Posted on 02/21/2008 7:47:47 PM PST by NormsRevenge
Ok, matter bends space - how does it become unbent? Is there some restoring force in the structure of space that rights itself when the matter goes away? Maybe this is some hyperbent space due to a black hole or something, and is in the process of unbending?
Yes. Normally space is flat. The curvature is the result of an interaction with an energy density. It's not just matter though, it's energy in any form that results in a curvature in space. That includes any particles, such as photons. The potential energy contained in the curved space that resulted from the creation of the distribution, is the potential energy of the gravitational field. So in a simple picture, space is acting like a spring, or an elastic sheet. The energy contained is rather large, since the distributed energy was once very close, and the energy is proportional to 1/r, where r is the initial separation. (∝∫1/r2dr... )
"Maybe this is some hyperbent space due to a black hole or something, and is in the process of unbending?"
It can't be a BH, because the energy distribution responsible for the curvature is not point-like. The energy distribution is given as in the pictorial plot shown in the article.
The response of space, or the vacuum to the presence of an energy density, or the change in the distribution of one, travels at the speed of light. The plot in the article, given in post 1, shows the energy distribution as is, at (distance in light years/c) years ago.
I guess I don’t know what I’m looking for in the picture. To me it looks like an inner and outer ring of gas separated by sparse space. For dark matter (or curled space), wouldn’t I want to see gravitational lensing? Or am I missing that?
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Some commentators have described the plague to not merely be an eclipse of the sun, but with the description of light emanating from the homes of the Israelites, while an inky dark fog would blot out even candlelight from the homes of the Egyptians. It additionally describes the darkness as a darkness which may be felt.
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That's the distribution of dark matter. In the center, it's roughly the shape of a sphere of denser lumps of the stuff, so it will bend light like an ~spherical lens. The outer ring appears as a slice of a hollow sphere, as if both the forward and back end of the sphere were cut off. So the viewer is looking down through a wall like section.
"For dark matter (or curled space), wouldn’t I want to see gravitational lensing? Or am I missing that?"
They've already noted the lensing and shaded the pic blue according to the density of matter that would account for the lensing. This article gives a good description. I think most of that plot of the dark matter density was made from analyzing weak lensing. I wouldn't know if any of the features of strong lensing, such as arcs, or multiple images of the same object appear in that pic.
"So, as matter travels through space, it bends it, then space unbends - doesn’t it start vibrating like a spring would as it is released? What kind of damping would stop it, or would it vibrate forevermore?"
Matter, or light will both do that, but it takes more than one object for the vibrations to propagate away from the objects. Otherwise the vibrations are localized with the object's wave packet, else the energy of the object would be lost with time and the object would just disappear. The natural frequency of the object and space are so different, that there is no net energy transfer/time to space from single objects. The object is simply retaining it's own energy. If the picture is composed of all particles and particle interactions, there's no mechanism that allows a net transfer/time of energy between a particle in this world and the vacuum. Only accelerations of particles relative to each other can do that.
Accelerations are what result in propagation of the vibrations away from the objects, which is a loss of particle energy to the g field. Those are gravitational waves, whose negative energy is carried by gravitons-particles that carry negative momentum. Large waves are generated by supernova explosions and tight orbits of very heavy objects like black holes. Those waves propagate at the speed of light and amount to a redistribution of the gravitational field. The only way to create the vibrations from a single particle, is to generate that particle of energy from nothing and have it's g field propagate in space, which can't happen.
Having said that, space is also expanding. That means in order to maintain the g field of a particle, some of that particle's energy must continuously be transformed into the potential energy of the field. That's the nature of the red shift connected to Hubble's constant.
So you are saying that as light propagates through space, it looses energy to space and is red-shifted as an observable result? And as a photon reaches the far extent of space it is depleted entirely of energy?
Yes. That's because space expands with time at ~72m/s/megaparsecs. That's why the light from the big bang appears in the microwave region, with a black body temperature of ~3.7 Kelvin.
"And as a photon reaches the far extent of space it is depleted entirely of energy?"
