Help Understanding the Hubble Constant's Units

[skynr13]

TL;DR

If the Hubble Constant is 45 miles (73 kilometers) per second per megaparsec. What is this converted to miles (or required specific length) per second, minute or hour?

If the Hubble Constant is 45 miles (73 kilometers) per second per megaparsec. What is this converted to miles (or required specific length) per second , minute or hour? The idea of this question is to find a basic speed of the Hubble Constant that anyone can relate to. Like if I was to say to someone the Hubble Constant is 45 miles (73 kilometers) per second per megaparsec, no one can easily understand how fast the Universe is expanding, because a Megaparsec is just too hard to conceive. But if someone in this Physics forum convert 45 miles (73 kilometers) per second per megaparsec into something more conceivable like one foot an hour then it is more understandable for a common non-scientist to understand.
Thanks for your help, kevin.

 

[Hill]

TL;DR: If the Hubble Constant is 45 miles (73 kilometers) per second per megaparsec. What is this converted to miles (or required specific length) per second, minute or hour?

If the Hubble Constant is 45 miles (73 kilometers) per second per megaparsec. What is this converted to miles (or required specific length) per second , minute or hour? The idea of this question is to find a basic speed of the Hubble Constant that anyone can relate to. Like if I was to say to someone the Hubble Constant is 45 miles (73 kilometers) per second per megaparsec, no one can easily understand how fast the Universe is expanding, because a Megaparsec is just too hard to conceive. But if someone in this Physics forum convert 45 miles (73 kilometers) per second per megaparsec into something more conceivable like one foot an hour then it is more understandable for a common non-scientist to understand.
Thanks for your help, kevin.

It can't be done because the units of the Hubble Constant are not the units of speed, but rather the units of 1/time.

 

[Filip Larsen]

The linear expansion rate corresponds to around 7.1⋅10^-11 1/year so you can get the "equivalent speed = distance/year" if you multiply this number by a distance. For instance, at the Moons distance from Earth the Hubble expansion would correspond to a speed of around 2 cm/year. (Note that this is just a change of scale and does not as such mean linear Hubble expansion is applicable to the Earth-Moon system or anything local. The Moon actually recedes from the Earth but due to other reasons).

 

[Ibix]

If the Hubble Constant is 45 miles (73 kilometers) per second per megaparsec. What is this converted to miles (or required specific length) per second , minute or hour?

It doesn't work like that. How it works is that something one megaparsec away recedes from us at 73km/s. Something two megaparsecs away recedes at 2 × 73 = 146km/s. Something ten megaparsecs away recedes at 10 × 73 = 730km/s. Recession speed increases with distance, so there isn't a single speed value that can be stated.

Note that there is significant random motion of galaxies on top of this pattern, and bound systems such as individual galaxies don't expand at all.

 

[Bandersnatch]

As has been said, you can't get a velocity out of the Hubble constant, because its dimension is that of a frequency. I can appreciate that it's not very helpful as far as making it relatable, though.

But maybe this will be - since H0 is stated as some speed per some distance, it tells you how long it'd take to cover that distance at the given speed. Let's call this time t.
So the 70-ish km/s/Mpc tells you how long it would take to cover a megaparsec while travelling at 70 km/s.
And, since a longer/shorter distance has a proportionally faster/slower speed associated with it - as per the Hubble law - that time t is the same for any distance in the universe.
2 Mpc at 140 km/s and 10 Mpc at 700 km/s and 0.1 Mpc at 7 km/s and 100 light years at 21 km/s - all these pairs of distances and speeds have the same t associated with them. That is because any and all distances in the universe change at the same rate, at a given time in its history, due to expansion. This includes whatever distance you pick for the size of the universe.

Which is to say, Hubble constant tells you how long it'd take for the universe to grow from 0 to its current size, if the rate of expansion had always been the same as today (it hadn't). If you were to run the numbers, the value of the Hubble constant in units of 1/t is something like 1/14.4 billion years.
I.e. it tells you that at this rate it'd take 14.4 billion years to grow/shrink the universe from/to zero size.

 

[sophiecentaur]

TL;DR: If the Hubble Constant is 45 miles (73 kilometers) per second per megaparsec. What is this converted to miles (or required specific length) per second, minute or hour?

But if someone in this Physics forum convert 45 miles (73 kilometers) per second per megaparsec into something more conceivable like one foot an hour then it is more understandable for a common non-scientist to understand.

The Hubble Constant tells you the speed of recession, related to the distance from the source. Forget about the specific units; numbers tend to add confusion. If you can come to terms with that then you can see that it's stated in terms of useful (spectroscopic) measurements (red shift tells you the distance - pretty useful and understandable). As far as units are concerned, it's probably best to stick to SI so m/s is worth getting into (if you want to follow this up).

There's nothing 'common' about a non-scientist; many of my friends fall into that category. However, the 'Scientist club' may not be accessible without some basics. Could you follow a football game without knowing how the scoring works?

 

[Jaime Rudas]

If the Hubble Constant is 45 miles (73 kilometers) per second per megaparsec. What is this converted to miles (or required specific length) per second , minute or hour? The idea of this question is to find a basic speed of the Hubble Constant that anyone can relate to. Like if I was to say to someone the Hubble Constant is 45 miles (73 kilometers) per second per megaparsec, no one can easily understand how fast the Universe is expanding, because a Megaparsec is just too hard to conceive. But if someone in this Physics forum convert 45 miles (73 kilometers) per second per megaparsec into something more conceivable like one foot an hour then it is more understandable for a common non-scientist to understand.

