## Scientists Say They Can Now Test String Theory

by Nancy Atkinson

The idea of the “Theory of Everything” is enticing – that we could somehow explain all that is. String theory has been proposed since the 1960’s as a way to reconcile quantum mechanics and general relativity into such an explanation. However, the biggest criticism of String Theory is that it isn’t testable. But now, a research team led by scientists from the Imperial College London unexpectedly discovered that that string theory also seems to predict the behavior of entangled quantum particles. As this prediction can be tested in the laboratory, the researchers say they can now test string theory.

“If experiments prove that our predictions about quantum entanglement are correct, this will demonstrate that string theory ‘works’ to predict the behavior of entangled quantum systems,” said Professor Mike Duff, lead author of the study.

String theory was originally developed to describe the fundamental particles and forces that make up our universe, and has a been a favorite contender among physicists to allow us to reconcile what we know about the incredibly small from particle physics with our understanding of the very large from our studies of cosmology. Using the theory to predict how entangled quantum particles behave provides the first opportunity to test string theory by experiment.

But – at least for now – the scientists won’t be able to confirm that String Theory is actually the way to explain all that is, just if it actually works.

“This will not be proof that string theory is the right ‘theory of everything’ that is being sought by cosmologists and particle physicists,” said Duff. “However, it will be very important to theoreticians because it will demonstrate whether or not string theory works, even if its application is in an unexpected and unrelated area of physics.”

String theory is a theory of gravity, an extension of General Relativity, and the classical interpretation of strings and branes is that they are quantum mechanical vibrating, extended charged black holes.The theory hypothesizes that the electrons and quarks within an atom are not 0-dimensional objects, but 1-dimensional strings. These strings can move and vibrate, giving the observed particles their flavor, charge, mass and spin. The strings make closed loops unless they encounter surfaces, called D-branes, where they can open up into 1-dimensional lines. The endpoints of the string cannot break off the D-brane, but they can slide around on it.

Duff said he was sitting in a conference in Tasmania where a colleague was presenting the mathematical formulae that describe quantum entanglement when he realized something. “I suddenly recognized his formulae as similar to some I had developed a few years earlier while using string theory to describe black holes. When I returned to the UK I checked my notebooks and confirmed that the maths from these very different areas was indeed identical.”

Duff and his colleagues realized that the mathematical description of the pattern of entanglement between three qubits resembles the mathematical description, in string theory, of a particular class of black holes. Thus, by combining their knowledge of two of the strangest phenomena in the universe, black holes and quantum entanglement, they realized they could use string theory to produce a prediction that could be tested. Using the string theory mathematics that describes black holes, they predicted the pattern of entanglement that will occur when four qubits are entangled with one another. (The answer to this problem has not been calculated before.) Although it is technically difficult to do, the pattern of entanglement between four entangled qubits could be measured in the laboratory and the accuracy of this prediction tested.

The discovery that string theory seems to make predictions about quantum entanglement is completely unexpected, but because quantum entanglement can be measured in the lab, it does mean that there is way – finally – researchers can test predictions based on string theory.

But, Duff said, there is no obvious connection to explain why a theory that is being developed to describe the fundamental workings of our universe is useful for predicting the behavior of entangled quantum systems. “This may be telling us something very deep about the world we live in, or it may be no more than a quirky coincidence”, said Duff. “Either way, it’s useful.”

Source: Imperial College London

“But, Duff said, there is no obvious connection to explain why a theory that is being developed to describe the fundamental workings of our universe is useful for predicting the behavior of entangled quantum systems.”

What? Is it a possible theory of everything or not? If so, then presumably quantum entanglement is included? Wait, let me quickly check the definition of ‘everything’…

Today: Scientists find way to test String Theory

4 Months From Now: Scientists disprove string theory. TOE advocates are found inconsolable.

Utter quackery! Experimentally attributing the phenomena of quantum entanglement or water being wet or exit signs being on the way out etc. to an extra-dimensional theory such as String theory requires an extra-dimensional laboratory. Good luck with that.

Maybe it’s still early days, but even as a theory of last resort, String theory still looks like specious reasoning thus far. Keep working on it.

