Shape of the wave of a single photon

[swansont]

To figure out the typical envelopes of photon waves in a light beam:

 

1: Set up double slit experiment were the path lenth difference is adjustable.

 

2: Start adjusting the path length difference.

 

2: Record the percentages of light that interfered and light that did not interfere at different path lenths.

 

3: The path length difference were half of photons did not interfere with itself is such a path length difference that makes half of the photon waves non-overlapping photon waves. Half of the photon waves are shorter than this length.

 

What path length difference can there be in a double slit? Or are you referring to an interferometer with two arms? In that case there's a coherence length issue. But for a double-slit experiment, the photon interferes with itself. This reveals nothing about any "shape" of the wave.

[Toffo]

 

What path length difference can there be in a double slit? Or are you referring to an interferometer with two arms? In that case there's a coherence length issue. But for a double-slit experiment, the photon interferes with itself. This reveals nothing about any "shape" of the wave.

 

How to do the adjustment of the length of one of the two paths:

 

With two periscopes connected in series .... With mirrors in other words.

 

 

If we want a simple proof that photon waves are not very short, we can cover one slit with thin sheet of glass, and observe that interference pattern does not disappear.

Edited October 16, 2013 by Toffo

[DParlevliet]

I'm really sorry to rain on your parade, but how many axes did your picture have and how many did you label?

According Wiki "A wave function that satisfies the non-relativistic Schrödinger equation with V=0. In other words, this corresponds to a particle traveling freely through empty space. The real part of the wave function is plotted here."

But I used it just to show the shape.

 

Of course my next question is about the other space axes, but I can easier proove that the time sinus exist (by the interference pattern)

[swansont]

 

How to do the adjustment of the length of one of the two paths:

 

With two periscopes connected in series .... With mirrors in other words.

 

There is only one path for the double-slit experiment

[Mike Smith Cosmos]

I have a question about the shape of the wave of a single photon .

If it is of any help.

When I asked the same question of my university professor, instructing us on wave mechanics.

His reply was similar to the vague answers that have come forth. He then took me aside for a coffee. I was a mature student in my .50's

He sort of confessed " nobody really knows! And he was well up in the field.

" if you want my personal ....." He started.

He described how the maxwell em field was set up near the antenna. At a certain frequency the field is unable to return into the antenna by self induction and return up the antenna or transmission line.

Instead the "bubble of EM" wave links back on itself and no longer requires the antenna and surrounding fields for its existence.

These bubbles of "EM " also having a succession of following " bubbles" the photon stream heads out into the blue horizon at break neck speed. The speed of light.

 

This sounded good to me. He did explain this was his personal visualisation.

 

I agree it needs mapping , but in the mean time " a string of photon bubbles vibrating in three dimensions at the frequency of oscillation of the wavelength of the relevant E.M wave haring off into the distance sounds good!

 

Whether anything other than an EM wave photon actually goes anywhere. Namely a wave goes somewhere but whether any particle go anywhere ? Certainly in every other phenomenon where waves are concerned, energy goes off into the distance, waves go into the distance but the medium of the wave stays put and supports the wave !

[studiot]

 

According Wiki "A wave function that satisfies the non-relativistic Schrödinger equation with V=0. In other words, this corresponds to a particle traveling freely through empty space. The real part of the wave function is plotted here."

But I used it just to show the shape.

 

 

So I am wasting my time, since you do not wish to address any of my comments.

[DParlevliet]

DParlevliet,

Am I wasting my time or do you want an answer to your original question?

 

I am sorry but I am not always availble to answer (my company would not allow that) so I cannot answer quickly. Also it seems that I don't understand you questions, because I really try to answer them. So let me start again, first keeping it simple.

 

If you search on the web for double slit images and animations you will always see flat (sinus) wavefronts moving to the slits. My question is: how does that look with only one photon?

 

Then seen from the double slit: this experiment is based on adding two parts of the same wave, which are separated in space (by the distance between the slit) with increasing phase difference. See the image before and picture in two of them with increasing phase. In the middle the phase difference is zero, so both add to double value. Going to the right the phase difference increases until the waves cancel each other. But when going much further to the right the shift between both waves becomes so large that only the tails interfere. Those are lower, so will cause smaller interference. Even futher to the right both waves misses each other completely and no interference pattern will be visible.

So my argument is, that the interference pattern on the detector is a kind of image of the original wave(packet).and can be calcuated back to the incoming wave. The fact that this pattern is clearly visible means that most photons which are detected has the same wave/packet/shape

[studiot]

It is still essential that if you draw a graph (which your sine curve is) you understand (and preferably label) the units on each axis.

 

You have not done this.

 

I repeat understanding this is the key to understanding your difficulty.

