Expert: Philip Stahl - 1/19/2006

Question
Thank you very much for your detailed answer. I appreciate the specifics about the answerable questions. As you say, I am asking about the absolute motion of the earth in the universe and maybe I have some false assumptions. I get it that we can't know if the universe is spinning or if it is moving relative to other universes in a larger scheme of things, or if it is just a small part of a moving body in a still larger scheme of things, but I don't quite get the impossibility of a coordinate system within our universe.

Wasn't there a big bang at the center of the universe and isn't all matter expanding outward from that point, with each galaxy cluster moving in a straight line away from that point at a steady and calculable speed (creating an increasingly larger void at the center of the universe)? Don't these straight lines of movement of the galaxy clusters all converge on the specific center point where the bang occurred? And wouldn't the line (or line segment) between our galaxy cluster and that center point be enough to define a coordinate system?

And while we are at it, how can all galaxy clusters be receding from each other? This could only be possible if the outer edges of the universe were moving away from the center more quickly than the inner edges and in fact the speed of everything in-between would have to be proportional to its distance from the center.

And I don't see how a simple formula could account for the speed at which any two galaxy clusters are moving away from each other. Galaxy clusters on opposite sides of the center would be moving away from each other more quickly than galaxy clusters on the same side. Also imagine galaxy cluster A which is ten thousand light years from the center, cluster B which is on the same line but a little further out, eleven thousand light years from the center, and cluster C which is on a different line, one thousand light years from A and ten thousand from the center. A starts equidistant from C and B but could not move away from them at the same speed…unless one or more of them is not traveling in a straight line. I do not know what Hubble's constant is, but does v = H_o (d) take all this into account?


Thanks,
Kevin

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Followup To
Question -
How fast am I going? This is composed of a number of questions, of which the last is probably the most difficult…but there might be a Nobel prize in it for you…unless somebody else figured this out already :)

How fast is our galaxy moving away from the center of the universe?
How fast is our solar system moving away from the center of our galaxy?
How fast is our solar system rotating around the center of our galaxy?
How fast is the earth moving around the sun?
How fast is my point on earth spinning around the axis of the earth?
Other than the movement of the universe itself, am I involved in any other types of celestial movement?
All these factors probably work in contradictory ways. For instance at night the spin of the earth may take me away from the center of the universe and during the day that spin may send me back. Given that it is 5 PM on Jan 18 and my location is near San Francisco, how do all these factors work together to create my aggregate speed in miles per hour away from the center of the universe?

Thanks for your time,
Kevin


Answer -
Hello.

The first (as well as last in the paragraph) cannot be answered and I will get to that.

The solar system motion wrt the galaxy is about 12 miles/sec toward the constellation Hercules.

The rotation rate sharing of motion (with neighboring stars) is about 150 miles/sec around the center of the galaxy.

The Earth is moving round the Sun at about 66,000 mph (~ 18.5 miles/sec)

A given (fixed) point on Earth- in terms of its rotation rate-  will depend on the latitude of the point. (So one can thereby calculate the circumference based on that lat.)

For example, for a lat. = 45 deg. (sin (45) = x/ R where R = 3,986 mi. is the radius of Earth at the equator and x is the radius of the latitude 45 deg circle, or x = R* sin 45 = 2,819 mi.)

Then: v = 2*pi*2819 mi/ 24 hr =  738 mi/hr

Now, particulars. Re: "movement of the universe itself" - there is really NO way of knowing that, apart from its expansion. That is, each galaxy cluster is receding from every other galaxy cluster at a rate which is proportional to Hubble's constant and the distance, or:

v = H_o (d)

Thus, if the universe were rotating we'd have no way to ascertain it.

What you are really getting at when you ask about some "aggregate motion" or speed is the absolute motion of the earth in the universe. This has indeed already been settled, and was the object of the Michelson-Morley experiment (you can google this, to learn more about it).

The experiment, to make a long story short, gave null results. This led to a fundamental postulate of special relativity theory, namely that it is not possible to define an absolute coordinate system with respect to the absolute speed of an object in space.

Such an absolute coordinate system would be based on the universe at large, but we have no way of ever doing that. Not the way we can impose a latitude, longitude coordinate system on Earth (or galactic longitude, latitude on the galaxy).

Since we can't define such a system, there's no way to ascertain the Earth's "aggregate" motion within it! The most we can do is to assay and compile the separate motions, but cannot ascertain what "resultant" these have in respect to the cosmos as a whole!

Hope this helps.  

Answer
Ok, lots of stuff to clarify.

First, one cannot ascertain a "center" to the universe, because there is no observational center that we can detect. The Big Bang was an explosion of space *as well as time* and in observing the expansion, we note that each galaxy cluster conforms to the recession like ink dots on the surface of an expanding balloon.

If you were an "ant" on one of those dots, you would surmise that you occupied a center, and all other dots were expanding from you. Ditto in the case of the cosmos at large. From each galaxy cluster it appears that all other clusters are receding- but this cannot a priori be used to infer a "center".

