Certain subsectors of the scientifically-oriented blogosphere are abuzz — abuzz, I say! — about this new presentation on Dark Energy at the Hubblesite. It’s slickly done, and worth checking out, although be warned that a deep voice redolent with mystery will commence speaking as soon as you open the page.
But Ryan Michney at Topography of Ignorance puts his finger on the important thing here, the opening teaser text:
Scientists have found an unexplained force that is changing our universe,
forcing galazies farther and farther apart,
stretching the very fabric of space faster and faster.
If unchecked, this mystery force could be the death of the universe,
tearing even its atoms apart.We call this force dark energy.
Scary! Also, wrong. Not the part about “tearing even its atoms apart,” an allusion to the Big Rip. That’s annoying, because a Big Rip is an extremely unlikely future for a universe even if it is dominated by dark energy, yet people can’t stop putting the idea front and center because it’s provocative. Annoying, but not wrong.
The wrong part is referring to dark energy as a “force,” which it’s not. At least since Isaac Newton, we’ve had a pretty clear idea about the distinction between “stuff” and the forces that act on that stuff. The usual story in physics is that our ideas become increasingly general and sophisticated, and distinctions that were once clear-cut might end up being altered or completely irrelevant. However, the stuff/force distinction has continued to be useful, even as relativity has broadened our definition of “stuff” to include all forms of matter and energy. Indeed, quantum field theory implies that the ingredients of a four-dimensional universe are divided neatly into two types: fermions, which cannot pile on top of each other due to the exclusion principle, and bosons, which can. That’s extremely close to the stuff/force distinction, and indeed we tend to associate the known bosonic fields — gravity, electromagnetism, gluons, and weak vector bosons — with the “forces of nature.” Personally I like to count the Higgs boson as a fifth force rather than a new matter particle, but that’s just because I’m especially fastidious. The well-defined fermion/boson distinction is not precisely equivalent to the more casual stuff/force distinction, because relativity teaches us that the bosonic “force fields” are also sources for the forces themselves. But we think we know the difference between a force and the stuff that is acting as its source.
Anyway, that last paragraph got a bit out of control, but the point remains: you have stuff, and you have forces. And dark energy is definitely “stuff.” It’s not a new force. (There might be a force associated with it, if the dark energy is a light scalar field, but that force is so weak that it’s not been detected, and certainly isn’t responsible for the acceleration of the universe.) In fact, the relevant force is a pretty old one — gravity! Cosmologists consider all kinds of crazy ideas in their efforts to account for dark energy, but in all the sensible theories I’ve heard of, it’s gravity that is the operative force. The dark energy is causing a gravitational field, and an interesting kind of field that causes distant objects to appear to accelerate away from us rather than toward us, but it’s definitely gravity that is doing the forcing here.
Is this a distinction worth making, or just something to kvetch about while we pat ourselves on the back for being smart scientists, misunderstood once again by those hacks in the PR department? I think it is worth making. One of the big obstacles to successfully explaining modern physics to a broad audience is that the English language wasn’t made with physics in mind. How could it have been, when many of the physical concepts weren’t yet invented? Sometimes we invent brand new words to describe new ideas in science, but often we re-purpose existing words to describe concepts for which they originally weren’t intended. It’s understandably confusing, and it’s the least we can do to be careful about how we use the words. One person says “there are four forces of nature…” and another says “we’ve discovered a new force, dark energy…”, and you could hardly blame someone who is paying attention for turning around and asking “Does that mean we have five forces now?” And you’d have to explain “No, we didn’t mean that…” Why not just get it right the first time?
Sometimes the re-purposed meanings are so deeply embedded that we forget they could mean anything different. Anyone who has spoken about “energy” or “dimensions” to a non-specialist audience has come across this language barrier. Just recently it was finally beaten into me how bad “dark” is for describing “dark matter” and “dark energy.” What we mean by “dark” in these cases is “completely transparent to light.” To your average non-physicist, it turns out, “dark” might mean “completely absorbs light.” Which is the opposite! Who knew? That’s why I prefer calling it “smooth tension,” which sounds more Barry White than Public Enemy.
What I would really like to get rid of is any discussion of “negative pressure.” The important thing about dark energy is that it’s persistent — the density (energy per cubic centimeter) remains roughly constant, even as the universe expands. Therefore, according to general relativity, it imparts a perpetual impulse to the expansion of the universe, not one that gradually dilutes away. A constant density leads to a constant expansion rate, which means that the time it takes the universe to double in size is a constant. But if the universe doubles in size every ten billion years or so, what we see is distant galaxies acceleratating away — first they are X parsecs away, then they are 2X parsecs away, then 4X parsecs away, then 8X, etc. The distance grows faster and faster, which we observe as acceleration.
