This is what science is all about; getting thrown a curveball by Nature and plunging in to find out what's going on. -Andy Albrecht
Imagine waking up in the morning and heading out into the sand dunes. They never look exactly the same from day to day. But each day that you go out, they'll look somewhat like this.
You consider yourself smart and well-informed, and you have a sense of adventure. So each morning, you venture out a little farther into the dunes. You find a variety of different features, but everything pretty much just looks like, well, sand dunes. One day, however, all of that changes. You venture out farther than you've ever gone before, and you see something that simply bewilders you.
Something like this, that appears to be dinosaur footprints! Well, suddenly you have this huge problem in front of you! On the one hand, you know that dinosaurs have been extinct for 65 million years. On the other hand, you examine these footprints, and you find that they're fresh. You walk around more, and you discover that this area is covered in dinosaur footprints. The tops of the dunes, the deepest valleys, the rolling straightaways, all of it.
So what do you do? How do you make sense of this? I mean, it seems that there are two major possibilities. Either these footprints were left by a creature that is going to cause you to drastically change your worldview,
or something -- perhaps a roguish person, a coincidence of unlikely natural events, or a poorly understood phenomenon -- is conspiring to make the land appear like it's inhabited by a creature that, according to your present understanding, doesn't and shouldn't exist.
This is the essential question in this situation: is what you're seeing indicative of what you're thinking, or is there another cause for the effect you observe?
If you're like me, your intuition in this situation will tell you that you need lots of hard, convincing evidence before you're ready to change your worldview so drastically.
Coming into that situation, it's probably fair to say that you didn't expect you'd be believing in the highly improbable, but now you've got a mystery to solve. While this dinosaur situation never actually happened, this is essentially what happened to cosmologists in 1998, when the first evidence for dark energy was discovered. We had measured the expansion rate of the Universe relatively nearby, and had figured out what the Hubble constant was. But at this point, we didn't know what the fate of our Universe would be. But we could figure that out, if only we knew what the contents of the entire Universe were. We looked at extremely distant supernovae, trying to discover what the expansion rate of the Universe was in the past, and hence, what the fate of our Universe would be.
Would the Universe recollapse, like the yellow line shows? Would it expand off into infinity, watching its size increase ever-so-slowly as the expansion rate drops to zero, begging for just one more proton, as that would be enough to cause a recollapse, like the green line? Or would it expand off into the abyss of emptiness, like the blue line? In any case, it would never follow that ridiculous curve shown by the red line; nobody even considered that. Yet in 1998, the data came in, and of those four cases, what did the data indicate?
Well, it was hard to tell, but it was more consistent with the red line than any others. You couldn't rule out the blue line, and the green line was pretty inconsistent, but it was hard to tell. When I started graduate school in 2001, more evidence had rolled in, but I wasn't ready to believe it yet. I needed to find out more information first, and I approached it the same way I'd approach the dinosaur footprint situation: assuming that there was an alternative explanation for why we observe this oddity.
Could something be blocking the light from back then? Could supernovae be intrinsically different when the Universe was so young? Could something be happening to the light (like photon-axion oscillations) that mimic the effect of dark energy?
I looked at these and other alternative explanations -- in incredible depth -- and it turned out that they just couldn't account for what we saw. (See my recent dark energy series.) In the meantime, data from other sources was rolling in. The cosmic microwave background, galaxy clusters, and many other distance indicators all pointed towards a Universe that was inconsistent with physics unless it had dark energy in it.
It took a little over three years to convince me to start to change my beliefs, and to accept dark energy, but it was coming along, and I certainly had moved from the "No way is this thing right" camp into the "Wow, there's a lot of evidence for it and no real wiggle room to get out of it" camp. The nail in the coffin (for me) came when a very smart man proposed an interesting alternative explanation for dark energy. While researching whether his explanation was feasible or not (and -- while it's an interesting idea -- I concluded that it's not), I really became very well-informed about dark energy, its alternatives, and its implications, among other things.
It suddenly occurred to me that if you wanted to eliminate this one thing, dark energy, it would take a minimum of six separate observations to be overturned. And that was it; it was suddenly unreasonable to me that I would reject dark energy. But it took three to four years of studying it intensely, becoming some type of expert in it (as much as one can be), and writing papers right on the cutting edge of the science to convince me. It's the only scientific conclusion I've had in my life where I've had to reject it and take up the antithesis of my original position, based on new observations.
And now, today, I defend dark energy, because I understand why we need it. So don't believe that dinosaurs exist just because you've found footprints. But when you've exhausted all other alternatives, and you've found lots more evidence for them, don't cling too dearly to your old beliefs in spite of the new evidence. And choose your experts wisely.
(And no, there aren't dinosaurs in the dunes; I made that part up.)
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Fantastic analogy. Of course as an outsider I'm still skeptical of dark energy. (Back when I last took a cosmology course there were still factors-of-2 disagreement between different experimental values for the Hubble constant, and that wasn't that long ago.)
But I hear what you're saying, and I'd agree that the dark energy evidence is currently the most exciting evidence for "new physics".
Nice post. Thanks for the personal point of view on the subject.
Sorry, you're wrong.
Read "The Big Bang Never Happened", by Eric Lerner; and
"Dark Matter, Missing Planets and New Comets" by Tom Van Flandern
@shhret: I am *not* a professional cosmologist, as Ethan is - but even I know that Lerner's and van Flandern's arguments are wrong... I've looked at them a few years ago, and even my level of knowledge about cosmology and General Relativity was enough to disprove their claims.
E. g. for Lerner's argument, see here:
http://www.talkorigins.org/faqs/astronomy/bigbang.html#lerner
http://www.astro.ucla.edu/~wright/lerner_errors.html
So, what's your level of knowledge about cosmology and General Relativity? How do you know that what Lern and van Flandern say is right, and what Ethan says is wrong?
@Ethan: Did really nobody expect an accelerating universe back then? I seem to remember several papers (about large-scale structure formation) even in the early 90ies which studied models with a non-zero cosmological.
And why is this discovery so hard to accept? Lambda is essentially simply another parameter in the Big Bang model. For decades, one assumed, as far as I can see, simply for simplicity and because there was no evidence saying otherwise, that Lambda = 0. The SN measurements showed then that Lambda isn't zero. Sure, that's not exactly what was expected - but also I don't see why such a result should be so controversial.
Especially when, on the other hand, there were theoretical reasons to suspect that Lambda might be non-zero. See e. g. Turner's article "Dark Energy: Just what theorists ordered"
(Physics Today, vol. 56, issue 4, p. 10)
Nice write up, Ethan. Thanks.
Am I correct that dark energy (since we don't understand its origin) violates the 1st Law of Thermodynamics (energy cannot be created)?
Or is considered an ongoing expansion of the Big Bang itself, balanced out by gravitational potential energy it necessarily creates?
"And choose your experts wisely"
And that is the hardest part for people like me (the layman). I often get really confused on which "expert" to trust.
@healthphysicist:
In General Relativity (and hence also in the Big Bang theory, which is based upon GR), it's in general not even possible to define the total energy of a system; and in most cases where that's possible, it turns out that that energy isn't conserved. So you could argue that GR altogether violates the 1st Law.
The reason is essentially that where Newtionan gravity talked about potential energy in a gravitational field, GR has nothing comparable - because according to GR, gravitational fields essentially not exist (they are replaced by curved spacetime).
For more details, see here:
http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html
Bjoern @5,
Mike Turner was one of the people who pushed for a Universe with some type of non-zero cosmological constant a few years before the SN data came in.
Why? The large-scale-structure data fit slightly better with a little dark energy than with none. But Mike Turner has made a long (and successful) career out of advocating for highly unlikely but not implausible positions, and this is perhaps the most stunning example where he turned out to be right. (And -- as a result, maybe -- he got to coin the term "dark energy.")
But it's fair to say that nobody "expected" dark energy in the sense that nobody had a compelling theoretical reason to expect that the vacuum energy of the Universe would have the value it does. In all fairness, that statement is still true, despite over a decade of work.
Thanks, Bjoern!
@Ethan: Thanks.
BTW, I've found one of the papers on structure formation I mentioned:
S. D. M. White, Large-Scale Structure at High Redshift, in The early Universe with the VLT (ed. J. Bergeron), Springer (1997) 219
Was this inspired by Turner's suggestions?
I agree that obviously nobody expected the exact value for the vacuum energy resp. could have calculated it; but I'd think that the idea that in principle, Lambda could be non-zero, has been around for a fairly long time.
