The color of stars

Most of the stars that you see in the sky are stars of our own galaxy. You can see that some are more yelow, some bluish, some reddish… But why do they have a color? Well, we first have to understand why material objects have color.

A rose is red because, if you illuminate it with some white light (which means some light with all the shades of the rainbow), it only reflects the red component.


A white rose reflects all colors, hence looks white.


A black object looks black because it absorbs all colors of light and reflects none.

If the surface of Mars looks red, it is because, illuminated by the light of the Sun, it only reflects red light.



But what makes the color of the Sun? What makes the color of stars?

The light that comes from them cannot be reflected by their surface, because there is no light source close by; this light must be emitted by themselves. Indeed, if you were sending some light beam to the surface of the Sun, it would be absorbed by this surface. In other words, the surface of the Sun -and of all stars for that matter- is a black body, in the sense that it is a perfect absorber of light. But why do we see colors?

Well, it was discovered at the end of the XIXth century that a heated black body emits electromagnetic radiation (light if you prefer), and the color of this light is characteristic of its temperature.

Somehow, you know this: take a piece of charcoal, it is black,; heat it: it will become red or even white; it thus emits a light which is characteristic of its temperature.charcoal_red




Similarly, the color of the light emitted by stars gives us precious information about the temperature of the star interior.
As for explaining this strange phenomenon called black body radiation, one had to wait till Max Planck in 1900. This was the birth of quantum mechanics…

Why test the equivalence principle?

Let us first remember what is the equivalence principle.


The equivalence principle expresses a property which is at the basis of Einstein’s general relativity: the equivalence between acceleration and a gravitational field. More precisely, observations made in a system in acceleration (e.g. a rocket) are indistinguishable from those made in a gravitational field (e.g. on Earth).


This allows to understand better the notion of mass, which is actually describing two apparently independent concepts:

  • the mass of a material object characterizes how it couples to a gravitational field; for example a more massive object is submitted to a greater attraction to the Earth, a greater weight. This mass is called the gravitational mass.
  • the mass of a material object characterizes its inertia, that is its resistance to changes of motion. This mass is called the inertial mass. Since acceleration corresponds to a change of velocity, hence a change in motion, it is this mass that appears in the famous law of motion: force = mass x acceleration.

The equivalence principle tells us that gravitational mass and inertial mass are identical. This is why it is at first so difficult to disentangle the notion of weight (related with the gravitational mass) from the notion of inertia (related with the notion of inertial mass).


This principle has some important consequences. Take for example a kilogram of gold and one of platinum. They resist to changes of motion in the same way: they have the same inertial mass. Hence they have the same gravitational mass and identical motions in a gravitational field; they are attracted in the same way by the Earth. This has been checked on ground to a precision of one part in 10 000 000 000 000 (in other words 10-13).


But theorists are not fully happy with the theory of Einstein. They would like to unify general relativity with the quantum theory which describes non gravitational forces. They thus have to change, even though in a subtle way, the description of the gravitational attraction. But by doing so, they often lose the precise identification between gravitational and inertial mass.

For example, let us consider string theory where the basic objects are no longer point particles but microscopic one-dimensional objects (the strings!): our good old particles are considered as grains of energy which correspond to modes of oscillation of these fundamental strings. We are used to (violin) strings emitting (sound) waves, but remember that, in the microscopic world, waves and particles are united in a single concept (the two sides of the same coin if you prefer). This is why different types of oscillations of the fundamental microscopic strings lead to different types of particles, with different energies E, hence different masses m (E=mc2).

Now in such a theory, the gravitational force between two particles/waves is understood as an oscillation, or a series of oscillations of the underlying string. It is thus not at all obvious that the gravitational force between say two protons is identical to the gravitational force between two neutrons, or between a proton and a neutron. Thus, if two material objects have the same inertial mass but different number of protons and neutrons, they may be falling differently in the gravitational field of the Earth. They would thus have different gravitational masses. This leads to a violation of the equivalence principle.

This is exactly what the Microscope mission aims at testing, gaining two orders of magnitude over the existing experiments on Earth (10-15).

How to test the equivalence principle in space? The Microscope mission

The goal of the Microscope mission is to test the equivalence principle to a precision two orders of magnitude better than is achieved on ground, more precisely 10-15 or one part in 1 000 000 000 000 000.

