Supersymmetry A Sinking Ship?

I really like supersymmetry, the idea there is some fundamental symmetry between fermions and bosons.  Unfortunately nature doesn't care what I think.  And even more unfortunately, the LHC has been running at very high energies for a while now and nobody is seeing so much as a hint for it.

A few quotes from this Nature article sum up the situation:

The LHC is now rapidly accumulating data at higher energies, ruling out heavier territory for the super particles. This creates a serious problem for SUSY... As the super particles increase in mass, they no longer perfectly cancel out the troubling quantum fluctuations that they were meant to correct. Theorists can still make SUSY work, but only by assuming very specific masses for the super particles — the kind of fine-tuning exercise that the theory was invented to avoid. As the LHC collects more data, SUSY will require increasingly intrusive tweaks to the masses of the particles. 

So far the LHC has doubled the mass limit set by the Tevatron, showing no evidence of squarks at energies up to about 700 gigaelectronvolts. By the end of the year, it will reach 1,000 gigaelectronvolts — potentially ruling out some of the most favoured variations of supersymmetry theory.

So basically, supersymmetry's biggest appeal is that it provides a "natural" solution to many problems in theoretical physics.  (Like why the Higgs mass so small.)  However, enough parameter space is being ruled out by the LHC that is appears that fine-tuning may be required to get SUSY to work correctly.  But the whole point behind SUSY's appeal is that it appeared to be a theory where fine tuning was not needed.

So by saying: "well supersymmetry may still exist if we do a bunch of fine tuning" seems to destroy the whole point for why we thought SUSY was a good idea in the first place.

Next:

Privately, a lot of people think that the situation is not good for SUSY... This is a big political issue in our field... For some great physicists, it is the difference between getting a Nobel prize and admitting they spent their lives on the wrong track... [Some have] been working on it for almost 30 years now, and I can imagine that some people might get a little bit nervous.

Now, before I get too hard on the theory, we are only in the first few years of the LHC operating at high energies.  Still, after 30 years you would hope that if SUSY was as "natural" as people have assumed, you would hope by now you would have a hint.  I mean, it's one thing to say we don't have enough to claim discovery but we don't even have enough evidence to suggest a hint!

So, is SUSY a sinking ship?  I think abandoning SUSY is still pre-mature.  However, if the LHC cannot see so much as even a hint in the next few years, I will think things will start looking really bad indeed.

Thoughts?

String Theory Is False If There Are No Gravitons.

Is it possible to falsify string theory?  Luboš Motl has just listed a few ways to do so. Though I think some are too impractical to be helpful, I think it is important for string theorists to try to find legitimate was to falsify the theory so that we don't have some Russell's Teapot theory on our hands. IE... a theory that may be false but one that you can never really know.

That said, I would like to highlight one that may be semi-practical: (From Zwiebach linked to the right.)

String theorists sometimes say that string theory has already made at least one successful prediction: it predicted gravity!

But actually I think the prediction string theory makes is that gravity is mediated by a spin-2 particle called the graviton. Therefore, if there are no gravitons then string theory is false.

Now, why am I claiming this may be semi-practical? Because in principle we can construct theories where gravity is meditated by something other than a spin-2 particle. One example, which I admit is probably garbage, is that gravity could be just a consequence of entropy as proposed by Eric Verlinde. And there are and will continue to be even more non-graviton theories proposed until a graviton is discovered.

Now, if one of these alternative-to-the-spin2-graviton theories are ever experimentally verified... I guess we will have done more then disprove the existence of a spin-2 graviton.... We will have also disproven string theory at the same time!

In the meantime, my money is still on gravity being mediated by a graviton as that is the most reasonable thing to believe.

What If Dark Energy Were A Phantom Energy?

Before we get too far ahead of ourselves, let's remember that dark energy being a cosmological constant fits the data very well and has for years. That said, experimental constraints allow for dark energy actually being an exotic form of phantom energy. (So for the time being we have to allow for the possibility and work out the details.) This was recently done by Dabrowski and Denkiewicz.