That all makes a sort of sense, and never once did we mention “negative pressure.” But it’s nevertheless true that, in general relativity, there is a relationship between the pressure of a substance and the rate at which its density dilutes away as the universe expands: the more (positive) pressure, the faster it dilutes away. To indulge in a bit of equationry, imagine that the energy density dilutes away as a function of the scale factor as R-n. So for matter, whose density just goes down as the volume goes up, n=3. For a cosmological constant, which doesn’t dilute away at all, n=0. Now let’s call the ratio of the pressure to the density w, so that matter (which has no pressure) has w=0 and the cosmological constant (with pressure equal and opposite to its density) has w=-1. In fact, there is a perfectly lockstep relation between the two quantities:
n = 3(w + 1).
Measuring, or putting limits on, one quantity is precisely equivalent to the other; it’s just a matter of your own preferences how you might want to cast your results.
To me, the parameter n describing how the density evolves is easy to understand and has a straightforward relationship to how the universe expands, which is what we are actually measuring. The parameter w describing the relationship of pressure to energy density is a bit abstract. Certainly, if you haven’t studied general relativity, it’s not at all clear why the pressure should have anything to do with how the universe expands. (Although it does, of course; we’re not debating right and wrong, just how to most clearly translate the physics into English.) But talking about negative pressure is a quick and dirty way to convey the illusion of understanding. The usual legerdemain goes like this: “Gravity feels both energy density and pressure. So negative pressure is kind of like anti-gravity, pushing things apart rather than pulling them together.” Which is completely true, as far as it goes. But if you think about it just a little bit, you start asking what the effect of a “negative pressure” should really be. Doesn’t ordinary positive pressure, after all, tend to push things apart? So shouldn’t negative pressure pull them together? Then you have to apologize and explain that the actual force of this negative pressure can’t be felt at all, since it’s equal in magnitude in every direction, and it’s only the indirect gravitational effect of the negative pressure that is being measured. All true, but not nearly as enlightening as leaving the concept behind altogether.
But I fear we are stuck with it. Cosmologists talk about negative pressure and w all the time, even though it’s confusing and ultimately not what we are measuring anyway. Once I put into motion my nefarious scheme to overthrow the scientific establishment and have myself crowned Emperor of Cosmology, rest assured that instituting a sensible system of nomenclature will be one of my very first acts as sovereign.
Neil,
The problem is that these spots amount to holes in the balloon that are letting the air out at the same rate it’s being pumped in. It was Einstein who originally proposed gravity would cause space(the balloon) to collapse to a point and it seems generally agreed that the rate of expansion and the force of gravity are in inverse proportion. I’m really not trying to say anything that isn’t being said, just pointing out that if these two points are true, it appears to be a stable cycle of some sort.
Greg,
Re the above point. I’m just making guesses as to how this might be. Obviously I don’t know squat, just pointing out the above situation. Gravity presumably causes space to contract, while inbetween gravitational vortexes it appears to expand. These two effects are supposedly equal. I just don’t see how this adds up to an expanding universe!
I live just outside of Baltimore, which has an active and world reknown medical community. On the local PBS radio station the other day, they were interviewing a neurologist on the ralationship between the brain and the mind. I called up and made my point that ‘if two atoms collide, it produces an event. While the atoms go from past events to future events, these events go from being in the future to being in the past.’ I pointed out that this is the difference between the brain, which is material and goes from past events to future ones, while the mind records these events and so sees time as narrative falling away into the past. His first response was that it was very deep, then he recovered his composure and start to explain how physics describes time as a dimension which we just happen to be at some point on. At which point the moderator cut to the next question.
John
“Supposedly equal”? Who ever said anything about the two effects being equal? Einstein once contemplated picking a value for the cosmological constant by hand, purely to balance gravitational contraction and ensure a static universe. But there was no reason whatsoever from first principles to compel the cosmological constant to take on such a value. Logically (at least as far as GR is concerned), it can have any value whatsoever. Empirically, it appears to have a value which is definitely not exactly balancing gravitational contraction. It is not open to you to say “hey, maybe it is exactly balancing gravity”, because what we observe is not what we would observe if that were the case.
If you want to think of time like that, go ahead; it’s a perfectly sensible account of people’s experience (and indeed is a predictable consequence of conventional physics). I’m not going to jump up and down and tell you that change is an illusion; if you’ve ever been away from Baltimore, then that was a change, not an illusion.
