Length Contraction & Galaxies: Time Dilation Adjustments

[vinven7]

Since galaxies are moving away from us, shouldn't they be contracted in length than they would be if they were at rest (wrt us)? In other words, are we observing increasingly shrunken galaxies as we look deeper into space?

When measuring supernova light curves, we do adjust for time dilation, so it seems natural that length would also be shortened. But I have not heard this explicitly mentioned as such.

 

[andrewkirk]

Since galaxies are moving away from us, shouldn't they be contracted in length than they would be if they were at rest (wrt us)?

Is it Lorentz contraction that you have in mind? Lorentz contraction does not apply here because it is only applicable to two objects that are in the same inertial frame. Galaxies are too far apart from one another to be in the same inertial frame, because there is too much curvature between them. A frame that was inertial for one galaxy would not even be approximately inertial for the other.

 

[mathman]

Unless the galaxy is going away from us at a significant fraction of the speed of light, there wouldn't be any noticeable contraction.

 

[PeterDonis]

Unless the galaxy is going away from us at a significant fraction of the speed of light

"Going away from us" in what sense? Spacetime is curved; there is not a single inertial frame that covers both us and the distant galaxy. So there is no invariant meaning to the "relative speed" of us and the other galaxy.

 

[PeterDonis]

When measuring supernova light curves, we do adjust for time dilation

No, we adjust for redshift, which is not the same thing. There is no way to properly define the "time dilation" of a distant object in an expanding universe. But we can directly observe the redshift of light emitted by a distant object, and adjust for that.

 

[sweet springs]

Since galaxies are moving away from us, shouldn't they be contracted in length than they would be if they were at rest (wrt us)? In other words, are we observing increasingly shrunken galaxies as we look deeper into space?

Yes, in the following sense. Let I be an agent from a galaxy far away. I am so cordial to my galaxy that I keep the distance to home constant. I can do that by adjusting observed hydrogen spectrum from home galaxy be normal. In this galaxy I was dispatched, I am moving very fast. I report home that time dilation and lengh contraction take place in this galaxy that is moving very fast.

 

[vinven7]

No, we adjust for redshift, which is not the same thing. There is no way to properly define the "time dilation" of a distant object in an expanding universe. But we can directly observe the redshift of light emitted by a distant object, and adjust for that.

Thank you. I think I misunderstood what the origin of "time dilation" is and PF has saved me yet again!

I have a follow up question. Let us say that we have a galaxy at redshift z and some Hubble velocity 'v'. This galaxy is observed to have a cosmological time dilation by a factor 'B' {ie, a supernova would fade in time B*T when observed in this galaxy as compared to a time T when observed in our rest frame, say}. Does the factor B work out to be the same as what we would observe if the galaxy had been in our inertial frame moving with a velocity v? ie, how does B compare with 1/sqrt(1-(v/c)^2)

 

[PeterDonis]

Let us say that we have a galaxy at redshift z and some Hubble velocity 'v'.

What is the "Hubble velocity"? Do you mean the speed of light times the redshift? In a curved spacetime, there is no well-defined meaning to the relative velocity of two objects that are spatially separated.

his galaxy is observed to have a cosmological time dilation by a factor 'B' {ie, a supernova would fade in time B*T when observed in this galaxy as compared to a time T when observed in our rest frame, say}

Once again, this is not "time dilation"; this is redshift. The factor B is just 1 + z, where z is the redshift.

how does B compare with 1/sqrt(1-(v/c)^2)

It has no relation, because v isn't well-defined to begin with. See above.

 

[PeterDonis]

I am so cordial to my galaxy that I keep the distance to home constant.

This only works if you are close enough to your home galaxy. If you are further away than the Hubble distance, you would have to move faster than light to keep the distance to home constant.