# What would be the best inertial reference frame to describe objects in the solar system (other than the solar system's barycenter)?

For the purpose of a project, I require the components that describe the inertial frame to be as independent as possible from solar system bodies itself. Since the solar system barycenter is itself determined by the positions and masses of the solar system bodies, it will not be a good choice.

I was thinking that the frame that I want could be described by some nearby star that does not have planets of its own or else the galactic centre itself.

If such an inertial frame exists, I would like the same to be expressed in heliocentric cartesian coordinates.

Any relevant thoughts would be much appreciated!

Use the initial Center Of Mass (COM) as an origin.

It's trivial to show that the COM of a closed N-body system (in Newtonian physics) moves with a constant velocity. This is a relatively easy system to work with and transforming to other coordinate systems, such as the heliocentric one you mention, is relatively trivial compared to computing the 3D N-body system with good accuracy. A word of advice : if the math of converting between coordinate systems is a problem for you, the mathematics and algorithms of an accurate simulation will be likely much worse. I'd suggest trying out such conversion mathematics as a warm up exercise and if you're comfortable with that then dive into the simulation.

COM can be shown to move at constant velocity because it's a closed system (or can be treated as such over the timescale you mention), and so net force on the COM is zero, meaning it has to move with constant velocity.

Adding a small body like an extrasolar asteroid makes next to no difference to the system as a whole. It's a minute change. You can treat such objects as special cases, ignoring their effect on the system and just calculating the effect of the system on them. If you're planning to add very large bodies and see what happens then you need to include them in the general system all the way through the simulation.

Note there are a lot of existing simulations out there that implement a wide range of approaches. This is a problem that has been extensively studied and a search online would yield a myriad of approaches.

The motion of the Barycenter is complex. I'd avoid this complication in what is already gong to be a messy mathematical system to simulate.

Your main priorities should be gathering accurate data for initial starting values (non trivial) and choice of algorithms. Choice or ordinate system is comparatively minor.

One of the postulates of General Relativity is that there is no absolute frame of reference. It's kind of an important one, and considered to be one of the standards for any other theory.

Speed of light is always a constant in all frames of reference, but it does not define a frame of reference. There is a lite cone transformation, but it's a bit of a complicated topic from relativity, and it doesn't change the answer.

Not all frames of reference are equal, however. There is a special class of these that are inertial. It is often convenient to choose an inertial frame of reference, because they are far easier to deal with. In an inertial frame of reference, energy and momentum are naturally conserved and the Newton's laws of motion hold without need to add fictitious forces. If you are dealing with relativity, in an inertial frame of reference you only need Special Relativity, which is far simpler than General Relativity.

Simplest example of a frame of reference that is not inertial is a rotating frame of reference. If you are inside a closed room and that room rotates, it appears that objects are acted on by some additional forces that seem to come from nowhere. There is the centrifugal force, pulling everything towards the outer edges of the room, and there is Coriolis force that makes thing move in a curve when they move towards/away from center. These are fictitious forces, because they are only there as a result of your coordinate system choice. But if things accelerate on their own under action of centrifugal force, the energy is not conserved. To fix that, you need to introduce an additional potential energy which is highest at the center of the room. That's called an effective potential. Same idea. It's only there because of a "bad" coordinate system choice.

Once you recognize that the room is actually rotating, however, and choose coordinate system that is not rotating with the room, you can describe all motion without these additional forces or potential.

If you know how to deal with these things, you can choose a coordinate system that's not inertial and work with it. You just have to be careful. And sometimes, this is a more convenient way to deal with it. If you are designing a space station that's going to generate artificial gravity by rotation, it's easier to go to a rotating frame of reference, so that the station is "still", and you just account for centrifugal and Coriolis effects in your design.

First off, what does "best" mean? My definition: The best frame of reference for some problem is that frame that make my job of solving that problem least intractable. With that definition, there is no single "best frame of reference." What constitutes the "best" frame for one problem will be quite different than the "best" frame for some other problem.

Suppose the problem at hand is to model the Earth's weather. This problem is hard enough when done from the perspective of a frame that rotates with the Earth. Choose a non-rotating frame and, woo-boy, you have an intractable mess.

Suppose the problem at hand is to model the dynamics of the solar system. This problem is hard enough when done from the perspective of a non-rotating frame with origin at the solar system barycenter. Do this from the perspective of an Earth-fixed frame and you once again have an intractable problem. Its worse than intractable: That polar motion is unpredictable means you have just thrown out high accuracy and future predictability with this choice.

No, because that would mean it would be possible to measure absolute motion, which violates SR.

It is impossible to measure motion relative to space. You can only measure motion relative to something else, because motion is only relative to something else.