Members of the mission like to say that this is the difference of weight of a 500 000 ton tanker when a 0.5 milligram drosophilia fly lands on the deck.

coaxial_cylindersIn order to do so, one needs to compare the free
fall of two objects of different composition (see why here). But the two objects must feel exactly the same gravitational field, and thus be placed at the same point in space. In the Microscope set up, they are two coaxial cylinders of different material – one is made of titanium and the other one of a platinum-rhodium alloy- which have coinciding centers of mass (as shown on the figure to the right).





As a matter of fact, the Microscope mission has two devices (see on the left): one with two cylinders of the same material, and one with cylinders of different materials. This allows to make sure that any effect observed with the two different cylinders is not observed with the two identical cylinders!



Actually, the cylinders are not in strictly free fall. Remember that an object in orbit keeps falling, with horizontal velocity. The satellite, and the two coaxial cylinders, are in orbit but they have slightly different motions: the satellite is submitted to non-gravitational perturbations (inducing friction or drag) which are compensated by micro-thrusters. And, in case the equivalence principle is violated, the two cylindrical masses should have tiny differences of motion. In the Microscope experiment, they are forced to follow the same motion at the center of the satellite by applying on them electrostatic forces, or if you prefer external acceleration on them. If the applied accelerations need to be different on the two masses, this means their natural motion is different: there is a violation of the equivalence principle. In other words, different accelerations on the two cylindrical masses mean different gravitational motions. Another beautiful illustration of the equivalence between acceleration and gravitational field!

It is very important to make sure that the effect observed must be attributed to a violation of the equivalence principle, and not to the set up malfunctioning. In order to do so, the physicists have a clever way of modulating the signal, that is of making the potential violation signal vary with time at a given frequency. Here is the trick.


The satellite is following a quasi-circular orbit at an altitude of 710 km. The axis of the cylinders is pointing in a direction fixed with respect to the distant stars, and the acceleration measurement is made along this axis. As you can see in the figure above, there are positions along the orbit where the gravitational attraction is perpendicular to this axis, and thus not active along this axis. There are other positions where it is parallel or antiparallel, and thus the effect is maximal. In this way, one modulates the effect at a known frequency which is directly related to the frequency of rotation along the orbit. Any effect of violation of the principle of equivalence must have such a modulation.

In order to further check the results, the physicists of Microscope have decided also to spin the satellite around the axis perpendicular to the orbital plane with a period of 1000 seconds. In this way, they introduce a further modulation of the signal.

If you want to watch the launch of the Microscope mission from Kourou, see here.


What is a graviton?

If the theory of gravity is fundamentally of a quantum nature, the graviton is the particle whose exchange between two masses is responsible for the gravitational force:


To understand this, one has to remember the traditional field/particle association that one encounters in quantum physics: a photon is at the same time a particle and an electromagnetic field (in fact an electromagnetic field is usually a superposition of many photons). The Higgs is a particle that is detected at CERN but it is also a field that is present everywhere and gives mass to the other particles.

Similarly, if the theory of gravity is a quantum theory, the graviton is a particle but also a gravitational field. On the field side, it can be seen as a field of deformation of space-time. On the particle side, it is the particle whose exchange leads to the gravitational force.


Now, the theory of general relativity as proposed by Einstein is not a quantum theory. So, the graviton is, in the strict sense, not part of this theory. But most theorists believe that eventually there will be a quantum generalisation of general relativity. In this context, there will be a graviton, and, even though we do not know this theory yet, because we know well the gravitational force, we can infer from it a certain number of properties of the graviton: for example, it has zero mass and travels at the speed of light.

If it turned out that gravity is not a quantum theory (a possibility not favoured today because it leaves many questions unanswered), then only the field interpretation is valid, not the particle interpretation, and there is no graviton.

Why is the horizon not expanding during inflation?*

Why is the horizon not expanding during inflation?*
Because the texture of spacetime expands in-between, regions which are very distant from us seem to recede from us at a velocity larger than the speed of light, and thus cannot send us information. The horizon separates these regions from the ones causally connected to us. This means that a photon emitted outside the horizon but towards us is actually receding from us because space is being created in the region in-between the photon and us (see figure below (*))


In the case of standard expansion, such a photon emitted just outside the horizon towards us will overcome the expansion and, after a while, move towards us. This means that the horizon will have overtaken it and moved away from us: it has expanded.

But in the case of inflation, the expansion is as fast as it can be (we say “exponential”): the photon emitted towards us just outside the horizon will never overcome the expansion: the horizon does not move.