Wow! I'm convinced! The stunning argumentation of this comment totally blows the original post out of the water!
--o--
Thanks, Ethan. It's good to have some real authority to refer to, when one is getting overwhelmed with uninformed waffle. (For my own sake - not as a club to 'win' an argument. Your explication of the evidence is the tool for that.)
Thanks for the personal history in this post. I appreciate very much seeing science in action -- a clear story (and one of very many, though not often told) of scientists with the curiosity, carefulness, and intellectual honesty to completely reverse their opinions on a topic that they care very much about over a few years, based on evidence.
Which is the process of science at its best.
I can only support, what Bard Bloom said: science at its best. I got to know some scientists in my life, and sadly there are several -- to many -- among them, who are not like you.
Am I correct that dark energy (since we don't understand its origin) violates the 1st Law of Thermodynamics (energy cannot be created)?
Look up the Casimir effect.
What's the "oddity"? I don't recognize the photo. And why is it odd?
Douglas Watts - I am familiar with the Casimir effect, in which the effect is either explained in terms of vacuum energy (virtual photons) or virtual particles.
The effect doesn't address energy conservation....how can these be creasted while maintaining conservation of energy?
It seems we have to toss out energy conservation in the Casimir effect (quantum realm) and dark energy (general relativity realm), and only apply it in "everyday" scales of systems.
That's was the point of my original question...do we toss out energy conservation, or can these phenomena be explained consistent with principles of energy conservation?
I didn't believe it at first, but I came around a lot faster than you did :) I also came around before most people heard about it....
I was on one of the two teams that announced the discovery of the accelerating universe in 1998. I remember in the last several months of 1997, I was busy working up the supernova lightcurves, double checking them, making sure all the data was in, making sure all the corrections and calculations had been done right. Then, at group meetings, Gerson Goldhaber told us that doing a quick analysis of the data, we were clearly seeing Lambda > 0. My response was, "yeah, that will go away when I finish checking all of the things to go with the lightcurve." (There was still the more careful statistical analysis to do, but the eventual signal was strong enough that Gerson's pen-in-the-notebook way of doing it could see the effect; to discount it on the basis of "we have a more sophisticated analysis to do" would be making the same mistake that led to the Hubble Space Telescope having an spherically aberrated primary mirror.)
Over the next weeks and months, as I checked the lightcurves again and again, and went through the data, and became more and more convinced that they were right, I sort of got used to the idea that the results we were getting were what they looked to be. So much so that in the January, 1998 AAS, when I gave a 5-minute talk and Saul showed the poster with our Lambda>0 results, I was a bit taken aback by how big the news was for everybody. Since I'd had time to get used to it, I didn't quite anticipate the huge splash that would come.
My nightmare was that we would find out that both teams had made the same (1+z) error in their K-corrections, and that would make it all go away... of course, we know that didn't happen.
I guess I was a "partisan" at that point. When I heard about things like grey dust, and other effects that might render the accelerating Universe result a systematic effect rather than evidence for dark energy, I'd tend to think, well, that's far more unlikely than what we really have. This is why you need multiple people with different biases doing science, and you need to share the results openly... so that people like Ethan who were more disinclined to doubt it will take the other ideas more seriously than people like me who were in on the original discovery. If one of the other ideas had turned out to be right, I would have eventually become convinced by it as Ethan was eventually convinced by Dark Energy.
Re: energy conservation -- General Relativity does *not* have a *global* energy conservation law.
It does have a local energy conservation law, which basically says that if you draw a small box in spacetime (small enough that it can fit within a valid "locally flat" coordinate systeM0, the change of energy in that box is equal to the rate at which energy is flowing in or out of that box.
But GR doesn't have any concept such as "the total energy of the Universe". As such, there's no total energy conservation law.
@Rob Knop, Ethan: many thanks for your personal accounts! Great read! :-)
@healthphysicist:
There are two ways to look at that - the first more used in popular science accounts and by experimental physicists, the second more by theoretical physicists...
1. One could say that Heisenberg's uncertainty principle allows temporary violations of energy conservation - simply because the energy of a given state isn't sure, but can only be determined up to a (usually small) interval; that's the larger the smaller the time interval is one considers.
(the crucial point here is that this isn't simply a measurement error - the energy *really* has no fixed, given value, but you can only give probabilities saying what the energy actually is!)
2. Or one says that energy is always conserved - but then you have to pay the price that virtual particles have rather unnatural properties, e.g. negative energy although they have positive momentum (in technical terms: they don't satisfy the "dispersion relations" of real particles).
E. g., in Quantum Electrodynamics, one of the simplest vacuum processes is the appearance of a photon, an electron and a positron out of nowhere at the same place, which travel a short time and then come together again and vanish.
According to the first point of view, the time interval they existed was so short that the total energy of the vacuum could have been a bit larger - and that explains the energy in the particles. According to the second point of view, one or two of the particles had negative energy, and in their total energy was always zero, equal to the vacuum energy.
Hi Bjoern - I'm glad I checked backhere.
I fully understand the points you've made, but on a macro-scale, the net result should be zero energy, since over larger periods of time and spans of space, negative and positive quantum energies (or energy uncertainties) cancel.
This "expectation" should lead to conservation of energy.
Dark energy seems to be one directional (expansion over contraction). So I think energy conservation must not apply at all and only be used within certain scales (not used in general relativity nor individual quantum mechanical phenomena, though averaged quantum mechanical phenomena should statistically cancel for the most part).
@healthphysicist: On a quantum level, energy conservation holds strictly. In General Relativity, it doesn't.
Quantum Field Theory predicts a non-zero "zero-point energy" density. Since this density is everywhere and at every time the same, it follows that if the volume of space increases, the total value of the zero-point energy increases, too. That increase is possible because, as mentioned, in GR global energy isn't conserved.
If I remember my QFT lectures correctly, this "zero-point energy" is *not* directly related to virtual particles; it exists even without those... I'll have to look that up again.
I found this fairly easy to read and states that zero point energy is assumed to be "created out of nothing", see paragraph "Dark Energy":
http://www.calphysics.org/zpe.html
Therefore, no energy conservation.
Typically, quantum mechanics equations can be applied to classical physics and you get the same classical answer (though simpler to go straight away with classical equations).
So I would expect, that Dark Energy theory, should also be consistent from quantum to classical interpretations. That suggests that there is no energy conservation at the quantum level (dark energy created out of nothing).
I need to go walk the dog and ponder.
The best current evidence shows that the expansion was decelerating in the past, and at some point (IIRC, relatively recently on cosmological scales) began accelerating, correct? As your last diagram shows?
So, without any certainty yet on what the mechanism of action called "dark energy" is, why do so many things I see about it talk about runaway acceleration. That is, why does no one seem to think that the acceleration may be a temporary phenomenon? I know that under some theories regarding what dark energy is, runaway acceleration is inevitable, but is it so in ALL reasonable theories? It just seems to me like if nature can surprise us once, it can do so again and again; and that no one I've seen seems to express that fact. I'm wonderig if it's due to a degree of certainty, or for other reasons (not wanting to overcomplicate things when talking to non-scientists or whatever).
@BenHead:
I'd think it's simply due to Occam's razor: the simplest model says that the acceleration will continue forever - and as long as we don't have evidence which says otherwise, we'll stick with the simplest model.
Obviously, that does not mean that research stops - other models are still actively investigated, but for now, there are no compelling reasons to actually use that models.
In the back of my mind is the book, The Black Hole War, about Stephen Hawking's conclusion that information is destroyed in a black hole.
Susskind, the book's author, couldn't accept this, because it was contrary to very fundamental physics (information can't be destroyed, and information can be related to energy...entropy is hidden information.
After decades of work, Susskind overturned Hawking. And information is NOT destroyed in a black hole.
It seems to me that dark energy poses the same sort of problem in reverse (creation vs. destruction).
@healthphysicist:
It would be more sensible to say that General Relativity poses the some sort of "problem" in reverse, because there are several cases where General Relativity says that (global) energy isn't conserved; dark energy is only one of them.
And I don't see why you call that a problem - why *should* global energy always be conserved? Sure, you could say that one never has observed a violation of the conservation here on Earth - but after all, we are not talking about ordinary circumstances here, but about really large scales!
Hi Bjoern:
If global energy is not conserved, then it comes from somewhere outside of our universe.