To make inferences one would require being at the actual 4-dimensional center of the original explosion. That is not possible since there is no 'center' in the observed expansionary framework.

As for the Big Bang itself, since it was an "explosion"
of space AND time, identifying its geometric center is not nearly so simple as you think. Indeed, the relic radiation from that event, the 2.7K background discovered by Penzias and Bell in 1965 is *isotropic* - meaning the same in all directions. There isn't one single scintilla or hint of a higher intensity in one region or place than another. Hence, no directivity or clue to ID a "center".

Now, it follows that if one can't identify a center, one has no basis to develop a 3- (or 4-dimensional) coordinate system. (For instance, imagine a possible expanding 'sphere' as the basis, this only works if one knows the *center* of the sphere!)

Your invocation of "straight lines of movement" vis-a-vis receding galaxy clusters sounds ok at first blush, but in practice isn't much use. First, again, we aren't talking about a simple 3-D geometry here, but a 4-D one. In addition, it isn't simply a matter of the Big Bang itself, one must also factor in inflation. This means an initial accelerated expansion phase - so all uniform motion extrapolations go out the window.

To make things worse, the Boomerang (balloon-borne) and MAXIMA UV measurements to do with type Ia supernovae. (See, e.g. Physics Today, July, 2000, p. 17) now disclose the universe may be accelerating again in its expansion - due to the presence of "dark energy".

Note, that this dark vacuum energy is no where observed in any earth physics lab, and hence only cosmology had shown it to be consistent with the observations made (e.g. on Type 1a supernovae in hundred of distant galaxies).

If you make a plot of absolute magnitude (vertical axis) against redshfit (z, for the galaxies they occur in ) then type Ia supernovae will be distributed in a particular way.

The axes for plotting 1a supernovae would appear:


M(ABS)
!
!
!
!
!
!
!
!
!---------------> Z
0


In the above graph, visualize a series of scattered points emanating from the origin up to the upper right. Also try to visualize an imaginary diagonal line going from the joined (M, Z) axes to the upper right. In terms of the real data, the type Ia points all fall to the LEFT of that line, or in what we call the 'accelerating universe' region. On the other side of the diagonal is the "decelerating region". An additional feature of the accelerating side is 'vacuum energy'.

The cosmological "equation of state" (think of something like the equation of state for an ideal gas, e.g. P = nkT) for this vacuum energy is:

w = (Pressure/ energy density) = -1

This is consistent with Einstein's general theory of relativity - which one could say approaches the status of a 'basic law of physics'.  In this case, the existence of a negative pressure is consistent with general relativity's allowance for a "repulsive gravity" - since any negative pressure has associated with it gravity that repels rather than attracts.

Specifically the term (rho + 3p) acts as a source of gravity in general relativity, (where rho = energy density).

If we set:  0 = (rho + 3p) then:

p =  -rho/3

and if:  p <  (-rho/3) we have gravity that repels

Looking back to the earlier equation for w, one finds:

p = - rho  (pressure = - energy density)

and -rho <  (-rho/3)

Some might argue that this shows a "new law" of physics, e.g. repulsive gravity, but in reality it's merely extending the existing concept of gravitation to show it has a repulsive as well as attractive aspect. And it always has been consistent with Einstein's general theory of relativity.

This indeed, shows the speed of expansion "need not be proportional to the distance from its center" (as it need not when inflation is operating).

However, in *normal* recession- expansion, given by the Hubble law, cf.

v = H d  =  (k) d    (k = H, a constant)

there is obviously a linear proportionality.

This is of the same form as the simple equation, y

y
!
!
!
!
!
!
!
!---------------> x

0

Which would yield a *straight line* of constant slope (k) from the origin 0,0 at a 45 degree angle toward the upper right.


Re: the recession effect, and any two galaxy clusters (say the Virgo cluster in relation to the Milky Way) - believe me that the "simple" Hubble law expansion does take this into account. The Hubble constant (H_o) does as well.

Let me again add a cautionary warning, however, that one cannot make extrapolations, assumptions, or inferences based on visualizing some presumed "center" for the reasons already given at the opening of this reply. Again, we can ascertain no "center" since it isn't a case of a simple geometrically symmetric event in space.

In practical terms, this means it is impossible to infer motions for recession between any two galactic clusters - ONLY between our own and others *in reference to us*. To obtain the kinematic recessional effect - say between the Virgo cluster and the Coma cluster- you'd have to peform redshift measurements from within Coma OR Virgo, with respect to the other. (e.g. obtain the redshift, z, from spectroscopic determinations, then compute v = zc = H_o (d))

A last point, for relativistic velocities of recession (v ~ c), the relationship is no longer simple linear, cf.  v = cz but rather:

v =  [(z^2 + 2z)/ (z^2 + 2z + 2)] c


Hopefully this response resolves your remaining questions.