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mkline55
2016-Feb-02, 09:17 PM
As I understand it, cosmological redshift occurs when the wavelength of emitted radiation is lengthened due to the expansion of the universe, and not due to the relative velocity of the emitter and receiver. I was willing to accept this definition until I wondered how this expansion could increase the wavelength of an individual photon. Does a photon have length which can be expanded? I think that answer is no, but I'm listening if someone has a different answer.

The real question I want to ask is, do the wave-like characteristics of photons have length? While we refer to wavelength and formulate that into velocity and frequency, is there really an actual "length" for an individual photon particle? If so, is there a limit to that length?

If the photon has no length, then what exactly is being stretched by cosmological expansion to produce redshift, and how does that occur?

kevin1981
2016-Feb-02, 09:32 PM
Good question !

Jeff Root
2016-Feb-02, 11:16 PM
I have wondered about the length of photons (and their width
perpendicular to their length, as well) for decades. My opinion
is that photons *do* have length even though it is fundamentally
impossible to measure the length of a photon, even in principle.
We observe the consequences of that length in the behavior of
statistically large numbers of photons. I think the wavelengths
in a beam of light are a direct consequence of the lengths of the
photons. The wavelengths are measured relative to the observer,
so the length of a photon is also relative. Meaning that the length
is not an intrinsic property of the photon.

I say it is fundamentally impossible to measure the length of a
photon because all that can be done with a photon is to detect
it or not detect it. The detection is a single event at a single time
and a single place. That doesn't permit the detection of the ends
of a photon passing a point at different times, or passing two
different points at the same time. The way wavelengths can be
measured is, for example, by measuring the angle of the peak
intensity of many photons which have passed through a prism
or been diffracted by a grating. Any single photon will exit the
prism or grating with an unpredictible angle, but together they
produce an interference pattern with a sharp peak.

As far as I can tell, the cosmological redshift is identical to a
combination of Doppler redshift and gravitational redshift.
There is no way to distinguish between the two other than
the context in which they are observed.

-- Jeff, in Minneapolis

John Mendenhall
2016-Feb-02, 11:19 PM
https://www.rp-photonics.com/spotlight_2008_05_05.html

Good limk.

Hint: attempting to ascribe macroscopic properties to fundamental particles is pretty much a waste of time.

efanton
2016-Feb-03, 03:36 AM
I have wondered about the length of photons (and their width
perpendicular to their length, as well) for decades. My opinion
is that photons *do* have length even though it is fundamentally
impossible to measure the length of a photon, even in principle.

Possibly a madcap idea, but here goes

if you had multiple photon guns and had a target to count the photons as they hit, then would it be possible to position this target at such a distance that the 'beams' could be aimed precisely to hit a single point. Obviously if these beams were fired from a very considerable distance in such a way as to hit the target at the smallest possible angles (in other words the beams being as close to parallel without actually being so) at some point if they had width some would collide and cause scatter before they hit the target. If you could identify the point of scatter then from simple trigonometry you have the width of a photon or at least an approximation.
I dont know if this experiment would be technically possible, the angle would be so very slight and I would imagine the distance to be very very long, but theoretically at least it seems to make sense. We can fire a laser at a target on the moon and measure its reflection would that be distance enough?

Jeff Root
2016-Feb-03, 07:12 AM
I don't see that it requires a small angle or long distance. What it
requires is for photons to collide. That doesn't happen, and it
doesn't depend on the size of the photons.

-- Jeff, in Minneapolis

mkline55
2016-Feb-03, 01:04 PM
https://www.rp-photonics.com/spotlight_2008_05_05.html

Good limk.

Hint: attempting to ascribe macroscopic properties to fundamental particles is pretty much a waste of time.

That link indicates that there is no length, so I'll ask again, If the photon has no length, then what exactly is being stretched by cosmological expansion to produce redshift, and how does that occur?

Ken G
2016-Feb-03, 04:02 PM
As I understand it, cosmological redshift occurs when the wavelength of emitted radiation is lengthened due to the expansion of the universe, and not due to the relative velocity of the emitter and receiver. I was willing to accept this definition until I wondered how this expansion could increase the wavelength of an individual photon. Does a photon have length which can be expanded? I think that answer is no, but I'm listening if someone has a different answer. No, photons by themselves do not have length. The "wavelength of a photon" actually refers to the wavelength of the wave we use to describe the photon behavior, and even that requires a reference frame, so it would be more accurate to say that wavelength is a function of the combination of a photon and an observer. Indeed, even saying that presumes we already have knowledge about the source of the photon, the conditions under which it was created. So cosmological redshift, like all redshift, is a comparison between a wavelength established by a source, and a wavelength established by an observer, both of which require reference frames. "The photon" is what we regard as the particle that mediates that comparison, and something that is different about the reference frames is responsible for the observed difference in wavelength.


The real question I want to ask is, do the wave-like characteristics of photons have length?When the source and observer are well described, yes. Change either, and the wavelength changes. Also, it is possible for the wavelength to be indeterminate to some degree, which we call a superposition state, specifically known as a "wave packet." This has a classical analog, say in analyzing sound.

While we refer to wavelength and formulate that into velocity and frequency, is there really an actual "length" for an individual photon particle? If so, is there a limit to that length?The limit comes from the nature of the source and detector, and invokes the Heisenberg Uncertainty Principle and all that jazz.


If the photon has no length, then what exactly is being stretched by cosmological expansion to produce redshift, and how does that occur?There is no model for "how it occurs," because there is no answer to what exactly is being stretched when the universe expands. However, increasing wavelength is an inescapable consequence of having a fixed number of "wavefronts" in some wave packet, while having the distance between the front and back of that packet increase with time. We have no idea how that distance is increasing, it just follows from our best model of how gravity works on the universal scale (with a few tweaks!), but we do have a good idea why the number of wavefronts doesn't change: there's nothing to change it.

mkline55
2016-Feb-03, 05:27 PM
There is no model for "how it occurs," because there is no answer to what exactly is being stretched when the universe expands. However, increasing wavelength is an inescapable consequence of having a fixed number of "wavefronts" in some wave packet, while having the distance between the front and back of that packet increase with time. We have no idea how that distance is increasing, it just follows from our best model of how gravity works on the universal scale (with a few tweaks!), but we do have a good idea why the number of wavefronts doesn't change: there's nothing to change it.