(*) Note that anyone measuring the velocity of the photon would obtain the standard velocity of light c; but, because of expansion, both the galaxy and the photon it emits recede from us, although this is not observable because they are beyond the horizon

What is a flat Universe?

What is a flat Universe?
First a word of caution: we physicists are using everyday words with a slightly different (or sometimes more precise) meaning. This helps at first because it sounds vaguely familiar but, when you go deeper (as we do in this course), this may make things more difficult.

For example, in everyday language, a flat surface is a 2-dimensional surface which is not curved.

For physicists, flat space could have more dimensions than 2 (actually 3 in our case). Flat space is a space where the familiar laws of ordinary geometry (the geometry of Euclid) apply: parallel lines never meet, the three inner angles of a triangle sum up to 180°, etc. In the case of a non-flat or curved space, all this has to be reconsidered: parallel lines meet, the angles of the triangle do not add up to 180°. Now you might think that we know that we are in a flat space because we learn all these rules at school. Well, Einstein tells us that this is true only locally, in our close vicinity. The question is whether this is true at the scale of the full universe. And it appears to be so!

Horizon and hydrogen recombination

Before the (re)combination of hydrogen, the Universe was opaque and light could not travel. Does this correspond to what one calls horizon?
The answer is no.

The black wall that one reaches when one watches far enough to observe the epoch of hydrogen recombination is opaque because, beyond it, light emitted is immediately trapped by charged particles. This means that light emitted before this epoch cannot be observed, but it does not mean that information cannot be obtained from earlier epochs. This information could be transported by neutrinos which interact very weakly very matter, or by gravitational waves. In other words, the black wall is opaque to light but not to other “messengers”.

On the other hand, an horizon corresponds to a surface which limits the region from which, at a given time, we cannot receive any information (whether in the form of light, neutrinos or gravitational waves).

What is the cosmic microwave background?

What is the cosmic microwave background?
The cosmic microwave background (CMB) is really the first light that emerged in the Universe, and that is still traveling across this Universe. It is called cosmic because it is of cosmic origin. It is called background because it is everywhere. And it is called microwave because it is an electromagnetic radiation (what we call losely “light”) which is in the microwave radiation frequency range. In this sense, it is similar to the microwave radiation present in your microwave oven. This microwave radiation is close in frequency to the electromagnetic radio waves. This is why the CMB can be detected nowadays by a simple dish antenna (an experiment that we do routinely on the roof of our lab in Paris).

Finally, let us stress that the CMB was produced at the time of Hydrogen recombination in a different frequency range but was redshifted to the microwave range by the expansion of the Universe.

Am I at the centre of the Universe?



Seeing distant objects is looking at their past. I could thus look at the Big Bang by looking far enough, and this in all directions. Doesn’t it mean that I am at the centre of the Universe?




The answer is no. Imagine a point (A) at 14 billion light-years from you (O), which corresponds basically to the Big Bang (left figure below). Then place an observer at point A today (right figure below), what does this observer see? Presumably, exactly the same thing as you.

But that seems impossible, because we (at O) are at a distance of 14 billion light-years from A, and we know that we are not at the Big Bang!


Well, you forgot that we see in time and space. In the left figure (see below), O corresponds to now, and thus A to the Big Bang era. In the right drawing, A is an observer now, and thus it sees the point O at the time of the Big Bang, 14 billion years before we appeared on Earth!


You may note that A sees a similar sky as O, but each star or galaxy is viewed at a different time (depending on the respective distances to A or O).

Problems with an infinite Universe?

How can the Universe be infinite if it was localized in a microscopic volume just after the Big Bang?
Well, this is absolutely right: if the Universe was localized in a small volume just after the Big Bang, it can have expanded to a large finite volume now but not to an infinite volume. But, the misconception lies in the mental image (carried by many, including physicists) of associating the Big Bang with a universe localized in a finite volume. Even an infinite Universe can undergo a Big Bang: each microscopic finite volume in this infinite Universe just after the Big Bang will eventually expand to a very large volume.

So, one should be cautious to make the distinction between the full Universe and the observable Universe (the portion of the Universe that we can observe, typically 14 billion light-years, since 14 billion years is the age of the Universe). The boundary of this observable Universe can be understood as an horizon.

Quite often, people say that they have difficulties picturing an infinite Universe. But, isn’t it more difficult to picture a finite Universe? What happens when we reach the boundary (unless the Universe is like a sphere)? Well, the notion of horizon should help you in this case: the observable Universe has a boundary, the horizon, but beyond the horizon begin the unchartered territories of the (infinite) Universe.

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