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The Hubble law v=Hd is basic to Cosmology. Among other good things, it teaches us an absolute criterion for motion and idea of time ("universe time") that are useful in Cosmology.
The Law refers to distances d between stationary observers---observers at rest relative to the Background of ancient light or equivalently at rest with respect to the expansion process as a whole. Think of a far-flung network of stationary observers scattered throughout the universe.
Stationary observers can agree concerning time---synchronize their clocks---agree on a common idea of the age of the universe. In the Hubble law distances are what you would get if you could measure distances instantaneously at some definite moment in time (something all the stationary observers can agree on). Since we can't actually measure instantaneously we have to estimate and work backwards, figure out what it would have been if we could.
The term d in the Law is a distance between two stationary observers measured at some chosen instant of time. The term v is the instantaneous rate that the distance d is increasing, at that moment. If you want to explicitly put the time t of measurement into the picture then the Law can be written v(t) = H(t)d(t).
So what is a good way to get your brain to assimilate this? How can you best "wrap your brain" around this picture.
One way is to draw the obvious and simple conclusion that since in Cosmology we have an absolute criterion of direction and speed of motion we can say exactly how fast and in what direction the solar system is moving relative to Background. So we can look out into the night sky at certain times of year and point in the direction the solar system is going.
It happens to be going 370 km/s in the direction marked by constellation Leo. Regulus is a bright star sort of at the front paws of Leo. Leo is overhead around 9 PM on nights in mid-April.
Here are some really simple easy-to-use starmaps for various months. Scroll down to the April one. You will see how easy easy it is to find Leo this month (around 9 PM), if you didn't already know that.
http://www.kidscosmos.org/kid-stuff/star-maps.html
Imagine you are at North Latitude 30 degrees and it is 9 PM in the early evening. You face south and tip your head back so you are looking not quite straight up. 15 degrees short of straight up. That means you are looking at celestial 15 North.
Or if you are at 35 degrees N latitude on the earth, and you face south and tilt your head back 20 degrees short of straight up, then you are looking at celestial 15 North. That is where Leo is. It is where the Sun and Earth and all the other planets are moving, relative to the Background of ancient light. That is where we observe the doppler hotspot in the CMB. The measured temp of the ancient light is warmer around Leo because we are moving in that direction.
This is, I think, the most basic fact in Cosmology. Fact One. The sky is about one tenth of a percent warmer in the Leo direction, and one tenth of a percent cooler in the opposite direction (because 370 km/s is roughly one tenth percent of c, a bit more but roughly.)
We have absolute time and motion in Cosmo and the cosmological data is actually adjusted to compensate for it. So that when sky maps of the CMB temperature and stuff are made they are adjusted so what you see is what a stationary observer would have seen, who happened to coincide with our location while the data was being collected. Our solar system (and earth) motion is factored out.
What the professionals want is a map of what it would look like to a stationary observer, not complicated by our own private individual solar system motion or our galaxy motion or any of those random details. So those are the mottled red and blue CMB oval maps you see in magazines---a stationary observer's view of the universe.
At least for some people the confusion about real motion on the one hand versus cosmological expansion of distances (Hubble Law expansion) on the other hand can be alleviated once they understand the idea of a network of stationary observers, and the idea of the time and distance measures appropriate to Hubble Law.
The Law refers to distances d between stationary observers---observers at rest relative to the Background of ancient light or equivalently at rest with respect to the expansion process as a whole. Think of a far-flung network of stationary observers scattered throughout the universe.
Stationary observers can agree concerning time---synchronize their clocks---agree on a common idea of the age of the universe. In the Hubble law distances are what you would get if you could measure distances instantaneously at some definite moment in time (something all the stationary observers can agree on). Since we can't actually measure instantaneously we have to estimate and work backwards, figure out what it would have been if we could.
The term d in the Law is a distance between two stationary observers measured at some chosen instant of time. The term v is the instantaneous rate that the distance d is increasing, at that moment. If you want to explicitly put the time t of measurement into the picture then the Law can be written v(t) = H(t)d(t).
So what is a good way to get your brain to assimilate this? How can you best "wrap your brain" around this picture.
One way is to draw the obvious and simple conclusion that since in Cosmology we have an absolute criterion of direction and speed of motion we can say exactly how fast and in what direction the solar system is moving relative to Background. So we can look out into the night sky at certain times of year and point in the direction the solar system is going.
It happens to be going 370 km/s in the direction marked by constellation Leo. Regulus is a bright star sort of at the front paws of Leo. Leo is overhead around 9 PM on nights in mid-April.
Here are some really simple easy-to-use starmaps for various months. Scroll down to the April one. You will see how easy easy it is to find Leo this month (around 9 PM), if you didn't already know that.
http://www.kidscosmos.org/kid-stuff/star-maps.html
Imagine you are at North Latitude 30 degrees and it is 9 PM in the early evening. You face south and tip your head back so you are looking not quite straight up. 15 degrees short of straight up. That means you are looking at celestial 15 North.
Or if you are at 35 degrees N latitude on the earth, and you face south and tilt your head back 20 degrees short of straight up, then you are looking at celestial 15 North. That is where Leo is. It is where the Sun and Earth and all the other planets are moving, relative to the Background of ancient light. That is where we observe the doppler hotspot in the CMB. The measured temp of the ancient light is warmer around Leo because we are moving in that direction.
This is, I think, the most basic fact in Cosmology. Fact One. The sky is about one tenth of a percent warmer in the Leo direction, and one tenth of a percent cooler in the opposite direction (because 370 km/s is roughly one tenth percent of c, a bit more but roughly.)
We have absolute time and motion in Cosmo and the cosmological data is actually adjusted to compensate for it. So that when sky maps of the CMB temperature and stuff are made they are adjusted so what you see is what a stationary observer would have seen, who happened to coincide with our location while the data was being collected. Our solar system (and earth) motion is factored out.
What the professionals want is a map of what it would look like to a stationary observer, not complicated by our own private individual solar system motion or our galaxy motion or any of those random details. So those are the mottled red and blue CMB oval maps you see in magazines---a stationary observer's view of the universe.
At least for some people the confusion about real motion on the one hand versus cosmological expansion of distances (Hubble Law expansion) on the other hand can be alleviated once they understand the idea of a network of stationary observers, and the idea of the time and distance measures appropriate to Hubble Law.
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