VEGF

a

VEGF

b

Normal sproutingNormal function

Increased sproutingDecreased function

Tumour angiogenesis

Normal Dll4/Notch

Reduced Dll4/Notch

alone, and was effective even against tumours that did not respond to anti-VEGF therapies. Anti-Dll4 treatment may therefore provide a good option for alternative or combinatorial therapy for solid tumours that are resistant to anti-VEGF therapies.

A host of issues remains before anti-Dll4 treatments reach the clinic, however. For example, despite the effectiveness of treatment of rodent tumours with antibodies against VEGF, treatment with these agents in clinical trials of several types of cancer provided an over-all survival benefit for patients only when they were combined with conventional chemother-apy9,13. Similar issues might arise as anti-Dll4 treatments progress into clinical trials. None-theless, with these new findings we now have

Figure 1 | The Notch pathway and angiogenesis. a, Vascular endothelial growth factor (VEGF) promotes Notch signalling, which normally suppresses formation of vascular tip cells (red). b, When Notch signalling is reduced (for example, by treatment with antibodies against Dll4), more tip cells form, reducing the numbers of non-tip cells (blue) and leading to increased blood-vessel sprouting and branching. But the new vessels function poorly, which in the case of tumour angiogenesis in mice stunts tumour growth1,2. (Photos from Fig. 2 of ref. 1.)

QUANTUM MECHANICS

The truth about realityGregor Weihs

Hopes of keeping quantum mechanics ‘real’ have been dashed by new measurements of neutrons’ quantum behaviour. Despite what our classical sensibilities require, the world is indeed fundamentally random.

another possible point of attack on cancer. ■ Thomas Gridley is at The Jackson Laboratory, Bar Harbor, Maine 04609, USA.e-mail: tom.gridley@jax.org

1. Noguera-Troise, I. et al. Nature 444, 1032–1037 (2006).2. Ridgway, J. et al. Nature 444, 1083–1087 (2006).3. Hellström, M. et al. Nature 445, 776–780 (2007).4. Siekmann, A. F. & Lawson, N. D. Nature 445, 781–784 (2007).5. Lobov, I. B. et al. Proc. Natl Acad. Sci. USA (in the press). 6. Suchting, S. et al. Proc. Natl Acad. Sci. USA (in the press). 7. Leslie, J. D. et al. Development 134, 839–844 (2007). 8. Coultas, L., Chawengsaksophak, K. & Rossant, J. Nature

438, 937–945 (2005).9. Jain, R. K., Duda, D. G., Clark, J. W. & Loeffler, J. S. Nature

Clin. Pract. Oncol. 3, 24–40 (2006).10. Krebs, L. T. et al. Genes Dev. 18, 2469–2473 (2004).11. Duarte, A. et al. Genes Dev. 18, 2474–2478 (2004).12. Gale, N. W. et al. Proc. Natl Acad. Sci. USA 101,

15949–15954 (2004).13. Ferrara, N. & Kerbel, R. S. Nature 438, 967–974 (2005).

Albert Einstein was convinced that “God does not play dice”; in other words, he could not accept quantum theory, with its inherent randomness, as a fundamental description of the world. Developing the theme in later work with Boris Podolsky and Nathan Rosen1, he hinted that he believed in a more basic layer of truth underlying quantum mechanics. This was to be expressed in ‘hidden variables’ that reconciled the purely statistical validity of quantum measurements with the classical, deterministic world-view. Writing in Physical Review Letters, Yuji Hasegawa et al.2 deal a fur-ther blow to these already beleaguered efforts

to inject some realism into quantum physics.Two theorems developed in the 1960s

put severe constraints on attempts to com-plete quantum physics as Einstein intended. First, John Bell showed that theories of local hidden variables, which don’t permit any remote influences, cannot explain certain quantum-physical observations3. Second, Simon Kochen and Ernst Specker independ-ently proved that more general, so-called non-contextual hidden variables (of which more later) are also untenable4. Many experiments have since used Bell’s theorem to invalidate local hidden variables. Much less work has

been done on the Kochen–Specker theorem, especially for particles other than photons.