What Is Phantom Energy?  Normal matter/energy in cosmology is classified according to the equation of state:

where p is the pressure and ρ the energy density of the matter/energy.  For radiation w = 1/3, for matter/dust w = 0 and for the cosmological constant w = -1.  What's interesting to note, looking at the image at the top, is the larger (more positive) w is, the faster it dilutes in the universe as the universe expends.  The cosmological constant is right at the point where it's density remains constant throughout the expansion of the universe.

Phantom energy is energy that has w less than -1.  If this form of energy existed, it would actually increase in density as the universe expanded!

Does It Fit The Data?  The best constraints on w for what is driving the dark energy is w = -1.05 +/- 0.29 from supernovae, CMB and 2dFGRS data and w = -1.001 +/- 0.0129 which hardly rules out dark energy actually being a form of phantom energy.

Furthermore, as the above plot shows, certain phantom energy models do fit current data, such as the supernova observations shown in this plot, and so we have to be willing to probe these models especially if they further go on to make experimental predictions. But do they?

Possible Experimental Prediction: A Sudden Big Rip.  First, as stated above, phantom energy models by definition predict w to be less than -1.  This itself can be measured and therefore tested.  Second, if we can somehow demonstrate that the energy density of the universe is is increasing with expansion, that would be a tale tale sign.

But lastly I want to discuss the big rip. It turns out, that if dark energy is driven by phantom energy, the universe gets ripped apart in finite time. More technically, the scale factor "a" controlling the expansion of the universe becomes infinite in finite time.  This means the distance between you and everything else in the universe goes to infinity without having to wait an infinite amount of time for this to happen.

In fact, a model discussed in this paper predicts the universe will experience this big rip in only 8.7 million years from now!

No wonder the authors call this model the "sudden future singularity" model. If the universe becomes singular, the scale factor "a" becoming infinite in only 8.7 million years, compared to the age of the current universe that will be one sudden singularity!

Conclusion.  I do want to remind people that the standard cosmology scenario where dark energy is a cosmological constant has worked so well for so many years that we have no reason to abandon it.  That said, dark energy being driven by phantom energy is technically a possibility and so we are justified looking into it, especially since it's existence may be experimentally verified/falsified.

Basically if we ascertain w is less than -1, see the energy density of dark energy increase with expansion, or find our universe suddenly being ripped apart we will know the dark energy is actually a form of phantom energy.

Let's hope that last one doesn't happen any time soon. :)

Mariusz P. Dabrowski, & Tomasz Denkiewicz (2009). Exotic-singularity-driven dark energy AIP Conference Proceedings, 1241 arXiv: 0910.0023v1

String Theory and Russell's Teapot

I don't want to be too hard on string theory because in reality I like the theory and hope it is correct.  That said, this cartoon by XKCD reminds me of the parallels between string theory and Russell's Teapot:

"The extra dimensions are really there we promise, they are just too small to observe...", "The supersymmetric partners that should exist for every particle are really there we promise, they are just at a high enough energy that they are out of our reach... ", "The 10^500 vacuum states leading to a multiverse...." etc...

I guess what I am worried about is that if string theory is not falsifiable in any practical way then you could never know if it is false or not.  Like Russell's Teapot.

Now, in defense of string theory, in principle these things may be able to be observed once we have built good enough detectors.  Therefore maybe it could somehow be falsified.

I guess another big difference is string theory employes hundreds if not thousands of physicists and the detection of Russell's Teapot doesn't. :)

The Scale Of The Universe and And It's "Best Theory".

Free Flash Games

Free Flash Games

Many of you have heard the phrase "use the right tool for the right job", and when it comes to physical theories the story is no different.  For example, I often hear that quantum mechanics is more fundamental and thus a better theory than Newtonian physics.  But is it always the better theory?  For example, does quantum mechanics describe the solar system better than Newtonian physics?  For all practical purposes the answer is a big "No Way!".

And, further, can Newtonian physics describe the large scale properties of the universe as well and general relativity?  Again the answer is no.

Look at the flash game above.  As you move the cursor back and forth, you see the universe at different scales.  And for each separate scale, a different physical theory becomes the best theory to use to describe that scale.  It really is the case that scientists are well advised, when describing the universe, to use "the right tool for the right job."

Question: But aren't the more fundamental theories are telling more about what is really going on?