But don’t kid yourself that this perspective implies that there’s something wrong with relativity’s concept of time. Relativity and thermodynamics (with a little help from basic evolutionary biology) have no trouble at all explaining (in general terms) what you’re able to perceive and remember at different times in your life; you’ll find that physicists are entirely unsurprised that you fail to remember the future, or to get confused between now and 20 years ago. It is of course physically possible for an organism to pay so much attention to its memories of 20 years ago that it confuses that time with the present, but that’s where evolutionary biology comes in; a creature like that would get eaten very quickly.
Greg,
Specifically I first came across the idea is Hawking’s, A Brief History of Time, where he went into the concept that Omega has to be very close to 1 for the universe to be as stable as it is. Later studies of the CMBR by Cobe and WMAP seemed to confirm that the various pertubations of space seemed to balance out to a basically flat or Euclidian space. Even if it isn’t exactly 1, a very close relationship would seem to cancel out expansion as a sinificant effect on the overall universe.
What is the Singularity other then a type of universal macro vacuum fluctuation. It would seem that dark energy is also a form of micro vacuum fluctuation, pushing the galaxies apart. It would seem that with sufficient dark energy, there would be no need for the singularity,other then as the point where it all started. But if X(expansion)+(-X)(gravity)=0, rather then X, there is no need for a beginning. This was how I first started organizing it in my head, if was only later that someone who described himself as a physicist in the Chicago area pointed out that light made a possible medium for the transfer of this energy from galaxies back out across the universe.
I did, among other escapades, hitch hike across the country at 17. It involved a lot of change for me, but probably not as much as the birth of my daughter.
I’m trying to make some sense of this, but it doesn’t really tie into my very simple observation that material change creates events, not the other way around.
P.S.
Well I’m afraid it’s not zero, so bad luck.
Perhaps this should attract the same penalty as describing yourself as a policeman or a doctor.
Nobody at this point in history has the last word on whether physical processes occur “because time passes”, or whether there’s no more content to the passage of time than the occurrence of such processes. Hopefully quantum gravity will eventually clarify this.
But you need to be aware that there are already highly successful ways for physics to deal with time in theories like general relativity, and though these are unlikely to be the last word on the subject, trying to insert a new concept of time into those theories when you don’t have a firm grasp of the existing one is not going to be productive.
Wow, go away for a day and lots of stuff happens
When it comes to gravity waves Egan points out the nonlocalizability of energy. To IMO give a bit of a picture of this imagine that you are trying to quantify some complicated gravitational system with gravity waves. You identify some region, analogous to a Gaussian volume, you want to measure things in. You find that this volume will change, and even in a source free region it may have the same volume but its boundary area will change. The nonlocalizability of energy is the ultimate problem of shooting at a moving target, where not only does the target move but the definition of range and space changes as well. The geometric construction you try to impose to define or measure physical quanitites is effectively a dynamical aspect of general relativity.
When it comes to:
The team’s proposal, which will be published in the journal Physical Review D, does away altogether with dark energy. Instead, Prof Senovilla says, the appearance of acceleration is caused by time itself gradually slowing down, like a clock that needs winding.
“We do not say that the expansion of the universe itself is an illusion,” he explains. “What we say it may be an illusion is the acceleration of this expansion – that is, the possibility that the expansion is, and has been, increasing its rate.”
—————-
The problem with this idea is similar to the old phrase about time being a river that keeps flowing on. By saying this one is referring to a rate of time by another form of time. This really is a sort of category error in my opinion.
When it comes to black holes and cosmic rays, and increasingly cosmic rays are thought to be due to these types of astrophysics, I have certain ideas in the works about aiming spacebased lasers at these sources. The purpose is to then have particle detectors down stream from the lasers. These very high energy protons, which can get up to 10^6 TeV, will scatter with these photons which in its frame are high energy gamma rays. Then with some fancy triggering we can measure the scattering products. In these way we might be able to do some high energy physics with cosmic rays and measure the physics of SU(3)xSU(2)xU(1) standard model at energies far above its symmetry breaking energy. Maybe if there is a framed Higgs field we can detect that as well at symmetry “recovery.”