I believe it's the "distance between the front and the back of that packet" I am trying to analyze. I believe you are saying that this distance increases with time. Is there a maximum limit to said distance?

Jeff Root
2016-Feb-03, 08:02 PM
Ken,

Can you explain what a "wave packet" is without having to explain
superposition states? If not, can you explain superposition states?
:)

Do you agree with me that ...

Given that the wavelength of a monochromatic beam of light can
be accurately and precisely measured,

- The wavelength of a single photon cannot be directly measured

- The wavelength of a single photon cannot be accurately and
precisely measured with any certainty.

To explain, through experience, we know that a certain
configuration of prism will change the path of a monochromatic
light beam by a specific amount. Nearly all the light in the beam
has its path changed by that amount, or very close to that amount,
making a precisely-located line on a screen. But if you put just one
individual photon through the prism, it has a significant chance of
taking any path and landing anywhere on the screen. Only by
sending a statistically large number of photons through the prism
will we be able to meaningfully relate the locations they hit the
screen to a wavelength. And similar arguments apply to all
methods of measuring wavelength.

-- Jeff, in Minneapolis

ngc3314
2016-Feb-04, 12:50 AM
I can't go with that, because there are astronomical applications for getting spectroscopy in which, say, only one photon is in the detection system at a time (or per second, for that matter) but the data still show very sharp spectral features (example: the Chandra X-ray Observatory crystal-grating spectrometer).

Ken G
2016-Feb-04, 01:34 AM
Can you explain what a "wave packet" is without having to explain
superposition states?Sure, it has a classical analog. When you analyze music, for example, you might consider its "waveform." That's not a single wavelength, it is a "wave packet"-- which is just the amplitude as a function of frequency, the Fourier transform of the amplitude as a function of time.


If not, can you explain superposition states?In the quantum picture, those frequencies are identified with particle states, and the waveform is a superposition of amplitudes of the particle being found with any of those frequencies when a frequency measurement is done on it.


Do you agree with me that ...

Given that the wavelength of a monochromatic beam of light can
be accurately and precisely measured,

- The wavelength of a single photon cannot be directly measuredThere really isn't the wavelength of a photon, but there is the wavelength of the wavefunction that is used to predict what will happen in the experiment, once you know the source and the observer. But if the source is highly monochromatic, then the wavelengths of each of the photons being emitted can be known with similar precision. This is what happens, for example, in a laser. It can also be directly measured, you simply measure its momentum. There is an important difference between a measurement that destroys the photon, and one that "prepares" the photon in a state, but in effect, a laser source is a type of direct measurement of the photon wavelength, of that latter type.


- The wavelength of a single photon cannot be accurately and
precisely measured with any certainty.
There are many techniques for knowing the wavelength associated with a single photon, some that destroy it, some that don't.


To explain, through experience, we know that a certain
configuration of prism will change the path of a monochromatic
light beam by a specific amount. Nearly all the light in the beam
has its path changed by that amount, or very close to that amount,
making a precisely-located line on a screen. But if you put just one
individual photon through the prism, it has a significant chance of
taking any path and landing anywhere on the screen.You can still measure its momentum using other devices. A classic way is called using a diffraction grating, aimed into a CCD. That destroys the photon, so you are measuring what its wavelegth "was." You can measure what it "is" by preparing it in a given state. Yes, there will be some uncertainty, but what measurement does not have uncertainty?

John Mendenhall
2016-Feb-04, 03:05 AM
I don't see that it requires a small angle or long distance. What it
requires is for photons to collide. That doesn't happen, and it
doesn't depend on the size of the photons.

-- Jeff, in Minneapolis

Jeff, here is th Wiki artcle on photon-photon collisions:

https://en.wikipedia.org/wiki/Two-photon_physics

which are quite possible, just expensive.

John Mendenhall
2016-Feb-04, 04:19 AM
That link indicates that there is no length, so I'll ask again, If the photon has no length, then what exactly is being stretched by cosmological expansion to produce redshift, and how does that occur?

Well, try this one:

http://cecelia.physics.indiana.edu/life/redshift.html

An aside here: mush of ccosmology requires GR. It is at least four senesters of calculus to figure out what is going on. For perceptive people such as yourself and many others on this forum, you can sense that there is something missing in the popular explanations, but can't quite put your finger on it. You might try the the general Wiki articles on GR and QM. Read a few paragraphs a day. They're a great cure for insomnia, also.

mkline55
2016-Feb-04, 03:32 PM
Well, try this one:

http://cecelia.physics.indiana.edu/life/redshift.html

An aside here: mush of ccosmology requires GR. It is at least four senesters of calculus to figure out what is going on. For perceptive people such as yourself and many others on this forum, you can sense that there is something missing in the popular explanations, but can't quite put your finger on it. You might try the the general Wiki articles on GR and QM. Read a few paragraphs a day. They're a great cure for insomnia, also.

Tried it. It's not very long, but it's also not very informative. Although the following quote seems simple enough, it's really the basis for my questions:


Light waves become stretched en route between the time they were emitted long ago, and the time they are detected by us today.

As written this indicates light waves have a length. Is that correct? It plays well with the expansion theory, since the leading edge of the wave travels through less space than the trailing edge, thus "stretching" the wave.

Lucretius
2016-Feb-04, 05:40 PM
As written this indicates light waves have a length. Is that correct? It plays well with the expansion theory, since the leading edge of the wave travels through less space than the trailing edge, thus "stretching" the wave.

