Paradoxes That Threaten to Tear Modern Cosmology Apart
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It's important to remember that energy conservation is not an axiom of basic physics. It is a consequence of Noether's theorem and temporal symmetry in the laws of physics. In the framework of GR, this means that any static metric will have some conserved quantity that corresponds to energy (though, in general, it will not be the same as the Newtonian energy). But if the metric is not static (as in the case of an expanding universe), there is no need for energy to be conserved.
Must energy conservation be local? Would it be "legal" for -- say -- energy to be spent/dissipated (entropy increase) at one location leading to an apparent over-unity effect ("free" entropy decrease) somewhere else? I'm not talking about energy transmission through wires or EM radiation... I mean something apparently disconnected yet coupled.
I ask because I've encountered such ideas in sci-fi before and couldn't think of a reason why they're forbidden -- though I have no idea how you would do such a thing.
Let me give you an example scenario:
Let's say (ignore the mechanism for now) that it's possible to send a small amount of information from point A to B. This information takes a tremendous amount of energy to generate at point A, and when it's received at point B it can be used to (somehow) unlock a tremendous release of energy. If you only looked at point B, it would look like you had an "over-unity device." But in reality the energy spewing out at point B is paid for at point A, and the information transfer by occurring at the speed of light does not violate causality.
Not claiming it's possible, just asking if it's expressly forbidden by fundamental physics or not.
(If it were possible it would of course open up all kinds of very amazing things like remotely powered space propulsion, a whole next level of power grid technology, or orbital solar power that actually worked, but I know of no effect that accomplishes anything like this so it's total sci-fi even if not forbidden by any known law.)
Edit: according to another response this likely is not possible. Oh well. :)
"The first puzzling feature of the space expansion physics is that the Friedmann’s equations Eq. (6, 5) in terms of the metric distance r(t) = S(t) · χ get the exact Newtonian form:
...
"where M g (r) = ... is the gravitating mass of a ball with radius r(t). So according to general relativity the dynamics of the whole universe is determined by the exact Newtonian acceleration and Newtonian kinetic plus potential energy conservation (here velocity of light c does not change the Newtonian character of the equations)."
Page 7, I believe. http://arxiv.org/abs/1501.01919
So from the perspective of energy conservation, why would it matter if new space has a non-zero amount of energy? It still does not increase the amount of energy available to do anything.
In many ways Science is 'unusually' honest which creates a lot of confusion. Ask everyone on the planet's name and age and you’re likely to find people that make mistakes. But, drop a mere 6 billion marbles and there likely all going to fall.
that's not a belief.You can experiment and reproduce that experiment.Whether you get all the variables right is the issue science deals with.
You can't "experiment" god,heaven,hell or angels.These are fairy tales which are based on nothing but ignorance.Their only purpose is power and control. Religion is useless. If you crave for spirituality,then philosophy is a better alternative.
This is interestingly put, and I would not completely agree with it. Let med give two examples:
1. Before Quantum mechanics we could measure the Photoelectric effect (that is, light that is energetic enough can shoot off electrons from metal plates). This is a Quantum phenomena, and we could measure it before the theory was discovered.
2. Before General relativity we could measure the precision of the elliptical orbit of Mercury. This could not be explained by Newtonian gravity, and is a relativistic effect. But could be measured before the theory was discovered.
And before these; Electric eels can shock you, and Magnetic rocks still attract each other, even before Maxwell, Ampere, or Coulomb were even born.
The problem now a days (for fundamental theoretical physics) is that we are mostly put in the categories: * There is no data we can't explain with theory. * Theory that is consistent with current data and only predicts new features at much higher energies than we can design experiments for.
There are some exceptions to these, but I will exclude these for now, since they are a bit technical. Example of the first one: There is no data directly implying a quantum nature of gravity [1]. Example of the second one: Supersymmetry might not be visible at LHC because LHC is too weak.