The gravitational effect in producing these jets and high energy processes is in a way secondary. Imagine that I might have some giant machine which I can squash a planet with. Now this planet might have a 1 Gauss magnetic field similar to Earth, but if I could squash it down to the size of a tennis ball the lines of magnetic field would be pressed together so the magnetization near this squashed planet is huge. The galactic sized black hole does something similar. A moderate or diffuse plasma with a weak magnetic field is gravitationally in an orbit around the black hole. A bit of friction due to interatomic or ionic collisions drains the energy from the plasma. This draws the plasma closer to the black hole with a faster orbit or orbital frequency (Kepler law). This then increases the heating of the plasma and tightens it closer to the black hole. This process accelerates until the plasma is intensely hot and the magnetic field lines of flux are compressed to huge magnetizations. So as this plasma goes deeper into the gravity well the energy E = 1/2mv^2 + GMm/r says constant and the kinetic part becomes very large. I use the classical term because curiously most of this is modelled using Newtonian mechanics. Extreme relativistic effects occur only very close to the black hole.
It might sound a bit strange, but it is actually rather hard to fall into a black hole. You have to pretty much aim right for it, or drop precisely in. The Earth orbits the sun at 29.5 km/sec. If we were to dump garbage into the sun (a slightly silly idea), the mass would have to be sent to a velocity v = 29.5km/sec so it comes to a dead stop in the heliocentric coordinate system. Then the stuff would just drop into the sun. Anything appreciably different will send the mass into an elliptical (Keplerian) orbit that avoids the sun. Also for this reason Earth is not constantly pummelled by the thousands of near Earth astroids that can come very close to Earth. Similarly for a black hole it takes a “dead-eye Dick” aim to actually hit the thing. So the plasma around the sun spirals in by losing energy and the above process occurs in a fairly adiabatic manner. This is why black holes, even collosal ones, can be fairly quiet and are not the star eating monster machines we sometimes think they are. The 10 million solar mass black hole at the Milky way center is actually rather quiet right now.
Lawrence B. Crowell
Lawrence, I am OK with the general concept of non-localizability (to whatever extent, I presume not “all over the universe”) of gravitational energy in various contexts. It does make me wonder, what then about the effective gravitational mass-energy of the radiating system? I presume that as time goes on, I would detect a little less attraction toward a radiating system. In that sense, the energy has been “carried off”, but I wonder about the details of how g would evolve at various r from a radiating system.
Also, isn’t there an issue with conservation of angular momentum in curved space? Make arbitrary Earth-style coordinates for a hypersphere. I can move an equator-parallel spin vector along a longitude to the arbitrary “pole”, then move it parallel to itself down the longitude 90 degrees away, then move it along (but now perp. to) the “equator” back to its original location – rotated 90 degrees with no torque put in. Would that really violate CoAM in the sense there really isn’t a trade-off somewhere, or is total AM thus ill-defined in principle?
(Uh, John, I guess you are waxing poetic up there about those “holes” in the balloon…? Or, do you mean sophisticated newish ideas that gravitons are leaking into other dimensions, etc? If the latter, that is a deep concept that really can’t be done justice to with intuitive models, IIUC.)
Galactic Einstein Lensing:
One of the things which many people do not realize is that this does not stand out as a clear test of general relativity. It can largely be understood with Newtonian gravity, and for a light ray that passes near an elliptical galaxy the dominant gravitational effect is essentially Newtonian — well sort of as I will show below.
So let us just consider this in the light of Newton. A photon which leaves the surface of a body of mass M will start out with a wavelength L. The frequency of this light is then f = c/L. The energy of a photon at the surface of the body is E = hf. Yet if we are to include the gravity field we then have to include that into the picture, and so the total energy is
E = hf – GM(hf/c^2)/r.
We are thinking of the photon as a ballistic object with mass m = hf/c^2 (by the infamous E = mc^2 formula). Now this photon leaves the body and reaches “infinity” or r —> infinity. We have by energy conservation that the total energy must be preserved, and so the photon has a different frequency, we will call f’, and E = hf’. So equate these and we find that
f’ = f(1 – GM/rc^2)
Now clearly f’
(for some reason this cuts these off sometimes)
Now clearly f’
It cut off again, but I will try once more. The prime frequency less than the unprimed and there is an inverse for the wavelengths.
Now for a light ray that comes close to a gravitating body the calculations are a bit complicated, but we can understand something of the net redshifting and blue shifting of light. If the photon starts out with a frequency f and falls into a gravity “well” it will be blue shifted as measured by an observer there. This would be the f in the above formula and by switching the definition of primed and unprimed we have that with binomial theorem (used for GM/rc^2
Well I got a little further, so let me see if the rest will go. It ended with my stipulation on the use of the binomial theorem. Anyway we get the blue shift
f’ = f(1 + GM/rc^2).
