EM fields exhibit cosmological redshift caused by the expansion of space.
Although the photon is considered a point particle, is it possible that single photons will experience any effects caused by the expansion of space?
Due to the fact that the light source and the observer are moving away from each other, yes. It’s called the Doppler effect. And the farther two objects are apart, the faster away from each other they’ll be moving, on average.
Um … could you be more specific here? It sounds like you’re asking whether the expansion of space could have any effect on a single particle by itself.
A single particle would not feel any effect because is there is none in its local rest frame. So for instance, if you got in your spaceship and headed for NGC 21190, you wouldn’t notice the space expanding as you went; instead you’d see the speed that that galaxy (as well as the Milky Way) is moving change as the expansion slowed down or sped up. Photons do not have rest frames, but the same holds true.
I don’t think it is quite true that the cosmic expansion has no effect on a local rest frame. The expansion of space applies universally. If you were to set two particles 1m apart in an inertial reference frame, and somehow eliminate all forces on and between the particles, then if you check back on the particles one billion years later, they will be 6.6 cm farther apart due to the expansion of the space between them (this experiment can’t be done in reality due to quantum uncertainty and the impossibility of blocking gravity). Strictly speaking a local inertial frame can only exist at a single point; there are generally no extended inertial frames permitted in general relativity.
I’m taking a class in cosmology right now, and my professor derived the general relativistic redshift formula by considering the effect of cosmic expansion on the wavelength of light between the time it is emitted and the time it is detected. I believe this is generally accepted.
Of course, the front end of your space ship is a small distance away from the back end of your space ship. Is your space ship expanding as the universe expands? If not, does that mean that the atoms that make up your space ship are very very slowly “falling” toward one another ad losing (gravitational? electromagnetic?) potential energy in order to keep the space ship the same size?
JasonFin, you are correct. However, I was treating the spaceship as a point, which is okay to a certain precision. If you want more precision, you simply make the spaceship smaller. If you want arbitrary precision, you make it a photon.
tracer, a human-sized spaceship does not expand with the Universe. However, I do not know if that means it’s losing energy, since I don’t know how we define zero-point energy in an expanding universe. Anyone?
tracer
It sounds like you’re asking whether the expansion of space could have any effect on a single particle by itself.
Yes. Perhaps there is more to just the effect of space expanding on waves of light. Can it affect the photon itself?
Jasonfin
I’m taking a class in cosmology right now, and my professor derived the general relativistic redshift formula by considering the effect of cosmic expansion on the wavelength of light between the time it is emitted and the time it is detected. I believe this is generally accepted.
Yes, but can you ask your professor whether the expansion of space can have an effect on a single photon?
What kind of effects? Remember that c is a constant.
Qeue, the problem with the idea that the expansion of space has an effect on a photon is the question, “from whose perspective does it have an effect?” A photon doesn’t have a perspective because it travels at c, so is not at rest in any local reference frame. We must provide a frame in which to answer this question. In cosmology people normally consider events from the perspective of “comoving” frames, which expand along with the universe, so over time the distance between points with fixed coordinates will increase (the coordinates themselves are unitless, but are multiplied by a scale factor with units of length to find proper distances). It has been demonstrated to my satisfaction that in such a frame the wavelength of radiation increases over time, and this must apply even to a single photon. Comoving frames are a mathematically neat solution to the problem of extending a local inertial frame to cover distant events, but I know it is not the only solution. I don’t know enough about general relativity to say anything about the properties of other types of extended reference frames. It is possible that in some types of global frames photons are not affected by the expansion of space.
JasonFin
Uh, I don’t think reference frames has anything to do with question. Look at this way:
Lambda = h*c / E
From this equation we can determine the wavelength of a photon, right?
So for a photon with 2eV energy we get:
6.625 x 10^-34 x 3 x 10^8/(1.6 x 10^-19 x 2) = 621 nm.
How does the expansion of space affect this measurement if the photon must travel millions or billions of lightyears?
The photon has less energy as measured by us because the expansion of space robs it of energy. Therefore its wavelength gets larger. It is like a ball rolling up an ever steepening hill, getting lighter as it goes in order to maintain the same speed.
Reference frames are crucial here. The equation you have there is true in any given frame, but the values Lambda and E are not frame-invariant. So there’s no such thing as “the” wavelength of a photon, only the wavelength in a given frame.
What would be the difference between a co-moving frame of the wavelength as compared with the rest frame of a lab on Earth?
Would it appear as a point particle in a particular frame?
There is no such thing as a comoving frame for a photon. Photons appear as point particles in every frame.
I’d just like to point out that according to Superstring Theory, there are no point particles - the most fundamental component of matter is a (1-dimensional) string or higher dimensional “p-brane”.
Achernar
If photons appear as point particles in every frame, how is it that they can have a wavelength?
I have read of experiments where they have measured the wavelength of 2 photons.
Okay, that’s a fair question. The thing is, wavelength is not a physical extension in space. So if a photon has a wavelength of 10cm in your frame, you can’t say that at time T it extended from point A to point B, where A and B are 10cm apart. Wavelength does behave like a Lorentzian distance to a certain degree, but if you were to apply that theory to it, the “rest wavelength” would be infinite.
Achernar
So what purpose does the concept of wavelength of a photon serve if photons must be viewed as point particles?
I would state that the wavelength of a photon is stretched proportionally to the stretching of space and that of the distance the photon traveled.
Why would this not be a valid statement?
It’s just a property of a particle. It describes the momentum and energy of the photon.