Neutrons are convenient guinea-pigs for the kind of delicate experiments needed to investi-gate these aspects of quantum physics: above all, they have no charge, which often makes it easier to observe the effects involved. Chief among these are the effects of spin, the prop-erty of a particle that makes it try to line up in a magnetic field. Quantum physics tells us that spin will be quantized: if you measure it along a chosen direction, it will point either in that direction or in the opposite one, but never in between. In addition, if you have measured spin in the vertical (z) direction and found it to be up, a subsequent measurement in the hori-zontal direction (x) will randomly yield a right or left value. Similarly, if you measure x first, the z value will be random.

It is this kind of randomness that was not to the taste of physicists such as Einstein. Hidden variables would allow the result of the z and the x measurements to be determined simul-taneously. In stark contrast, quantum physics nonchalantly declares that the z and x compo-nents of the spin cannot be quantified at the same time. It is, in fact, a matter of principle that the two measurements require different experiments.

Other characteristics, such as a neutron’s position, can be measured at the same time as spin. The procedures for measuring position and spin don’t interfere with each other, and the measurements are said to be compatible. It would therefore be natural to want any hid-den variables that are introduced to explain the spin-component measurements also to explain the results of simultaneous spin and position measurements: the value governed by the spin’s hidden variable shouldn’t depend on a specific position measurement, and vice versa. This is the condition known as non-contextuality: that the result yielded by any hidden variable should not differ according to any compatible meas-urement being performed at the same time.

But it seems that, as always, quantum theory wants to have the last word: it stub-bornly refuses to admit hidden variables even under such seemingly innocent conditions. It turns out that neutrons can be prepared in such a way that spin and position measurements, although nominally still independent, are so strongly correlated that non-contextual hidden variables cannot explain them. Unsurprisingly for connoisseurs of quantum weirdness, entan-glement — the mysterious holism in which the state of one quantum object is tied to the state of a second, separate object — is the key to this trick.

The fact that non-contextual hidden vari-ables cannot explain the spin–position corre-lations of entangled neutrons is a variant of the Kochen–Specker theorem. It was long thought to be untestable because, in its original form, it required infinitely precise measurements. With a statistical treatment, however, an in equality could be derived5–7 that restricted the

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Polarizer Incident neutrons

Spin turner

Spin analyser

Port 1 detector

Port 2 detector

Magnet yoke

Neutron interferometer

Phase shifter

Spin rotator

The developmental biology of the mammary gland is a fascinating process — from its origins in the embryo to the many dynamic changes in later stages of life. But it is thought to be perverted in breast cancer. The gland consists of a tree-shaped network of ducts, with the outer layer of the tubes consisting of myoepithelial cells, and epithelial cells lining the inner lumen. During pregnancy, some of the luminal epithelial cells develop into lobulo alveolar cells, which, given the right hormonal cues, secrete milk. The overwhelm-ing majority of breast cancers arise from these luminal cells.

In two new papers, Kouros-Mehr et al.1 and Asselin-Labat et al.2 show that a gene-regula-tory factor called GATA-3 guides immature breast cells on their developmental path to

form luminal epithelial cells. Moreover, they have uncovered a link between GATA-3 and two additional gene-regulatory factors, FoxA1 and oestrogen receptor alpha (ERα). Their results indicate that this pathway may be involved in mammary tumours.

The GATA-3 protein is an old acquaintance of developmental biologists, as it regulates the lineage determination and differentiation of many cell types. These include neurons of the sympathetic nervous system, immune cells called T helper 2 (TH2) cells, the inner root sheath of hair follicles, fat cells, the nephritic ducts of the kidney, and the ear cochleae3,4. Because GATA-3 is such a central player in development, fetal mice cannot survive to term without it5, and in humans a mutation in one of the copies of the GATA-3 gene leads to many

DEVELOPMENTAL BIOLOGY

Cell fate in the mammary glandQiang Tong and Gökhan S. Hotamisligil

Most breast cancers have their origin in the luminal epithelial cells of the mammary gland. Defining how a master regulator controls the development of this cell lineage could provide important hints about why this should be.

pre dictions for measurement results made by any non-contextual hidden variable model.