Then if that photon travels through the well and then out of the well it is redshifted by the first formula. It should not be hard to see that the blue shift is then completely taken away by the redshift as the photon goes of to “infinity.”
In this Newtonian perspective what we see is that the gravity field is conservative. It does no net work on a body that it interacts with, but simply transfers kinetic energy to potential in a periodic manner in the case of an orbit, or in a transient manner for a body that comes in, is then deflected by the field and goes off on its merry way.
In a full general relativistic setting this situation is complicated somewhat, but the ultimate outcome is not significantly changed. The gravity field does nothing to change the energy of the photon as detected far away. Similarly for a cosmology, say a large spherical S^3 space that evolves with “time,” what ever “higgly piggly” gravitational bumps (hills or valleys etc) due to galaxies or gravity waves or … , that might exist do not change the energy of the photon as measured “far away.”
Finally, what might be noticed by anyone familar with the Schwarzschild metric is that the redshift formula above looks about right, but that it really should read
f’ = f(1 – 2GM/rc^2),
with the “2GM” instead of just “GM.” This reflects a significant departure from an expected Newtonian effect, and was found in 1919 in the famous Eddington expedition to measure the abberation of light around the limb of the sun in an eclipse.
Lawrence B. Crowell
The parallel transport of a vector in a spacetime differs from there being a “force.” Remember, general relativity removes the gravity force. So any vector that is changed by parallel transport along a path does so without there being a force applied. It is the whole coordinate frame which is being rotated. This means that any local observer on that frame will conclude that angular momentum is perfectly conserved.
Lawrence B. Crowell
Lawrence,
You’re right, it does take some digesting.
Those quotes didn’t come out quite right. Been a long day.
Lawrence,
That would be a photon originating from that well.
A photon leaving the surface of a gravitating body would be redshifted. This has been of course detected in the spectra of radiation leaving the surface of the sun.
Lawrence B. Crowell
Lawrence,
I guess my theory has been something along the lines that light is redshifted by climbing over the hills between gravitational wells, as opposed to the Big Bang model, which says it is because these wells are flying away from each other.
You are saying significant redshift is due to climbing out of these wells.
Since the lines between where the well ends and where the hill begins is a matter of perspective, especially since Newton says the wells extend to infinity, can you see why I think the Big Bang model may be overlooking some factors?
John M: Again you need to read what I wrote. If you drop a ball down an elevator shaft it will accelerate, or equivalently its kinetic energy increases. Also its potential energy decreases. Now assume it hits the bottom without loss of energy. We assume a perfect loss-less impact and it bounces back up to the top. It will then reach its point of origin with zero velocity. A similar thing happens to light which traverse local gravity wells. The photons will blue shift locally, but then in climbing back out of the well will then redshift so that the local gravity field results in no change in the energy (equivalently the wavelength) of the photon.
A static gravity field with force F = GMm/r^2 becomes very small as r becomes very large. Its influence is negligable. The potential energy for this force is U = -GMm/r, and if you think about it with a bit of calculus
F = -dU/dr.
The total energy of a mass is the kinetic plus the potential
E = 1/2mv^2 + U.
If this total energy E > 0 then the mass will then leave the gravitating mass and go off to “infinity.” If you set E = 0 you can easily calculate the minimal velocity where this happens, called the escape velocity.
It is best to review some basic Newtonian physics IMO. While Newtonian mechanics has been surpassed by relativity and quantum physics classical mechanics is in many ways very deep and profound. It will also help to clarify some of these issues. Also it really should come as no surprise that people looking at cosmology tend to be pretty bright and are not likely to be tripped up by the issue you appear to be citing.
Lawrence B. Crowell
Lawrence,
I understand that you are saying whatever blueshift created by a photon falling into a gravity well is compensated for by the redshift of it coming back out of that well.
My point is that if the photon originates from within that well in the first place, it is redshifted by exiting it, according to your description. Whether this would explain all of the redshift is another matter, but it would seem to explain redshift as having other possible causes then only recession. If we are detecting redshift of light coming from the sun, it doesn’t mean it is moving away from us.
Astronomers have only been able to seriously examine these effects for what amounts to a moment in time and from one rather small point in space. That limits our perspective. These are effects that have happened over hundreds of millions and billions of years and barely imaginable distances. As Greg said of dark energy, it wouldn’t take much, given the volume of space and lengths of time involved, to add up to serious effects.
The problem with assigning gravitational redshift to stars in galaxies is this is less parsiminous. We might identify a galaxy moving away at 10% the speed of light as interpreted by Doppler shift. This is not too extreme and is a common result for galaxies in the multi-100 mP range. We would also identify the stars in this galaxy, at least by some statistics of light spectra as similar to stars in our galaxy. If we were to interpret the red shift as due to a change in gravity this leads to two difficulties.
