# B How fast is Earth traveling due to the Hubble constant?

1. Mar 11, 2017

### Nick Levinson

I'm trying to figure out or find how fast Earth is moving due to the Hubble constant. I'm runnng into two answers and have difficulty understanding either one.

--- One answer is a number of kilometers per second per megaparsec. But that's a distance per time unit per distance unit. I don't understand why the number is not reduced to one distance unit per time unit, much as we say for aircraft (a number of miles per hour or a number of kilometers per hour). My problem seems to center on the "per megaparsec" part. When I look it up, I see that a megaparsec is a number of light-years, which is the distance traveled by electromagnetism (e.g., light) in a year, and it relies on electromagnetism because, as far as we know, it's the fastest thing traveling. So I don't understand why the distance units are not being combined.

--- The other answer is that the constant measures the expansion of the universe, which I'm fine with, but then it's assumed that we decree an arbitrary center and then find that everything else moves away from that center, so that the center is arbitrarily assumed to not be moving. That's fine when we want to be arbitrary, but Earth is not at the center of the Milky Way and the Milky Way is not at the center of either the universe of known and observable matter and energy or, as far as we know, at the center of the infinite universe (the universe as understood by children). So, even just from the Hubble constant, there should be a speed number for Earth's travel from the center of a universe.

I understand that, without counting the Hubble constant's effect but counting Earth's travel toward the Great Attractor (I just learned about that and don't know if that's still in a scientific consensus), Earth is traveling at about two and a half million miles an hour. I expect to get an upper speed by adding the Hubble constant's speed at Earth's location to the non-Hubble combined speed, much as we'd add the speed at which someone climbs a rope located in an elevator to the upward speed of the elevator itself, even though sometimes one speed would be subtracted from the other, such as when Earth is moving around the sun in a direction of travel opposite of that of the universe's expansion.

2. Mar 11, 2017

### phinds

It isn't. As you seem to understand, but aren't following through on, there is no such thing as absolute motion, just motion relative to other things. You can get the motion of the Earth relative to the CMB, but there is no such thing as the motion of the Earth due to the expansion of the universe.

3. Mar 11, 2017

### John Park

Mainly tradition, I think; km/s and megaparsecs are familiar units for cosmological quantities (and a megaparsec is just a large number of kilometres); so collapsing the units of H into an inverse time makes some things less intuitive. (Note that H represents a rate not a velocity.)

No. There is no centre of the Universe (as far as we know). But it's a fairly simple consequence of uniform expansion that any observer will see the universe expanding around them. It's sometimes compared to an inflating balloon, where the 2D surface of the balloon represents the 3D expanding universe. Every point on the balloon sees all its neighbouring points moving away from it as the balloon inflates. (This does assume that if the universe has an edge, we're nowhere near it.)

(The Great Attractor is something inferred from the motions of galaxies; it's an interesting cosmological phenomenon, but it does not represent the centre of the universe, either.)

Since the universe does not appear to have a centre, it doesn't make sense to ask how the Earth is moving with respect to it. And in any case the expansion measured by the Hubble parameter doesn't operate within the solar system or even within the Galaxy--just on an intergalactic scale. I'm not sure where you get the Earth's speed is about two and a half million miles an hour. That might be its speed around the centre of the Milky Way (I haven't checked)--but that's a legitimate speed, measured against a relatively well-defined centre.

4. Mar 13, 2017

### Nick Levinson

OK.

I thought the known universe had a measured distance across it (counted in billions of light-years) and therefore that its center is implied and locatable and therefore that Earth's location could be determined relative to the universe's center's location, all at least approximately, and I thought the Earth's locus had been calculated as not at the center of the universe, but if all that is not the case, then so be it.

The two and a half million is a sum of speeds including motion around the sun and motion of the Milky Way. I'd have to re-research it to list the components; those may be the only ones.

5. Mar 13, 2017

### rootone

The Earth IS at the center of the observable Universe.
Nobody expects that to be everything which exists.