With this theory at hand, Hasegawa et al.2

passed a beam of neutrons through a specially designed interferometer that splits the incom-ing neutrons into two beams with opposing spin states (Fig. 1). The path that a particular neutron takes thus becomes entangled with its spin. The paths are recombined after the neu-tron passes a phase shifter (inducing a variable delay), and the neutron leaves the interfero-meter through one of two exit ports, depend-ing on its phase shift. The end result is that you can measure a neutron’s position — the port it exits from — as well as its spin along one of two orthogonal directions.

The exit port measurements for two differ-ent phase shifts follow the same rules as z and x spin measurements. You cannot measure both simultaneously, and if you measure one after the other, the second measurement will randomly reveal the neutron in one of the two ports. By analogy, we could call them the port z and x measurements.

Hasegawa and colleagues performed z and x measurements of both the spins and the exit ports of the neutrons as they emerged from the interferometer. To no great surprise, they dem-onstrated convincingly that the correlations between the measurements are stronger than anything allowed by the theoretical inequality5,6 for models involving non-contextual hidden variables. In essence, the spin measurements fix the spin values of the hidden variables, and the port measurements fix the port values. That leaves no more room for manoeuvre. But for the hidden variables to be compatible with the result of the joint measurement of spin and

Figure 1 | Neutron interferometer. Hasegawa and colleagues’ latest experiments2 on quantum reality reuse an earlier experimental set-up of theirs8. Neutrons are spin-polarized before they enter the interferometer, where the neutron beam is split into two possible paths before recombining and exiting through one of two ports. An entanglement between path and spin is established by changing the spin of the neutrons on one of the paths. The phase shifter determines the type of port measurement by exploiting neutron interference at the point where the two beams recombine. A spin rotator after the interferometer selects the direction in which spin is measured for one of the beams. The correlations between spin and exit port measurements can be determined from the numbers of neutrons detected per unit time for each setting. (Figure after ref. 8.)

port, more latitude is just what is required.Even though experiments of this type are

very difficult — Hasegawa and colleagues’ neutron beam is about as dim as the light of a candle seen 16 kilometres away — the data are amazingly clean and leave nothing to

interpretation. Thus, unless one allows the exist-ence of contextual hidden variables with very strange mutual influences, one has to abandon them — and, by extension, ‘realism’ in quan-tum physics — altogether. We knew this for photons already, but the corroboration in a dif-ferent system should help to convince doubting Thomases, as well as assure the rest of us.

At a time when quantum information processing is becoming an established field in physics and computer science, it is important to experiment on the foundations of the under-lying theory. This might seem strange, given that the past 100 years have shown that quan-tum theory is very good at predicting the results of experiments. But if you agree with Einstein, then it doesn’t matter how practical the theory is: it can still just not real be enough. ■ Gregor Weihs is at the Institute for Quantum Computing, and Department of Physics and Astronomy, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada.e-mail: weihs@iqc.ca

1. Einstein, A., Podolsky, B. & Rosen, N. Phys. Rev. 47, 777–780 (1935).

2. Hasegawa, Y. et al. Phys. Rev. Lett. 97, 230401 (2006).3. Bell, J. Physics 1, 195–200 (1964).4. Kochen, S. & Specker, E. J. Math. Mech. 17, 59–87 (1967).5. Cabello, A. & García-Alcaine, G. Phys. Rev. Lett. 80,

1797–1799 (1998).6. Simon, C., Weihs, G. & Zeilinger, A. Phys. Rev. Lett. 84,

2993–2996 (2000).7. Simon, C., Brukner, D. & Zeilinger, A. Phys. Rev. Lett. 86,

4427–4430 (2001).8. Hasegawa, Y., Loidl, R., Badurek, G., Baron, M. & Rauch, H.

Nature 425, 45–48 (2003).

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