The first is that it would mean that any sun-like star in such galaxies is similar to our sun with a larger gravity. Yet a larger gravity would mean a larger pressure in the stellar interior, which would change the internal physics of nuclear energy production. Yet these stars on some average appear no different from star in our galaxy — just redshifted.
The second problem is that the Hubble relationship was derived by looking at Cepheid variables. These are stars with a pretty strict empirically known luminosity-periodicity relationship. We can identify these in galaxies that are reasonably close and we infer their distances with this “meterstick.” If we were to interpret the redshift as due to the gravity of these stars we would conclude that gravity is stronger the further out you look. This would mean that we exist in a very special region of the universe. Yet a crucial aspect of physics is that things are Point Of View Independent (POVI). This interpretation is not POVI, but a model with has galaxies receeding away from each other is POVI.
Lawrence B. Crowell
Lawrence,
The theory I’ve been suggesting is that redshift is a function of the space, a genuine cosmological constant. Say that space really is expanding. Possibly something like a positive vacuum fluctuation that is more field effect then particle production. The redshift of the original space it crosses is further magnified by all the subsequent space and so on, so the further away it is, the faster it appears to recede. Since relative space is essentially as fluid as what is defining it, this field condenses out as particles, which eventually gravitationally clump.
This model would be point of view independent because every galaxy would appear to be flying away from each other, with speed proportional to distance, since we can only measure the light which has actually traveled the distance, not all that which has been intercepted, deflected, absorbed, etc. We only see what has been the most redshifted, not everything blueshifted as it fell into gravitational vortexes and didn’t manage to come back out the other side. Which is most of the energy and which released the pressure, keeping the universe from actually expanding. Consider the effect attributed to dark matter, the spin of the outer bands of galaxies that cannot be attributed to gravity. An external pressure on these gravitational systems and the gases that are their initial stages might solve the problem as well as adding additional internal attractive forces. On the stellar level, it may explain the Pioneer effect.
Obviously I’m proposing a field/wave/particle relationship that is beyond my ability to explain at the microcosmic level, so its basis is on how it explains the macrocosmic phenomena. I realize I’m not going to get any support on it either, but it certainly isn’t any more fantastical then many of the other theories, both establishment, quack and many of those somewhere inbetween.
Do we really undertstand the relationship of light and electricity as particles, as waves and as fields to say that radiation doesn’t interact at levels we are unable to measure with current techniques? It does seem to me that we have become convinced that reality at the quantum level is discontinuous digits more then analog fields, but maybe it’s only that particles are easier to detect then what holds them together.
This is a most interesting thread. Seans initial assertion that “dark energy” is “stuff”, and has a gravitational moment is, I believe very correct.
Dark energy is singular massed space…observed as a quantum Planck Realm at differing scales directly related to local energy density…it is completely non-particulate, but has a cumulative mass equal to 74% that of the universe…perhaps as much as 96% if we assume “dark matter” to be the combined mass of all macroscopically (from our frame of reference in scale) identifiable singular objects…10 solar masses up.
I’m not the only person who seriously doubts that the cosmological red shift is doppler related…even though we all know that motion DOES cause a doppler redshift in light. Some galaxies nearby actually have their light blue shifted.
From our frame, today, we observe space to be almost flat (Omega total 1.02).
However as we observe outward, we observe a universe where by General Relativity (and Big Bang concept) space time was more curved than today; the universe was smaller in terms of its present size and more gravitationally dense. The farther out we look with our telescopes, the greater this observational effect becomes.
At 2 million light years “distant”, the Andremeda glaaxy fills about 30 minutes of arc in the sky. At 10 billion light years “out”, that same 30 minutes of arc contains millions of galaxies. The combined mass of the space between us and these galaxies and to a much lesser extent, the baryonic mass of the galaxies themselves cause the light we observe to be gravitationally red shifted.
From our frame of reference, we feel that the universe is more vast with distance. It is not. Rather the universe becomes progessively younger and smaller, space becomes more curved and dense, and we observe the same gravitational redshift with the universe itself which we can identify with single astronomical objects of extreme density…quasars for example.
Since quasars are distant, we observe them to be gravitationally redshifted in much the same way as the distant galaxies which surround them.
LC,
In following this thread, I gather that you have a strongly temporal interpretation and concept of the universe.