I would find that very profound to have something entering our universe from beyond it. Much more profound than Susskind's restlessness with information being lost in black holes.
I guess I don't understand what prompted Susskind's decades-long uneasiness with information loss, but no similiar uneasiness with GR/dark energy. It seems inconsistent. Susskind felt that ALL of physics was at stake based on information loss, but doesn't even mention the similar conundrum posed by GR/dark energy in his book.
I have no real sense of "should" (though it would be my first intuition, that energy is conserved). But I would have a great sense of profoundness if energy were entering our "closed system" of the universe.
@healthphysicist:
Huh?!? Why? How does that follow?
BTW, if one, as is often done, defines "universe" as "all that exists", the phrase "outside of our universe" makes no sense.
Methinks this is not "intuition", but that you simply think so because you've been told all your life that energy is always conserved.
Bjoern-
Told, yes..but also experienced (ie. the food we metabolize, gas in car engine, etc.). And intuition is just a guess based on past experiences (what one has been told included).
A formulation of the First Law of Thermodynamics (energy conservation law), is that in any process of an isolated system, the total energy remains the same.
If global energy (throughout the universe) is not conserved in our isolated system (the universe), and if at the quantum level within our universe, energy conservation holds (from your post 1/17 @ 3:40)...then it seems to only follow that the energy comes from outside our universe.
@healthphysicist: Wrong. *If* energy indeed came from somewhere else, (1) the universe would *not* be an isolated system (by definition, a system is isolated if no energy is exchanged with its "outside"), and (2) overall energy (universe + outside) would be conserved. So your conclusion does not follow in the least.
"energy is not conserved globally in the universe" means "the 1nd law does not hold for the universe". This doesn't imply in the least that energy has to come from somewhere else. "energy is not conserved" means the same as "energy can be created out of nothing" (or destroyed).
I just (re)discovered something.
In Susskind's book, he does mention dark energy, it's just not in the index, and only mentioned once (as far as I can tell). He equates it to the cosmological constant.
So if you go back to my first post (1/16 @ 9:35 a.m.), I've answered my own question (at least if I use Susskind's answer).
Dark energy is considered (by Susskind) to be part of the Big Bang itself and therefore, does not violate the First Law of Thermodynamics (ie. energy is not added to the universe).
i think i will reserve judgment until i hear what sarah palin and jenny mccarthy have say about dark energy when they are on the next oprah show.
Bjoern -
The energy can't be "created out of nothing" and at the same time be conserved quantum mechanically, as you yourself stated.
I didn't really think that the dark energy originates outside the universe, but that is the unreasonable conclusion if energy is not conserved. Sort of like assuming information becomes missing in a black hole...where would it go? The answer, of course is that it is not missing, it goes nowhere, it stays in our universe.
Nor is dark energy created continuously out of nothing, but is the cosmological constant of the original Big Bang. And this gives the universe a net energy of zero.
@healthphysicist:
Huh? That's a non sequitur.
The cosmological constant is equivalent to a constant energy *density*, and hence to an *increasing* energy - not to a constant energy.
Why?
No one knows the cause of the Big Bang.
By equating dark energy with the cosmological constant, the expansion of the universe is "accounted for" from the very beginning (which envelopes it into the mystery of the Big Bang...not an answer, but pushes it back).
As you state, the energy density is constant, but is driven by the cosmological constant. The dark energy increase is balanced out by the change in gravitational potential energy. Energy conservation applies.
http://www.astrosociety.org/pubs/mercury/31_02/nothing.html
@healthphysicist:
What is that supposed to mean?!?
And that?!?
As I told you already *way* above (January 16, 2010 11:02 AM), in General Relativity, the concept of "gravitational potential energy" doesn't exist (one can't define it in any meaningful way).
The article you quote
1) uses Newtonian physics, whereas you can only explain the development of the universe as a whole using General Relativty; a Newtonian approach gives some clues, but can't be the final answer
2) doesn't even mention dark energy or a cosmological constant.
No, but you are up against some pretty credentialed cosmologists if you want to make energy not be conserved, and have a net universal energy increase... Fillipenko, Susskind, and Krauss, to name a few.
Good luck with that!
Here's Krauss on the same subject:
http://www.youtube.com/watch?v=7ImvlS8PLIo
Bjoern and healthphysicist,
You two are having quite the back-and-forth. I thought I'd interject a bit.
Energy has a good classical definition: the ability to do work. We can measure it, convert it from one form to another, and use it. But that definition only holds within a fixed, finite amount of space.
When you come over to general relativity, where space no longer means what you're used to on Earth, those definitions break down. People can argue all they want as to whether energy conservation holds or not, but the fact is -- at least on the scale of the observable Universe -- we don't have an agreed upon definition of Energy, which makes it hard to argue about whether it's conserved or not.
Susskind and Krauss' arguments hold based on one specific definition of energy, which may or may not be true. (Filipenko's argument is circular, defining energy as the thing which makes the sum of the whole shebang=0.) It's not that any of them are wrong, per se, just that it's reliant on the definition of something we don't know how to define, at least not yet.
Thanks Ethan, that was helpful, but also woeful, if we don't have an agreed upon definition of energy.
I also thought that the Landau-Lifshitz pseudotensor allows energy (whatever it means) conservation laws to be extended to general relativity.
If energy isn't conserved....where does it go/come from?
@Ethan: Thanks for interjecting. I thought that "healthphysicist" was already aware of the things you pointed out, because they are explained at the webpage I cited - but apparently this was news for him...
@healthphysicist: I may have Fillipenko, Susskind, and Krauss against me - but as Ethan said, their definition of energy is not unique and not agreed-upon by everyone. And I have Baez, also a quite knowledgeable physicists, on my side... (see the link I provided in the comment on January 16, 2010 11:02 AM)
The problem with the pseudotensor is also explained there. Haven't you looked at that page so far, or have you already forgotten that?
Hi Bjorn:
Yes, I looked at & remembered the link. I got out of it that in GR there is non-equivalence of energy-momentum conservation in local, flat spacetime (Eq. 1 under Expansion of The Universe...paragraph) and large scale spacetime (Eq. 3), but that this inconsistency could be overcome by the use of the pseudotensor, though there are some pro's and con's with it (I probably don't have a good math appreciation for the pro's and con's since I've never done any GR work).
It does this in the context of looking at the EFFECT of universal expansion, in trying to explain what happens to the energy of red-shifted photons. Without really understanding pseudotensors, I would have just intuited that the lost energy isn't lost and becomes gravitional potential energy. To say the energy is lost, forces me to ask to where?
But I can't pull out of the link anything regarding the CAUSATION of the expansion. Is it assumed to be the cosmological constant, which was, afterall proposed in GR? And if true, wouldn't it be consistent with what I've (my references) have been saying? Maybe what I'm missing is the other "can of worms" issue at the end, which isn't elaborated on.
Slightly aside, I understand that if one calculates the vacuum energy, it works out to be 10^120 times greater than the measured dark energy. There would then have to be a cancelling effect, leading to the observed value of dark energy. But why should the cancelling effect be expansive over long periods of time and not, at least periodically contractive? Since for any vacuum energy pushing say, two galaxy clusters apart, there would exist vacuum energy pushing them back together.
I'm not sure how that calculation was done, because inherent in the concept of vacuum energy is that it exists within very short time intervals (within uncertainty principle). Why would it manifest itself over such long time spans as the age of the universe?
I know the Casimir effect is used as evidence of this manifestation, but that may actually be van der Waals forces, and even if truly quantum vacuum energy, it is contractive, not expansive, and requires inducing a field between conductive plates (not at all representative of galaxy clusters).
I find that equating dark energy with the cosmological constant has the fewest inconsistencies (because it really just pushes the explanation back into the unknown of the Big Bang, while maintaining many consistencies).
@healthphysicist:
I think this is particularly important (from that webpage):
This shows quite clearly, IMO, that the pseudo-tensors aren't sensible descriptions of energy density.
I don't understand. If you could say where the energy went, it wouldn't be "lost"! "lost" means (here) "it doesn't exist anymore", not "it went somewhere else".
I'd say that no one actually knows the original cause... if you read Ethan's recent series, one could say that the "momentum" the universe gained from inflation makes it expand more and more; but as Ethan already pointed out, the cause of inflation isn't known so far.
The cosmological constant does not cause the expansion; it causes the *acceleration* of the expansion. (in mathematical language: if you call the scale factor a, then the cosmological constant does not cause adot to be greater than zero, but adotdot to be greater than zero).