Moving at a constant speed of any value and staying "still" are all the same thing, physically.

One of the postulates of General Relativity is that there is no absolute frame of reference. It's kind of an important one, and considered to be one of the standards for any other theory.

Speed of light is always a constant in all frames of reference, but it does not define a frame of reference. There is a lite cone transformation, but it's a bit of a complicated topic from relativity, and it doesn't change the answer.

Not all frames of reference are equal, however. There is a special class of these that are inertial. It is often convenient to choose an inertial frame of reference, because they are far easier to deal with. In an inertial frame of reference, energy and momentum are naturally conserved and the Newton's laws of motion hold without need to add fictitious forces. If you are dealing with relativity, in an inertial frame of reference you only need Special Relativity, which is far simpler than General Relativity.

Simplest example of a frame of reference that is not inertial is a rotating frame of reference. If you are inside a closed room and that room rotates, it appears that objects are acted on by some additional forces that seem to come from nowhere. There is the centrifugal force, pulling everything towards the outer edges of the room, and there is Coriolis force that makes thing move in a curve when they move towards/away from center. These are fictitious forces, because they are only there as a result of your coordinate system choice. But if things accelerate on their own under action of centrifugal force, the energy is not conserved. To fix that, you need to introduce an additional potential energy which is highest at the center of the room. That's called an effective potential. Same idea. It's only there because of a "bad" coordinate system choice.

Once you recognize that the room is actually rotating, however, and choose coordinate system that is not rotating with the room, you can describe all motion without these additional forces or potential.

If you know how to deal with these things, you can choose a coordinate system that's not inertial and work with it. You just have to be careful. And sometimes, this is a more convenient way to deal with it. If you are designing a space station that's going to generate artificial gravity by rotation, it's easier to go to a rotating frame of reference, so that the station is "still", and you just account for centrifugal and Coriolis effects in your design.

I don't think there is absolute frame of reference. you would have to define it in each situations.
if it's for calculation, it seems like a useful "absolute frame of reference" (if you must make one, but it's probably not necessary) is location where inertia frame of reference does not change.
In another words useful absolute frame of reference is location where it does not accelerate.

I suppose my opinion that an absolute frame of reference doesn't exist is more of an innate conclusion of my own.

## Turning the tables?

The reason the case of the travelling twins is also known as the “twin problem” or even the “twin paradox” is the following. From the point of view of the twin on Earth, one can explain the age difference by appealing to time dilation, a basic concept of special relativity. It involves an observer (more precisely: an inertial observer), for instance an observer that lives on a space station floating through empty space. For such an observer, special relativity predicts the following: For any moving clock, that observer will come to the conclusion that it is running slower than his own. Whether it is a clock on another space station floating past or a clock on an engine-driven rocket, in the time it takes for a second to elapse on the observer’s own clocks, less than a second will have elapsed on the moving clock. This slowdown is true not only for clocks, but for everything that happens on the moving space station or in the flying rocket. All processes taking place on these moving objects will appear slowed down for our observer.

Characteristically, there are situations where time dilation is mutual. For instance, if there are two observers drifting through space, each on his or her own space station, and if those two space stations are in relative motion, then for each observer, the time in the other space station appears to run slower than for himself. (If that already sounds like a paradox to you, you might want to read the spotlight topic The dialectic of relativity.)

With the help of time dilation – often abbreviated to “moving clocks go slower” – one can try to explain what happens to the twins. No wonder the travelling twin ages less! After all, the twin on Earth can invoke time dilation: Moving clocks go slower, and so do the clocks of the moving twin. On these slower-moving clocks – and, by extension, in the whole spaceship – less time passes than on Earth, in other words: when the travelling twin returns, he is younger.

No paradox so far. But why can’t the travelling twin turn the tables on her sibling? After all, motion is relative. Why can’t the twin in the spaceship define herself as being at rest? From that point of view, it would be Earth that moves away before returning to the spaceship. And if that is so, couldn’t the travelling twin apply time dilation (“moving clocks are slower”) to everyone who remained on Earth? By that argument, shouldn’t it be the humans on Earth that are younger than expected once the twins are reunited? If both twins are on an equal footing, then each one should be allowed to onsider herself at rest and invoke time dilation. But in the end, when the twins meet again, only one of them can be right – then, there cannot be any ambiguity: either the one twin is younger, or the other (or, of course, both twins’ arguments are wrong, and they have aged exactly the same). A contradiction – a twin paradox?

## What is an inertial frame of reference ?

An inertial frame of reference is a set of measuring devices, which moves with constant velocity along a straight line and without rotation.