Don't we first need to pin down exactly what kind of a wave light is? That is, is it transverse, longitudinal, or perhaps some other form that we're not familiar with? The idea of a sine wave, that transverse wiggly thing so often used to represent light, and which is presumably able to "stretch," or "shrink," is certainly only an abstraction of light's true nature. At most a sine wave could only represent the "path" that the photon is taking.

And what about radio waves? Are they really the same kind of animal as a light wave? Isn't a radio wave actually made up of myriad photons moving in synch? Isn't a radio wave longitudinal, and therefore subject to doppler shift just like a sound wave?

mkline55; I tend to agree with your original assessment that a light wave or photon has no length, and therefore cannot be "stretched."

Jeff Root
2016-Feb-04, 06:46 PM
I can't go with that, because there are astronomical applications
for getting spectroscopy in which, say, only one photon is in the
detection system at a time (or per second, for that matter) but the
data still show very sharp spectral features (example: the Chandra
X-ray Observatory crystal-grating spectrometer).
Can a wavelength be measured from only a single photon
hitting the detector, though? One photon at a time is fine.
Limited rate is not the problem. The problem is the limited
number of photons. And generally, the more energetic each
photon is, the fewer that should be needed to get an accurate
measure of their wavelength.

-- Jeff, in Minneapolis

Ken G
2016-Feb-04, 06:58 PM
As written this indicates light waves have a length. Is that correct?As I said, what has a length is the wavelength of each component in the superposition involved in the wave packet that describes the state of the photon. This has a well quantified meaning in both quantum mechanics, and even in classical electrodynamics, so I recommend thinking in terms of the latter and forget the quantum altogether. Regular old elecromagnetic waves, in an expanding universe, will have their wavelengths "stretched", so if you can understand that, does that not answer your question?

It plays well with the expansion theory, since the leading edge of the wave travels through less space than the trailing edge, thus "stretching" the wave.Exactly, the distance over which the trailing "crest" traveled is longer than the distance over which the leading crest traveled, resulting in the perception of a "stretched" wavelength. But there is no known "cause" of the increasing distance, it is simply the solution to the dynamics of general relativity of the universe as a whole. You can't really say "the cause of the increasing distance is that the universe is expanding", because the increasing distance is all we mean by the phrase "the universe is expanding." We have no idea why the distance is increasing, and in recent times, that increasing distance seems to be receiving an important contribution from a completely unknown effect called "dark energy."

Jeff Root
2016-Feb-04, 07:44 PM
Don't we first need to pin down exactly what kind of a wave
light is? That is, is it transverse, longitudinal, or perhaps some
other form that we're not familiar with?
There is no question that light behaves like transverse waves.
The observations which show light to behave like waves show
it to behave like transverse waves, not any other kind. The
waving is oscillation of the strengths of the electric and
magnetic fields. When observing large numbers of photons,
the two fields are found to be perpendicular to each other,
and perpendicular to the direction of propagation. They are
also found to always be in phase. When the strength of the
electric field is increasing, the strength of the magnetic field
is increasing, and so forth.



The idea of a sine wave, that transverse wiggly thing so often used
to represent light, and which is presumably able to "stretch," or
"shrink," is certainly only an abstraction of light's true nature. At
most a sine wave could only represent the "path" that the photon
is taking.
The idea that the sine wave represents the path of a photon is
one I never saw until a few years ago, and only a few times since.
It is one of the most ludicrous misconceptions about the natural
world that I've ever seen. It clearly shows the failure of a simple
geometric illustration to communicate a simple geometric idea.
The light (or photon) travels in a straight line. The strengths of the
electric and magnetic fields vary. The variations are represented
by the sine curve.



And what about radio waves? Are they really the same kind of animal
as a light wave?
Of course. It is a continuum. Everywhere along the continuum, the
properties of the electromagnetic radiation at that wavelength are
similar to the properties at slightly shorter and longer wavelengths.



Isn't a radio wave actually made up of myriad photons moving in
synch?
Of course!



Isn't a radio wave longitudinal,
Good heavens! No. Certainly not! Electromagnetic waves are
transverse waves. The real question might be whether anything
is moving transversly. I am as close to certain as I can be of
anything that there is no transverse motion involved, but I can't
prove it, and I'm not going to try to explain it.



and therefore subject to doppler shift just like a sound wave?
Longitudinal waves and transverse waves can both be stretched
or compressed, or be observed to be stretched or compressed by
an observer in relative motion, so both are subject to Doppler shift.

-- Jeff, in Minneapolis

Jeff Root
2016-Feb-04, 08:10 PM
I don't see that it requires a small angle or long distance. What it
requires is for photons to collide. That doesn't happen, and it
doesn't depend on the size of the photons.
Jeff, here is the Wiki artcle on photon-photon collisions:

https://en.wikipedia.org/wiki/Two-photon_physics

which are quite possible, just expensive.
My apologies. I was thinking about one thing and wrote about
another thing. Two photons with sufficient total energy can
collide to form a pair of other particles, such as an electron and
a positron. I would expect that to mean that two photons with
less total energy can also interact, even though they can't form
any other particles, but I'm not aware of such an interaction
ever being observed. The experimental setup that efanton
described doesn't strike me as being useful or necessary for
the purpose.

-- Jeff, in Minneapolis

mkline55
2016-Feb-04, 08:31 PM
Is there a maximum limit to wavelength? Could a wavelength be so long that the "leading edge" arrives seconds before the "trailing edge"?

Jeff Root
2016-Feb-04, 08:45 PM
Can you explain what a "wave packet" is without having to explain
superposition states?
Sure, it has a classical analog. When you analyze music, for
example, you might consider its "waveform." That's not a single
wavelength, it is a "wave packet"-- which is just the amplitude as
a function of frequency, the Fourier transform of the amplitude
as a function of time.
It sounds like "wave packets" are just the sum of all the EM
radiation at a given place and time, either in total, or in a signal,
or that are detected, or that you are interested in. So it might
be described as what the complex waveform is doing at a
particular place at a particular instant. Or maybe within a
particular small, brief window. It might not even contain any
detectible photons, or any photons of interest.