I think people should read the paper

http://arxiv.org/PS_cache/arxiv/pdf/1005/1005.4915v2.pdf

Four-qubit entanglement from string theory

L. Borsten, D. Dahanayake, M. J. Duff, A. Marrani and W. Rubens

Of course this paper is typical of Duff’s papers, in that it is dense with group theory. If you are familiar with Young Tableaux calculations then this is paper is tractable. The paper involves coset constructions of gauge groups and moduli for certain symmetries, in particular U duality. U duality involves compositions of S and T duality. S duality involves a dualism between a gauge charge q and its magnetic-like corresponding charge g (electric and magnetic charges, but the latter do not exist at low energy) according to a Bohr-Sommerfeld rule qg = n-hbar. The term hbar is the Planck unit of spin or “action,” for those familiar with Lagrangian dynamics. The T duality is a dualism between a distance or radius R and 1/R.

The problem is that I fear there is some confusion on just what is meant by entanglement. I thought I would break this out some, which might be more understandable than string theory stuff, though I will try to illustrate this connection towards the bottom. Entanglement is most interesting with respect to the subject of teleportation. Teleportation of quantum states is a “hot topic” in physics these days. The simplest case is a spin system, such as two electrons, or two polarization states of photons. A spin system has in the basis of the Pauli matrix sig_z the states |+> and |-> for spin up and down, or for polarization up versus side. The Pauli matrix acts on these states as

sig_z|+> = |+>, sig_z|-> = -|->, where I will use +/- for “plus or minus.”

Now these states are complex numbers, which means there are 2 variables for each state and thus 4 altogether. However, there are constraints, such as the probability Born rule 1 = P_+ + P_-, P_+/- = |a_+/-|^2 for a state |psi> = a_+|+> + a_-|->, and irrelevance of a phase in real valued measurements. So this reduces the number of variables from 4 to 4 – 2 = 2. That is just what we would expect.

Now let us consider two spin systems, say two electrons. The use of electron spin state is not concrete, for these arguments hold just as well for polarization direction of photons. So we have two sets of states and operators {sig_z, |±>}^1 {sig_z, |±>}^2 denoted with an additional index i = 1,2 and we still have

sig^i_z|+/->^i = +/-|+/->^i.

We can form two independent states |psi>^i = a^i_+|+>^i + a^i_-|->^i for the two spin systems. For each there are 4 variables and 2 constraints. This gives 4 degrees of freedom in total. Yet we can compose these spin states in various ways. One way of doing this is

|psi> = (1/sqrt{2})(|+>|-> + e^{iz}|->|+>),

where I have dropped the index i, and we just implicitly see the first and second |+/-> as i = 1 and 2. This makes reading things clearer. The e^{iz} is a phase which for it equal + and – the state is not an eigenstate of sig^i and is an eigenstate of sig^i respectively. So these are singlet and triplet state configurations. I probably should not have mentioned this, but it does have some subtle implications. This is an entangled state. If you have access to |+/->}^1 then you also have access to |+/->}^2, and this holds no matter how far apart these states end up as. You can entangle two electrons by overlapping their wave functions. One that is done you can separate them arbitrarily far and they are still entangled.

Now let us count the degrees of freedom for this state. We have again 4 variables for each |+/->}^i but now we have one constraint from Born rule and another from the “mod-out” of phases. So you have 6 independent variables. Now if you are Alice your part of the EPR pair (this entangled states between spins) you have half of these variables which is 3. This is more information than with just having access to a single spin locally with 2 variables. So something funny is going on. If you attempt to access this information as spin up or down there is then an additional variable you have no information about, thus the state of the system is undetermined and Alice can’t access the quantum bits which may be teleported by Bob from his part of the entangled state. The additional bit of information needed is the manner by which Bob has selected his eigenstates, or the orientation of the Stern Gerlach apparatus (or apparatus appropriate for the observables measured. This is the key which needs to be transmitted by Bob to Alice. This must be communicated as classical information.

This is the basic nature of quantum entanglement. It means that if you have a measurement of a spin then that outcome tells you something about the spin your partner has with the entangled spin. However, you don’t know what choice of measurement your partner will choose to make, so there is a loss of information without that classical bit of data communicated between you and your partner. This involves something called entanglement entropy. Because you have one part of the total wave function, there is some loss of information here. In effect the information explicitly available to you is that of the entire wave function “modulo” some bit which involves the entanglement. This connects up with the Duff et al in their string theory calculation with these coset constructions. At this point I have to leave this in a sort of qualitative situation, for if you think what I just wrote is complicated try reading this paper. 🙂

I am writing up a paper right now on something similar to this. It involves the exceptional group F_4, which is the automorphism of the E_8 group. A coset construction between that and B_4 ~ so(9) gives a renormalization group flow where the fixed point or end of the flow is the Einstein field equation. Further, the structure of this group involves the Heisenberg group of quantum mechanics.

