# If objects don't move when the universe expands, how can the expansion result in redshift?

I am approaching this topic from a layman's perspective and view this as a logic puzzle, but when someone tries to get me to accept the logic, I'm never convinced by their arguments.

According to the wiki page on the expanding universe, the universe is expanding (which is how we see redshifted light from distant galaxies), however this expansion does not result in the movement of objects across space away from each other. Instead, this expansion is the formation of new space such that all of the objects in space maintain a static relationship with space.

This should mean, that as light produced by a distant light source that is expanding away from us, it is not moving away from the photon. The photon then travels across space, and this trip takes longer as a result of the expansion, but once the photon is in space near to Earth, the earth is not moving away from the light. By the time the light is at the same distance from the telescope as a flashlight held in front of the telescope, the telescope is not moving away from the photon any more than it is moving away from the photon produced by the flashlight.

So, IF the expansion is not the result of motion across space, HOW do we show redshift??????

Another comment, laymans perspective
The whole reason it can make sense that objects far enough away can expand away from us FASTER than the speed of light (which is the reason why telescopes can't see further) is that these objects are not moving across space to achieve this expansion.

Another comment in reference to the Raisin Cake. understanding the expanding universe as a raisin cake swelling, therefore the actual cake that is in contact with any raisin stays in contact with that raisin,, the raisins do not move through the cake,,, APART. BUT, in space, the raisins actually ARE moving through the cake. Also, the PHOTON that travels across space from the distant light source to the telescope, travels across space. additionally, it's NOT useful to think of this transaction of energy in a raisin cake, because the raisins DO travel across space away from each-other as the cake swells, but this is NOT how we can possibly understand objects in space expanding away from us on Earth faster than the speed of light.

• Because saying that space between two objects expands can be formulated also as new space forms, and it is equivalent with respect to doppler to saying that one object moves with respect to the other one. The rest is of relevance in a full cosmological point of view. Space expansion is different than a system expanding in space. But the point is irrilevant in your discussion. Also a simple Doppler formula does not apply as for the history between emission and observation must be taken in account. Both both can be regarded as kind of doppler shift. – Alchimista Apr 8 '19 at 8:28

The redshift is indeed not caused by the movement of the objects, but by the expansion itself. This is a theoretical result from considering the FLRW metric for a light ray traveling on a null geodesic.

A derivation can be found here.

The cosmological redshift $$z$$ is given by $$z+1 = 1/a$$, where $$a$$ is the scale factor (the size of the Universe) at the time the light was emitted. Notice that this result doesn't care how the Universe expanded. In principle, you could imagine a universe which was static when the light was emitted, and static when the light is observed, but expanded by the factor $$a$$ at some point in between, and you'd observe the same redshift as if that universe had expanded gradually in the meantime. This is in sharp contrast to a normal Doppler shift, where in such a hypothetical case, the would be no observed redshift.

Note also that galaxies receding faster than the speed of light $$c$$ is no hindrance for us to see them; all galaxies with a observed redshift larger than $$z\simeq1.4$$ recede faster than $$c$$. The most distant observed galaxy GN-z11 has a redshift of $$z=11.09$$, and recedes at $$v\simeq2.2c$$. When it emitted the light we see, it receded even faster, namely at $$v \simeq 4.3 c$$. See the ant on a rubber rope "paradox" for an intuitive explanation.

If objects don't move when the universe expands, how can the expansion result in redshift?

Because the objects are moving in relation to one another. Neither is moving through space, but space is expanding. So two galaxies that used to be 1 billion light years apart are now 2 billion light years apart.

According to the wiki page on the expanding universe, the universe is expanding (which is how we see redshifted light from distant galaxies), however this expansion does not result in the movement of objects across space away from each other. Instead, this expansion is the formation of new space such that all of the objects in space maintain a static relationship with space.

Yes, they maintain a static relationship with their local space, but not with each other. See the raisin cake analogy. The galaxies are moving apart because they're embedded in space which is expanding.

This should mean, that as light produced by a distant light source that is expanding away from us, it is not moving away from the photon. The photon then travels across space, and this trip takes longer as a result of the expansion, but once the photon is in space near to Earth, the earth is not moving away from the light. By the time the light is at the same distance from the telescope as a flashlight held in front of the telescope, the telescope is not moving away from the photon any more than it is moving away from the photon produced by the flashlight. So, IF the expansion is not the result of motion across space, HOW do we show redshift?

Because space expands, so two galaxies are moving apart, so they have a relative speed, so the photon looks redshifted. It hasn't actually been redshifted. It hasn't lost any energy. When you move away from a source of light it looks redshifted, but the light didn't change, instead you changed. Cosmologist Tamara Davis says the same thing in the 2010 Scientific American article Is the Universe leaking energy?:

Image by Tamara Davis and Scientific American, see Is the Universe leaking energy?

The whole reason it can make sense that objects far enough away can expand away from us FASTER than the speed of light (which is the reason why telescopes can't see further) is that these objects are not moving across space to achieve this expansion.

We can see galaxies that have always been receding from us faster than light. See Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe by Tamara Davis and Charles Lineweaver. Also see the ant on the rubber rope

• Well, all Ive done yet is go to work and read these relpies, but i do plan to look up some of the recommended reading. ,,, – tsmspace Apr 9 '19 at 2:37
• however,,, i still want to rebutle, that still in my perspective, I see it this way. If the galaxies are now further apart, it has no bearing on the speed of the photon relative to the telescope on impact. As the photon nears the telescope, space is expanding less between them, until just before the photon hits the telescope, there will be virtually no expansion between them, therefore the photon should still impact as if it were travelling the speed of light and the earth is not moving away from it significantly. – tsmspace Apr 9 '19 at 2:41
• @tsmspace : don't overthink it. Tamara Davis was describing galactic redshift as something that can be likened to Doppler shift, and I think that's the correct approach. Do read the article. I think the wrong approach is to think that the CMB photon somehow loses energy via some mysterious mechanism. I say that because I know of no situation wherein energy is not conserved. – John Duffield Apr 9 '19 at 22:19