The reference frame should not spin (rotate) around its own axis. In other words, looking from this frame, distant stars should not be seen in a circular motion (unlike we see it on Earth).

Actually, I don't think it is possible to give an unambiguous, exhausting, and rigorous definition of the inertial reference frame, simply because it is such a fundamental notion in physics, than it cannot be reduced to anything simpler. However, I don't think there is any controversy. We will all agree whether the frame is inertial or not when we see it.

Again: rotate respect to what ?

Are you shure that distant stars ( the universe ) are not rotating ? Why ?

Do you know the paradox ( Newton ) of a bucket whith water. If the bucket rotates nothing happens but if the water rotates the surface of the water is like a "V". Newton said: the next book I will explain that. He never explained it.

Its Ok to say: inertial frame of reference ? ( frame, just geometry )
Shoudnt we talk about material frame of reference ?

Forget about fictitious forces for a bit. Suppose you can see some object, and you know there no forces act on this object. If the object moves along a straight line with a constant speed you are in an inertial reference frame. This is Newton's first law of motion. You are not in an inertial reference frame if the object appears to undergo some kind of acceleration. Newton's first law essentially defines an inertial reference frame.

Newton's second law talks about what happens to objects that are acted upon by some force as seen from an inertial observer. The first law defines an "inertial reference frame" in terms of behavior. The second law similarly defines "force" in terms behavior.

Newton's second law is a very powerful device. It can be used to determine the state (location and velocity) of some object at any point in time based solely on state at some particular point in time and knowledge of the forces acting on the object. However, Newton's second law is valid only in an inertial frame. Because of its projective powers, it would be nice to extend this law to non-inertial frames.

Return again to the force-free object, but this time we observe it from a reference frame known to be non-inertial. The object will appear to accelerate. Dividing the observed acceleration by the mass yields something with units of force. By relating this force-like parameter to some attribute of our reference frame (its rotation or acceleration), we can use this force-like parameter as if it were a force in Newton's second law. The force isn't real (the object has zero external forces), so it is "fictitious".

## From what frame of reference does the Earth orbit the sun?

We can. But it is difficult to use such a coordinate system. For example, there is an enormous fictitious force whirling the sun around the earth. It is far better to pick a coordinate system where the motion looks simple, and the sun-centered one is that system.

We can. But it is difficult to use such a coordinate system. For example, there is an enormous fictitious force whirling the sun around the earth. It is far better to pick a coordinate system where the motion looks simple, and the sun-centered one is that system.

Yes, it is a question of classical mechanics. Newton's mechanics is approximately valid for inertial reference systems, wrt which motion makes sense physically (no assumption of fictitious forces). As a bonus the equations are simpler as well.

Special relativity relates to those reference systems of classical mechanics, see the intro of:
http://www.fourmilab.ch/etexts/einstein/specrel/www/

No, the units are different.

We do feel forces of acceleration while sitting on Earth. Take an accelerometer and you will see that we feel an upwards acceleration of magnitude g.

The laws of physics dictate that the equations of motion will take a relatively simple form in some reference frames but a rather ungainly form in other frames. Those extra terms in the ungainly form are fictitious forces. (Or fictitious accelerations. There is no need to multiply by mass to yield a force because the very next step is to divide by mass to yield acceleration.)

While one could describe the behavior of the solar system from the perspective of an Earth-centered frame, you hit the nail on the head in the original post when you asked "Why is any reference frame more accurate than another?" The "best" (read: most accurate) frame of reference for computing the orbit of a satellite orbiting the Earth is an Earth-centered frame. You'll still get fictitious forces, but nonetheless the propagated orbit will be more accurate when computed in an Earth-centered versus a solar system barycenter frame.

Suppose instead the vehicle is transiting from Earth to Jupiter, and once at Jupiter, goes into orbit about Jupiter. To obtain the greatest accuracy you need to be quite adept with your frames of reference, switching integration frames along the way. The key to this switching is the gravitational sphere of influence.

Imagine two donut-shaped spaceships meeting in deep space. Further, suppose that when a passenger in ship A looks out the window, they see ship B rotating clockwise. That means that when a passenger in B looks out the window, they see ship A rotating clockwise as well (hold up your two hands and try it!).

From pure kinematics, we can't say "ship A is really rotating, and ship B is really stationary", nor the opposite. The two descriptions, one with A rotating and the other with B, are equivalent. (We could also say they are both rotating a partial amount.) All we know, from a pure kinematics point of view, is that the ships have some relative rotation.

However, physics does not agree that the rotation of the ships is purely relative. Passengers on the ships will feel artificial gravity. Perhaps ship A feels lots of artificial gravity and ship B feels none. Then we can say with definity that ship A is the one that's really rotating.