That second category is why people jump on new results directly, like the BICEP or the super-luminal neutrinos, and the hep-th/ section of arxiv.org is flooded with papers trying to explain it. However, for both these cases, the measurements turned out be be wrong.
> every day what you thought you knew is now obsolete.
This is what many people say, but I would not agree (in fundamental physics). For example:
* One can say Newtonian mechanics is wrong because we have Special relativity now. But one should say: There is a regime (high velocities) in which Newtonian mechanics breaks down. This regime is determined by the speed of light, c. Newtonian mechanics is still correct for velocities much smaller than c. * One can say that Quantum mechanics makes Newtonian mechanics wrong. But one should say: There is a regime where Newtonian mechanics breaks down and Quantum mechanics governs, which is determined by the Planck constant.
and so on. It is not "obsolete", or have not turned out to be wrong. One only needs to append new aspects in various regimes.
[1] See e.g. http://backreaction.blogspot.fr/2013/11/big-data-meets-eye.h... > Those of us working on the phenomenology of quantum gravity would be happy if we had data at all [...]
I guess another interpretation of that statement is more along the lines of "We can't measure how much we are currently unaware of", which seems to make more sense.
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> But one should say: There is a regime where Newtonian mechanics breaks down and Quantum mechanics governs, which is determined by the Planck constant.
I find this completely unsatisfying. I used to think that a theory is either proven wrong or not proven wrong, and Newtonian mechanics is proven wrong. However, I got a new confidence in Newtonian mechanics when I had explained to me that Quantum mechanics yields Newtonian mechanics in a make-believe world where Plack's constant is exactly zero. So, while Newtonian mechanics is proven wrong, it is also (nearly) identical to our best current theory in many circumstances.
That is: According to Quantum mechanics, Newtonian mechanics is correct within the bounds of this exact forumla: insert super complicated formula here
In yet simpler terms: Newtonian mechanics is Quantum mechanics (except that it is always off by a miniscule, totally ignorable, amount. Except in extreme circumstances)
I believe we are saying the same thing.
Your "as Planck's constant approaces zero" is the same as me saying "in the regime where Planck's constant is irrelevant" (not quote from above, but those are the words I would use).
As you say, one can think of it as an expansion like:
QM = NM + \hbar C_1 + \hbar^2 C_2 + ...
(QM = Quantum mechanics, NM = Newtonian Mechanics, \hbar = Planck's constant, and C_i are correction factors (your "insert super complicated formula here")). Take \hbar to zero and you are get what you just said. But if you go into a regime where \hbar is significant, "Newtonian Mechanics breaks down", e.g. corrections are of same size (or perhaps even larger).
It might be "unsatisfying" how I try to describe it, but I tried to say the same thing as you did (I think). :-)
We are certainly in agreement about the facts of the matter :)
The thing I find unsatisfying is specifically the phrasing "Newtonian mechanics breaks down". Breaks down how? Breaks down why? "There is a regime (...), which is determined by the Planck constant." to me reads like, and I am adding color here for effect, "The governor has decreed that on Mondays, Quantum Mechanics shall be in effect. All other days are to be executed with Newtonian mechanics only, except when Max Planck has a belly ache!"
You make it look like QM is a special case of NM, while in reality, QM describes all the phenomena that NM does, not the other way around; NM is a special case of QM. I'm trying to explain it that way instead:
Quantum mechanics is correct. Always, always, always[1] use Quantum mechanics!!! Newtonian mechanics is obsolete!
[1]: Well, this is where my lack of knowledge about Special relativity comes in.
PS: Did you know that in specific circumstances you can use these much simpler formulae instead: (...), and the error is within these totally acceptable bounds: ... ?