-- Jeff, in Minneapolis

Lucretius
2016-Feb-06, 05:45 PM
It seems as though light is still a very mysterious phenomenon.

It also seems that trying to explain the workings of light without some type of medium through which it propagates is akin to trying to explain the workings of aerodynamics while leaving out the air.

Forgive me for muddying the waters still further with this quote from Maxwell, found near the very end of his two volume "Treatise on Electricity and Magnetism":

“821] ...whatever light is, at each point of space there is something going on, whether displacement or rotation, or something not yet imagined, but which is certainly of the nature of a vector or directed quantity, the direction of which is normal to the direction of the ray...the magnitude of this vector remains always the same, but its direction rotates round the direction of the ray so as to complete a revolution in the periodic time of the wave...the direction and the angular velocity of this vector are perfectly known, though the physical nature of the vector and its absolute direction at a given instant are uncertain...This vector is always perpendicular to the direction of the ray, and rotates about it a known number of times in a second...” (bold added)

Of course Maxwell believed in the aether so we really can't take anything he says seriously, right?

Lazer
2016-Feb-06, 07:16 PM
It seems as though light is still a very mysterious phenomenon.

It also seems that trying to explain the workings of light without some type of medium through which it propagates is akin to trying to explain the workings of aerodynamics while leaving out the air.

Forgive me for muddying the waters still further with this quote from Maxwell, found near the very end of his two volume "Treatise on Electricity and Magnetism":

821] ...whatever light is, at each point of space there is something going on, whether displacement or rotation, or something not yet imagined, but which is certainly of the nature of a vector or directed quantity, the direction of which is normal to the direction of the ray...the magnitude of this vector remains always the same, but its direction rotates round the direction of the ray so as to complete a revolution in the periodic time of the wave...the direction and the angular velocity of this vector are perfectly known, though the physical nature of the vector and its absolute direction at a given instant are uncertain...This vector is always perpendicular to the direction of the ray, and rotates about it a known number of times in a second... (bold added)

Of course Maxwell believed in the aether so we really can't take anything he says seriously, right?

In the light of dark energy, the idea of an aether is not entirely farfetched.

mkline55
2016-Feb-08, 08:58 PM
As I said, what has a length is the wavelength of each component in the superposition involved in the wave packet that describes the state of the photon. This has a well quantified meaning in both quantum mechanics, and even in classical electrodynamics, so I recommend thinking in terms of the latter and forget the quantum altogether. Regular old elecromagnetic waves, in an expanding universe, will have their wavelengths "stretched", so if you can understand that, does that not answer your question?
Exactly, the distance over which the trailing "crest" traveled is longer than the distance over which the leading crest traveled, resulting in the perception of a "stretched" wavelength. But there is no known "cause" of the increasing distance, it is simply the solution to the dynamics of general relativity of the universe as a whole. You can't really say "the cause of the increasing distance is that the universe is expanding", because the increasing distance is all we mean by the phrase "the universe is expanding." We have no idea why the distance is increasing, and in recent times, that increasing distance seems to be receiving an important contribution from a completely unknown effect called "dark energy."

This description involves something I could only interpret to be longitudinal waves. Yet, Jeff Root states emphatically that light behaves like transverse waves, and not longitudinal waves. Which is it? If the waves are transverse, then what is it about them that the expansion model stretches? If they are longitudinal, then what is the maximum wave length?

Jeff Root
2016-Feb-08, 09:09 PM
Are you having a problem with the idea of transverse waves
getting stretched? I don't see why that would be a problem.
Certainly not a bigger problem than the idea of longitudinal
waves getting stretched.

-- Jeff, in Minneapolis

Ken G
2016-Feb-08, 10:58 PM
This description involves something I could only interpret to be longitudinal waves. Yet, Jeff Root states emphatically that light behaves like transverse waves, and not longitudinal waves. Which is it?Nothing I said involved longitudinal waves, I was only talking about the distance between crests. It doesn't matter what kind of "crest," be it longitudinal or transverse, because if it's transverse, you simple define the "crest" to be when the phase of the wave is some given thing, like 0 mod 2pi. The only relevant thing here about a "crest" and "the next crest" is the return to the same phase in a snapshot of the wave amplitude.


If the waves are transverse, then what is it about them that the expansion model stretches? The distance between the phase=0 points along the wave.

mkline55
2016-Feb-09, 04:39 PM
Are you having a problem with the idea of transverse waves
getting stretched? I don't see why that would be a problem.
Certainly not a bigger problem than the idea of longitudinal
waves getting stretched.

-- Jeff, in Minneapolis

Isn't a transverse wave just an oscillation that is perpendicular to the direction of travel? How do you stretch the wave? You would have to lower the oscillation rate, wouldn't you? How does stretching space lower the oscillation rate yet maintain a constant velocity?

Hornblower
2016-Feb-09, 07:14 PM
Isn't a transverse wave just an oscillation that is perpendicular to the direction of travel? How do you stretch the wave? You would have to lower the oscillation rate, wouldn't you? How does stretching space lower the oscillation rate yet maintain a constant velocity?

The question of how the velocity of propagation of an electromagnetic wave remains constant relative to an observer despite the stretch may be unanswerable, even in principle. Nevertheless our observations are best fitted by a model in which that occurs. Since the time interval between successive crest passages is increased in a redshifted waveform, it follows that the distance between crests is increased as reckoned in the observer's frame of reference. Whether the oscillations that create these crests are transverse or longitudinal is beside the point. I do not understand why you have difficulty with one and not the other.

mkline55
2016-Feb-09, 07:53 PM
The question of how the velocity of propagation of an electromagnetic wave remains constant relative to an observer despite the stretch may be unanswerable, even in principle. Nevertheless our observations are best fitted by a model in which that occurs. Since the time interval between successive crest passages is increased in a redshifted waveform, it follows that the distance between crests is increased as reckoned in the observer's frame of reference. Whether the oscillations that create these crests are transverse or longitudinal is beside the point. I do not understand why you have difficulty with one and not the other.