So motion in physics is not all relative. There is a set of reference frames, called inertial frames, that the universe somehow picks out as being special. Ships that have no angular velocity in these inertial frames feel no artificial gravity. These frames are all related to each other via the Poincare group.

In general relativity, the picture is a bit more complicated (and I will let other answerers discuss GR, since I don't know much), but the basic idea is that we have a symmetry in physical laws that lets us boost to reference frames moving at constant speed, but not to reference frames that are accelerating. This principle underlies the existence of inertia, because if accelerated frames had the same physics as normal frames, no force would be needed to accelerate things.

For the Earth going around the sun and vice versa, yes, it is possible to describe the kinematics of the situation by saying that the Earth is stationary. However, when you do this, you're no longer working in an inertial frame. Newton's laws do not hold in a frame with the Earth stationary.

This was dramatically demonstrated for Earth's rotation about its own axis by Foucalt's pendulum, which showed inexplicable acceleration of the pendulum unless we take into account the fictitious forces induced by Earth's rotation.

Similarly, if we believed the Earth was stationary and the sun orbited it, we'd be at a loss to explain the Sun's motion, because it is extremely massive, but has no force on it large enough to make it orbit the Earth. At the same time, the Sun ought to be exerting a huge force on Earth, but Earth, being stationary, doesn't move - another violation of Newton's laws.

So, the reason we say that the Earth goes around the sun is that when we do that, we can calculate its orbit using only Newton's laws.

In fact, in an inertial frame, the sun moves slightly due to Earth's pull on it (and much more due to Jupiter's), so we really don't say the sun is stationary. We say that it moves much less than Earth.

(This answer largely rehashes Lubos' above, but I was most of the way done when he posted, and our answers are different enough to complement each other, I think.)

yes, you may describe the motion from any reference frame, including the geocentric one, assuming that you add the appropriate "fictitious" forces (centrifugal, Coriolis, and so on).

But the special property of the reference frame associated with the Sun - more precisely, with the barycenter (center of mass) of the Solar System, which is just a solar radius away from the Sun's center - is that this system is inertial. It means that there are no centrifugal or other inertial forces. The equations of physics have a particularly simple form in the frame associated with the Sun. $M_1 d^2 / dt^2 vec x = G M_1 M_2 (vec r_1-vec r_2) / r^3 + dots$ There are just simple inverse-squared-distance gravitational forces entering the equations for the acceleration. For other frames, e.g. the geocentric one, there are many other inertial/centrifugal "artificial" terms on the right hand side that can be eliminated by going to the more natural solar frame. In this sense, the heliocentric frame is more true.

This was going to be a comment on Luboš Motl's answer, but it would be more appropriate as a full answer now.

His answer says: Laws of physics can be written more simply for the solar system's center of mass (barycenter) than for a point on Earth (geocentric).

Just one thing! One mustn't neglect the non-idealities of the barycenter itself, which has a location in the Milky Way that biases it gravitationally at least. On the surface this is splitting hairs, but the greater point is that the idealness of any reference frame is also relative, and no "ultimate" frame exists.

Likewise, choosing a point on the skin of an elephant over a geocentric point is sacrificing universality just as much as choosing a geocentric point over the barycenter is. To a flee however, consideration of physics formulated at a point beyond the surface of the elephant may be just "academic". Sound familiar?

There may be a confusion : it is wrong to say that the Earth is the centre of the Universe, that is, the (unique) point from which the Universe is to be (fundamentally) described (the fact that the Sun turns around the Earth is only a consequence of this) what actually matters is that there is no centre of the Universe : there is no such point the description of the Universe from any point is equivalent to the description of the Universe from any other (then you are allowed to describe motions either from the Earth or from the Sun).

Mathematically, in classical mechanics, the Universe is said to be an affine space.

Yes, the proposition: "the sun moves around the earth" had the earth immobile. This suited the theology of the times which was completely anthropocentric and that is why it prevailed over other theories coming from antiquity, like Aristarchos', who had a heliocentric proposal.

The relativity of motion was explored, as Lubos describes, when equations could be written down, and one chooses the heliocentric for its beauty and simplicity. The epicycles exist if one plots the solutions in a geocentric system, but they are so cumbersome and "ugly" as a shorthand of physics.

Both Sun and Earth move in circles around their barycenter i.e. centre of mass.

The trick is that since Sun is too massive, the center of mass is too close to the sun, actually beneath the surface of the Sun, which makes the motion of Sun negligible. And, we say that Earth moves around the Sun.

The sun, moon, earth (and so on) all move around each other.