Actually, it's hard to say!  For example, I've already posted on how some of the theoretical machinery going into our most fundamental theories of nature could just be clever mathematical models that just so happen to fit nature.  Not necessarily what is actually going on.   Furthermore: I'll give another example: is spacetime really curved, like general relativity says, or is something else going on like the interaction of a spin-2 graviton?  (Or something else entirely and yet the math just happens to work out making them clever models as opposed to the true reality!)

So, my advice to those who want to classify (and many do!) which physical theory is most superior or "most correct": I advise you to first ask what scale of the universe you are trying to describe.  Because, it turns out that each scale of the universe has it's own best theory.

A best theory for describing the cosmos at large... a different best theory for describing how a planes and rockets fly through the air or how bridges stand... a different best theory for describing how elementary particles interact... a different best theory etc...

Finally: It is this observation that allows cosmologists to think there may be a better theory than general relativity for describing scales larger then have been examined thus far.   Or: one reason why string theorists have good case for why there might be a better theory than standard quantum theories for describing the smallest of scales.

In short: the idea of a best theory is really scale dependent!

Click on the image to the right from XKCD.

What Would Happen To Particle Physics If The LHC Finds Nothing?

Apparently Tommaso Dorigo, bet $1000 in 2006 that no physics will be found at the TeV scale (the energy scale the LHC is shooting for) before 2011 and even titled that post This 1000$ says there ain’t new physics at the TeV scale.  Back in 2006 that probably would have been seen as a pretty bold bet.  (Now less then a week away, not so much. :) )  It also appears he is still convinced there may not be much to look forward to in 2011 by way of new discoveries.

All this has got me thinking: what would happen to particle phsyics if the LHC finds no new physics beyond the standard model?  Or: what if the LHC finds nothing new except the standard model Higgs? 

A few things come to mind:

First:  I wonder if that would spell the end of accelerator physics for some time to come do to a withdrawal of funding.  The US and UK already appear to have taken some steps to cut funding for future accelerator experiments even in the face of the potential discoveries of the LHC.  In fact, the UK may still cut some funds for the LHC itself.  How can this funding landscape do anything but get worse if the LHC finds nothing?

It will be difficult to appear before governments and argue "Funny thing HaHa... moving up in energy with the Tevetron yielded no new physics beyond the standard model despite claims that it might... Then moving up in energy even further with the LHC yielded no new physics beyond the standard model despite a barrage of theory papers arguing it should... But, interestingly enough it turns out that if we build an even more expensive/elaborate accelerator then we really believe this time we will find something. :) "

Second:  All the theory papers will be rewritten to demonstrate that the natural energy scale for new physics beyond the standard model is really just above the TeV scale. :)

Now don't get me wrong, I sincerely hope that the LHC (and perhaps still the Tevatron) finds new physics beyond the standard model.  The world would be too boring if the standard model is all us humans can ever uncover with accelerators.  Furthermore, I have a hard time thinking we can go up orders of magnitude in more energy and find nothing. (Although my personal opinions don't effect the reality of the universe.)

Nevertheless, I still wonder what will happen to particle physics if the LHC finds nothing beyond the same standard model that has been around for decades.

Any of you have a any thoughts/guesses?  More money for Cosmology? :)

How The Twin Paradox Of Relativity Changes In An Expanding Universe.

I'm sure most of you have heard of the twin paradox "in which a twin makes a journey into space in a high-speed rocket and returns home to find he has aged less than his identical twin who stayed on Earth."  This paradox has been worked out for special relativity in Minkowski spacetime.  Recently, Boblest et al. worked out the details using general relativity for an expanding universe. (de Sitter spacetime.)

First a review of the standard Minkowski version:  In this case the whole universe is flat Minkowski spacetime and can therefore be handled with special relativity.

The twins in the paper have names: Eric and Tina. Eric stays on Earth while Tina accelerates away from Earth with constant acceleration α = 9.8 m/s²  until her clock shows 5 years have past.  Then she decelerates by the same magnitude coming to a complete stop after ten years then begins her journey back to earth accelerating then decelerating in the same 5 year intervals.  Finally, after 20 years has transpired on her clock she has returned to earth being now 20 years old.  The plot above might help make this more clear.  It shows how far she she is compered to Earth versus the time recorded on her clock.