Sorry, I don't understand the question. Since the laws of physics and the constants of nature don't change with time (as far as we know), how *could* the cancellation have different effects at different times?
Vacuum energy density is constant, the same everywhere - so how could it do different things at different places?
As I said: don't confuse vacuum energy with virtual particles. The concepts are related, but not the same. Vacuum energy is constant all the time, it doesn't exist only very short time intervals.
Nope. The physicists doing these experiments know what they are doing, and obviously have checked for this. E. g., the van der Waals force has a different dependence on distance than the Casimir effect.
The Casimir effect isn't the same as the cosmological effect of the vacuum energy. These are two different manifestations of the same underlying phenomenon. In the Casimir effect, what one uses are essentially *differences* in energy density of the vacuum energy (and you can only obtain such differences using conductive plates), whereas in the cosmological case, the vacuum energy is everywhere the same, and its *gravitational* effects are important. Not the same thing at all!
Hi Bjoern (didn't mean to leave the "e" out last time):
Oh..I thought you were trying to express that vacuum energy is the cause of the universe's expansion. But now I see you are saying no one knows the cause.
So I think we agree on much.
I now see you are saying that the cosmological constant causes the acceleration of the expansion.
We agree. This is the "dark energy", which accelerates the expansion. This is what I intrepreted Susskind, et. al. to mean.
In other words, the cause of inflation is a mystery (perhaps a phase transition). The cosmological constant comes into play right after the mystery inflation and accelerates the expansion towards a Big Rip, rather than allowing gravity to perservere in a Big Crunch.
The expansion creates empty space, which contains vacuum energy. If the use of a pseudo-tensor is accepted (and you've pointed out why it shouldn't be), then we have energy conservation as the vacuum energy balances gravitational potential energy (or gravitational radiation).
I think we agree on all that. Right? I can also agree the Casimir effect is due to vacuum energy differences, but the vacuum energy creation is driven by the mystery inflation and cosmological constant of the Big Bang.
What I think we're still left with is, what if a pseudo-tensor is not used? In that case, energy is not conserved.
And that's where you say it ceases to exist.
I can't wrap my head around that at all in a physical sense, but I'm guessing it follows from the tensor math.
How would that happen physically? Energy has mass equivalence, so isn't it similar to making an object cease to exist?
I Here is what's not clicking:
In the Casimir effect, conductive plates move due to vacuum energy density differences. (I accept not van der Waals and not virtual particles)
This is hardly the case for the universe..vacuum energy density is the same...it does not seem to me it should induce expansion. The vacuum energy "pushing" something in one direction, should be balanced by vacuum energy pushing the same thing in the opposite direction.
Bjoern:
Please ignore the "I Here is what's not clicking:" and following paragraphs.
They are remnants of an earlier draft.
@healthphysicist:
Good that we agree on most things now... apparently we have partly talked past each other.
Actually, there is so little mass in the universe that even without dark energy the universe would expand forever. It would decelerate, but nevertheless there wouldn't be a Big Crunch.
Agreed. Note that I gave two reasons why I don't like this explanation:
1) The gravitational energy pseudo-tensor isn't well-defined, and gives strange results for many circumstances.
2) There is no gravitational field in General Relativity, so it seems not sensible to talk about "gravitational potential energy".
Depends on what you mean with "mass", and with "object". ;-)
In particle physics (where I come from), "mass" means "rest mass" (of a particle). E. g. photons have no rest mass, and therefore I'd say they have no mass (although they have energy). So I would say that dark energy also has no mass. OTOH, I've heard that people in General Relativity mean the "relativistic mass" when they say "mass". So people in GR probably would say that dark energy has mass... So you see that there isn't even a definition of "mass" everyone agrees upon. Talking about "objects" will be even more problematic... is e. g. a photon an object, in your opinion?
As mentioned, you have to consider the gravitational effects of dark energy. According to GR, energy (and momentum, and pressure) are "sources" of gravity.
I think that "pushing" is a bad metaphor. Think of it like a compressed spring: if you let it loose, it will expand at each location along its length, not compress somewhere and expand at other places.
Hi Bjoern:
Ok, virtually (HA!) all issues behind us...I think we were projecting thoughts that didn't actually exist in the other's mind.
But back to how something "ceases to exist"...a photon is a "thing" or "object" in the sense that it exists. We can measure the physical effect of its existence (it has no rest mass, but has momentum).
If there was no physical effect, we'd conclude it didn't exist!
A photon can continue to degrade becoming the smallest possible existence, but this existence still exists. It is the smallest piece of information (1 vs. 0), leading to the maximum entropy (but not infinity). Physicist John Wheeler sloganized this as "It from bit".
And this was the theme of Susskind's dilemma and book. Information (which is energy, which is photons) cannot cease to exist.
I assume Susskind et. al. must accept pseudo-tensors over their weaknesses. He doesn't mention this at all in his book, and I don't have the background to choose a side from a mathematical perspective. But from a philosophical perspective, I would not easily accept that something can cease to exist.
Maybe tensor manipulation could provide for the energy to enter extra-dimensional space rather than ceasing to exist? Or tunnel back to the Big Bang? That would not be as profound philosophically as ceasing to exist. Ceasing to exist requires a mechanism, before it can be "easily" accepted, it seems to me.
There were various attempts to get a nonzero cosmological constant; for instance, Steven Weinberg gave an argument (http://adsabs.harvard.edu/abs/1987PhRvL..59.2607W) which does roughly get the value right, in 1987. That attempt, incidentally, is an intellectual forefather of the "SUSY landscape".
My own recollection, having been an experimental particle graduate student in 1998, was that the cosmological constant came out of absolutely nowhere, and that absolutely nobody believed it. I will also say it took a while for everyone to understand the distinctions among flatness, omega_tot=1, cosmological constants, and inflation, so at first many people incorrectly thought the result was incompatible with inflation.
A lot has happened in experimental astronomy and cosmology since that time, so that people may forget. But even just 12 years ago, "everybody knew" that uncertainties in astrophysics measurements applied to the exponents. Nobody believed that an astronomy experiment could control their systematic uncertainties to the kind of precision that was needed to believe these results.
That's part of why the accomplishment of the measurement was so great. It took a lot of intestinal fortitude and intellectual courage for people like Ron Knop above to believe in their own results, and they were right to.
@healthphysicist:
So love is an object, too, because love exists, too? Do you see the problem? ;-)
Okay, that's better. Although "physical effect" is still a bit unclear. ;-)
Yes, and that nicely shows where your thoughts go wrong: You implied that "energy is lost" is the same as "an object is lost". If you consider the case of cosmological redshift, you immediately see that's wrong: the photons lose energy (i. e. it disappears, it does not exist anymore - if one doesn't wants to use the gravitational energy pseudo tensor), but nevertheless the photons themselves still exist.
Huh? Why should a photon be the smallest bit of information, and why should that lead to maximal entropy?
Did Susskind really say that information = energy = photons?!? Or did you invent these equalities on your own? Because I strongly beg to differ here!
Well, you probably accept that electrons and positrons can annihilate each other. Or that unstable particles can decay. So obviously, you accept that "objects" can cease to exist. The only question which remains is if *energy* can cease to exist. As I said: energy is not the same as an object.
Sorry, this doesn't look like a sensible physical suggestion, but like word salad.
Bjoern -
You have given me some understanding with where you are coming from...I think we are very close, and I appreciate the mental calisthenics.
I see "transformation" as being different than "ceasing to exist". In transformation, whatever you start with (which originates with the energy of the Big Bang, which is still a mystery) can be transformed into something else. But the original energy of the Big Bang remains, whether today, yesterday, or a few billion years ago.
In e-/e+ annihilation the particles transform their masses into energy. In particle decay, a parent particle transforms into a daugher particle and/or energy.
It seems to me, another way to conceptualize the GR issue is that as the universe expands there is a transformation of energy. A particular photon may be red-shifted to zero, but vacuum energy increases by equal amounts over the time period.
So the Big Bang energy itself, does not cease to exist, it just transforms. "Ceasing to exist" means, to me, that the energy of the Big Bang leaves our universe, which it doesn't do. In fact, rather than leaving, it just makes our universe expand, creating empty space with its increasing vacuum energy and forcing red shifting of other photons.
