Testing Alternative Theories of Gravity with Atomic Clocks

Modelling the Dark Side of the Universe

Most our instruments are built to detect light (e.g., stars, dust, galaxies), and so we still know very little about the dark sector, which comprises more than 95% of the universe and neither emits nor absorbs light. The simplest type possible type of dark matter particles are those represented by a spin zero scalar fields. Scalar fields can arise from not-yet understood physics such as compactified extra dimensions. The Higgs particle is believed to be the first fundamental scalar field ever detected. In cosmology, the initial rapid inflation of the universe is also best modelled by a scalar field called the inflaton, while the quintessence scalar field generates a form of dark energy that may account for the accelerated rate of expansion of the universe. It is reasonable to believe that similar to the visible sector, the dark sector is rich and contains particles of different kinds with various masses.

Alternative theories of gravity and PPN parameters

The solid line corresponds to 10^-16 clock stability. 

Einstein's theory of gravity alone cannot account for dark matter or dark energy. Instead, a scalar field that may couple in different ways to different kinds of matter enters the theory of gravitation in addition to the metric tensor of general relativity. This field couples to matter and therefore violates General Relativity. The standard way to describe deviations from General Relativity in weak gravitational fields is via the Parametrized Post-Newtonian (PPN) formalism. The most commonly constrained PPN parameters are 𝛄 and β.

In Einstein's General Relativity 𝛄=β=1. When the scalar field is massless, the 𝛄 and β parameters are constant. The introduction of a mass term causes the 𝛄-parameter to become distance dependent. It is thus natural to expect that PPN parameters may depend on both the distance from and the composition of the mass they are tested around, e.g.,  their value measured around the Earth would be different than around the Sun. The strongest constraint on the 𝛄 PPN parameter comes from the Cassini spacecraft, which limits the size of the parameter around the Sun to 2.3 x 10-5 (1-sigma confidence level). Null results from planetary ephemerides place similar constraints on the  β parameter.

Testing Alternative theories of Gravity with Clocks in Space

Performing accurate timing experiments with satellites carrying state-of-the-art atomic clocks in Earth orbit can test alternative theories of gravity such as scalar-tensor theories. The Hydrogen Maser placed aboard the International Space Station as part of the Atomic Clock Ensemble in Space (ACES) mission is expected to reach  a frequency inaccuracy of 10^-16.  

We calculate the gravitational redshift for an eccentric Earth orbit induced by varying PPN parameters and compare it to the one predicted by GR.  We find that a clock with the stability that should be achieved by the ACES mission placed in an elliptical orbit would constrain 𝛄 and β to the 10-6 level (see figure). We take an eccentric orbit with the same parameters as that proposed for the orbit of the originally proposed STE-QUEST satellite.  Choosing an  eccentric orbit makes the signal stronger since the relativistic effects are larger than for a circular orbit due to the higher velocity at perigee.

PPN parameters for general scalar-tensor theories
We compute the PPN parameters γ and β for general scalar-tensor theories in the Einstein frame, which we compare to the existing PPN formulation in the Jordan frame for alternative theories of gravity. Note that there are infinitely many possible frames, but these two frames are the ones that are typically chosen. In the Einstein frame, the Ricci scalar appears alone and the matter fields couple to a conformally related metric, while in the Jordan frame, the scalar field multiplies the Ricci scalar and any matter fields present couple directly to the frame metric. This computation is important for scalar-tensor theories that are expressed in the Einstein frame, such as chameleon and symmetron theories, which can incorporate hiding mechanisms that predict environment-dependent PPN parameters. 

Extended Point Source?
The PPN parameters are typically calculated for a space-time consisting of a point source surrounded by vacuum, which is not accurate for experiments performed around extended objects like the Sun. Instead, we add a parameter that measures how much the exterior gravitational field deviates from that of a point source with the same mass.  To check our assumptions, we recompute the Cassini constraint modelling the Sun as a homogenous sphere instead of a point source for massive Brans-Dicke theories, and find that the 𝛄-PPN  constraint becomes more stringent.

The article this post is based on was led by PhD student Andreas Schaerer.  The paper is published in Physical Review D. I have also written a conference proceeding that describes tests of gravity with space-based atomic clocks and atom interferometers.

Dear Immigration Offices Worldwide

I do not love you and I have never feigned affection for you, but I somehow I still feel the need to make my feelings clear. I would like more time away from you.  I can understand visiting you once when I move to a new country. However, seeing your representatives and going through the associated tons of paperwork so often is tiring, and, of course, counter-productive. All my energy feels drained after interacting with you. You often fail to see me as human and yet I have to go through this seemingly endless process of registering, reregistering, and re-re-...-registering myself.

Until next time,

Your lawful immigrant who generally submits most documents on time.

What is the origin of the Kreisburo(s)?

My understanding is that careful registration of individuals and their addresses originated in the period before the Holocaust.  It appears that immigration offices are some of the numerous vestiges from that era that exist outside museums. In the past, authorities needed to know the exact address of Jewish individuals so that they could find them and arrest/kill them later, which, while not reassuring, made sense in that political climate.