This plot above shows the time on Eric's clock versus the time on Tina's clock.  As you see, Eric is nearly 350 years old when Tina returns.  Furthermore, he ages quickest relative to Tina when she is traveling at peak velocities.

Now consider an expanding universe:  For an expanding de Sitter spacetime, the universe is no longer flat and so the authors have to appeal to general relativity.  The Hubble expansion parameter, quantifying how fast the expansion is happening, is denoted by H.  For our universe, H =  H₀ = 71 km/s/Mpc.  Larger H means faster expansion.

The plot above shows how the results change in an expanding universe.  Interestingly H must be greater than 10⁷ H₀ , before we see significant differences compared with the flat case.  One very important thing to notice is that, since the universe is expanding quickly, after 20 years Tina is not able to return home.  This should make sense since the distance she has to travel in an expanding universe is further then in the flat case.

This next plot above shows how Eric's clock changes compared to Tina's in the expanding universe case.  As you can see, Eric does not age compared to Tina nearly as much.  This should also make sense because the expansion of the universe inhibits Tina's relative velocity to become to significantly different from Eric's.

Now For A Proper Round Trip. Now let us demand Tina accelerates and decelerates in such a way that Tina is able to return home in 20 years.  Now Tina must turn around before the 10 year mark.  Here the authors compare three "trips" where the constant acceleration/deceleration is greater for each trip.  IE, Tina accelerates faster for trip 3 than trip 2 which is faster than trip 1.  In each case, H =  10⁹ H_0.

The plot above shows how Tina's position compared to earth changes with time in an expanding universe.

And lastly, the plot above shows how Eric's clock changes compared with Tina's for the three trips.

Conclusion:  This paper shows how the twin paradox is altered for an expanding universe.  Interestingly, the expansion of the universe lessons the distance Tina can travel in 20 years and makes it so that Tina's change in age changes much more closely to how Eric's age changes.  However, it should also be noticed that to see significant differences compared to the special relativity case the universe must be expanding significantly faster than our own universe is.

Sebastian Boblest, Thomas Müller, & Günter Wunner (2010). Twin Paradox in de Sitter Spacetime E-Print arXiv: 1009.3427v1

A Great History Of The Evidence For Dark Matter.

In the paper Dark Matter: A Primer Garrett and Dudagives give a nice historical background to the accumulating evidence for dark matter.  Lets go through the history they lay out.

1.  J. H. Oort:  Astronomers have come to tust what is known as the mass to light ratio, M/L, that does a good job telling you what the mass of luminous matter should be based off of the luminosity of that matter.  This relation is normalized such that for the sun, M/L = 1.  In the 1930, Oort found that the stars moving on the galactic plane were moving faster than the galaxy's escape velocity!  He knew what the mass of the visible matter should be from M/L and discovered stars in the galatic plane are moving too fast to be bound by that much mass.   He postulated more mass must be present in the galaxy than can be attributed to the visible matter.

2.    F. Zwicky:  Zwicky studied the Coma Cluster and found that the stars had much more kinetic energy than they should from the viral theorem, KE = - 1/2 PE, assuming that the cluster had te amount of mass predicted by M/L.  He then worked out how much mass this cluster must be to have that high of a kinetic energy and found the mass should be about 10 times more mass than the visible matter. (Again, from M/L measurements.)

3.  Vera Rubin:  Vera Rubin studied the rotation curves for 60 galaxies.  These curves should obey the well known relation v(r) = sqrt(G m(r)/r) where v is the velocity, r is the radius, m is the mass and G is the gravitational constant.  Instead, she found that the velocity was not consitant with the amount of mass seen in visable matter.  Instead, new unseen matter is needed to explain the rotation curves.  (See plot above.)

4.  D. Walsh et al:  in 1979, D. Walsh et al. were among the first to detect gravitational lensing.  They watched how the light was bent by certain distant galaxies.  The problem was that the galaxies had to have more mass to bend the light as profoundly as it did than come from the M/L relation.  Dark matter could explain this discrepancy.