Now is this practical? In principle yes, for the LHC may give quantum amplitudes that have black hole content. In other words there is a small amplitude or probability at high energy that the scattering outcome is what is expected for the quantum decay of a black hole. This is found by Duff et al to have some quantum logic similar to entangled states. So there is a prospect for this.

LC

TERRYG: huh?

Making sense, you are not. All I see is a kneejerk emotional ( some would say, emorage ) response to the article, while actually explaining nothing.

A Theory made a prediction. Scientists can test that prediction to see if the Theory works for *that* prediction. No claims beyond testing that prediction were made.

*please* read the article carefully before emoraging in the comments section.

Well, you would think that a unique prediction would test the theory.

But it has happened before, when string theory was born it was the only theory explaining strong interactions in the atomic nucleus (say). The next year (IIRC) QCD, a more predictive theory, came around and did the same.

And of course predicting black hole entropy is not unique for string theory (and here never was).

Similarly string theory predicts quark-gluon plasma and solid state system properties that AFAIU no other theory does. But here the predictions are not fundamental but of the “convenient math” type.

Hopefully this sticks.

That would make predicting black hole properties somewhat tautological, wouldn’t it? Not exactly wrong, but ad hoc. But we know string theory is claimed to be fundamental.

I think this is confusing ordinary strings with cosmological topological singularity strings.

@ Beckler:

Exactly, I suspect you know this: “Theory of Everything” is the misnomer the ellipsis hint at.

It is a fundamental theory, in fact perhaps of everything gravity and field, but would both add on other theory and need add ons. (Add ons for emergent phenomena like chemistry or solid state physics which is likely impossible to practically predict from fundamental principles.)

Actually there is a better (simpler, massively predictive) contender for “TOE” in the sense implied by the misnomer, which is the quantum mechanics it relies on. All systems are QM systems at the basis.

[Interestingly, “fundamental theories” are claimed to have similar problems by people like David Deutsch, that of being misnomers. He presents these ideas in “The Fabric of Reality” if you are interested.]

@ Dave Finton:

Good for them in that case, because that is _huge_ progress!

If anyone here smells burning rubber, don’t worry; it’s just the insulation of my synapses overheating as a result of reading that paper provided by LBC above! 😉

I anyone else having trouble understanding what LBC wrote above? Waaaaaaaay over my head! An interesting article, however.

if you want to make contact, get a hold of a quantum mechanics text, or look up Pauli matrices — which is what those sig symbols stand for. Also look up the Born rule in quantum mechanics. If you follow what I wrote then you will understand the basic idea of quantum entanglements. The coset stuff that Duff et al. wrote is far more abstract and deep, and as i read it I agree with the conclusion.

As for practical experimental physics the biggest problem is in detecting entanglements at such high energy. Normally to set up entangled states and to do experiments you need things to be very cold, or to work with massless particles such as photons. High energy entanglements with 100-1000 GeV mass particles is a tough nut to crack.

LC

Lawrence,

I hope you didn’t misunderstand my post above. I wasn’t implying that your writing didn’t make sense; simply that from my lay perspective it was difficult to understand. I much appreciate that you take the time to provide your expertise on a number of subjects offered at UT. The reason I come to this site is my love of astronomy, and to learn. Your comments, while at times a bit over my head, foster additional research and learning on my part.

Hello GekkoNZ

We embrace theories closer when they pass lots of tests. Relativity theories account for orbital effects, gravitational lensing, frame dragging, time dilation etc. and if they are ever observed, gravity waves. Similarly QM is successful in describing a whole bunch of stuff and there are even attempts to commercialise it with quantum computing, quantum cryptography etc.

While a unique prediction would test Mr Duffs theory, he rightly allows the possibility of “no more than a quirky coincidence”. Hence, more (some might say a lot more) work is required. Good luck to him.

No doubt UT will keep us in the loop and thanks as always LC for the write up.

The story of Ludwig Boltzmann comes to mind. He founded his theory of statistical mechanics on the atomic theory. At the close of the 19th century the idea was highly controversial, where Ernst Mach opposed the theory on positivist grounds. Nobody had found any experimental evidence for atoms, though the chemists used the idea to make sense of chemical calculations. String theory is in a similar situation, where the tests of the core concept have not yet come about.