The reason we say the earth moves around the sun is because the effects are more visible on a macro scale, and easier to predict with reasonable precision. Yes, it's most correct to say that all motion is relative, but it gets a lot more complicated to explain it if you're speaking to a layman.

I have to use this as a chance to repeat a great story about the philosopher Wittgenstein, related by his student Elizabeth Anscombe:

[Wittgenstein] once greeted me with the question: "Why do people say that it was natural to think that the sun went round the earth rather than that the earth turned on its axis?" I replied: "I suppose, because it looked as if the sun went round the earth." "Well," he asked, "what would it have looked like if it had looked as if the earth turned on its axis?"

But what about physics? In terms of actual physical theories, does the sun really go around the earth, or does it only appear to do so because we're viewing it from the rotating reference frame of the earth?

A rotating frame is distinguishable from a nonrotating frame, without reference to anything external. This is true both in Newtonian mechanics and in special and general relativity. There are various ways to tell if you're in a rotating frame, including a Foucault pendulum, a mechanical gyroscope, or a ring-laser gyro of the type used in commercial jets. The Foucault pendulum as a proof of the earth's rotation dates back to about 1850. (Long before then, heliocentrism had become accepted among physicists on less definitive grounds, such as the fact that Kepler's laws have a simple form in a heliocentric frame.) As a relativistic example, the analysis of the famous Hafele-Keating test of general relativity required the introduction of three effects: kinematic time dilation gravitational time dilation and the Sagnac effect, which is sensitive to the rotation of the earth.

There are other theories in which you can't detect a frame's rotation except relative to distant matter, e.g., Brans-Dicke gravity. The original paper on B-D gravity is available online http://loyno.edu/

brans/ST-history/ and is very readable even if you're not a specialist. The positive results from the techniques listed above would then be interpreted not as evidence of absolute rotation but as evidence of rotation relative to distant galaxies. But B-D gravity is no longer viable based on solar-system tests dating back to the 1970's. So if you like, you can say that Galileo was only finally proved right in the 1970's.

A very late answer, one that I hope adds to the excellent answers by Mark and Luboš.

From the perspective of Newtonian mechanics, there's nothing wrong per se with using a geocentric point of view. Such a point of view does require adding fictitious forces and torques that would otherwise be absent in an inertial perspective, but if makes sense to do that, that's okay. That said, there's a world of difference between choosing to use a geocentric perspective when doing so makes sense such as predicting the weather compared to a now non-scientific mandate that one must always use a geocentric perspective. There's a nice explanation of those fictitious forces and torques that result from choosing to use a geocentric perspective: They're a fiction that results from that choice of perspective. This mandate would instead somehow make all of those fictitious forces and torques real. What makes these forces occur, and why in the world do they disappear when we choose to look at things from a different perspective?

Even though a geocentric perspective is conceptually valid from a Newtonian perspective, the concept of parsimony (aka simplicity, aka Occam's Razor) says we must reject the idea of returning to a mandated geocentric point of view (and thereby forgo half a millennium of scientific progress). Parsimony has played a very important role in science since Galileo's time. Scientists much prefer simple explanations over complex ones. Using a geocentric perspective to describe the motion of an exomoon about an exoplanet is a ludicrous proposition.

From the perspective of general relativity, there is something wrong per se with using a geocentric point of view to describe the entire universe. While coordinate systems are global in Newtonian mechanics, they are local in general relativity. Coordinate systems are local charts on Riemannian space-time in general relativity. They do not have universal extent. A mandated geocentric perspective does not make sense in terms of general relativity.

There are experimental evidences of absolute motion of the Earth around the Sun. There is a dipole anisotropy in fine measures of the Background Radiation temperature that is known from the analysis of the COBE satellite measures, in the early 90s. See for instance this paper.

In order to make the adequate corrections, so that the Cosmic Background Radiation "seems" isotropic, the absolute velocity of the Local Group against the Cosmic Background Radiation must be accounted for, but that correction depends on the month of the year, because a small part of the correction comes from the orbital speed of the Earth around the barycentre of the Solar System (among other terms).

That small part of the corrections needed is exactly what you would expect if you assumed that is the Earth who is going around the Sun, and not vice versa.

(the cosmic background dipole anisotropy, image from map.gsfc.nasa.gov)

Here is an extract from the abstract of the quoted paper:

We present a determination of the cosmic microwave background dipole amplitude and direction from the COBE Differential Microwave Radiometers (DMR) first year of data (. ) The implied velocity of the Local Group with respect to the CMB rest frame is $v_=627 pm 22 km s^<-1>$ toward (. ). DMR has also mapped the dipole anisotropy resulting from the Earth's orbital motion about the Solar System barycenter, yielding a measurement of the monopole CMB temperature (. ) $T_0=2.75 pm 0.05 K$

This doesn't mean however, that there is an absolute reference frame in the Universe. Other comoving observers will detect another dipole anisotropy. The Last Scattering Surface, as well as the cosmological horizons are different for different comoving observers. But nevertheless it proves that it is the Earth that moves around the Sun, and not vice versa. Since the 90s this is no more a philosophical issue: WE are moving certainly, absolutely, surely and gloriously, around the Sun.