No quick and general definition is very much good, but for JM’s benefit, and as “temporal” relates to this discussion, the temporal approach regards the universe as an object which is evaluated by a separate, objective observer- and this is very important- has an identity of its own…it essentially exists as it is whether I (we) are here to observe it or not.
I get this impression from the way you (LC) have discussed biological existence, and its role in the universal order on this thread.
I believe reconciling General Relativity and Quantum Mechanics can only be achieved by disgarding the “temporal” view and adopting an “atemporal” approach, in which the universe ONLY exists in tandem with observation and in which the observer is an integral part of the cosmic system.
From what I have studied about what modern physics has learned over the last 75 years or so, I believe a temporal view of the universe is not justified by the field evidence..the facts…presently at our disposal.
Best Wishes…Sam Cox
A gravitational blue shift is only observed if you are at the “bottom” of the gravitational well.
The dark energy, a moniker we give it, may well be due to a Higgs-like particle that in four dimensions gives an action
S = int d^4x sqrt{-g} (k + H^2)(R – A*H^2),
where k is or related to the gravitational constant and A is another constant. The Higgs field evaluated on the physical vacuum (after the Goldstone has been absorbed) and so H^2 —> . Th value of H^2 on the vacuum expectation defines what we call the cosmological constant. How this action is arrived at, which is a rather canonical form, has to do with the nature of quantum gravity and unification. There are a number of ways to look at this, such as string theory, Loop Quantum Gravity, or maybe some other approach.
Again to say that dark energy is a “stuff” is problematic. It is similar to the temptation to consider space and time as a physical “something” in general relativity. If we have a point “x” and define this in two metrics for spatial surfaces (two different frames) g_{ij}(x) amd g’_{ij}(x), then by “pushing” the spatial metric forward in time this will give two different points. That this is the case it indicates that spatial quantities are frame dependent and not physically real. This is an aspect of general covariance. General relativity is really about the relationship between particles, not between abstract geometric objects such as points in space or spacetime. In the case of dark energy it is likely a manifestation of the physical vacuum expectation of the Higgs particle H, and is then something which gives a relationship between physical particles.
An atemporal approach to quantum gravity is probably somewhat on the mark. Time is a curious quantity. In quantum mechanics it is regarded as conjugate or complementary to energy. Yet for those who understand classicl physics and Hamiltonian formalism there are not Poisson brackets between time and energy. Quantum mechanics exploits a Fourier relationship between frequency (or energy by E = h*freq) and time, but quantum mechanics does not define an energy operator. Time exists in a manner not entirely equivalent to spatial quantities which have a strict dual to momentum in classical mechanics.
Consider a quantum wave equation i&Y/&t = iHY, for the wave function defined for the metric as the configuration variable Y = Y[g]. Then for two states Y[g] and Y[g’], we might expect that a superposition of these two states is possible
Y” = AY[g] + BY[g’]
for A and B amplitudes with 1 = sqrt{A^2 + B^2}. But this really is not possible in a completely covariant manner. To form such a superposition is to define a coordinate map between two metrics g’ = g + &g. Yet this is really a “bimetric” abuse.
The Einstein field equation R_{ab} – 1/2Rg_{ab} = – k T_{ab} in the trace reversed form is R_{ab} = k(T_{ab} – 1/2Tg_{ab}). For a source free spacetime, T_{ab} = 0 the Ricci curvature is zero. In a source free region R_{ab} = 1/2Rg_{ab}, but under the assignment of two metric in &g assume a small violation of the Einstein field equations means a nonzero Ricci curvature is determined by a “potential,”
R_{ab} = nabla_a nabla_bV =/= 0
where the potential is a metric difference V = (g’ – g)_{ab}g^{ab}. The perturbed vacuum Einstein field equation may then be written as
nabla_a nabla_bV = 1/2 nabla^2V &g_{ab}
or according to the difference in the metric
nabla_a nabla_b& delta g = 1/2&g_{ab}nabla^2 &g.
When contracted on indices and integrated over a region volume in M^4 we find that using the Greens theorem
int_{vol} dv &g nabla^2 &g = -int_{vol}dv nabla &g nabla &g = -int_{vol} dv (nabla g’ – nabla g)^2,
which is the source of the energy error functional &E_g = |nabla g’ – nabla g|^2.