 

Are you with me thus far?

[Strange]

If you search on the web for double slit images and animations you will always see flat (sinus) wavefronts moving to the slits. My question is: how does that look with only one photon?

 

I think you are wasting your time trying to visualise a photon. You might as well, for the purposes of this experiment, think of it as a little fuzzy ball. After all, the same experiment can be done with reasonably macroscopic objects (I think a C60, buckyball, might be the largest) with the same results.

 

The resulting pattern reflects the probability of photons reaching various points on the screen. This can be calculated mathematically, and this precisely matches the results. If you want to try and visualise the photon as a wave going through both slits, then there will be other experiments that make that meaningless. If you think of it as a particle, then there are other experiments that contradict that.

 

So what is it? It's a photon. It does what photons do.

[DParlevliet]

It is still essential that if you draw a graph (which your sine curve is) you understand (and preferably label) the units on each axis.

The graph image has: x-axis is time, y-axis is "the real part of the wave function" according Wiki. I don't know what that is.

 

In my question X-axis is time, y-axis is what interferes in the double slit experiment, whatever that is.

[Toffo]

 

How to do the adjustment of the length of one of the two paths:

 

With two periscopes connected in series .... With mirrors in other words.

 

 

If we want a simple proof that photon waves are not very short, we can cover one slit with thin sheet of glass, and observe that interference pattern does not disappear.

 

Oh yes, as DParlevliet has has been pointing out, when moving away from the center of the interference pattern on the screen, the path length difference to that point increases.

 

The path length difference approaches the distance between the slits, which may be arbitrarily large, in principle.

 

There is only one path for the double-slit experiment

 

Path1: Through slit A

Path2: Through slit B

[studiot]

 

The graph image has: x-axis is time, y-axis is "the real part of the wave function" according Wiki. I don't know what that is.

 

In my question X-axis is time, y-axis is what interferes in the double slit experiment, whatever that is.

 

 

 

Suppose I take a journey from A to B and plot a graph of the distance travelled en route.

 

Can I say that this is the shape of any physical object?

Of course not.

It has a definite shape on paper, that's all.

If pushed I could observe that it must never be decreasing, unless I went back towards A at some stage.

 

A shape is a surface in 2 or three spatial dimensions. Like the surface of a football tells us it is round, or more accurately a sewn together polyhedron of flat (ish) sides.

My graph above is a shape on paper in two spatial dimensions. I am just using one to represent time.

 

This is the source of my query about what you are asking.

 

Now can you see why the question "What is the shape of a photon?" makes no sense in that context?

Edited October 16, 2013 by studiot

[DParlevliet]

I think you are wasting your time trying to visualise a photon.

 

But I also explained how the double-slit measurement shows how the waves which interfere look like. Then it is just simply calculating back with interference rules.

 

So if anyone knows the formula of the interference result on the detector, then we know the shape of the wave which did cause the interference.

[swansont]

Path1: Through slit A

Path2: Through slit B

The slits are next to each other, and if you know the photon goes through one slit and not the other, there is no interference pattern.

But I also explained how the double-slit measurement shows how the waves which interfere look like. Then it is just simply calculating back with interference rules.

 

So if anyone knows the formula of the interference result on the detector, then we know the shape of the wave which did cause the interference.

Where in the interference equation does the shape appear?

[DParlevliet]

Now can you see why the question "What is the shape of a photon?" makes no sense in that context?

 

A bit. Perhaps the word shape is chosen wrong. Englisch is not my native language and certainly not the scientific use. Therefore later on I use "looks like", which is of course not scientific either. For instance if my previous used is an EM wave with x = time and y = E, then I would have called that the shape of a sine with amplitudes as a gausian curve. So perhaps must I call it a curve, or the envelope of the amplitudes.

I agree it needs mapping , but in the mean time " a string of photon bubbles vibrating in three dimensions at the frequency of oscillation of the wavelength of the relevant E.M wave haring off into the distance sounds good!

 

Do you mean with the bubbles the particles in their indeterminable position?

[Strange]

But I also explained how the double-slit measurement shows how the waves which interfere look like.

 

No it doesn't. The interference pattern depends on the wavelength and the distance between the slits.

 

In the classical version of the experiment, the wave is a sinewave. In the photon version ... well that doesn't make sense. There is no wave, just photons (Or electrons, or atoms, or buckyballs).

[DParlevliet]

Where in the interference equation does the shape appear?

 

Do you know the interference equation? Please read above, perhaps my use of shape is wrong and confusing. Better is perhaps to call it just the wave itself. Or how does the wave look like when you plot E (in an EM wave) against time.

[Enthalpy]

An excited hydrogen atom, decaying spontaneously to the ground state from the 2p state decays in 1.6 x 10^-9 seconds, or 1.6 nanoseconds.