There is no far extent of space. The space we're in is like a patch on the surface of a balloon in 3d. Each of the spacial coordinates curve all the way around to the same spot. The radius of that balloon just keeps increasing, so that space continues to expand and that expansion is accelerating. The photon will never leave space, or find an "edge".
ooops... 7.2m/s/parsec.
...was right the first time...72
Say we had a chunk of bent space, how would it release its energy?
The expansion has a measurable effect in regions of space where matter isn't gravitationally bound. The fundamental phenomenological evidence is the decrease in momentum of a particle/object moving through essentially free, or flat space. Photons are the only particles that are well known to lose momentum in traveling long distances, because the emission lines(energies) at the source are known.
Since the momentum lost is so small compared to the total conserved momentum within a gravitationally bound system, the effect will not be noticed within the system. It will be noticed between systems not gravitationally, or otherwise bound, because it will not be buried in magnitudes larger binding energies. An analogy would be a breeze acting on a naval vessel. The breeze effects no relative motion between parts of the ship, only the motion of the entire ship as one unified object.
"Has anyone made a measurement in local space to decide this (is it even detectable?)?
It wouldn't be detectable, other than the loss of momentum objects in very flat space, or in splittings of degeneracies in extremely high energy processes. Those HE processes would be at energies far above the Large Hadron Collider.
"Say we had a chunk of bent space, how would it release its energy?"
The space is bent, because of the presence of an energy density, a particle, or system of particles. As that energy density propagates through space, the energy contained in the bending follows the propagation.
The release in bending that accompanies the expansion of space as the particle's momentum and energy decrease is a lowering of the gravitational field energy. That has the effect of an increasing expansion rate. At each point in time, the total energy remains zero. The positive energy of the particles is balanced by the negative energy of the gravitational field, so the sum is zero. The energy density of the terms just gets smaller as hte universe ages.
Perhaps you would indulge me an answer to a paradox that has bugged me for a long time. They say that if one of a pair of twins speeds off in a spaceship traveling near the speed of light then returns to earth, he has aged much less than his earth bound brother. Suppose they both speed off in opposite directions near the speed of light, and then return to earth - are they now both the same age? Howcome?
Time for a moving object is given by:
tmov=trest*sqrt(1-(v/c)2)
trest is the clock rate seen in the rest frame. The rest frame is the nonmoving frame. An observer in the moving frame will see their clock run at the rest frame rate, but it will be running at tmov. The fastest the clock will run is in the rest frame and runs slower as the particle accelerates to higher velocities, or is held in the curved space of a gravitational field.
The effect can be seen by measuring the decay rate of fast moving particles with very short lifetimes, like Kaons, Muons, ect... To a slow moving observer in a lab watching the results of particle collisions, or particles generated by incoming cosmic rays, the lifetimes are much longer than they are for the same particles at, or near rest. The particle sees it's own clock though as a rest frame clock, and transforming the long decay time according to the particle's velocity results in obtaining a decay rate consistent with the rest frame clock.
Clocks also run slow in the curved space of gravitational fields, even if the particle isn't moving in translation. THe effect can be seen with stuff "falling" into a black hole. The stuff just hangs on the event horizon. The clocks for those particles go to a zero clock tick rate.
In your example of two particles moving away from each other at the same speed, symmetry says both clock will slow down the same amount. That means the age of the stuff on both ships will be the same, but "younger" than the stuff on Earth. So the crew's tritium watch dials will last longer than 12, or so, years from the manufacture date. To the crew though, the watches will seem to last ~12 years, because their clock has always been a rest frame clock. They just think folks on Earth got old and the date on the sales slip is funny...
That is depressingly far away.
So, it makes no difference whether or not the two moving objects are moving in the same direction or not? They are moving relative to earth - that is the only criteria?
That's right.
"They are moving relative to earth - that is the only criteria?
For calculating the clock rate difference, yes. That doesn't mean Earth itself isn't moving. It only provides a reference for the rest frame clock, because the moving clock can't be it's own reference. Everything on the moving object looks like it's in a rest frame.
Nothing can be seen directly.
I’ve seen bigger.
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