PPS: Did you know that these simplified formulae were already known under the silly name "Newtonian mechanics"? The more you know! :)
The reason that I am adding it as a comment is not to correct you -- you are already right -- but to maybe help other readers. QM vs NM did not sit right with me until I understood that NM's equations actually fall out of QM's equations in specific, nameable, circumstances :)
Okay, so when we talk about use we are talking about tools. A lot of the tools we got from Newtonian mechanics are pretty reasonably accurate. If I see a ball bounces 3 feet when I drop it from 5 feet up, there's no reason to use anything particularly fancy to guess how high it will bounce if dropped from 10 feet. These are simpler tools I can use, and they may not be great (gravity is weaker at ten feet, for instance, so it's clear I'd be wrong to some extent, forget my ignoring just about every pertinent detail of the ball), but it works. Right tool for the job doesn't need to be fancy.
> You make it look like QM is a special case of NM, while in reality, QM describes all the phenomena that NM does, not the other way around; NM is a special case of QM.
Quantum Mechanics is continuous and differentiable at all points, including in descriptions of e.g. mass. To make Newtonian Mechanics a special case, you'd (at the very least) have to put some gnarly integrals in place of almost every variable in your formulas. They don't _really_ agree, one isn't a subset of another. One is an approximation (and not even specifically of Quantum Mechanics, just an approximation of things-seen-on-earth, some of which have compelling quantum mechanical stories, some of which, like gravity, don't). And sometimes approximations are useful.
I suppose my use of the word "regime" is unconventional. What I mean is a "parameter regime", or "for a certain range of a parameter".
For example, for the range in which \hbar is much smaller than one (in some units), this is the "parameter regime" in which QM and Newtonian mechanics agree quite/indistinguishably well. And for the range in which \hbar is close to one, "Newtonian mechanics breaks down", in the sense that QM effects are large -- i.e. where Newtonian mechanics is no longer a good approximation to QM.
> Quantum mechanics is correct. Always, always, always[1] use Quantum mechanics!!! Newtonian mechanics is obsolete!
I would not agree with phrasing it like that, and it is indeed Special relativity (or a part of it).
If quantum mechanics makes Newtonian mechanics (NM) "obsolete", then what does that imply for Special relativity (SR)?
QM makes corrections to NM with the parameter \hbar. SR makes corrections to NM with v/c (velocities you make experiments at over speed of light). So say that we are doing a mechanics experiment on our desk (say dropping something on a spring, or whatever). And we go with your "always use QM", it would take a long time to write down what happens, the same (although a bit faster) if we were to go with "always use SR".
Before you start writing down what is going on for that experiment, you make an assumption/approximation of which range of parameters is relevant for you. An apple dropped on a spring bed would not have relevant corrections from QM nor SR.
> The reason that I am adding it as a comment is not to correct you -- you are already right -- but to maybe help other readers.
Absolutely! Thats is also my goal in discussing these things. I do not always know how to make them "popular"/less technical, so I'm very interested in hearing other ways of explaining it.
Ah. That's unsatisfying :)
It would be super satisfying to have one coherent theory of everything. [1] Why hasn't anybody thought of that before? ;)
[1]: And then, again, it is of course useful to have efficient ways to work within subsets of the grand theory, such as NM.
The Newtonian model is wrong in some very important ways. Not just 'not quite right' but 'fundamentally in error.'
The fact that gives good-enough answers for a whole class of problems is misleading. So did the old theory of planetary epicycles.
Relativity and Quantum Field Theory use different models which give accurate predictions for a much wider class of problems. But the models make the difference. The math comes afterwards.
It's true if you make some simplifying assumptions in the equations they reduce to Newtonian mechanics. (Well - relatively does. QFT is weirder. Part of it reduces to plain vanilla Maxwell, but it also includes forces and interactions Maxwell never had to worry about.)
That doesn't mean the Newtonian model is just as good. It means it's been demoted to a simpler toy model you can use for certain problem - as long as you understand it's just a toy.
Science is really about model making, not math or approximation. The math just gives you ways to use a conceptual model for practical predictions.
The concepts behind the model always come first. And the concepts underlying GR and QFT are much richer and more explanatory than the concepts underlying Newtonian mechanics.