Earlier I was given to believe that "stretching" occurs because "trailing wave crests" have to cross more space than "leading wave crests", which requires a photon have some sort of length in the direction of travel. How can that logic apply when the waves are transverse?

Hornblower
2016-Feb-09, 09:11 PM
Earlier I was given to believe that "stretching" occurs because "trailing wave crests" have to cross more space than "leading wave crests", which requires a photon have some sort of length in the direction of travel. How can that logic apply when the waves are transverse?

Whether what we call crests are attributes of transverse or longitudinal oscillations, the spacing between successive crests is still reckoned along the direction of propagation of the waveform.

It appears that you may have been led down a path of confusion by bad writing on these topics. Some of the misconceptions created by this bad writing have been well addressed in posts early in this thread. As I think I understand it, the particle-like portion of the quantum-mechanical model does not have a linear size corresponding to the wavelength of the wave-like portion of the model. I am too rusty on this to go any farther, after being away from it for over 45 years. I will leave it to others to elaborate, and to correct any bad writing on my part, should there be any.

Ken G
2016-Feb-09, 09:15 PM
Earlier I was given to believe that "stretching" occurs because "trailing wave crests" have to cross more space than "leading wave crests", which requires a photon have some sort of length in the direction of travel. How can that logic apply when the waves are transverse?The photon does not need a length, its "wave packet" does. You can think of the wave packet as being a kind of spread in the location where the photon would be found if you did an experiment to locate it. So if you want to think of uncertainty in the location of the photon as a kind of "length" of the photon in the direction of travel, so be it, but it has nothing to do with whether the wave is transverse or longitudinal. That has to do with the direction of the associated oscillating electric field (which appears in the classical analog when you have many photons in the same wave packet).

mkline55
2016-Feb-10, 12:42 PM
The photon does not need a length, its "wave packet" does. You can think of the wave packet as being a kind of spread in the location where the photon would be found if you did an experiment to locate it. So if you want to think of uncertainty in the location of the photon as a kind of "length" of the photon in the direction of travel, so be it, but it has nothing to do with whether the wave is transverse or longitudinal. That has to do with the direction of the associated oscillating electric field (which appears in the classical analog when you have many photons in the same wave packet).

So the frequency of a photon is directly related to its location uncertainty, which is increased by expansion? What is the formula?

Ken G
2016-Feb-11, 02:47 AM
So the frequency of a photon is directly related to its location uncertainty, which is increased by expansion? What is the formula?It's not the frequency of the photon that is related to its location uncertainty, it is the uncertainty in the frequency. More correctly, the uncertainty in the momentum, but that is easily related to frequency for a photon. The formula is called the "Heisenberg uncertainty principle."

Grey
2016-Feb-11, 02:13 PM
I think you're making this more complicated than it has to be. Let's just look at this classically for a moment (general relativity is, after all, a classical theory). Let's say we fire a 1000 meter long pulse of infrared laser light from some distant galaxy a billion years ago. We'll make our laser emit light at exactly 1000 nm (I'm picking all my numbers to make the math convenient). So there would be exactly 109 wave crests in the pulse, and in a non expanding universe, we'd receive that same 1000 meter pulse, with exactly the same number of wave crests, and we'd measure the same wavelength. But if, say, the universe expands by 10% during the billion years the light travels over that distance, the total distance is now 1.1 x 109 meters. A beam of light isn't a gravitationally bound system, so it will expand right along with the rest of the universe over cosmological time. No new wave crests are created when that happens, so those same 109 wave crests have to fill a greater length, and the only way for that to work is if each wave is a little bit longer.

A photon doesn't have a length, but it does have a wavelength, and that wavelength is increased by cosmic expansion. Note that this isn't unique to photons. Every particle has a wavelength, based on its momentum, and if it's a free particle not interacting with anything else, that wavelength will increase slowly over time due to cosmological expansion. (Actually, even if it is interacting with other things, it's momentum will still change because of this, but generally the momentum changes from its other interactions would be so much larger that it would be hard to notice.) Normally, this is only significant for highly relativistic particles, where a significant part of their energy is kinetic energy, rather than being mostly the rest energy of the particle.

mkline55
2016-Feb-11, 03:04 PM
I think you're making this more complicated than it has to be. Let's just look at this classically for a moment (general relativity is, after all, a classical theory). Let's say we fire a 1000 meter long pulse of infrared laser light from some distant galaxy a billion years ago. We'll make our laser emit light at exactly 1000 nm (I'm picking all my numbers to make the math convenient). So there would be exactly 109 wave crests in the pulse, and in a non expanding universe, we'd receive that same 1000 meter pulse, with exactly the same number of wave crests, and we'd measure the same wavelength. But if, say, the universe expands by 10% during the billion years the light travels over that distance, the total distance is now 1.1 x 109 meters. A beam of light isn't a gravitationally bound system, so it will expand right along with the rest of the universe over cosmological time. No new wave crests are created when that happens, so those same 109 wave crests have to fill a greater length, and the only way for that to work is if each wave is a little bit longer.

Take a close look at your example. The "pulse" you describe consists of 109 separate photons, each of which is fired off at exactly the time when the preceding photon should be 1000 nm away. That's about 3.34-15 seconds. The first crest belongs to the first photon. The second crest belongs to the second photon. The photons are independent of one another. An expanding universe model would separate the photons from one another, so that they would arrive at greater intervals than they were sent. What you seem to be saying is that the intrinsic independent frequency of each individual photon is altered by the arrival rate, but I don't think that's what you mean. How does expansion also reduce the frequency of each individual photon?