Since it is a recurrent question, I have rather to add my answer here than to more recent ones.

I hope I can make more clear some points which was not completly well focused in some previous answers.

Kinematic description

Once we have chosen whatever reference frame we like (here does not matter if inertial or not) and we have a description of the trajectories of N bodies, say N vectors $<f r>_i(t)$ , we can always use a reference frame centered on one of the bodies, say the a-th, by simply subtracting the position vector of the chosen body to any other position vector. Therefore, in this new reference frame the trajectories of the original system of N bodies will be: $<f r>^_i(t) = <f r>_i(t) - <f r>_a(t). [1]$ It is clear that in this new frame $<f r>^_a(t)=0$ by construction, i.e. the a-th body is at rest forever.

An example of such transformation of coordinates is the change of reference frame required if we want to find the proper description of the Solar system as seen by an observer on the Earth, starting from trajectories in the (inertial) reference frame where the center of mass of the Solar system is at rest. Notice that an observer at rest on the surface of Earth is not only translating with the planet, with respect to the center of mass, but she/he is also rotating, so the actual transformation would be more complicate than eqn. [ $1$ ]. However we can ignore the need of an additional rotation of our vectors if we confine our considerations to reference frames which do not rotate relatively to the original frame.

At this point it should be clear that there is nothing wrong to describe the motion of the Solar system bodies from the Earth. It is just one of the infinite possible choices of the origin of the reference frame, an probably the most useful for Earth based observers. It has the same right to be used as a reference frame fixed on a moving car to describe what passengers see.

However, the possibility of changing point of view, does not imply that different choices would provide the same description of the trajectories in an N-body system. Quite interestingly, if we start from a reference frame where body $a$ is at rest, i.e. $<f r>_a(t)=0$ , where a second body b moves according to $<f r>_b(t)$ , and we move to a new reference frame based on body $b$ , in the new system body $a$ will be described by the vector $<f r>^_a(t)=-<f r>_b(t)$ . This implies that motion of $a$ as seen by $b$ or motion of $b$ as seen by $a$ differ only by an inversion and therefore they have the same synthetic description.

What about applying the above consideration to the Earth-Sun system? In the case of the two-body system things are quite simple. The shape of Earth trajectory as seen from Sun or that of Sun as seen from Earth are the same. In addition, since the center of mass of the Sun-Earth system is within Sun, Earth trajectory as seen from Sun is almost coinciding with the same orbit as described from the center of mass.

In the next two figure I have plotted the orbit of the two bodies in the reference frame of the center of mass

and in the reference frame of (non-rotating) Earth. Distance units are millions of kilometers.

Things change a lot when we describe motion of other Solar system bodies. THe next two plots show the motion of Sun, Venus, Earth, Mars and Jupiter, as seen from the center of mass of the system or from (non-rotating) Earth.

Even at this kinematic level, the greater simplicity of the description in the center of mass frame is evident. Nevertheless, I want to stress once more that nothing is wrong with this description. It is the closest to what we get frome Earth-based observations.

Dynamic description

From the point of view of solving a problem of Newtonian dynamics, we all know that the center of mass reference frame of an N-body system is convenient. Since it is an inertial frame, we can use Newton's law $<f F>=m<f a>$ in connection with Newton's gravitional force law, without need of introducing additional inertial forces.

Notice however that once one has written the set of differential equations of motion for the gravitational N-body problem: $<f a>_i = Gsum_ m_j frac<(<f r>_j - <f r>_i)>_j - <f r>_i ight|^3>$ it is trivial to write down the equations of motion referred to body $a$ : $<f a'>_ = Gsum_ m_j frac<(<f r'>_j - <f r'>_i)>_j - <f r'>_i ight|^3> - Gsum_ m_j frac<(<f r'>_j - <f r'>_a)>_j - <f r'>_a ight|^3> [2]$ where $<f r'>_i = <f r>_i - <f r>_a$ and $<f a'>_i = <f a>_i - <f a>_a = frac<^2 (<f r>_i - <f r>_a ) ><t^2>.$ There are two interesting things to notice in eqn. 2, the first one could help to clarify some statements present in other answers:

## Fundamentals of Physics I (221)

Classical physics provides a framework for making quantitative predictions, and an explanation for phenomena that could seem puzzling. Galileo's observation that everything falls in the same way, regardless of how much of there is or even what it is made from, is an example. We are led to ask, what is the "natural state of things", why is there motion, and why and how does it change?