Last edited: Mar 13, 2017
6. Mar 13, 2017

### Staff: Mentor

Here's my attempt to explain this without butchering the whole thing:

The problem is that expansion isn't a velocity. It's an acceleration that depends on distance. In SI units, regular acceleration has units of $\frac{m}{s^2} = \frac{m}{(s)(s)} = \frac{m}{s}*\frac{1}{s}$. The first fraction in that last part represents velocity and the 2nd represents time. So if you are accelerating at a rate of : $\frac{10m}{s^2}$ that means your velocity is increasing at a rate of 10 meters/second every second. If the rate of change of your acceleration is zero, then you have a constant acceleration and if you accelerate for 10 seconds your velocity will increase by 100 m/s.

But the expansion of space isn't an acceleration of time. Well, not directly at least. The rate of acceleration has units of velocity per distance, or $\frac{km}{s}*\frac{1}{Mpc}$. The problem here is that we can't directly cancel these units because the 2nd term is actually changing over time since things are moving away from us. So breaking it down further it should be: $\frac{km}{s}*\frac{1}{\frac{ΔMpc}{Δs}}$, where Δ (delta) is a symbol that represents a change in a quantity. Calculus tells me that 2nd term should probably be $\frac{1}{\frac{dMpc}{ds}}$, where 'd' represents an infinitesimal change in a quantity. You could rearrange the 2nd term to get a change in time over a change in distance and maybe cancel out units, but that's a little confusing as it takes away the benefit of being able to immediately tell that you're still working with a change over time.

Unfortunately, I don't know if you can cancel units in this case and I don't know if my analysis is 100% correct. But the general idea is that the rate of expansion is an acceleration over distance (which itself can depend on time since you'll be moving), not purely an acceleration over time. So if you just sit there inertially (with respect to the hubble flow) and let the expansion of space carry you away from another object, your recession velocity will gradually increase over time. But if you're also moving relative to the hubble flow in addition to moving away from the other object, your recession velocity will increase even faster with respect to time than before.

Hopefully that's mostly correct. As always, someone correct me if I'm wrong.

7. Mar 14, 2017

### phinds

The center of the observable universe is your left eyeball when you close your right eye. As rootone said, it would be rather silly to think that's the center of the universe.

8. Mar 14, 2017

### John Park

As I recall, if you do cancel the units you get the inverse of the "Hubble time", which is of the same order as the age of the universe. I believe that in some of the simpler cosmological models, it is the age of the universe, but, like you I'm open to correction on that.

9. Mar 14, 2017

### Bandersnatch

While I mostly agree with what you were getting at, I'm not sure it's a good idea to call it 'acceleration over distance', since acceleration is by definition the change of velocity over time. Furthermore, 'acceleration over time' kinda implies jerk. A more correct description, IMO, would be the change of velocity over distance.

This bit is not correct in general. The recession velocity of some generic galaxy increases over time only in universes undergoing accelerated expansion, which while true for our universe at the present epoch, wasn't true in the past, and does not follow just from the statement that there is expansion. In particular, universes without dark energy have recession velocities always decelerating, or - in case of completely empty (i.e. 'Milne') universes - constant in time.

Yes. The Hubble time is the age of the universe in Milne universes, where recession velocities are constant over time. It is simple to see why that is so:
Recession velocities are given by the Hubble law: $V=dH_0$ Let's take an arbitrarily chosen distance d from the observer, and ask how long does it take for a galaxy at d to cover that distance. From the definition of velocity we have $V=d/t$, so combining the two equations we get $dH_0=d/t => t=d/(dH_0)$
The above gives meaning to eliminating the two distances in the dimensions of the Hubble constant (a galaxy twice as far will recede at twice the velocity, so the time to cover both distances is the same and independent of the particulars of the distances). And the meaning of the inverse of $H_0$ is the time for any receding galaxy to get to where it is now.

It tells you how the recession velocity scales with distance. It's 67.9 km/s every 1 Mpc. A galaxy at 1 Mpc will recede with 67.9 km/s, at 10 Mpc with 679 km/s, at 1 Gpc with 67 900 km/s. You can't reduce it to just km/s (like for aircraft), since the expansion does not have just one speed. It has a rate - much like percentage rate of growth of money on your savings account. Just as a bank could tell you that according to current rates, you'll be getting 6 dollars a year for every 100 dollars you deposit (so the dimensions are $/t/$ - just as with the Hubble constant which has d/t/d), or equivalently tell you that you'll be getting 6% increase/year (and if you eliminate the distances from the Hubble constant, you get a percentage rate as well: roughly 1/144th% per million years).
* note for clarity: in a bank, the percentage rate tends to remain constant, so you can get exponential growth of savings. The Hubble constant is not in general constant in time (rather, it falls down).