A photon doesn't have a length, but it does have a wavelength, and that wavelength is increased by cosmic expansion. Note that this isn't unique to photons. Every particle has a wavelength, based on its momentum, and if it's a free particle not interacting with anything else, that wavelength will increase slowly over time due to cosmological expansion. (Actually, even if it is interacting with other things, it's momentum will still change because of this, but generally the momentum changes from its other interactions would be so much larger that it would be hard to notice.) Normally, this is only significant for highly relativistic particles, where a significant part of their energy is kinetic energy, rather than being mostly the rest energy of the particle.

Is the wavelength nothing more than a mathematical application of frequency and velocity? How is it different from this example: Take a tiny magnet. Spin it pole over pole, at say 10 times per second. Now move it along its axis of spin at a velocity of 1000 meters per second. What is the wavelength? It's 1000/10 = 100 meters. Spin one twice as fast, and move it at the same velocity. It's wavelength = 1000/20 = 50 meters. Is there actually a wave?

I'm asking the same question about photons. Is the light wave similar to the example with magnets?

Grey
2016-Feb-11, 03:28 PM
Take a close look at your example. The "pulse" you describe consists of 109 separate photons, each of which is fired off at exactly the time when the preceding photon should be 1000 nm away. That's about 3.34-15 seconds. The first crest belongs to the first photon. The second crest belongs to the second photon. The photons are independent of one another. An expanding universe model would separate the photons from one another, so that they would arrive at greater intervals than they were sent. What you seem to be saying is that the intrinsic independent frequency of each individual photon is altered by the arrival rate, but I don't think that's what you mean. How does expansion also reduce the frequency of each individual photon?Well, again, because this is an effect from general relativity, and that's a classical theory, it's really better to understand this looking at the waves classically, rather than individual photons. However, even if you do insist on doing so anyway, you can't just say that if you send a billion photons that each one gets a single wave crest. Each photon has a definite wavelength (you definitely can't "divide up" the wave crests in the classical description so that each photon gets a single wave crest), and wavelengths are increased by cosmological expansion. It actually is true that the fractional amount of separation between photons will be increased by exactly the same proportion as the redshift itself (i.e., if the wavelength is increased by 10%, the mean separation between photons will also increase by 10%).

I'd agree that the "mechanism" by which this takes place for a single photon isn't intuitive. Trying to do so is kind of mixing a classical effect with quantum theory; maybe a quantum theory of gravity would provide a better picture. But we run into this kind of thing all the time. For example, a photon of a specific frequency always has a certain amount of energy. Why is that? What is the mechanism that requires this, and makes it impossible to have a photon with more energy but a different frequency? There's no good answer, and there's not necessarily an intuitive reason why this has to be the case. It's just something we've determined through observation.



Is the wavelength nothing more than a mathematical application of frequency and velocity? How is it different from this example: Take a tiny magnet. Spin it pole over pole, at say 10 times per second. Now move it along its axis of spin at a velocity of 1000 meters per second. What is the wavelength? It's 1000/10 = 100 meters. Spin one twice as fast, and move it at the same velocity. It's wavelength = 1000/20 = 50 meters. Is there actually a wave?

I'm asking the same question about photons. Is the light wave similar to the example with magnets?Wavelength, frequency, and velocity are indeed all tightly related. There are only two independent parameters among those three variables (i.e., set any two of those, and that will determine the third). You could technically talk about your flipping magnet as a wave with a wavelength and frequency, but I don't think it would provide you any meaningful information. We generally use wave mechanics to describe something when doing so will give us useful information about how it behaves.

mkline55
2016-Feb-11, 04:20 PM
Thanks for your input Grey. I appreciate your time and effort, but I'm not seeing any clear answer yet to the question. So I'll restate it.

As I understand it, the widely-accepted expansion theory exists primarily as a model to explain cosmological redshift. In short, the expansion model says that space-time expands, and the longer distance/time a light wave travels, the more it gets "stretched", producing cosmological redshift. It seems clear then, that the model depends on a wave extending a distance/time in space in order to be "stretched". Photons are what make up light, so in order to "stretch" the wavelength of photons, it appears that each photon must have some length with can be stretched. However, I am told that photons have transverse waves, not longitudinal waves. What that means is that photons have one state at one location, and another state at another location, but not that photons exist simultaneously in both locations in both states as well as all locations and states between. That leads to the question of what it is that expansion theory stretches. Clearly, if this is WHY the expansion model exists, then it must have a good explanation of how it stretches transverse photonic waves.

Grey
2016-Feb-11, 05:00 PM
Clearly, if this is WHY the expansion model exists, then it must have a good explanation of how it stretches transverse photonic waves.To some extent, I disagree the there must be a good explanation. General relativity is a classical theory. It's great for describing strong gravitational effects and the evolution of the universe as a whole, including cosmological expansion. Quantum theory is what introduces the idea of light as individual photons, and is excellent at describing interactions between individual particles on the smallest of scales. One of the great frustrations of modern physics is that we don't have a single theory that encompasses both of these, allowing us to describe both quantum effects and gravitational (or cosmological-scale) effects at the same time. We'd like there to be such a theory, and we know some of the features it would have to have, and we have some predictions based on trying to combine the two (such as Hawking radiation), but nobody has been able to come up with one combined theory.

So for now, we go along as we've done, using general relativity to describe cosmological expansion (and in these cases, light is essentially treated as a classical electromagnetic wave most of the time), and when we want to talk about individual photons and their interactions, we use quantum theory. We don't worry that it doesn't make intuitive sense that cosmological expansion (or gravitational interactions of any kind, really) could redshift photons when they don't have a size, because neither general relativity nor quantum theory really make intuitive sense about anything anyway.

This continues to work very well, and both theories continue to be well supported by observations, but obviously we'd prefer something more complete. Although, actually, we do this kind of thing more than you might think. We continue to use classical electrodynamics to describe many interactions with electricity, magnetism, and radiation, without worrying about that radiation being "really" made up of individual photons. We use Newtonian mechanics to deal with most questions of basic mechanics and gravity, treating gravity as a force, without worrying about the fact that it's "really" curved spacetime (or maybe it's "really" an interaction with a massless spin-2 boson!).