If the Earth were expanding at the same rate as the current expansion of the universe, then two cities 1000 kilometers apart (Paris and Madrid, for example) would move 7 millimeters apart every 100 years, while two cities 2000 kilometers apart (Budapest and Madrid, for example) would move 14 millimeters apart every 100 years, and two cities 3000 kilometers apart (Dakar and Madrid, for example) would move 21 millimeters apart every 100 years. In other words, the cities would move apart by 7 millimeters every 100 years for every 1000 kilometers of distance between them, which is roughly 70 kilometers per second per megaparsec

 

[Jaime Rudas]

red shift tells you the distance

Redshift tells you the distance only if you already know the rate at which the universe is expanding.

 

[sophiecentaur]

Redshift tells you the distance only if you already know the rate at which the universe is expanding.

The Hubble constant contains that information. Or not? if you know how to apply Doppler correctly. What other measurement than red shift could have been used for distant galaxies?

 

[Jaime Rudas]

The Hubble constant contains that information. Or not?

Yes, but to measure the Hubble constant, you need to know the distances.

 

[Jaime Rudas]

The idea of this question is to find a basic speed of the Hubble Constant that anyone can relate to. Like if I was to say to someone the Hubble Constant is 45 miles (73 kilometers) per second per megaparsec, no one can easily understand how fast the Universe is expanding, because a Megaparsec is just too hard to conceive.

Another way to visualize what 70 km/s/Mpc is equivalent to is to show that something expanding at that rate will double its size in about 14 billion years.

 

[sophiecentaur]

Yes, but to measure the Hubble constant, you need to know the distances.

This is very true. As with all astronomical measurements, existing measurement methods are used to find the distances of nearer objects (starting with measuring the diameter of the Earth and distances in the Solar System). Cepheid Variables (look it up) in our galaxy gave a distance measurement to galactic stars and that was extended to find distances to other galaxies.

Hubble's data showed that distance away and red shift were related pretty reliably and suggested a 'constant' relationship which works for huge distances. Of course, it runs out after measurements of many billions of light years.

 

[timmdeeg]

If we talk about cosmological distances, aren't these spacelike? So, we would need the knowledge of the expansion history to know them if I see it correctly.

 

[sophiecentaur]

If we talk about cosmological distances, aren't these spacelike? So, we would need the knowledge of the expansion history to know them if I see it correctly.

You could say the same about any measurement unit. We rely on past calibrations and our graphs etc. to give the distance from a given galaxy by looking up the red shift. There are many other forms of data which justify the use of the Hubble Constant (within the limits that it works for). This sort of measurement doesn't just pull itself up by its own bootstraps. Needless to say, our concept of cosmological 'history' relies on a very brief time for actual observations (not much longer than my personal lifetime). One century observations in a few billion years is a very short time to conclude anything about changing positions with time. The whole framework of cosmic measurements relies on many interrelated measurements to support each other.

Do ou have a problem coming to terms with that 'inconvenience'? I think we are rather stuck with it.

 

[Jaime Rudas]

If we talk about cosmological distances, aren't these spacelike? So, we would need the knowledge of the expansion history to know them if I see it correctly.

Yes, when we talk about cosmological distances, we generally refer to space-like separations between comoving objects.

 

[sophiecentaur]

Yes, when we talk about cosmological distances, we generally refer to space-like separations between comoving objects.

This is true and introduces an apparent paradox when considering the age of the universe and the distance separating us from some early objects. And there's that idea of the expansion phase at the formation. I'm not being a 'fussy customer' about this but it's quite hard to swallow / appreciate.

But Hubble's idea applied to times after these awkwardnesses needed to be introduced. JWST has made some fantastic measurements available of those really early times. I haven't enough of a clue about this stuff to be at ease with it yet but, in time, it'll be another of 'those things'. I mean, why should we insist that a constant, invented a hundred years ago would necessarily be a constant constant.

 

[Jaime Rudas]

I mean, why should we insist that a constant, invented a hundred years ago would necessarily be a constant constant.

Actually, that constant wasn't just 'invented' 100 years ago; it's a direct consequence of applying general relativity to a homogeneous and isotropic universe, as Lemaître demonstrated in 1927. Not 'insisting' on it would imply not insisting on general relativity, or not insisting on the cosmological principle, or both.

 

[PeterDonis]

This is true and introduces an apparent paradox when considering the age of the universe and the distance separating us from some early objects. And there's that idea of the expansion phase at the formation. I'm not being a 'fussy customer' about this but it's quite hard to swallow / appreciate.

I'm not sure what the issue or apparent paradox is here. Can you elaborate?

why should we insist that a constant, invented a hundred years ago would necessarily be a constant constant.

Nobody thinks it is. Our current standard model of the expansion history of the universe includes variation of the Hubble parameter with time. What Hubble called his "constant" is really just the value of the Hubble parameter "now".

 

[Jaime Rudas]

What Hubble called his "constant" is really just the value of the Hubble parameter "now".

Yes, the Hubble constant $H_0$ is constant in space, not in time.