Cosmological Inflation: If Photon expands, why not other matter?

I keep repeatedly reading in many Stack Exchange and Quora questions that space of universe expands but particles (matter) don't, see e.g. this Phys.SE post. The reason given is that particles are governed by much stronger Electromagnetic and Nuclear forces, where space expansion is relevant to only on much larger inter galactic scale where all natural forces including gravity is weaker.

How come photons in CMB (Cosmic Wave Background) which is also a kind of matter has expanded to radio wave range from gamma range? Is photon not affected by nuclear, Electromagnetic forces?

If the answer is Photons are weightless while subatomic particle like electron has mass, then does it mean space expansion affects other massless particles as well? Have the other massless particles proven to show expansion since big bang?

I am confused why space expansion affects Photons but not other forms of matter.

• BTW, the CMB hasn't expanded from gamma. The temperature of the universe at recombination was around 4000 K, so the CMB spectrum had its peak in visible light when it was originally emitted. You can see an approximation of the orange colour of the universe when it was starting to become transparent at the end of this answer: physics.stackexchange.com/a/133943/123208 – PM 2Ring May 13 '19 at 2:22
• By the photon "expansion" you are referring to the cosmological redshift. However, this redshift is only the effect of the frame of reference. In our frame of reference these photons were emitted already redshifted and the redshift did not increase during their travel. Also, in the frame of reference of the emitter, these photons are not redshifted at all while traveling through the expanding space. So the wavelength of light is not stretched by the space expansion per se (neglecting the acceleration). It only looks to us this way in our reference frame. – safesphere May 21 '19 at 5:24

The photon does not expand, his wavelength does. Wavelength of the photon is simply width of one period of the wave. This distance is completly determined by the nature of photon and geometry. The naure of photon doesnt change due to equivalence principle in GR, but the geometry does and so does the wavelength.

To compute the change in the period you would imagine that you started to send wave of period $$T_0$$ from some event $$(t_0,x_0)$$. This wave will travel with speed of light to some event $$(t_1,x_1)$$ where it is recieved. But sending full period of wave is not instanteneous. The transmition of one period would end after a time $$T_0$$ passed at the event $$(t_0+T_0,x_0)$$. This will also travel with speed of light until it is recieved at $$(t_1+T_1,x_1)$$. But because the space is expanding, the space between these two "points of wave" exapnds too and when they come to reciever, they will be further appart that they have been when they were first sent.

Here it is in the detail:

Let us have photon traveling in expanding universe in direction of x-coordinate. Forgetting other spatial coordinates, the metric in expanding universe (FLRW) metric is:

$$ds^2=-c^2dt^2+a(t)^2dx^2$$ where $$a(t)$$ is some positive function of time.

The photon moves on null curves, that is: $$0=-c^2dt^2+a(t)^2dx^2\rightarrow dx=\frac{c}{a(t)}dt$$

Now asume that the light signal was send from an event $$(t_0,x_0)$$ and that the period of the light is $$T_0$$. That means if the signal was started to be sent in $$(t_0,x_0)$$, the sending of one period was finished in $$(t_0+T_0,x_0)$$.

The light travels through space, where observer starts recieving the signal in the event $$(t_1,x_1)$$. How long it takes for him to stop recieving the signal (which would be one period $$T_1$$)? The equation for moving photon gives: $$\int_{x_0}^{x_1} dx=\int_{t_0}^{t_1}\frac{c}{a(t)}dt=\int_{t_0+T_0}^{t_1+T_1}\frac{c}{a(t)}dt$$ or: $$0=\int_{t_1}^{t_1+T_1}\frac{dt}{a(t)}-\int_{t_0}^{t_0+T_0}\frac{dt}{a(t)}$$

from which $$T_2$$ can be computed. Since the integral tells you the area under a curve $$1/a(t)$$, this equations is an equation for width of two equal areas at two different points so the $$T_0$$ and $$T_1$$ wont be equal in general.

The photon does not expand. Photons are always size-zero (or at least, "smaller than we can measure") particles. What increases is the photon wavelength. Wavelength is not the physical size of an object, but rather a characteristic related to, but not the same as, the energy it carries and which physically determines the length scale at which similarly-configured particles will, in aggregate (either together in space or sequentially in time, or some mixture), manifest wave phenomena like diffraction.

Quantum mechanically, wavelength is related to how information-poor the particle position is: particles with shorter wavelength can have higher-information positions. But not having a highly-precise position is not the same thing as being a physically large object.

The same thing would occur if you shot an electron into deep space and it persisted for ages as well. The electron is point-sized as well, and massive, but its wavelength will expand just same.

• Good answer, but more precisely, the wavelength does not expand with the space expansion. The redshift we see is only the effect of the frame of reference. Consider a mirror on a hypothetical long solid rod attached to a source of light. The light travels through the expanding space, reflects back, and travels again through the expanding space. It will arrive back to the emitter with a zero redshift (assuming no acceleration). – safesphere May 21 '19 at 5:48

You are right, this has been observed with photons. As photons travel through intergalactic voids of space, where expansion dominates, the wavelength of the photons gets stretched with the expansion of space itself, so the photons frequency gets smaller, they lose energy.

Now inside galaxies, where gravity dominates, space is not expanding. Photons' wavelengths traveling inside galaxies do not get stretched, so they do not lose energy. The important thing is, that matter does have gravitational effects, and these effects become dominant if matter exists in large amounts, thus it will dominate over expansion (dark energy).

Now you are asking, whether if a single atom is traveling through expanding space, does it get stretched? The answer is what you suggest, since an atom is dominated by strong and EM forces, and those are dominating over dark energy, the atom will not get stretched. The protons do not get stretched either that we receive from far away galaxies. The reason is the same, the proton is dominated by the strong and EM forces.

• I was repeatedly told the redshift is due to a Doppler effect. What's going on here? – Winston May 12 '19 at 5:09
• I don't understand why you would ask if matter expands in your next question if you answer here that it does not. Any reason? – Winston May 12 '19 at 5:11
• @Exocytosis The other answers are talking about point particles like the electron. I am talking about composite particles, like the proton and atom. Maybe I will ask a separate question about the strong force and dark energy. – Árpád Szendrei May 12 '19 at 16:06
• Ah ok I see, thank you. – Winston May 12 '19 at 18:01
• "inside galaxies, where gravity dominates, space is not expanding" - Space itself is expanding everywhere, including inside galaxies. However, galaxies are not expanding with the space expansions, because they are held together by gravity. – safesphere May 21 '19 at 5:06