5.  Microlensing:  Several MACHOS studies went into effect and all came to the same conclusion: the missing matter could not be attributed to brown dwarfs, neutron stars, black holes, planets or other "dark" objects made of matter that we are familiar with.  This extra mass had to be coming from some exotic type matter thus far unknown.

6.  BBN:  Big Bang Nucleosynthesis is one of the great achievements of modern cosmology.  It turns out, the Deuterium to Hydrogen ratio (D/H) is heavily influenced by the overall density of baryons in the universe.  Using D/H, one finds that the amount of baryons in the universe is much smaller than the total baryonic matter.  The rest must be coming from some extra dark matter.

7.  The CMB: The power spectrum taken from the Cosmic Microwave background is highly sensitive to the amount of baryonic matter in the universe.  See the plot above.  As the amount of baryons, \Omega_b, changes, so does the power spectrum... by a lot!  The red error bars show the measured value.  As can be seen, baryonic matter only makes up 4.6% of the universe.  From the same power spectrum on finds that the total matter in the universe is more like 25% of the universe indicating that the vast majority of the matter is matter we don't understand.

8:  N-Body Simulations and SDSS:  Numerical simulations of large structure formation have been performed.  Only those that include dark matter give results that match what we observe from large structure surveys such as the Sloan Digital Sky Survey.

9.  The Bullet Cluster:  "Smoking gun" evidence for dark matter, as some would say, came from a recent experiment involving the Bullet Cluster.  The Bullet Cluster recently collided with a larger galaxy.    In such a collision, dark matter should just pass through without interacting and the visible matter heated up giving a tremendous amount of X-Ray emissions.  It was clear that the matter causing the majority of the lensing was not centered in the same spots as the luminous matter.  This showed convincingly that the amount of baryonic matter in galaxies is not as large as the amount of dark matter.  Furthermore, in 2007 another team confirmed a ring-like structure of dark matter was found after the collision of two massive galaxies.

10.  Penny et al:  In 2009, Penny et al. found that a significant amount of dark matter would be needed to hold certain galaxies together that were experiencing a significant amount of tidal forces.  These galaxies were surprisingly stable given how little luminous mass they had.

As you can tell.  This is a great article and I recommend everyone read it.

All images taken from the article cited.

Katherine Garrett, & Gintaras Duda (2010). Dark Matter: A Primer Eprint arXiv: 1006.2483v1

Does Ignoring Small Scale Physics Hurt Cosmology? Probably Not.

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When cosmologists study the universe they usually assume it is homogeneous and isotropic with linear perturbations.  On large scales this turns out to be a very good approximation.  Fortunately, these assumptions greatly simplify the math since:

1. The equations are linear and therefore easily solvable.
2. (Related to #1.)  Fourier modes decouple meaning you can solve for each mode independent of the others.

(If #1 and #2 above don't make sense it's fine.  Just know that the math becomes simple and solvable with the above assumptions.)

Recently, Baumann et al. asked a very interesting question: "Are we sure that small-scale non-linearities do not induce a large backreaction?"  In more lay terms: The physics on small scales is not linear, homogeneous and isotropic.  Are we ignoring important effects that physics on these small scales may place on the physics on large scales when we assume the universe has these nice properties on all scales?  

This isn't a new concept.  In particle physics one faces the same issue.  Physics that happens at high energies (or small scales) may have non-trivial effects on low-energy physics. (or large scales.)  These are often called non-perturbative effects and a good low-energy prediction must to take them into account.  "Integrating out" these small scale effects is at the heart of renormalization in particle physics.

Fortunately for cosmologists, Baumann et al. found that any back-reaction effects are very small.  Second, at most the these effects exert a slight positive pressure on the universe.  Therefore, backreaction effects cannot account for something like dark energy that has non-trivial negative pressure.  Lastly, they found the small scale effects completely decouple from large scales confirming that applying linear theory to large scales is well motivated.

Therefore, doing cosmology with the above simplifying assumptions appears to pass yet another important test.

(Image: Credit: NASA / WMAP Science Team)

Daniel Baumann, Alberto Nicolis, Leonardo Senatore, & Matias Zaldarriaga (2010). Cosmological Non-Linearities as an Effective Fluid eprint arXiv: 1004.2488v1