Sooner or later there's going to be another update, and relativity and QFT will be demoted in turn. But they'll be demoted by another conceptual revolution expressed in math, not by more math based on the same concepts.
> Well - relatively does. QFT is weirder. Part of it reduces to plain vanilla Maxwell, but it also includes forces [...]
Indeed. QFT is usually referred to as the more general framework, the actual models that explain our physics are usually called Electroweak theory (QED (Quantum electro dynamics) as a special case) and QCD (Quantum chromo dynamics). These are all QFTs with associated gauge groups (a.k.a. Gauge theories). QED reduces to Maxwell, more or less, in a classical limit.
> That doesn't mean the Newtonian model is just as good.
Oh, absolutely not. But for certain experiments it is preferable to use. The same goes with every theory so far, say GR or QFT, non of them are the final "theory of everything", but I wouldn't say that they are "wrong" or "misleading".
- Mechanism for baryon asymmetry
- Mechanism for ultra high energy cosmic rays
- Mechanism of high temp superconductors
- Black hole information paradox
- Finding solutions to the Schrodinger equation in various situations
You might mean something very specific when you say "Fundamental physics" though.
0: https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_p...
> - Black hole information paradox
This is indeed a big question, but I would discard this in what I wrote since: What is the experiment here? There is theoretical evidence for the Black hole entropy, but even if we could create black holes, which has so far not been accomplished by the LHC, how would you measure it? It is a bit more difficult than a gas where you could deform it and measure temperature etc.
So this I would discard because I was considering discrepancies between theory and experiments.
> - Mechanism for...
some of these I would exclude in what I wrote because they might be explained by current theories, but it is just not known how exactly. Take ultra high energy cosmic rays, there are Shock-front acceleration mechanisms, Supernovae explosions etc that are candidates, and if I understand the formation of that unsolved problem correctly it is to among these candidates identify the correct one or the main one (or if the candidate is not among the ones we know now, find a new one and explain it).
The orbit of Mercury had some attention from the physics community, but it just wasn't important enough for them to stop declaring that physics was complete. Also, the black body radiation had lots of attention from the engineering community, just nearly nobody tought it culd lead to any new physics, and the photoelectrical effect by its turn, was about as iportant as a toy.
Today we have plenty of data that isn't explained by physics. It's just that it isn't important enough to lead to new things.
Bollocks. Particle physicists and cosmologists are intensely aware of the need for new theories. They are, as near as I can tell, scrounging in every corner they can find for explanations, including a lot of corners that don't really even exist. It's just about the only thing they've got to talk about right now, and so it is just about the only thing they talk about, not something they think "isn't important". But we either don't have the brains to put together the data we have, or lack the data to figure out what the answer is.
"There are some exceptions to these, but I will exclude these for now, since they are a bit technical."
Take for example the Anomalous magnetic dipole moment of the muon [1], it is a measurement that do not agree with theory, but it is far from being the centre of attention for physicists (certainly some people do have that as their main goal to explain, but in general).
So indeed, there are things that do not match up, as well as the need to find a new experiment that gives something new (in the sense: The anomalous magnetic dipole moment of the muon is not enough of a hint to find the "new theory" (it seems).)
[1] https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_p... The 11th point under that section of that article.
Cosmologists by their turn have plenty of empirical problems to solve, but keep dismissing them as "probably just a particle we didn't see yet", and "yes, that's just a fundamental property of space (that no theory depends upon... applications?!? what do you mean by applications? it's too fringe to be usefull)".
As it is, we don't have any "important" empirical problems that we expect to completely rewrite theory. What's completely fair because most of the time what looks like "just another particle that we didn't see yet" is indeed just another particle that we didn't see yet. But completely dismissing all known problems is wrong.