Newton proposed three laws, or let's say three statements, that give us answers of a sort (and raise questions of their own!). Most books on fundamental physics would say that you have to learn them, so here they are.

1. Objects at rest stay at rest, objects in motion stay in motion at a velocity that is constant in direction and magnitude, unless acted upon by a force.

2. A object of mass (M) , subject to a force (vec) , alters its motion with an acceleration (vec) in response to the force where

3. For every applied force between two objects there is an equal and opposite reactive force.

Actually, Newton's second law embodies the other two, but all three describe how nature works in classical physics. Let's look at them, and then linger on the second law and learn how to use it.

The first law in effect says that the natural state of things is for them to continue in whatever motion they have. If they don't, then there is a force that has changed that motion. As Newton himself put it written here in modern English, (today's international language of science), while he wrote his Principia in Latin:

Every body remains at rest or moving uniformly on a straight path, except when its state is changed by an applied force.

It is paradoxical to our experience, where we know that things seem to slow down no matter what. Ride a bicycle, stop pedaling, and the thing comes to a rest. Throw a ball, it sails for a while, rolls along the ground, may be returned by your dog, and eventually, inevitably, seems to come to a rest. Newton's first law says the reason is that there are are "forces" acting on the objects, and that without those forces they just keep on going. In our everyday world we have frictional forces, air resistance, friction in bearings, friction where surfaces slide, and those slow things down and ultimately cause the motion to stop. Newton explains this in his second law, as we shall see.

Cats have done extensive experiments with Newtonian physics, especially the first law.

So, in space, no air and no friction, start something moving and it just keeps on going.

Newton's First Law on the International Space Station

The idea seems simple enough, but what happens when I try an experiment and I'm accelerating (with respect to the universe), that is, what if my frame of reference is not moving at a constant speed? In that case, I would see objects apparently accelerating backwards with no obvious force. Newton's First Law would not work.

That objects in motion in a straight line at uniform speed (which could be zero) keep going along that line at that speed is "inertia", and a frame of reference in which this is true is called an inertial frame of reference. The perfect inertial reference frame is the entire universe, taken on average. To change motion with respect to everything else, to create an acceleration, there must be a force that acts on the object.

Thus the behavior of moving objects is reduced to (a), finding the right frame of reference, (b) identifying the forces, and (c) calculating the resulting acceleration or change in velocity.

This first of Newton's Laws, truly a law of inertia, tells us that we have to use special "inertial" reference frames. Fortunately, although the Earth is on a curved path in its orbit around the Sun and is spinning on its axis while we on its surface are doing physics experiments, it's a good approximation that locally a good reference frame is fixed on Earth's surface where we are. When there are exceptions, we have to move out and take a wider view to understand what happens, or to invent a force that isn't real.

An example you experience all too often on the highway is what happens when you're driving along at 80 km/h and suddenly up ahead someone brakes for a deer dashing across the road. You brake too, to avoid crashing into the slowed car in front of you, while the deer makes a safe getaway into the woods (we hope). You seem to have been pulled forward with respect to the car. It feels as if there is a force pulling you, while in fact it is the slowing of the car while you continue going forward at the same speed you had. Newton's First Law says that unless you have a seatbelt or airbag applying a force to slow you down, you will crash into the car's interior. The inertial reference frame that describes this is one that is stationary with respect to the highway.

The second law says that in an inertial reference frame there will be no acceleration if there is no force (that's actually the first law as a consequence of the second). If there is an a force, than the velocity of the object to which the force is applied will change in proportion to the force, the famous

where "F" and "A" are vectors, that is, they have direction as well as magnitude. That's why when we are careful with notation we might put an arrow over the symbol (vec) to keep us aware it has direction too. Alternatively, in books just writing in boldface may be enough, like F, or A.

• The larger the force, the more the acceleration.
• The acceleration has the same direction as the force.

The proportionality between these vector quantities is the "mass" of an object, and since it is determined by the object's "inertia", this mass is best called "inertial mass". It is a measure of how much matter there is in the object. As you know from experience, the more matter there is, the more force is required to change its motion. Notice how mass appears along with the change in velocity. The product of mass and velocity is called "momentum", and it too is a vector. Here it is for reference:

However, acceleration is the rate of change of velocity. We use (Delta) to mean "change in" and with it

and with that we have another way of stating the second law in terms of momentum rather than acceleration

The force is equal to the rate of change of momentum. In the absence of an external force, the momemtum does not change. The concept of momentum is so important we will spend a week on it later in the course.