I did not invent the info=energy=photons on my own. It may be poor wording on Susskind's part that has led me to understand it that way. Or my own mental foibles, since I had some awareness of Shannon's formula which equates entropy (energy per temperature) with missing information (bits).
From Susskind, pg 168: "Temperature is the increase in energy of a system when you add one bit of entropy".
pg 295: "The maximum entropy in a region of space is one bit per Planck length"
If you add one bit, then you increase the energy. Energy is quantized (photons). That there is a maximum entropy (not infinity), says that bits or quanta cannot disappear.
His book is really about his formulation of the Holographic Principle and this may give you a better sense of where he is coming from:
http://en.wikipedia.org/wiki/Holographic_principle
great post!
@healthphysicist:
It's easy to show mathematically that the energy of photons lost due to redshift is not equal to the dark energy gained due to a larger volume: radiation energy density decreases proportional to the inverse of the fourth power of the scale factor, hence total radiation energy decreases inversely to the scale factor. In contrast, total dark energy increases proportional to volume, hence proportional to the third power of the scale factor. Doesn't add up.
What Susskind says in your quotes is quite correct (although I suspect he meant a "Planck volume", not a "Planck length") - but how you interpret it makes little sense. That's absolutely not what he expresses in these quotes!
For starters, the photons are quantized, that's right. But that isn't the same as saying that energy in general is quantized (there are lots of other things with energy, not only photons!). Additionally, "one bit of entropy" is not the same as "one quantum of energy". And I don't see how you get from "there is a maximum entropy" to "bits or quanta can not disappear".
Sorry, I had a typo...he said Planck area, not length nor volume. That is the whole point of the Holographic Principle...that the information in a volume of space is encoded within the boundary of its area. Just like a hologram is a 2 dimensional surface (basically), but provides a 3 dimensional image.
Yes, there are lots of things with energy, not only photons. But how does one describe a change in energy to those things? To take 1 MeV particle to 2 MeV, you add a quanta of energy equal to 1 MeV. Whether that quanta is the result of a photon interaction or a particle collision, it is still a quanta, which exists in the universe. Since the one bit causes an increase in energy, what do you call that increase in energy? Whatever you call it, it exists in the Universe.
To go back to your e+/e- annihalation..assume no initial kinetic energy...rest masses of 0.5 MeV each.
If you said these particles "cease to exist", then I would ask what happened to the 1 MeV of energy that previously existed in our Universe? It would be profound to have that 1 MeV leave our Universe. It was essentially introduced into our Universe by the Big Bang (which is itself a mystery). It seems to profoundly compound the Mystery to have energy disappear.
You might repeat that they simply "cease to exist", which I would say is word salad. It has no explanatory power...like "magically disappear".
Of course, the 1 MeV of energy from the annihilation actually continues to exist in our Universe as a photon. The quanta of energy (call it what you will)...does not cease to exist.
With all that said, I appreciate you pointing this GR paradox out. It is summarily pointed out here (a little easier to read than your original link):
http://en.wikipedia.org/wiki/Physical_theories_modified_by_general_rela…
I don't know why Susskind failed to discuss this, he discusses quite a bit of GR in the book, and is very orthodox on energy and information conservation.
When we typically look at energy-mass relationships, we don't consider dark matter. Is it possible, that the excess loss of radiation is interacting with dark matter? And so, energy appears to not be conserved?
Oh yeah...the bits/entropy/non-disappearance issue.
If entropy is constrained (Susskind says it is, one bit per Planck area), then it doesn't reach infinity.
In a minute region of space, if a bit (or quanta) could cease to exist (or disappear), the entropy would be infinite...it would no longer be constrained to one bit per Planck area, since the bit no longer exists!
Thanks for the explanation about the holographic principle.
Yes. But my point was that the *energy* of that quantum ("quanta" is plural) is not an object in itself, so your argument that "objects don't simply disappear" doesn't lead to "energy can't disappear". Photons can change to photons of different energies.
Err, I call it an increase in energy?!? What do you want to call it?!? And why do you still seem to equate "bit" with "photon" or "quantum"?
Err, why does that "compound the Mystery"?
Balderdash. The explanatory power is in the math of GR, which tells us precisely under which circumstances energy can appear or disappear. There is nothing magical about that. This is simply the consequence of a law of nature. Simply because this contradicts your intuitive notions about energy, objects, bits or whatever does not make it wrong. You could as well say that an increase in entropy of a system is "magical"!
And I also don't see why you call this a "paradox". What exactly is paradoxical, i. e. self-contradictory about this?
If you mean the formula E=mc^2, then you are wrong - that formula holds (and is used, AFAIK) for dark matter as well.
So you suggest that cosmological redshift is due to photons scattering with dark matter particles, or what?!?
Non sequitur. If the universe is infinitely large, there is an infinite number of Planck areas, and hence an infinite number of bits. And hence entropy is infinitely large.
Huh? Susskind says that the maximum entropy is one bit per Planck area. How do you get from that "if a bit could cease to exist, the entropy would be infinite"?!?
I'd say that if the bit ceases to exist, entropy is zero there! Perhaps Susskind means something different with "bit" than I assumed - could you please tell me what exactly he means, and what he says about the relationship between the number of bits and entropy?
Yes, photons can change to photons of different energy, but they do so by radiating other photons or losing energy to particles, etc. Energy continues to exist.
The photons don't simply change energy.
When you add water to a tub, you've added either liters, or drops or molecules...these all represent discrete amounts, regardless of what unit you choose. Likewise, when you add energy to a system, it can be thought of as units of energy, regardless of what the discrete energy unit is.
I understand the math of GR explains the phenomenon, but I wouldn't say entropy is magical, because I observe it (add cream to coffee). I don't see things disappear! Even in the annihilation example, I can see the resulting photon (when its energy is absorbed in a detector).
Yes, if universe is infinitely large, there is an infinite number of Planck areas. But the principle applies to ANY volume of space!
Think of a small volume of space, which is bounded by a small area..if it has maximum entropy, then it is constrained to 1 bit per Planck area. Now suppose a few bits disappear, the remaining bits could rearrange positions. Entropy has increased within this area..and as more and more bits are removed, entropy continues to increase.
The paradox for me is how in GR energy can be lost, but how in Q.M it can't be. Energy is energy. I found this gem, which I think can give you some insight on where I'm (via Susskind) is coming from.
Note his aversion to "disappearance" and his insistence on maintaining energy conversion and his interchangability between bits and photons/quanta, etc. Certainly he understands GR....so another paradox is why he doesn't mention my first paradox.
Maybe there are two reference frames...like he mentions in this video with black holes. To an outsider, a black hole horizon is seething hot...to someone passing the horizon, it is not. Maybe photons are red-shifted in our reference frame, but not in another, thereby allowing two distinct realities. Energy is both conserved and not conserved at the same time!
If you don't mind watching this, you'll have a sense of my (mis)understanding:
http://fora.tv/2008/07/23/Leonard_Susskind_-_The_Black_Hole_War
In cosmological redshift, the energy does *not* continue to exist - that was the whole point!
Water naturally has smallest building blocks (molecules), energy has not.
Come on, you are a bit above the argument "I only believe in things / processes I can personally see in my usual surroundings", aren't you? And as I mentioned several times now, e. g. in annihilations, things indeed *do* disappear. Yes, the energy stays the same in annihilation processes - but the *things*, the *objects* have disappeared!
Err, yes, but the *things* have disappeared. That was the point.
Your argument says essentially "things can't disappear, therefore energy can't disappear". I counter with (1) things can disappear, and (2) energy is not a "thing" in this sense - and you say only "things may disappear, but the energy stays the same". I counter then with "there are processes where energy disappears, e.g. redshift", and you say only "can't be, things can't disappear, therefore energy can't disappear". We are going in circles - and that's not my fault!
The problem is essentially that you insist that energy is like a thing or an object and therefore can't disappear. And that simply an unsupported assertion, contradicted by actual evidence.
Energy is energy, yes - but why does that exclude the possibility that in different situations, it will behave differently?!?
I asked you to explain what Susskind means with "bit"; you didn't do that. So I can't say anything about what you wrote about bits here. Does he explain that somewhere in the video you mentioned? I'll see when I have time to watch it (almost 53 min!)...
Hi Bjoern:
I've put 2 + 2 together...I think (I think, therefore I am, HA!). I was confused, but no longer.
I wasn't previously thinking enough from a GR perspective, more from a quantum or particle perspective. And re-watching that video has helped clarify things for me (as well as your great comments), so I shall explain what I think is going on.