Here's my count:
* General relativity describe the universe's dynamics quite accurately, been around for almost a century * Dark matter has been around for 80 years (http://en.wikipedia.org/wiki/Dark_matter) * Dark energy was discovered in the 1990's (super cool, but current measurements put it in the vanilla category). * ns != 1 (support for inflation) detected by WMAP, verified by Planck. The idea of inflation comes from the 1980's. * Inflationary gravitational waves discovered but turned out to probably be dust (http://www.bbc.com/news/science-environment-31058529)
"What’s more, there is an energy associated with any given volume of the universe. If that volume increases, the inescapable conclusion is that this energy must increase as well. And yet physicists generally think that energy creation is forbidden."
is regarding vacuum energy = dark energy = cosmological constant, etc, and continues to discuss it after that.
Another thing I find annoying is when they (this article and also others I have seen linked here on HN) paint the picture of that breaking energy conservation is some kind of magic going on -- it is far from it.
In General relativity (GR) you can construct conserved quantities from Killing vectors [1]. For example, if you have a time-independent metric (the GR tool for measuring lengths in space-time) you get a time-like Killing vector, which is associated to a certain conserved quantity; Energy. (Another example is when the metric has certain angular independences and you get conservation of angular momentum.)
Now in metrics that mimics cosmological evolution (that is, evolution in time), you have to break time-independence, hence your time-like Killing vector is gone and your energy conservation law is gone!
This is portrayed as some magic-like thing (at least that is how it sounds to me when I read these popular cosmology articles), but it is simply a consequence of the mathematics of GR. It might break some usual physics intuition, but I would not say that physicists (at least in this field) are surprised by it.
So it does not really "contradict basic physics", one just needs to know more about the details to get a good view of it. We do not need to figure out (or "conjure into existence") a way to break conservation of energy (as is the example here), it is already there in GR.
[1] https://en.wikipedia.org/wiki/Killing_vector_field#Geodesics The article on wikipedia is quite lacking on this point, but I link it here anyway.
> It might break some usual physics intuition,
It really shouldn't in light of Noether's theorem: The fact that time independence of the action S gives rise to energy conservation in the first place tells us pretty clearly: If your action has time dependence, you don't have conservation of energy.
Anyone have an idea what that's supposed to mean?
Edit: Ah, thanks to both of you, it seems obvious now
'Every year, the velocity of the distant quasars (going away relative us) is increased by 1 cm/s.'
"The MDI (Michelson Doppler Imager) images shown here are taken in the continuum near the Ni I 6768 Angstrom line. The most prominent features are the sunspots. This is very much how the Sun looks like in the visible range of the spectrum (for example, looking at it using special 'eclipse' glasses: Remember, do not ever look directly at the Sun!). The magnetogram image shows the magnetic field in the solar photosphere, with black and white indicating opposite polarities. " from: http://sohowww.nascom.nasa.gov/data/realtime/realtime-update...
Anyone know what I'm doing wrong?
Edit: this might be a better resource, and can automatically show you an animated sequence: http://sohodata.nascom.nasa.gov/cgi-bin/data_query
The successor instrument is called HMI, which returns 4096^2 images on a pretty fast cadence (45s or 720s depending on your purposes). It is much superior to MDI. The HMI instrument team is at Stanford University, so I'd point you there for data rather than to the NASA site, which offers a lot of sources and seems to suffer from a least-common-denominator effect.
Recent HMI quick look products are here: http://jsoc.stanford.edu/data/hmi/images/latest/
There is a back-catalog of JPEG images for browsing: http://hmi.stanford.edu/data/hmiimage.html
For science purposes, you can get FITS data from http://jsoc.stanford.edu . There are a lot of data products -- intensity, magnetic field (line-of-sight and vector), velocity, tracked regions, etc., as well as near-real-time analogs of much of this data (not as well-calibrated, but arrives within a couple hours of being taken).
There is no embargo on this data. They just expect acknowledgement (http://sdo.gsfc.nasa.gov/data/rules.php).
"The final elements, a pair of tunable Michelson interferometers, enable MDI to record filtergrams with a FWHM bandwidth of 94 mÅ. Normally 20 images centered at 5 wavelengths near the Ni I 6768 spectral line are recorded each minute."