### STAR Scientific Overview

STAR will test Special Relativity (SR) by searching for violations of Lorentz invariance that would affect the behavior of matter and the propagation of light through space-time. This search supports the NASA science goals of the 2010 Science Plan for the SMD: *“How do matter, energy, space, and time behave under the extraordinarily diverse conditions of the cosmos?”* and: *“Discover how the Universe works, explore how the Universe began and evolved…”*

These goals are critical to the development of astrophysics and cosmology, and the answers depend both on observation and our understanding of physics at large and small scales. STAR will probe the limits of accuracy of Lorentz invariance (LI), a critical assumption in Einstein’s relativity theories and in the Standard Model (SM) that encapsulates the interactions of matter and energy in all phenomena.

#### What is STAR’s value to science?

Einstein’s SR posits that speed of light (c) is exactly constant, rigorously independent of the magnitude and direction of the velocity of the observer relative to the emitting source, and further that there is no preferred universal rest frame. Basic to SR is that the constancy of $c$ ties space and time together, giving them the same units and forming the basis of the rod-clock comparisons essential to STAR. STAR will test these assumptions that lead to the famous Lorentz transformations of SR. These ideas work remarkably well, but difficulties appear when one tries to combine Einstein’s theories with the SM. Since some fundamental theories of this type (such as quantum gravity) allow large violations of LI at high energies such as those encountered in the Big Bang era, a natural question is: can remnants of these effects be detected in today’s universe? If successful, STAR could uncover new phenomena beyond the SM of particle physics and provide evidence for a preferred universal direction or reference frame in the cosmos. A new fundamental understanding of space-time and matter would result, and our view of many astrophysical phenomena could be altered. Dramatic advances are likely in areas directly connected to this physics: behavior of matter and radiation in extreme physical conditions such as the Big Bang, very near black holes, and in the early Universe – as informed by observations of electromagnetic and gravitational radiation. Cosmology could be revolutionized if the frame in which the Cosmic Microwave Background (CMB) is isotropic were found to be preferred in some other way.

Lorentz Invariance has two components

**Directional invariance**—tested by the Michelson-Morley (MM) experiment of 1887—states that if a rod and a clock are rotated relative to an identical pair, the rods retain identical lengths and the clocks remain in synch.

**Velocity invariance**—tested by the Kennedy-Thorndike (KT) experiment of 1932—predicts that if a rod and a clock travel at a constant velocity relative to another pair, the moving rod will be shorter and the moving clock will run slower, per Einstein’s theory of Special Relativity.

#### How will STAR test Special Relativity?

Macroscopic tests of LI generally fall into two classes, MM and KT indicated in the box above, where experiments are designed to search for small deviations from directional or velocity change invariance. Analyzed by Robertson and by Mansouri and Sexl, the RMS model of Lorentz violations is parameterized as:

\delta c/c=\varepsilon_{KT}(v/c)^2+\varepsilon_{MM}(v/c)^2\sin^2\theta

where the quantities $\varepsilon_{KT}$ and $\varepsilon_{MM}$ are small dimensionless coefficients, $\theta$ is the angle of propagation of light relative to some preferred direction, $v$ is the velocity of the apparatus relative to the frame, and $\delta c$ is the deviation of $c$ from an exact constant. In SR the terms on the right hand side are zero. In the RMS model a MM experiment can be viewed as measuring the quantity $\varepsilon_{MM}$ via the $\theta$-dependence of $c$, while a KT experiment measures the quantity $\varepsilon_{KT}$ via the velocity dependence of $c$, independent of $\theta$.

A weakness of the RMS model is that it is not linked to the physical processes occurring in real clocks and rods used to make the measurements. The modern approach to LI violation is based on cataloging all possible sources of violation in the SM. Colladay and Kostelecky developed the Standard Model Extension (SME) with this task in mind. This work has produced many new insights to existing experiments and has been shown to include the RMS model. The number of parameters has been greatly expanded to include effects from the entire fermion and boson sectors of the SM. From the perspective of this proposal estimating the SME parameters is an alternative data analysis to using the RMS model, giving deeper physical insight into any phenomena detected, that pertain to the actual rods and clocks used. The same data is used for both analyses.

Detection of anisotropy of $c$ would likely identify a preferred direction in space. A remarkable development of modern cosmology is that the CMB suggests a possible identity for a preferred reference frame of matter and radiation in the Universe, defined as that in which the CMB is exactly isotropic. The blue and red-shifted regions in the CMB all-sky map indicate the Earth’s velocity relative to an isotropic microwave distribution. The most likely speed-oflight anisotropy that STAR might uncover can be envisioned as a similar shape but of much smaller amplitude. In the rest of this proposal when a specific frame is required, especially for data analysis issues, we use this CMB frame, but of course the actual analysis will identify whatever direction is associated with any detected anisotropy. Expectation is high that the direction on the sky would agree with the CMB, but this is not a prejudice of our experiment: STAR will make an all-sky search for directional effects in c.