I think GR says that photons are red-shifted to zero near black holes or at cosmic horizons (where things moving away faster than light from them can reach us). And I think that traditional GR theory allows this, and that is what you have been trying to explain to me.
But this is exactly what Susskind is arguing against. He understands your point (I had either forgotten or perhaps never knew that traditional GR allowed for non-conservation of energy) and is explaining why it is wrong. This is the essence of his war with Hawking...Hawking was arguing what you're arguing, but in the end Hawking admitted defeat.
Now to the neo-GR physics....
Photons do NOT actually cease to exist at these horizons, they only seem to. They are degraded down into the smallest piece of existence, a bit.
We can't physically observe a single bit, we can only measure their collective temperature. And temperature is thus defined as the increase in the energy of a system if one bit of entropy is added.
Susskind (in the book) considers a bit may be like a string, but much smaller than the strings of String Theory. "These miniature, swift, and terribly powerful threads of energy are called fundamental strings."
-------
I don't have the GR background to argue in GR terms (tensors or pseudo-tensors) why Susskind's argument makes more sense than the traditional GR argument. His book doesn't include the underlying math (which I wouldn't understand), but I would guess he's published papers.
I can only say he's convinced many others of it (Hawking, T'Hooft, many more names in book).
I was originally considering his argument from my understanding of photon interactions...energy is always transferred, it never disappears. So his argument was very consistent from my perspective.
Thanks for helping me get things straight!
@healthphysicist: I've watched the part of the video where Susskind gives his talk; the rest are apparently only questions from the audience. So far, he hasn't talked anywhere about energy conservation - he merely pointed out repeatedly that information isn't lost. So where do you get all that strange stuff from like
Does this come up somewhere in the questions? Or did he only say that in his book? Or did you make that up on your own based on your understandings of what he said?
Additionally, the talk in the video was *very* qualitative. E. g. he never defined what "information" is actually supposed to mean here; I know of at least two different meanings of this term in information theory: Kolmogorov or Shannon information. So, what does he actually mean? Does this become clearer in his book?
Hi Bjoern:
I asked you to watch the video before I put the parts of the puzzle together myself.
You have re-sensitized me to what a black hole is...a place in space-time where energy appears to be redshifted to zero. This is what it means to "fall into a black hole". I got mentally lost in all the other aspects of talking about energy/particles.
But our discussion is at the heart of the Black Hole War. I got lost by the trees and didn't see the forest.
If you do a few quick things and then re-watch the video, things should click.
First, read this quick paragraph...go to the "High Level Summary" paragraph of this link (note the two physicists mentioned worked with Susskind):
http://en.wikipedia.org/wiki/Holographic_principle
Both energy and matter are considered to be incidental, and composed of information. The smallest unit of information is the bit.
Susskind is saying that a bit cannot be destroyed.
A photon (composed of many bits), can shed and transfer those bits in different ways (radiate them, conversion to mass), but eventually, it is a single bit, and the bit cannot be destroyed. Nor can any of the shed or absorbed bits that were spun off be destroyed. This is because the very fact that something exists, is information. It tells you something about the state of the universe.
Read this article, with the above in mind:
http://articles.latimes.com/2008/jul/26/science/sci-susskind26
Note Susskind states "nothing is ever completely lost" & "it is converted into a different form". In other words, energy (at the level of bits) is always conserved.
The paradox, where energy seemed to go to zero in traditional GR is now described as the Black Hole Complementarity in the article (and book and video).
The bits remain at the black hole horizon, which has a massive temperature.
Now, if you rewatch the video with all the above in mind, it should click.
Hi Bjoern:
I posted once, but it hasn't shown up...strange. So this is a shorter version.
You have to keep in mind that in traditional GR when energy goes to zero, that that occurs at the horizon of a black hole.
In information theory, energy and matter are large scale composites of bits:
http://www.sciamdigital.com/index.cfm?fa=Products.ViewIssuePreview&ARTI…
Susskind has modified traditional GR with Black Hole Complimentarity...bits are conserved. A photon cannot go to zero, because its existence is information. The photon can shed bits in macro forms (like lower energy photons), but eventually it is a bit.
The bits accumulate at the horizon of a black hole and raise it's temperature:
http://articles.latimes.com/2008/jul/26/science/sci-susskind26
Watch the video again with all this in mind.
I hope this posts!
Testing to see if this will post...
Bjoern -
I tried to respond to you twice yesterday, but my posts would not post. If you're still checking in, let me know and I will respond.
@healthphysicist: I don't want to dispute Susskind's point that information can't be destroyed. What I want to dispute is your continued insistence that photons (and other things) are "composed of information", and therefore can't disappear, because the information can't disappear. As far as I can see, none of your cited sources says actually anywhere that photons are "composed of information". So I'd say that you made up a non sequitur.
@healthphysicist: A clarification: I'd say that a photon (and other particles) *can* be destroyed, but its information can not - it is simply transferred elsewhere. I. e. when a particle falls into a black hole, the particle can cease to exist, but its information is then contained in the BH - and when the BH evaporates, the information can be re-released into the environment.
Hi Bjoern:
Good to see you're back....there are two ways to think of "existence". If I have a loaf of bread, and break it in half, such that I now have two half-loaves of bread...I can agree that the "loaf of bread" has been destroyed...only two "half loafs" exist. This is a philosophical meaning of existence and if that is the level you are arguing from, then we can agree.
But since this blog is physics based, I was arguing from a physics meaning...ie, the loaf of bread has been transformed into two half loaves...nothing has ceased to exist. The two halves came from something and they will eventually become something else, but throughtout the processes (even those yet to be undertaken) the sum of the parts equals the whole.
After all, that is what the physic's energy conservation law says...energy (in its various forms including matter) cannot cease to exist or be created (after the Big Bang). Particles can become photons (e+/e- annihilation) and vice-versa (pair production).
So, if you want to say (in your clarification) that a photon's information is contained in the BH...how so? If it's another transformation, than nothing has really ceased to exist (just transformed)and physic's energy conservation stands, and we finally agree on the phyics meaning as well.
Here quite simply (from another great physicist on the same subject) is where it says energy/matter are composed of information:
http://www.sciamdigital.com/index.cfm?fa=Products.ViewIssuePreview&ARTI…
This truly is what everyone agrees on, it's not a non sequitor.
So I think we finally agree, though I'm not sure.
@healthphysicist: We are apparently continuing to talk past each other... Sorry, but I see no further sense in discussing this.
The book synopsis you cited does *not* say that energy/matter is "composed of information". It only says:
which IMO does mean something different than "energy/matter is composed of information".
So, let's agree to disagree, o.k.?
Sure...but you owe yourself an answer to my question on your clarification...how is the information (from the photon which fell into the BH) contained? You acknowledged the information isn't destroyed, so what is it?
When you answer that question, we'll no longer disagree.
@healthphysicist: I don't know how exactly a BH contains information - I suggest you ask Susskind, since he is the one who says that information is conserved (which I don't dispute).
But the original question was "can energy vanish?" (e. g. due to cosmological redshift), and this question came itself from "can energy appear out of nowhere?" (e. g. dark energy). This whole stuff about things disappearing into a BH isn't very relevant to these questions. As already pointed out, in cosmological redshift, no photons vanish - only their energy vanishes.
So if you want to claim that this isn't possible due to conservation of information, you first have to explain why a photon with less energy should automatically have less information. I'd say that all photons have the same amount of information, no matter what energy they have. If you think otherwise, please present some arguments or, even better, a calculation or a formula which gives the relation between the energy of a photon and the information "contained" in it.
Superb Bjoern...you are a thinker! I'm glad I didn't misjudge you. If you can actually get to understand this stuff, you will be glad you stuck in there. It is very cool because it integrates QM & GR with things like computing and biology. It hints at QG (quantum gravity) and a theory of everything.
First let's define "information". In everyday language we use "information" to mean something like "data which represents reality".
If I tell you I am 6 foot tall and weigh 150 lbs, that data is traditionally called information. But where does the information actually originate from? From the physical reality of the universe...from my actual existence in the universe and the fact that I have unique characteristics in that physical reality at a point in time. The letters in "6 foot tall" and "150 lbs" are just composed of pixels on your screen, the information is in my physical characteristics.
I hope you can grock (Susskind's uses this term to mean "wrap your head around") this...this is what Susskind was referring to (in video) when discussing where the information resides regarding Grant's tomb.
