B What is conformal time?

[Dark85]

TL;DR Summary

The wikipedia pages for the Particle horizon of the universe has the following statement:

"Due to the expansion of the universe, it is not simply the age of the universe times the speed of light (approximately 13.8 billion light-years), but rather the speed of light times the conformal time."

What is conformal time in simple terms? Why can't we just multiply the age of the universe times the speed of light?

The wikipedia pages for the Particle horizon of the universe has the following statement:

"Due to the expansion of the universe, it is not simply the age of the universe times the speed of light (approximately 13.8 billion light-years), but rather the speed of light times the conformal time."

What is conformal time in simple terms? Why can't we just multiply the age of the universe times the speed of light?

 

[phinds]

Why can't we just multiply the age of the universe times the speed of light?

Please stop and think about what "expansion" means. The galaxies at the edge of our observable universe emitted the light that we now see some 13+ billion years ago, BUT ... they have been moving away from us for all of those years and are now about 50 billion light years away.

 

[PeroK]

What is conformal time in simple terms?

There's a discussion about how to calculate conformal time here. I'm not sure it meets your criterion of simple.

https://physics.stackexchange.com/questions/455693/how-exactly-is-conformal-time-eta-calculated

 

[Ibix]

What is conformal time in simple terms?

See figure 1 in Taylor and Lineweaver, which is a distance-vs-time chart of the universe.

The top chart has a horizontal scale in units of measured distance and the vertical scale in units of wristwatch time for an observer in a galaxy. Notice the particle horizon is not a straight line, which is why you can't use your linear assumption.

The middle chart is the same thing but rescaled into comoving coordinates - so the horizontal scale is stretched by different amounts at different times so that galaxies have constant coordinates. This is why the fine grey lines representing galaxies in this diagram are vertical while they were curved away from our location (the origin of coordinates) in the first one.

The bottom chart is the same as the middle one except that the vertical scale has been stretched so that light travels on 45° lines. This is the definition of conformal time - it is a rescaled time coordinate chosen so that for light the comoving coordinate distance travelled per unit conformal time is constant.

 

[Ibix]

The point is that the scale factor of the universe is time varying in a non-trivial manner. Sometimes maths is easier if we move that complexity into the definition of our coordinates, and in those cases we use comoving distance and conformal time.

 

[Jaime Rudas]

I think conformal time could be interpreted as the time it would have taken for light to reach us if the universe were static, that is, if throughout its history the galaxies had been at the same distance from us as they are currently.

 

[phinds]

I think conformal time could be interpreted as the time it would have taken for light to reach us if the universe were static, that is, if throughout its history the galaxies had been at the same distance from us as they are currently.

Hm ... given that the recession velocity varies with distance, I don't think so.

 

[Jaime Rudas]

Why can't we just multiply the age of the universe times the speed of light?

The particle horizon refers to the current distance of the most distant (comoving) object that we can, in principle, observe today. The light coming from that object was emitted 13.8 billion years ago and, since the speed of light is constant, we can conclude that this light has traveled 13.8 billion light-years. However, during those 13.8 billion years, the universe has expanded so much that the object that emitted that light (and, therefore, the particle horizon) is currently about 46.5 billion light-years away.

 

[Jaime Rudas]

Hm ... given that the recession velocity varies with distance, I don't think so.

I don't see how this affects what I proposed. However, if you look at the bottom panel of Figure 1 in Davis & Lineweaver (which is where conformal time is plotted), you can see that the light cone is a straight line, that is, compatible with the Minkowski metric.

 

[phinds]

I don't see how this affects what I proposed. However, if you look at the bottom panel of Figure 1 in Davis & Lineweaver (which is where conformal time is plotted), you can see that the light cone is a straight line, that is, compatible with the Minkowski metric.

Well, I was taking your statement

I think conformal time could be interpreted as the time it would have taken for light to reach us if the universe were static, that is, if throughout its history the galaxies had been at the same distance from us as they are currently.

to mean that the time would be equivalent to a static universe where the edge of the O.U. was ~50billion LY away, implying a 50billion year age. Guess I interpreted it wrong.

 

[Jaime Rudas]

Well, I was taking your statement

to mean that the time would be equivalent to a static universe where the edge of the O.U. was ~50billion LY away, implying a 50billion year age. Guess I interpreted it wrong.

Yes, that's more or less it: conformal time would be equivalent to the time in the last 46.5 billion years of a static universe, as shown in the bottom panel of Figure 1.