The STAR spacecraft will search for variations in $c$ at the level $\delta c/c \sim 10^{-17}$ over the entire sky with the possibility of higher resolution depending on clock performance. It will be able to make a factor of 100x improvement of the limit on the KT coefficient and a factor of 15x improvement on some of the parameters in the SME. The MM coefficient and other SME parameters will also be measured with resolutions at least as good as on the ground. The MM data also support the KT measurements by providing crosschecks and cover the possibility that measurements in space may be different to those on the ground for reasons as yet unknown. The concept for the STAR KT experiment is illustrated in § E of the Science Foldout. The MM measurements are obtained by spinning the spacecraft at a low rate and are also illustrated on the foldout.

#### Why expect STAR to be successful at 2e-17?

It has been suggested that the appropriate scale for remnants of Big Bang physics will be near the ratio of the electroweak mass to the Planck mass (quantities in the SM), $\sim 2\cdot10^{-17}$, implying the likelihood that there will be modulations of the velocity of light $\delta c/c$ on this order. While not a firm prediction, this consideration makes plausible a discovery in the window opened up by STAR -- with the concomitant exciting physics.

#### Why space?

Performing the experiment in space offers a number of advantages over ground experiments:

- Quiet environment: seismic vibration is eliminated (spacecraft has no moving parts)
- Elimination of mechanical distortions due to gravity
- Higher orbital velocity: spacecraft moves 16x faster than a ground laboratory
- Different systematic errors
- Faster orbital period: 90 mins vs. 1440 mins

The last point is very valuable for reducing thermal effects: filtering of orbital thermal effects can be greatly enhanced at 90 mins vs. 1440. STAR should gain at least a factor of 100x from these advantages, relative to a similar ground experiment.

#### What is the technology status?

- The technology for the clocks and cavities is well understood and in use in both laboratory and commercial instruments for more than one decade.
- The Iodine clocks were developed in the 60's are in use in many laboratories, in particular Berlin, Konstanz University, University of Colorado, Stanford (all STAR participants)
- Performance is a factor of ~5 from the STAR requirements and the path to this improvement is clear and in progress.
- Most components of the clock are in the range TRL 5-8

- The optical cavities were developed in the 90's are in use in many laboratories and in particular in Berlin, University of Colorado, Stanford, Ball (all STAR participants)
- Their performance exceeds the STAR requirements
- Flight versions of optical cavities have been developed by Ball to TRL 7-8
- Commercial versions are available from Advanced Thin Films for standard lab instrumentation for about $20,000

- Thermal isolation systems using multiple shells have been developed in laboratories and for flight.
- A 6-shell system that meets STAR requirements exists at Humboldt University (STAR participant).
- Multi-shell models have been flown on the Shuttle with microkelvin stability (ZENO, CVX).

### Scientific Goals and Objectives

#### NASA Goals

The primary NASA science question addressed by the STAR mission is given in the 2010 Science Plan for the SMD: *“How do matter, energy, space, and time behave under the extraordinarily diverse conditions of the cosmos?”*

This is derived from the goal:*“Discover how the Universe works, explore how the Universe began and developed…” *

STAR’s objective is to probe the limits of accuracy of Lorentz invariance, a critical component of Einstein’s relativity theories and a cornerstone of the Standard Model of matter and energy. A signal of such a violation could show up either as an apparent angular dependence of $c$ or an apparent dependence of $c$ on the velocity of the apparatus. STAR’s objective is to improve our current knowledge of the velocity dependence of $c$ by 100x, and verify its apparent lack of angle dependence in space.

The foremost Astrophysics Research Objective in the NASA Science Plan for 2007-2016, is to *“Understand the origin and destiny of the universe, phenomena near black holes, and the nature of gravity”. *

The second Baseline Objective for Astrophysics is:*“Investigate the nature of space-time through tests of fundamental symmetries; (e.g., is the speed of light truly isotropic?)”*

STAR directly addresses this compelling objective. An LI violation can be viewed as a symmetry breaking effect and would undoubtedly transform physics on all energy scales, while an improved null result could constrain theories attempting to unite particle physics and gravity. If STAR discovers a violation then modifications to the SM, SR and General Relativity would be required. Since theoretical considerations point to a violation being more important at the high energies characteristic of the Big Bang, the impact on our view of the birth and evolution of the universe would be dramatic. For example, the long standing idea that nothing but Hawking radiation can leak out of black holes may turn out to be incorrect, leading to a new view of phenomena at galactic centers. Even a null result is of value because it puts limits on the size of a violation that can be allowed in new theories attempting to unify the SM and General Relativity.

#### Mission Objectives

##### Anisotropy of Velocity of Light

Anisotropy, by definition, refers to any departure from being the same in all directions. STAR’s basic objective is to measure any small variation of $c$ as a function of velocity of the apparatus and as a function of direction. These are the only sets of science data generated. To distinguish the two data classes, the apparatus rotates at a period that is incommensurate with the changes in its velocity vector. The classes can then be analyzed as a function of direction in inertial space, independent of velocity, and as a function of direction of the spacecraft velocity vector. The angular measurement must include at least one ‘rod’ and the velocity measurement must involve both a ‘rod’ and a ‘clock’. The analyses are free of model assumptions and represent the most general interpretations of the data.