A definition: "Information" distinguishes one state of affairs in the universe from another, measured in bits.
Humans use data (figures and numbers) to conceptualize and communicate the information, but data are just representations of information.
You should be able to see straight-off, that a 1 eV photon is in a different state (t=0) than if it loses energy and becomes a 0.5 eV photon (t=1). The state of the universe has changed.
You should further be able to see, that the information of the photon resides within its existence, and therefore conservation of information requires conservation of the photon.
I'll continue....
Thought experiment - imagine a universe outside our own, which is completely empty. Pretend you are a huge binary computer. Maybe you represent that universe with a long string of "0"'s.
Now suppose I put a photon in that universe. The state of the universe has changed. You might switch one of your "0"'s to a "1" in order to represent that universe.
Information cannot disappear...you cannot change the "1" back to "0" which infers mechanistically that the photon cannot cease to exist. The "1" has to represent the photon as it loses energy in this very crude case (analogy - crude laws of physics (physics = physical description of reality)).
A less crude case (analogy - better physics) would be to have a "1" flash across your bins, so that a "1" in one bin represents the photon in one state (which flips back to "0" when the state is changed) and the "1" in another bin represents the new state. Regardless, you can never have all zeros again, the photon cannot cease to exist.
Maybe an even less crude case (analogy - even better physics) would be to have a ten bin "byte", within your system, and the "1"'s & "0"'s whirl about as the photon changes state. Again, the byte cannot contain all "0"'s. The photon cannot cease to exist.
In the above example we used true bits (0 & 1) to crudely represent reality. Now you are probably ready to argue that GR says that the photon energy can go to zero, but the photon is still considered to exist.
But the very reason it's considered to exist is to overcome the difficulty with its seeming disappearance, which otherwise causes a discontinuity in physics. It's a forced contrivence overcome by the Holographic Principle.
I need just a bit (HA!) more elaboration and things should start to gel, but I have to run...I'll have to finish later.
That definition is quite qualitative. As long as we don't know how to actually calculate the amount of information, this isn't very helpful.
Yes, the "state" has changed. But why shouldn't different states have the same amount of information? I see no more or less information in a universe with a 1 eV photon than in a universe with a 0.5 eV photon.
I don't think so. You could change the 1 back to 0, but simultaneously change another 0 to a 1. Then the total amount of information stays the same, although the state has changed. Hence a photon can change (or transfer its information elsewhere), and nevertheless the amount of information stays the same.
We do know how to calculate the amount of information! Not me, but Susskind et. al. which you'd have to find in their papers. I'm trying to describe conceptually what goes on...:
In the thought experiment, the computer's bits were data, representing reality (reality - the universe itself - actually contains the information). In other words, if something in reality doesn't exist then it doesn't exist(0). If something in reality does exist it is something. What is the smallest something that can exist and still actually be something and not nothing?
We call that a bit (conceptually a "1", but physically something that really exists in the universe).
The bit itself is the smallest existence of energy that can exist (mass = energy). We'll never be able to measure it, but Susskind calls it a "thread of energy". These bits are real. They cause the BH horizon to heat up when photons fall in (other matter gets heated, breaks down, and becomes photons when it falls in and those photons become bits).
So, a 1 eV photon would generate more total bits when it falls into a BH than a 0.5 eV one.
Another way to think about it...if BH is at max density (a fixed volume) and you add a photon it will grow. What's the smallest thing you can add to the BH where it just exceeds its fixed volume by the smallest possible amount? That's a bit. More bits = more energy = eV's.
That's the direction taken in this talk:
http://www.youtube.com/watch?v=GHgi6E1ECgo
In traditional GR, the BH was only described by mass, angular momentum & charge. This inferred that as things fell in, their entropy decreased. A BH was seen as a very ordered state. This was troubling...entropy should always increase.
In Neo-GR, we see the BH as a highly chaotic state, entropy increases as things fall in, and this is manifest in the energy of the bits. The max entropy = 1bit/Plank area.
In conclusion...what EXISTS started with the BB (we already agreed vacuum energy is the result of the "momentum" of inflation/BB, it doesn't come from nothing).
Everything that EXISTS, can TRANSFORM (energy to mass, mass to energy, mass to mass, energy to energy) and in the process entropy increases. The smallest existence of everything that EXISTS is the bit, a small thread of energy.
I didn't hear Susskind say anything like that in his talk. Is this somewhere in his book, or did you make that up on your own?
Where?
Why should there be such a "smallest possible amount" for volume increase? Why shouldn't any amount, no matter how small, be possible? And again: do *you* call this smallest thing a bit, or does Susskind himself say so somewhere?
I don't want to listen to another 54 minutes of talk, and again not find what you claim is there. Please be more specific: where exactly in the talk does Susskind say:
1) That the smallest possible thing in the universe is a bit.
2) That there is a smallest possible amount for increase in the volume of a BH.
3) That "a bit" is "a thread of energy".
4) That photons are bits, contain bits, are composed of bits, or whatever.
5) That photons of different energy contain different amounts of information.
As far as I can see, you make all of these statements up on your own, and Susskind actually said quite different things.
Entropy increases as things fall in, right. But it would be news to me that BHs are therefore "highly chaotic states".
I also don't remember hearing that in the last talk you directed me to. So, where did you get this from? From his book? Or did I miss it in the video? If the latter, when exactly does he say that?
I don't remember that I ever agreed with that. When did that happen, in your opinion?
The answer to most of your questions is the same...in the book. If it was in the video, I wouldn't have had to type it out. I'm trying to back-up the video with info from the book.
Also if you go back and read the L.A. Times link that I've already provided, which apparently you haven't read or you've forgotten, you'll see the consistency. (1/24 @ 12:01). Pg 1 - "...nothing is ever completely lost....It's just converted into a different form."
In video @ Chap 5 "seething super hot soup of information" is literally billions of degrees (see article, Page 2). That's chaotic.
The entropy limit (1b/Planck area) is in the book and also in the YouTube video I just linked to today in my earlier post.
Last question...1/21 @ 9:55 a.m. you say "Agreed" based on my previous comment, which was based on your previous post where you used the word "momentum".
You said:
The only *remotely* similar thing I ever said in this thread is (in comment 45):
But that has nothing to do with "vacuum energy is the result of the momentum of inflation"! Apparently you totally misunderstood my comment! That doesn't speak to well about your interpretations of what Susskind says...
The quote from the L. A. times article (no, I haven't forgotten that) does simply point out that information is not lost - something I already agreed upon. It does however not in any way support your claims about "photons are composed of bits" etc.
The "seething super hot soup of information" you quote isn't part of the BH, but on its horizon. So the BH itself isn't chaotic, there only is chaotic stuff around it. And that isn't in any way news - accretion discs etc. have been known for decades.
As I said, I don't want to look through another 54 minutes of video merely to find out that Susskind doesn't actually say what you claim you say. So, where exactly in the video does he say that?
Your comment 48 clearly says "Agreed" to what I wrote:
"The expansion creates empty space which contains vacuum energy".
And your comment 45 clearly states the "momentum" the universe gained from inflation makes the universe expand more and more.
Apparently we are talking over one another.
My understanding of the Holographic Principle is consistent whether in the book, the video, the article, and the latest video (which isn't Susskind), any webpage on the subject, etc. with no contradictions.
It is also consistent with all the laws of thermodynamics and QM.
If you want to learn more, study it. If not, don't.
Let me quote from the New York Times, Jan26, 2010 page D2 (top of 4th collomn).
"Lawrence Krauss, a cosmologist from Arizona State, said that most theories were wrong. "We get the notions they are right because we keep talking about them," he said."
This seems like a most sensible admission of our extreme ignorance about the extremes of the universe including "dark energy". To paraphrase Lawrence Krauss, "We get the notion that dark energy is right because we keep talking about it."
I wish I had time to read all of this blog and comments more carefully, but let me add an unskeptical remark. Reading 74, 76 and 78 Bjoern carefully; I must say that as usual Bjoern is a voice of reasoned scientific thinking even when I choose to disagree with his conclusions. I choose to disagree not because I am an expert; but perhaps because I find underlying assumptions too extraordinary for me to accept. Nevertheless Bjoern's reasoning always educates me and brings me closer to his view (i.e. I understand it's sound basis better)and that is much appreciated.
And further, I don't think, "In the book" is a fair answer whatever the book or topic of discussion; it's kind of like saying, "Because Willie Wonka says." or "It's obvious, dah!"