If you find this a frustrating state of affairs, well, now you know how physicists feel, and why a quantum theory of gravity is something so many people have worked on trying to develop. ;)

mkline55
2016-Feb-12, 01:07 PM
To some extent, I disagree the there must be a good explanation. General relativity is a classical theory. It's great for describing strong gravitational effects and the evolution of the universe as a whole, including cosmological expansion. Quantum theory is what introduces the idea of light as individual photons, and is excellent at describing interactions between individual particles on the smallest of scales. One of the great frustrations of modern physics is that we don't have a single theory that encompasses both of these, allowing us to describe both quantum effects and gravitational (or cosmological-scale) effects at the same time. We'd like there to be such a theory, and we know some of the features it would have to have, and we have some predictions based on trying to combine the two (such as Hawking radiation), but nobody has been able to come up with one combined theory.

So for now, we go along as we've done, using general relativity to describe cosmological expansion (and in these cases, light is essentially treated as a classical electromagnetic wave most of the time), and when we want to talk about individual photons and their interactions, we use quantum theory. We don't worry that it doesn't make intuitive sense that cosmological expansion (or gravitational interactions of any kind, really) could redshift photons when they don't have a size, because neither general relativity nor quantum theory really make intuitive sense about anything anyway.

This continues to work very well, and both theories continue to be well supported by observations, but obviously we'd prefer something more complete. Although, actually, we do this kind of thing more than you might think. We continue to use classical electrodynamics to describe many interactions with electricity, magnetism, and radiation, without worrying about that radiation being "really" made up of individual photons. We use Newtonian mechanics to deal with most questions of basic mechanics and gravity, treating gravity as a force, without worrying about the fact that it's "really" curved spacetime (or maybe it's "really" an interaction with a massless spin-2 boson!).

If you find this a frustrating state of affairs, well, now you know how physicists feel, and why a quantum theory of gravity is something so many people have worked on trying to develop. ;)

Here's the definition of classical electromagnetic radiation from Wiki (https://en.wikipedia.org/wiki/Electromagnetic_radiation):

Classically, electromagnetic radiation consists of electromagnetic waves, which are synchronized oscillations of electric and magnetic fields that propagate at the speed of light through a vacuum. The oscillations of the two fields are perpendicular to each other and perpendicular to the direction of energy and wave propagation, forming a transverse wave.

That is exactly what we've been describing, and which you throw aside with the statement, "We don't worry that it doesn't make intuitive sense that cosmological expansion (or gravitational interactions of any kind, really) could redshift photons when they don't have a size," in order to make the inflation process palatable.

The inflation model is intrinsically tied to explaining cosmological redshift. Without cosmological redshift, the inflation model would not exist. In simple terms it explains cosmological redshift as a stretching of space which stretches light waves. It seems that at its core it must explain how stretching space can stretch light waves. If that explanation flies in the face of other mainstream theories, then shouldn't the model explain why that is acceptable? How can "We don't worry about it" be an acceptable answer?

Cougar
2016-Feb-12, 04:43 PM
The inflation model is intrinsically tied to explaining cosmological redshift.

I don't follow. The redshift-distance relation was known for 50 years before the idea of inflation was brought forward. Inflation explains three glaring problems that simple expansion couldn't explain, but inflation doesn't exactly explain the ongoing expansion.


Without cosmological redshift, the inflation model would not exist. In simple terms it explains cosmological redshift as a stretching of space which stretches light waves.

The expansion alone "explains" that, although that's a GR analogy, which, as Grey has very eloquently written, does not address the QM perspective.

Grey
2016-Feb-12, 04:57 PM
That is exactly what we've been describing, and which you throw aside with the statement, "We don't worry that it doesn't make intuitive sense that cosmological expansion (or gravitational interactions of any kind, really) could redshift photons when they don't have a size," in order to make the inflation process palatable.No, you've been talking about photons, which don't have a size. Classical electromagnetic waves definitely have a length (you might be able to say they don't really have a width, I suppose, since the transverse oscillations are in the electromagnetic field, not in any physical dimensions, but even the most tightly focused beam of light will have some extent in the transverse direction). General relativity works just fine to describe how classical electromagnetic waves redshift during cosmological expansion. I gave the "mental picture" version of that above: as space expands, the distance between successive wave crests get farther apart. The argument you presented to that picture was to try to break the light into photons, a quantum picture. But if you're looking for a "mental picture", then redshifts of all types are really visualized better as an issue of classical electrodynamics, rather than trying to view light as made of photons. Both views are useful, and I don't think it's reasonable to say that either is more "real", any more than it makes sense to say an electron "really is" a particle or "really is" a wave. An electron is an electron, sometimes best understood as a wave and sometimes best understood as a particle. Similarly, light is light, and it's sometimes best viewed as a classical electromagnetic wave, and sometimes best viewed as made up of discrete quanta. We use whichever picture best helps us understand a given phenomenon, rather than insisting that only one of them is "real".

It's true that general relativity and quantum theory don't work together as they stand. We do indeed find that extremely frustrating, and there are always people working on trying to come up with a way to modify one or both so that they can be combined into a single theory. Nobody has managed that yet. We also keep trying to extend our observations of both theories, hoping to find a place where observations don't match the prediction, possibly giving us some further clues about how theory should be modified. But so far, that hasn't worked either. Every test just confirms those theories to better and better degrees (for example, see the recent observations of gravitational waves that match the predictions from general relativity beautifully, or the recent confirmation of the Higgs boson as support for the standard model of particle physics). The cases where you need both theories at the same time are things that are hard to engineer (they generally involve extremely high energy density), so we aren't likely to be able to do any controlled experiments in the near future.