Since the apparatus must have sensitivity to direction, it will act as a form of broad beam antenna converting a general distribution of anisotropy into measurable signals when projected on the sky. From the amplitude and phase of this distribution a crude form of anisotropy ‘map’ can be constructed. This map is not expected to show fine detail, but primarily an overall dipole-like asymmetry as discussed above.

The distribution of $\delta c/c$ variations on the sky as seen at the first harmonic of the spin rate and at the orbital period represent the raw data obtained from the STAR instrument from which all other results are derived.

##### Kennedy-Thorndike Coefficient

The KT coefficient is obtained from a data analysis that compares a rod length to the ticking rate of a clock as a function of velocity direction. It uses Eq. 1 to look for a preferred frame effect manifested by the velocity dependence of $\delta c/c$ independent of orientation. From the form of (Eq \ref{eq1}) this signal will be at orbital period. The derived quantity is then the $\theta$-independent term, $\varepsilon_{KT}(v/c)^2$. Since it is very difficult to measure $c$ directly with high precision, the only way this analysis can generate an observable $\delta c$ is if $v$ varies. To obtain extra sensitivity over ground we make use of the orbital velocity of the spacecraft to maximize the change in v, denoted dv. By convention $v$ is taken as the velocity relative to the CMB and any signal detected is referenced to this frame. To get the sensitivity to the KT coefficient we then multiply the $\delta c/c$ data by $c^2/v\delta v$. In a circular orbit at 650 km altitude we obtain 2.2e7 for this quantity giving a high sensitivity to small effects. The resulting limit on $\varepsilon_{KT}$ is $\sim 4\cdot10^{-10}$. This can be compared with the ground limit of $\varepsilon_{KT}\le 4\cdot10^{-8}$ supporting our claim of 100x improvement in the resolution of this parameter. Testing for other potential preferred frames would involve examining the ‘map’ data for small signals aligned with other directions of interest.

##### Coefficients of Lorentz Violation

The SME provides a more general formalism than RMS for interpreting the STAR data. The coefficients of Lorentz violation represent the most general set of Lorentz violations that can occur within the SME. To obtain these coefficients the $\delta c/c$ data is reanalyzed to derive first and second harmonic information in two orthogonal planes. The fitting equation is of the form \delta c/c=A\sin\Phi+B\cos\Phi+C\sin{2\Phi}+D\cos{2\Phi}

where the amplitudes A, B, C, and D contain linear combinations of the coefficients of Lorentz violation and $\Phi$ is a phase angle relative to inertial coordinates. The coefficients of Lorentz violation measured by STAR will be for mixed photon and electron sectors. They are relevant as the first order, velocity-independent terms in the SME as applied to cavities. These are important results for theorists attempting to unify the SM with gravity because they are linked directly to the interaction fields currently assumed to be Lorentz invariant. These terms will be measured with a resolution similar to ground, $\sim 3\cdot10^{-17}$. Velocity-dependent terms also enter (Eq \ref{eq2}) and are purely from the photon sector. These are bounded by STAR at the $10^{-13}$ level, a factor of ~15 improved resolution over ground measurements. In this case $\Phi$ is a phase angle representing the direction of the velocity vector.

In the case of the KT-style measurements the SME coefficients are not yet quantified but are expected to be analogous to the terms described above. Theoretical work to define these parameters in the SME and their impact on the underlying physics is in progress elsewhere.

##### Michelson-Morley Coefficient

The MM coefficient is obtained by comparing the apparent lengths of two rods perpendicular to each other using light beams as the yardsticks. The data is the dc/c signal as a function of orientation, but now one assumes (Eq \ref{eq1}) is correct and computes the coefficient of the $\sin^2(\theta)$ term: $\varepsilon_{MM}(v/c)^2$. The MM coefficient $\varepsilon_{MM}$ is larger by a factor $(c/v)^2$ relative to the basic measurement, $\delta c/c$, to give a parameter that can be compared directly with other experiments. As mentioned above $v$ is taken as the velocity relative to the CMB and any signal detected is referenced to this frame. We expect to resolve $\varepsilon_{MM}$ to $\sim 1\cdot10^{-11}$. Alternatively, one can search for a $\sin^2(\theta)$ dependence along any axis, in which case the total amplitude of the MM term would be constrained. This would amount to a generalized search for a preferred frame in any chosen direction.

While it is unlikely that the MM measurement will be better than on the ground, it does serve as a useful diagnostic for the anisotropy measurements because it provides a cross check on the behavior of the ‘rod’. Also, as mentioned earlier, there has been speculation that LI violations might be different in space because of the near absence of matter surrounding the apparatus.

Last modified Mon, 6 May, 2013 at 19:34