10. Mar 14, 2017

### John Park

In some of the books I've seen it's been called the "Hubble parameter" for that reason. I was trying to remember to do that myself, but I think I just called it H.

11. Mar 15, 2017

### Nick Levinson

On Earth being the center of the observable universe and no one doubting that other universes exist beyond the reach of our technology-independent observational powers (post #5, above, by rootone): It's reasonable to expect more universes, but, ignoring them and focusing on this one, unless the distance from Earth to the edge of the observable universe is equidistant for all directions, Earth is not at the center. If Earth is, then the moon is not. And if Earth is, it's not at most times of the year. While Earth being at the center (presumably throughout the year) was accepted for centuries, I think that is no longer considered true. I also think we're not near the edge of the observable universe; we may be closer to the center than to an edge. But I'm not an expert on this.

12. Mar 15, 2017

### phinds

Quite the contrary, unless you subscribe to the highly speculative many-worlds interpretation, there is only one universe. In any event, even if there ARE other universes, they are not casually connected to ours.

The center of the observable universe is your left eye, when you close your right eye. Mine is too. If you were on the moon, the center of the observable universe would STILL be your left eye.

13. Mar 15, 2017

### Bandersnatch

Being in the centre of the observable universe is like being in the centre of the circle of the horizon on Earth. If you move around, the horizon moves with you, and you're always at the centre.

14. Mar 15, 2017

### Staff: Mentor

That's not what 'observable universe' means. The observable universe is simply the portion of the universe visible to any observer at a give time. You and I, looking up into the night sky, are observing slightly different observable universes. Not that we can notice the difference since we can't see into the infrared and microwave range. If we were a few billion light years apart, then we would have noticeably different observable universes. Every observer is, by definition, at the center of their own observable universe.

There is nothing special about the observable universe. There's no physical line or change delineating the observable universe from something else. We just talk about it as if there's only one that's centered on the Earth because it's a convenient shorthand instead of having to talk about a specific reference frame every time we say "observable universe".

15. Mar 15, 2017

### Nick Levinson

I do not subscribe to the many-worlds interpretation, since it seems to support there being infinitely much matter and energy, but that some number of other universes, perhaps one or perhaps some other finite number, can exist seems very plausible. I understand that the Big Bang theory applies only to our observable universe and does not rule out another universe of matter and energy pre-existing and existing with the Big Bang.

I thought what we can observe today with our present technology is the observed universe. If that's the observable universe, then I need a term for the universe that includes what can be observed only if there were no technological limit on observation. Maybe that's the known universe, thus including our best theory about what's in it. Relative to that known universe, the one we're in, then, if I'm always at the center of the universe and you're always at the center of the universe and we're not at the same place, then we're being approximate. If "circle of the horizon" means that I can stand on Earth and turn 360 degrees and always see the horizon and thus the horizon is a circle, okay, but that's not an adequate analogy to what I'm calling for the moment the known universe. It is that known but not entirely observed universe that I understand we are not at the center of.

16. Mar 15, 2017

### Staff: Mentor

The big bang applies to the entirety of the universe, not just our observable portion. It doesn't rule out the possibility that our universe in another state prior to the big bang, but "existing with the big bang" makes no sense.

The maximum diameter of our observable universe has a hard limit governed by the speed of light. Light or other particles traveling towards us from portions of the universe outside our observable portion simply haven't had the time to reach us. This diameter is then reduced by what we can actually see with our eyes and instruments. However, when we speak of the observable universe, we are almost always talking about the portion limited by the speed of light. So the term you're looking for is simply "the observable universe".

17. Mar 15, 2017

### Staff: Mentor

We are indeed at the center of the "known" universe, because the known universe is the same thing as the observable universe. The two terms mean the same thing in the context that you've been using "known universe" in this thread.

18. Mar 15, 2017

### John Park

I assume you're referring to post #13:
Bandersnatch said "move around", not "turn around".