So I suppose you could try to argue that general relativity doesn't make sense because it doesn't fit with quantum theory, and quantum theory is so well tested. But you could argue equally well that quantum theory doesn't make sense because it doesn't fit with general relativity, and general relativity is also very well tested. But the truth is that it doesn't make much sense to throw out either of them, because in their own domains, they both work extremely well. We definitely observe cosmological redshift. Light from distant galaxies really does change its wavelength on the way over here, and using various distance markers it really does work well to describe that as a result of cosmological expansion. Moreover, other predictions from general relativity (for example, that not only should distant events be seen as redshifted, they should also be time dilated from our perspective) are likewise borne out by observation. Alternate explanations have been tried, and don't work well.

mkline55
2016-Feb-12, 05:16 PM
When the most sensitive telescopes are collecting data from very distant sources, are they measuring streams of light waves to determine frequency, or are they accumulating individual photons to determine frequency?

Grey
2016-Feb-12, 05:32 PM
When the most sensitive telescopes are collecting data from very distant sources, are they measuring streams of light waves to determine frequency, or are they accumulating individual photons to determine frequency?These days, we're using CCDs, which definitely interact with light as though it were made of individual photons. But the interactions with the lenses or mirrors that focus that light onto the CCD are probably best understood thinking about light rays classically. ;)

This isn't really any more mysterious than the fact that in a double slit experiment, light acts very wavelike in the sense that it produces an interference pattern, but also very particle-like when interacting with a typical detector. Which is to say, it's actually pretty mysterious, but also seems to be the way the world actually works, and we've known about it long enough to kind of get used to the idea.

mkline55
2016-Feb-12, 06:14 PM
Does the expansion theory indicate a maximum wavelength for electromagnetic radiation?

Grey
2016-Feb-12, 06:29 PM
Does the expansion theory indicate a maximum wavelength for electromagnetic radiation?I don't think there's any theoretical upper limit, from either general relativity or quantum theory. We've actually used radio waves in the ELF range (wavelengths of 10,000 km to 100,000 km) to communicate with submarines, since shorter wavelength radio waves don't travel well through water. But it's hard to detect such low frequency radiation. It's easy to emit low frequency radiation, though. Just take a charged object and wiggle it back and forth very slowly, and you can, in principle, make radiation with a wavelength as long as you'd like.

mkline55
2016-Feb-12, 07:03 PM
I really appreciate your input Grey. I don't know how people put up with me sometimes. If I may, I'd like to summarize in my own words. Please feel free to correct my errors.

The expansion model says redshift occurs because space itself expands while light waves propagate through it. These waves "stretch" because leading wave crests travel through less space than trailing crests. The basis for this is the wave-like property of light, and the theory does not address any fundamental nature of photon structure like size, length, etc. except for velocity, frequency and wavelength.

mkline55
2016-Feb-12, 08:03 PM
Okay, now I have a problem. I created an analog model of wave expansion using the above information. It's just a spreadsheet where I show where the leading and trailing wave crests would be as the wave travels through an expanding space. Sure enough, the distance between crests increases with distance. The only problem is that the expansion is not linear. The farther apart the crests become, the faster they recede from one another. In effect, the whole stretching process accelerates over time. Just to verify, I tried using different starting wavelengths, and the bigger waves expand at a faster rate. If, for example, I compare two waves starting at the same point and time where one has twice the wavelength, the one with twice the wavelength expands twice as much. If I understand the expansion theory correctly, the expansion should be linear, and should be the same amount for any wave, not be proportional to the wavelength. What part of this am I getting wrong?

Grey
2016-Feb-12, 10:13 PM
If, for example, I compare two waves starting at the same point and time where one has twice the wavelength, the one with twice the wavelength expands twice as much. If I understand the expansion theory correctly, the expansion should be linear, and should be the same amount for any wave, not be proportional to the wavelength. What part of this am I getting wrong?Actually, you got this right. When light is redshifted, the change in wavelength is proportional to the wavelength. So for a z of say, 0.5, all wavelengths are increased by 50% (you'd multiply the emitted wavelength by 1 + z, or 1.5 in this case, to get the expected received wavelength). This isn't just true for cosmological redshifts, it's also true for gravitational redshifts and Doppler redshifts based on velocity. For that matter, this is also true of Doppler shifts for sound waves.

mkline55
2016-Feb-16, 01:37 PM
Thanks Grey.

Does this mean that cosmological redshift has a compounding effect as well? For example, if a wavelength doubles from 10 units to 20 units through first "half" of its journey, wouldn't it double again from 20 units to 40 units over the second "half"? I put "half" in quotes, because that's either a time or distance value, but in whose frame of reference I don't know. At least that's what my analog model shows. I believe I need to add a factor to my model to include the expansion ahead of the wave - meaning that the space between the current location of the wave front and the ultimate destination is expanding as well. It should come out as a decreasing recession of some sort. Is there a specific name for that effect?

Grey
2016-Feb-16, 05:21 PM
Does this mean that cosmological redshift has a compounding effect as well? For example, if a wavelength doubles from 10 units to 20 units through first "half" of its journey, wouldn't it double again from 20 units to 40 units over the second "half"?Pretty much, assuming that the universe expands by a factor of 4 during that time period. One of the convenient things about cosmoglogical redshift is that it's just the same as the change in scale factor of the universe during travel.


I put "half" in quotes, because that's either a time or distance value, but in whose frame of reference I don't know.The easiest time frame to use when dealing with cosmology is "comoving coordinates", where you imagine clocks spread out through the universe all moving with the Hubble flow, and measure time by them. Since all of them are "stationary" (even though they get farther apart), they all read the same time in their respective local frames.


At least that's what my analog model shows. I believe I need to add a factor to my model to include the expansion ahead of the wave - meaning that the space between the current location of the wave front and the ultimate destination is expanding as well. It should come out as a decreasing recession of some sort. Is there a specific name for that effect?I'm not sure if there is. And yes, this does have an indirect effect: the light takes longer to get there than it would in a non-expanding universe. That's why you end up with varying ways to state the distance of some distant galaxy. You could use the distance it was at when the light was first emitted, the distance it would be now, or the distance the light itself travelled, all three of which will generally be different.