The energy error functional may be written according to a variation in the Ricci curvature, where the contributing term will be R_{44} = -nabla^2 Phi/c^2, for Phi the newtonian gravitational potential
int_{vol} dv &g nabla^2 &Phi/c^2 = -int_{vol} dv (nabla Phi’ – nabla Phi)^2/c^2
Hence the relevant quantity is a fluctuation in the Newtonian force. The variation in the Newtonian force will then manifest itself as the variation in the angle of swing for the torsional balance. The energy error functional is &E_g = hbar/&T. This error functional is a measure of our “ignorance” in assigning a coordinate map between the two metrics. It also indicates a potential relationship between the uncertainty principle and spacetime physics.
This appears to be an indication of how one relationship system, gravity and a geometric relationship between particles, and another system of relationships, quantum mechanics and entanglements etc, are related to each other in a general relationship system. This appears to require that time be regarded as “derivative.” the energy error functional for zero energy uncertainty (a fine grained description) has the time uncertainty &T —> infinity. In other words time is so uncertain that it effectively does not exist.
Lawrence B. Crowell
Lawrence,
Why is there no loss? Some of the light falling into the well doesn’t re-emerge at all, so why wouldn’t that which does loose some energy?
Are particles the reality, or are they the equivalent of the crests of waves that cannot otherwise be measured? They would still be another layer of abstraction in that case.
Temperature is a derivative of energy, but that doesn’t mean it doesn’t exist. It seems that relativity recognizes the subjective nature of time, but still assumes there must be one absolute dimension of it along which everything ultimately travels. If time is a consequence of motion, like temperature, rather then a basis for it, then the only absolute time would be the complete absence of it, like temperature.
Sam,
It seems from the above that you are describing a non-expanding universe, where redshift is due to crossing non-particulate energy of space, while the following seems to describe an expanding universe?
QUESTION: Why is there no loss? Some of the light falling into the well doesn’t re-emerge at all, so why wouldn’t that which does loose some energy?
The set up is artificial with loss-less impact of a ball at the bottom of a shaft, and of course assuming it bounces right back up vertically. But it is a matter for illustration. Gravity is a conservative for F = -GMm/r^2, assumed in the radial direction — I’d prefer not getting into vector notation. Kinetic energy is defined by the displacement of a mass projected on the force T = int F*dx, or for a linear (eg eacy) displacement FX. So consider the change in the kinetic energy from going between the radial point R and R’
T = -GMm in_R^R’ dr/r^2 = GMm(1/R’ – 1/R).
Now consider the displacement of the mass upward back to R
T’ = -GMm in_R’^R dr/r^2 = GMm(1/R – 1/R’).
Now clearly T’ = -T and so the change in energy of the particle falling down the shaft, bouncing at the bottom and returning is zero. Similarly this is why two gravitating bodies can remain in orbit “eternally.”
QUESTION: Are particles the reality, or are they the equivalent of the crests of waves that cannot otherwise be measured? They would still be another layer of abstraction in that case. Quantum waves are complex valued, which means they are not real valued in mathematics. Physically the quantum wave is not regarded as real either, but more as an abstraction which contains all possible information about a quantum system in a measurement. Now a quantum wave Y defines a probability amplitude dP = Y^*Y dV, where dV is an infinitesimal unit of volume of space. This leads to
P = int dP = int_V’ Y^*Y dV = 1
over all space. A sufficiently peaked wave function or a probability weighted heavily around a point appears similar to a particle. In fact classical mechanics is similarly probability wave mechanics, but where the position is weighted by xY^*Y and if Y^*Y = delta(x-x’) then under integration gives x’ and the classical dynamics of a particle x’ = x'(t).
As for temperature, that also has relationships to energy as well. The euclideanization of a wave function with t —-> it (i = sqrt{-1}) converts exp(i*freq*t) to exp(freq*t) so that freq*t appears formally equivalent to E/kT, k = Boltzmann constant, T = temperature.
At the Planck scale unification there is an absolute upper temperature, given by the equipartition theorem E = kT and for E = sqrt{hbar c^3/G} = Planck energy, then T = E/k. This Planck temperature is about 10^{37}K — huge and appears to represent an upper temperature limit. In string theory there is the Hagedorn temperature, related to this, where all string modes contribute. This extreme temperature is tied to the origin of time in some way, and it is the temperature of the earliest part of the big bang, or a temperature associated with the singularities of black holes. Hot Stuff!!!
As for the curvature of the early universe, if it is a sphere then at earlier epochs it has a higher radius of curvature. So as we look further out, since light travels at its locally finite speed we see earlier into time. So far the universe looks very flat, so if the universe is a sphere we see only a tiny portion of it. The inflationary period converted a region of the universe a billionth the radius of a nucleus into a meter or so in size. The curvature of the universe was drastically reduced.
Lawrence B. Crowell