There are several possible tests of string theory that are fairly direct. The first is with AdS or BTZ amplitudes at high energy, where some AdS/QCD evidence has already been found at RHIC. This amounts to detecting back hole amplitudes at the TeV domain in energy, where string theory does predict a renormalization group flow to these IR low energy domains which continues high energy amplitudes. These amplitudes will be logarithmically suppressed in scale ~ 1/log(E/E_p), for E_p the Planck energy 10^{16}TeV and E ~ TeV. So in spite of the huge energy difference the physics should still be detectable. There are other empirical connections with cosmology, though at this point these are somewhat more oblique.

LC

I also read that if we are lucky, then one of the dimensions might be as big as 0.7mm and within this range the gravity would not follow the inverse square law if string theory would be correct. Finding this would also give a clue that string theory might be onto something. The question is how to you measure the gravity formula at 0.7 mm scale…

2 and 3 entangled qubits proved in lab fully applies fits perfectly for black holes. 4 qubits doesn’t quite apply for the universe theory of everything, because there will be many more then the 4 proven entangled cubits to possibly discover. Using Lie Algebra three-dimensional geodesics motion that we perceive is stationary D=4 is the “4th dimension of time” which is Supergravity after a further time-like reduction to D=3. What causes this time-like reduction could be that complex qubits appear automatically by black holes. Four Qubits relates to D=4 STU blackholes. Four Qubits is : large/small values of CHARGES, Absolute zero TEMP or not, Zero or not zero ENTROPY, and ORBITS nilpotent or semisimple : this leads to 31 nilpoint orbits which are ENTANGLEMENT families that reduce to 9 up to permutations of the 4 qubits. Eight charges are 4 Electric and 4 Magnetic. Qubit computers robots will do better then binary bit robots like the old heath kits that had a mobile robot wih infrared sensor and mobile arms voice recog hah Hero

This is based on the Randal-Sundrum idea, which has some merit. I tend to think that in D = 10, with six extra dimensions gravity will depart from Newtonian 1/r^2 into 1/r^8 at around 1TeV of energy or 10^{-16}cm. This fixes the scale for Planck physics from 1TeV at the IR low energy scale up to 10^{16}TeV at the UV high energy scale. The scale of this interaction involves a power law on the string parameter, which for higher powers means a fairly small number is reduced a lot.

For gravity to exhibit behavior departing from 1/r^2 of Newton some additional things have to be going on. It requires that two of the six compactified dimensions renormalize at a different “flow” than the rest. In this way the power or exponent on the string parameter at larger distances is only a square term, which is much larger than a power of 6. This is possible, and it would mean gravity departs from the standard rule at around 1mm.

To detect this requires some delicate work. It means building Cavendish type experiments which are extremely sensitive and able to detect this gravitational attraction on this scale. I think that so far things are close to this scale and nothing has been found. I don’t know if things have probed to the sub-mm length scale as yet.

LC

We live in existing times.

I don’t like Dr. Michio Kaku on his string theories. He is making it popular but he is still guessing and give claims that might be completely false when tested to reality.

I would love string theory to be true, but I am also realistically that it can be completely wrong direction and have no problems to dispose it when it proves to be wrong. Experimental evidences is what I base on.

LBC sometimes my brains gets fried trying to read your math stuff, but that is actually good since it forces me into a deeper understanding of the material instead of the basic stuff you find elsewhere.

For those that are interested to understand a bit of what LBC is saying, check out the DeMYSTiFieD books from Mc Graw Hill.

The easiest book is “relativity DeMYSTiFieD” to start with because you get the maths basis you never learned in school.

A harder one is “Quantum Mechanics DeMYSTiFieD” where you find this kets (Dirac) notation. |a> so LBC starts to make sense.

LBC what does |+> and |-> mean? I assume Dirac notation but it is a first time I see a + and – sign.

The |+> and |-> states are up and down. Or it could be polarized up and side — which ever is the case it just signifies two different states. In quantum mechanics we do also have

= 1 = and = 0,

which means these are orthogonal (perpendicular) vectors in an abstract vector space of states. Here the vector space is two dimensional — a plane with unit vectors that point to a circle centered around the origin.

LC

Lee Smolin (“Not Even Wrong”) has an interesting blog entry on this paper, interesting as much for the comments of String Theory mavens (e.g. Ed Witten) as for his own comments: http://www.math.columbia.edu/~woit/wordpress/?p=3127

Woit is too conservative and curmudgeonly for me.

LC