates it because of the wavelength and time it takes to radiate.

Please note again this is all totally classical physics and was in effect observed and accepted long before quantum theory was considered.

The metastable states are a bit like resonant cavities where the electron that is trying all the time to radiate its energy is in effect having energy fed back to it from the fields that it is creating in a continuous feedback loop.

Quantum mechanics just explains this classical process in a slightly different way and allows the energy levels to be calculated to a great degree of accuracy via quantum electrodynamics the most accurate physical theory that we have at the moment.

As an interesting aside let me add one other fact.   It can be observed that although electrons are particles they can also behave like waves and show interference patterns etc.  The wavelength of the waves depends on the momentum (mass times velocity) of the electron.  If one considered the metastable states of the electron and work out the "wavelengths" of the electrons as waves when they are in these orbits you find that the metastable states correspond to whole numbers of wavelengths of the electron that is the electrons are resonant structures then.  Again all this is classical physics and measurable without ant recourse to quantum theory for an isolated hydrogen atom.

Similarly all quantum processes have a solid bedrock in classical physics although once you get more electrons in an atom the calculations become incredibly complex.

Nowadays physics teaching tends to dive straight into quantum processes without fully explaining the classical physics background and this causes severe confusion in some peoples minds.

[yor_on]

Soul Surfer, let's call my expressions about photons and wavepackets as born out of frustration here And let me add that I'm glad you took it this way.

As for if a photon has a frequency in a mathematical sense bound to it's energy I know, actually I do even though i tend to forget it as i look at it. But what's interest me are those 'single ones' aka 'what the he* is a photon?' and those I think to be non-classical, and in that motto it, to me that is, becomes impossible to understand how they are thought to act as common waves in their single state?

I will read you and see how you think.
Nice.

[yor_on]

Thanks for your lecture Soul Surfer. A nice view of a classical approach.
And single photons will in your eyes then be a bell formed (Gaussian)wave packet with its 'cutoff's' decided by what? And should I understand that as a classical approach too?

And your use of 'free space' I assume to include some sort of particles, not being a 'perfect vacuum' as it's normally defined in classical physics? Or do you mean that electromagnetism will propagate in a free space in the classical sense. That's one of my main questions in fact, as if we define that 'space' as containing nothing, and consider an EM wave as something obeying our macroscopic arrow of time (above Planck time/size) then, for this question, I will ignore 'virtual energy/particles'. As I believe that everything needs an interaction (medium if you like) to propagate, be it billiard balls or waves, that one is quite interesting to me?
==

I'm presuming that you are using 'free space' here in the meaning of how it relates to electromagnetic theory (Maxwell). In that idea 'virtual energy or particles' (quantum vacuum) have no place, as I understands it?