You can go from the North Pole to the Equator or anywhere else on the Earth, and you'll still be at the centre of the observable "universe" that extends as far as the horizon around you. And that is the analogy to our position in the real universe.

Last edited: Mar 15, 2017
19. Mar 16, 2017

### Nick Levinson

I'll hold up (for now) using terminology that's causing a problem herein (which maybe I caused) and go to definitions, in order of greater size:

A) The universe that we can observe with today's technology from Earth or near it. (What we could observe only with century-ago technology was smaller and presumably what we'll be able to observe a century from now will be bigger, although perhaps not.)

B) The universe that we could observe if we could put our technology far away and await results. If we could put it, say, a billion light-years away (waiting two billion light years from launch to result), we might find this universe to be appreciably bigger, but if we found a lack of matter and energy at the new maximum distance then we might doubt the universe of matter and energy to be spherical. This univere might be larger than the 93 billion light-years in diameter now said to be the case.

C) The universe that we could observe if our technology were unlimited. There'd still be the limits of physics. That could be bigger and, in the past, always has been bigger than our past technology let us find.

D) The universe that extends forever in all four dimensions of space and time and, beyond the matter and energy we can perceive, could be mostly empty. This universe, which extends forever, is what children learn about. By definition, it is bigger than either of the other two.

In this thread, I'll call them A, B, C, and D, respectively.

It seems that A (or B) and C are being conflated in this thread into one. That would make what technology measures the same as what physics tells us, and that would mean that technology introduces no limits that physics has not already introduced. But while technology has a concept of tolerance or degree of precision, I think physics without technology does not. Once technology stops introducing a limit that is not required by pure physics, tolerance or degree of precision becomes unnecessary.

I read that a beam of light tends to disintegrate over distance, as individual photons tend to veer off (I don't recall if an individual photon could disintegrate but I think not), so that the maximum perceivable distance is that beyond which a beam of light would have disintegrated before getting to us. I don't know if that's also true for lasers, but I think that it is, although maybe at a greater distance.

By "pre-existing and existing with the Big Bang" I meant that matter and energy could have existed before and during the Big Bang while nowhere near the location in space where the Big Bang occurred. Since expanding balloons are a popular analogy, I'll use that here: Assume a balloon (with vacuums inside and out) was expanding and in the center there occurred a big bang creating a new vacuous balloon that also was expanding. The two balloons might never come close to each other. If they were big enough and an observer was on either balloon's surface and was using available technology, the observer might be unable to perceive the other balloon, and perhaps could do no more than hypothesize that the other balloon could possibly exist. I don't think the Big Bang meant that any prior matter and energy far from the spatial location of the Big Bang had to have ceased existing or that the Big Bang could not have occurred until it did cease existing.

On the distinction between moving around and turning around, in the context of universe C the likelihood that we're precisely at the center is statistically almost infinitesmal, even before we adduce evidence of our location. Perceiving matter and energy in all spatial directions, so we therefore perceive that we're at the center of what we have observed, is not enough to justify saying we're at the exact center of the universe that could be perceived if we could put sensors far enough out to make a difference in our perceptions of the size and shape of the universe. In that context, my left eye being at the center and my right eye being at the center cannot both be true at the same time, regardless of whether the other eye is closed. I don't think it's true even for universe A, although the difference would likely be too small for present technology to measure.

20. Mar 16, 2017

### John Park

It is routinely pointed out in semi-popular accounts of cosmology that looking out into space is looking back in time. The microwave background was formed a few hundred thousand years after the big bang (when it was of much shorter wavelengths), and we observe that in fair detail now, observe galaxies that are (I think) only a few million years younger than that. It's not clear whether we could observe much beyond the formation of the microwave background--the universe was very opaque until then--but if the big bang is real, there isn't very much further (in time or distance) to go. There might be a lot more matter to examine, but the actual boundary is defined by the time since the big bang.

It is also routinely pointed out in semi-popular accounts of cosmology that there is no such location. The big bang happened everywhere.

This analogy would represent another universe outside our space-time continuum--a kind of many-worlds model. It's not clear that even in principle there could ever be communication between two such universes or any way for one to deduce the existence of the other. Unless some observable effects of other universes can be hypothesised, speculations about them are philosophy rather than physics.