You'll be glad to know that I have no more time at the moment.
Thomas:
I am not commenting to argue. I cannot derive the math and even if I could, I probably couldn't get the symbology to post in the comments section. I am only relating what Susskind et al. are saying.
It's pretty frustating to do so when you are told by someone who hasn't read the book, that you are misinterpreting it.
It's one thing to be skeptical...it's another to be so skeptical as to be close minded.
The Holographic Principle gives continuity on many things as I've outlined.
Bjoern, who doesn't understand it, prefers to reside in a world of discontinuity...where things magically appear and disappear, entropy decreases, and energy is not conserved.
In essence, Bjoern is sticking with early Hawking and you are sticking with Bjoern. Hawking, after reading and understanding Susskind, admitted defeat.
@thomas: Thanks for the flattering remarks. :-)
@healthphysicist:
Yes. But these two statements taken together still aren't the same as "vacuum energy is the result of the "momentum" of inflation/BB".
You could say that the *increase* in vacuum energy with time is due to the expansion of the universe, and that the expansion could be the result of the "momentum" of inflation / the BB. But then still, knowing one ultimate cause for the increase in vacuum energy with time is not the same as (1) knowing the direct cause of its increase nor (2) the cause of its existence.
I don't remember ever disputing the Holographic Principle; I only dispute your claims about "photons are composed of bits of entropy", "bits of entropy are threads of energy" etc.
I already told you that due to the usage of pseudo-tensors, the 1st law of thermodynamics doesn't really hold consistently in General Relativity.
Well, why don't you simply do what I aksed you for several times now? Tell me where exactly in the videos Susskind says the things you claim he says. Or provide quotes from his book where he says these things. Not some vaguely related things which you then interpret to mean what you want to mean them - but quotes which directly support your claims!
Well, since you keep providing only quotes which don't actually say what you claim, and since you apparently also misunderstood at least one of my arguments, the suspicion that you perhaps misunderstood something in the book is warranted, I'd say. Why don't you provide quotes which support what you say, but only quotes which say some vaguely similar things?
I don't disagree with the quotes you provide; I don't disagree with anything I've heard Susskind say in the video or read in the interview - I disagree with your interpretation of what the things he says are supposed to mean!
(1) You still haven't explained why things appearing or disappearing should be "magical". On the other hand, you yourself have agreed that some things do indeed appear or disappear (e. g. virtual particles).
(2) Where did I say that entropy decreases?!? Have you again misunderstood something I said?
(3) I have outlined in detail, with supporting math, why "energy is in general not conserved in General Relativity" is a sensible position.
Wrong. I'm sticking with what Susskind actually says in that video and that interview. I simply disagree with your interpretations about what Susskind means by saying that.
Bjoern:
I cannot make something in the video magically appear. The video was all I had found up to that point in time to provide you with some insight and I had already given you quotes and links. I'm sorry Susskind didn't use exactly the same words he used in the book, I was trying to fill in what is not on the video.
Examples of my frustration:
I quoted you from the book on 1bit/P-area in comment 52, which you asked me about again in your comment 78.
In comment 52 I also provided a Wiki link, I'll quote a bit (HA!) from it:
"The holographic principle thus implies that the subdivisions must stop at some level and that the fundamental particle (1 or 0) is a bit of information"
The subdivisions being referred to are of the fundamental particles (use hyperlink in same paragraph) of quarks, leptons and bosons (bosons include photons).
That link also mentioned Susskind and strings, though vaguely. And energy, matter, information equivalence. Clicking the hyperlink "string theory", tells us that any particle (including photons) can be thought of as a vibrating string:
http://en.wikipedia.org/wiki/String_theory
In comment 60, I gave you a quote from Susskind, which clearly describes what strings (which may be bits) are. I didn't include a page number, but it's on Page 327.
Susskind acknowledges we'll never truly know what a bit is, because it is so small.
He does not specifically discuss photons with zero energy.
MY INTERPRETATION is that in traditional GR when photons get red shifted to zero energy at the horizon, in the Holographic Principle they exist as a bit on the BH horizon. Because a bit adds to the horizon's temperature, it isn't quite zero energy and can be reemitted later. I don't see how a massless/energyless thing can increase temperature.
Virtual photons are created and destroyed within the uncertainty principle...energy is conserved.
2 cents more.
Leonard Susskind & James Lindesay's book titled:
An introduction to black holes, information and the string theory revolution (is fully viewable online at google online books.)Chapter 12 The Holographic Principle and Anti de Sitter Space (is viewable)
follow the link and go to chapter 12 to read:
http://books.google.com/books?id=cxJCBRUNmVYC&printsec=frontcover&dq=su…
But warning, not much of his book is written for a layman like me.
By the way, I learn from Bjoern, Hawking, Penrose, Susskind, Ethan, Cooperstock, Scientific American, New York Times, etc. and YOU. I don't stick with anyone; rather I try to respect everyone. But respect of professionalism; does not imply agreement; I decide for myself. I particularly respect if a professional physicist takes the time to listen, discuss and educate a curious layman like me. I still choose to disagree with Bjoern, Ethan and Hawking on many things. But I disagree as in a discussion sense rather than as in an argument sense. Meaning that I will continue to watch the science for 5, 10 , 20 or more years until something more definitive is achieved. (by the way Bjoern has broken some of my favorite ideas and I thank him for that. I still may choose to disagree with him but I also realize that my idea is sitting on a 2- or even 1-legged stool rather than a 3-legged one. And it is good to know how solidly my ideas sit or NOT).
As for the holographic principle, it is an idea that I have NOT tried to be informed on. Maybe I should.
But if Bjoern or Ethan tells me that I am misinterpreting some physics statement by some other physicist (e.g. Susskind); then I will listen (and I assume they are correct); because as professional physicists (I am not), they may notice important pesky little details that I miss or I may be using a word like holographic in too narrow a way.
I'm out of time, you'll be glad to know.
Sorry, I forgot that.
I don't see why the holographic principle, as explained in that article, would imply that. One could argue that it implies that the fundamental particle *has* one bit of information only, but I don't see why this bit should be the particle itself! I. e., I'd say that particles (or things in general) *carry* information, but not *are* information.
And nothing in that whole article anywhere (as far as I could see) says that photons of different energies have different amounts of information.
I know that in String Theory, particles are envisioned as vibrating strings, thanks. (and although I personally think that String Theory is probably right, I here also have to point out that it is a totally untested theory, and many physicist think it is mere idle speculation and has nothing to do with reality).
You probably mean that?
Could you please provide a bit more context to this quote? It is unclear to what "these" refers here.
I didn't catch this so far, but what is this supposed to mean? Where does traditional GR say that? Are you here talking about photons which "try" to move away from the BH, or what? But judging from context, you instead mean a photon which is falling into the BH. Where does traditional GR say that a photon falling into a BH is redshifted to zero energy at the horizon?!?
*sigh* And yet again you move the goalpost around. This was not about the question if energy can appear or disappear; this was about the question if *things* (and you consider photons to be things, don't you?) can appear or disappear. So, do you admit that things (like virtual particles) can appear and disappear, or don't you?
@Thomas: Thanks for the link, looking into the book is very helpful!
@healthphysicist: I'll quote from the book: (page 6)
I'd say that supports my point: photons of different energies can have the same information content (here: one bit).
Consider also the thought experiment described at pages 75-77, especially the sentence
Obviously, it follows that not every photon which escapes the box means that information has escaped the box, and hence photons can't "consist" of information bits, as you have asserted several times now.
Summarizing: the energy of a photon apparently has no fixed relationship to its information content; photons can carry no information or one bit (and probably more), and photons carrying one bit can have different energies.
great article, and very interesting discussion guys! unfortunately, i'm pretty far from natural science topics, but i found this post extremely interesting.
Most links on this article are DEAD.
Very unfortunate, I was eager to read further, since you don't really go into detail as to what specific reasons led you to your change of stance in this matter (pun not intended).
Dark energy/dark matter are one of those areas in recent astrophysics that really defy belief, specially considering that to fit the data, everything in the Universe we've been studying for millenia, every ounce of "real matter", only amounts to 4% of what exists.......
I suspect our very incomplete knowledge of black holes, gravity and the not so unthinkable possibility that our universe is interacting with an exterior medium (maybe expanding with certain "environmental" or geometric constraints), give me hope that this matter will probably be debunked in the not very distant future.