What will the future bring?
We believe to be better now, but is that true? or is the hatred just focused in other directions? will we ever build a world without wars and so much discrimination in seemingly all directions? I, of course, do not know the answer to these questions, but I believe in the power of information flow, which is made instantaneous by the internet. In the meantime, like in most love-hate affairs, people on both sides have to continue to avoid being bitter, and, in particular, avoid placing blame on the wrong shoulders until the many problems resolve and others appear.

Getting back to today

As long as my paperwork is done, I should not complain. Immigration is a complicated problem. Immigrants keep the economy growing as long as they are controlled and underpaid. It naturally makes sense to continue to keep them that way as long as possible and then blame their condition on the views of the public.

The tons paperwork and the many interviews that sometimes make me feel a cross-bred between a criminal and a moron are good practice - each in its own way. Sometimes, I am interviewed by people who have no understanding of who I am or what I do. At other times, I am interviewed by very kind people who make me feel good about my achievements, and try to solve my often atypical paperwork problems.  The stressful part is not knowing which kind of person will be at the other side of the desk. I try to respect them all. I also understand that they are not to blame and generally have no power to change the laws.

Bye, Bye Fallanden

Under the rainbow

We'll miss the lake, the mountains, the corn, the swans, the ducks, the fox (dear fox - we've only seen you once, but I have to say you are very pretty and graceful, and even though you destroyed our trash bags on a regular basis you were my favourite neighbour), the hunting lodge, the various parks, and, of course, the house we lived in.  For once, I have very little to say other that I am tired of moving and of not having a home of my own. I suppose the right attitude is to be grateful for the experience, but somehow I am tired of being tired, which may make little sense.

The swans

The corn was about 3 meters high.

On rollerblades

The hunting lodge

The rainbow up the hill

A view of cloudy Fallanden

Edward and the ducks

Stereotypes

http://economydecoded.com/2013/09/stereotypes-just-humour.html

We are taught that stereotypes are always wrong. I see them as approximations based  on 'data' gathered by people from interactions with each other. Approximations help us build simplified models of the world we live in.   They are always wrong when compared to an exact result. However, in order to improve our understanding of the world, we have to simplify it.  Even simplified models that are in good agreement with data are valid only with many ifs and buts. Yet because we are human we forget the assumptions where the "general statement" is valid, and take it as true - always. Such errors are unavoidable. The same flawed logic goes into the many "theories of everything" that I get via email.

Ideally, one could systematically get rid of the stereotypes/models/approximations that are based on inaccurate data or hear-say, and build models with a scientific basis that are adjusted when new data comes in. But we cannot expect to restrict thinking to the scientific community, which is very tiny.  Otherwise, we stall progress. I believe it's important that regular people, who now have access to huge amounts of data via the internet, keep creating new models/approximations for the world around us. Some models will be wrong, some will be almost-right in certain situations, and some of the wrong ones will end up widely accepted for some time. It's important to retain the courage to not only question existent models, but to create new ones.

So, does this mean that I like it when people tell me how easy everything is for me vs. them because I am a woman in a field with almost no-women? (especially when data suggests the opposite) Or when they assume I don't understand what they are saying because of how I look or who I am? Do I like my yearly visits to the immigration office where I am treated as an unwanted entity who is a cross between a criminal and a moron?  Of course, not. I am not masochistic. I leave that for the female protagonist of Fifty Shades of Grey. But I try not to get too upset when I receive such treatment. Life is hard for everyone in different ways. Gratuitously offensive words/statements mean that most of us (including me sometimes) should think more before speaking to avoid being offensive.

Should we aim to understand "everything"?

No! The idea is to easily see what's important. This is what school is supposed to teach us. Over the course of my life so far, I have met a few people who are smart enough to almost always understand the main points of any conversation or seminar. I classify them as "out of this world smart".  

Does my understanding of science correlate with my looks or with the way I dress?
Obviously, my ability to understand an idea has no correlation to the color of my hair or to the length/shape of my skirt/jeans/dress-pants on a given day. If I do not understand something, often my colleagues do not understand either. This is happens when (1)  the research work is not explained clearly, (2) I don't know enough of the background material, (3) a combination of both (1) and (2), or (4) I an not paying attention. 

Am I bitter?

No, or at least I do not think so. I've always had good relationships with my bosses, my co-authors, and the students I work with. They are each very talented. I admire them, learn from them, and consider them my friends.  The letters my professors write for/about me are praising, and I think they like me as a person, too.

Then why do I write on this topic?
Sometimes I feel the need to write on topics that are not science. I have thought about giving up making philosophical statements on this blog. However, somehow when I have not made palpable progress in other ways, writing gives me comfort and a sense of accomplishment. It's partly a way to procrastinate getting scientific work done.  It's easier to write blog posts than scientific papers. I cannot seem to completely abstain from writing, and I am not sure I want to try.