1.6 x 10^-9 seconds * speed of light = 0.48 meter. 0.48 m is some kind of average length of these photon waves.

I'm pleased with that explanation.

The hydrogen 2p-1s transition has an energy of 10.2 eV, which gives it a wavelength of 121.5 nm, just as your link says. There's nothing there that implies it has a length of half a meter.

Two different time scales here. The transition energy defines the photon's period, frequency, wavelength. The duration of the transition defines the frequency breadth, wavelength width, and stretch of the photon over time and distance.

[Strange]

 

Do you know the interference equation?

[math]f = \frac{z \lambda}{d}[/math]

Where:

[math]f[/math] is the separation of the fringes

[math]z[/math] is the distance from the slits to the screen

[math]\lambda[/math] is the wavelength of the light

[math]d[/math] is the distance between the slits.

 

 

Or how does the wave look like when you plot E (in an EM wave) against time

It is a sine wave.

Edited October 16, 2013 by Strange

[Enthalpy]

...the shape of the wave of a single photon [...]

With really a single photon, the wave function cannot be measured, I believe. You detect the photon once, it happened to be here, or there, or there.

 

Some experiments tell "single photon" but use many of them, so that the number of photons detected around each position permits to reconstruct a wavefunction. It's rather "one photon at a time", which just needs faint light intensity, but is conceptually difficult, because we use to ignore when the photon was emitted. Most often, we just know at what mean rhythm photons are detected.

[DParlevliet]

[math]f = \frac{z \lambda}{d}[/math]

 

I mean the intensity of the detector against the position on the detector.

[Mike Smith Cosmos]

Waves. 2 different waves.

 

Surely we are getting our waves confused.

 

There is the straight forward constant amplitude sine wave, which is the signal.say 100 MHz ( radio signal or 1 THZ very high frequency light) A normal sign wave.

 

Then because everything in the universe has a de broglie wave or probability wave as part of its nature, particularly if it is a particle , like an atom. A world, a photon there is this second wave not having constant amplitude, defining the particle position either side of a mean point. Like the one you keep showing from Wikipedia.

Edited October 16, 2013 by Mike Smith Cosmos

[DParlevliet]

Some experiments tell "single photon" but use many of them, so that the number of photons detected around each position permits to reconstruct a wavefunction. It's rather "one photon at a time", which just needs faint light intensity, but is conceptually difficult, because we use to ignore when the photon was emitted. Most often, we just know at what mean rhythm photons are detected.

 

In the double slit the propability is measured of detecting a photon on a certain position on the detector. Because for each photon this is the same propability, you can use multiple photons to get a full curve.

Then because everything in the universe has a de broglie wave or probability wave as part of its nature, particularly if it is a particle , like an atom. A world, a photon there is this second wave not having constant amplitude, defining the particle position either side of a mean point. Like the one you keep showing from Wikipedia.

 

That is what I think. The question is now: what is the formula of this not-constant amplitude. I would already be happy with a approximation of (for instance) its FWHM.

[swansont]

Two different time scales here. The transition energy defines the photon's period, frequency, wavelength. The duration of the transition defines the frequency breadth, wavelength width, and stretch of the photon over time and distance.

 

The decay time will limit where you might expect the photon to be, but that's not the same as any "size" of a photon. I could have the hydrogen atom between two mirrors in a cavity, and the photon would quite happily be emitted toward a mirror, even if they were a few mm apart. The mirrors would not have to be .48m apart for this to happen. If the mirrors were closer than half a wavelength (plus whatever correction is necessary because the atom is there), though, then the photon could not appear.

 

For instance if my previous used is an EM wave with x = time and y = E, then I would have called that the shape of a sine with amplitudes as a gausian curve. So perhaps must I call it a curve, or the envelope of the amplitudes.

 

 

I refer you back to my earlier response: all you know is that it must obey the wave equation.

 

The curve you show here is not a sine curve; for that to be true it must be infinite in time and space. So even here you have a superposition of sine curves, which allow the wave packet to be of a finite extent. It would not be a "pure tone", i.e. there would be an uncertainty in the frequency, and there would be multiple frequencies represented in a Fourier analysis of the wave. To have a chance to know that you need to know where the photon came from.

[Mike Smith Cosmos]

Dergbi123vr said

-----------------------

That is what I think. The question is now: what is the formula of this not-constant amplitude. I would already be happy with a approximation of (for instance) its FWHM.

------------------------

I think if it is a separate particle like en electron or photon you look up de broglie, and use his formula.

 

If it is in association with another particle like an electron in an atom with a nucleus. You have to use shreonigers equation.

Edited October 16, 2013 by Mike Smith Cosmos