Newton described his Second Law using the idea of momentum which at the time he simply called "motion". With a little editing for clarity he said:

The alteration of motion is always proportional to the force and is in the direction in which that force is applied.

Newton's Second Law on the International Space Station

Often stated that for every action there is an equal and opposite reaction, the Third Law really only applies between two objects interacting with one another and not with anything else. Here's how Newton put it, (translated from his Latin into our English):

To every action there is always opposed and equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

It means that of object B1 exerts a force on object B2, then the opposite also occurs: object B2 exerts and equal and opposite force on B1. A classic example would be two skating partners on ice. If they do not push on the ice with their skates, then when the first one pushes on the second, the second pushes back on the first.

The result of the Third Law is that these internal forces balance. A system of two bodies cannot mutually accelerate with respect to the universe by pushing on one another. They exert the same magnitude of force on one another, but it is oppositely directed. Consequently, those forces do result in accelerations of the bodies with respect to one another.

## Inertial reference frames

This property of massive bodies to resist changes in their state of motion is called inertia, and this leads to the concept of inertial reference frames. An inertial reference frame can be described as a 3-dimensional coordinate system that is neither accelerating nor rotating however, it may be in uniform linear motion with respect to some other inertial reference frame. Newton never explicitly described inertial reference frames, but they are a natural consequence of his First Law of Motion.

When we say that a body is in motion, one might ask, in motion compared to what? Could you catch a baseball going 100 mph in your bare hand? You could if you were riding on a train going 100 mph, and someone on that train gently tossed you the ball. The train and the track both exist in their own inertial reference frames, and the speed of the ball depends on the inertial reference frame from which it is viewed. If you were standing on the platform, and a passenger on that train tossed the ball out the window to you, it would not be wise to attempt to catch it in your bare hand.

When you're trying to understand the mechanics of a system it's usually convenient to choose coordinates that reflect the symmetry of the system. The solar system is roughly centrally symmetric because the Sun is by far the largest mass in it, and the coordinates that reflect this symmetry are polar coordinates with the Sun at the centre.

For example in these coordinates if the Earth was the only object apart from the Sun, the Earth's orbit would be (nearly) a ellipse. The presence of the other planets (mainly Jupiter) perturbs the Earth's orbit, but we can handle this by perturbation theory starting with the elliptical orbit and adding on the perturbations caused by the other planets.

So taking the Sun as a reference point is a reflection of the symmetry of the Solar system.

As noted in other answers, if we're describing the galaxy the Sun is no longer the best place to set the origin of our coordinate system, and we'd use polar coordinates centred on the centre of symmetry of the galaxy. Likewise to describe a galaxy cluster we'd choose the origin to be the centre of mass of the cluster. At the very largest scales the universe is isotropic and homogenous, so it doesn't matter where we place the origin.

It's all about the context in which you want to analyze particular issue.
If you are studying the solar system, the most suitable, would be to consider the sun as the center of the system.
If you are studying the Milky Way, the sun is not a good reference point, you should take the center of the galaxy.

Similarly, to locate the stars from an observer on earth, the "celestial sphere" is used, and that does not mean returning to the model of Ptolemy.
It's all about the scope that is intended in a particular analysis.

why not relative to the Earth?

Scientists do express things relative to the Earth, where that makes sense. I couldn't imagine trying to forecast the weather or model the global circulation of the Earth's atmosphere from the perspective of a non-rotating frame with it's origin at the solar system barycenter. Astronomers, at least those dealing with Earth-bound equipment also have to express things relative to the rotating Earth. They need to know where to point their Earth-bound equipment, after all.

Meteorologists not only represent the weather in terms of a geocentric point of view, they model the weather from that perspective. This means that all kinds of fictitious forces arise in their models because the Earth is both accelerating and rotating. There's nothing wrong with that per se, so long as one does the mathematics correctly. Since any alternative (e.g., a non-rotating frame) is even worse, meteorologists make sure they do the mathematics correctly.

On the other hand, using an Earth-centered, Earth-fixed perspective to describe the behaviors of the distant objects that astronomers observe is even more ludicrous than is trying to describe the Earth's weather from the perspective of a non-rotating, barycenter-based perspective. It's much easier to describe the behaviors of solar system bodies from the perspective of a non-rotating, barycenter-based frame. That frame similarly isn't all that good for describing the behavior of the galaxy as a whole.

A reference frame at rest with the Sun is, with a good approximation, an inertial system (much better than one at rest with our planet or other bodies in the Solar system, essentially in view of the hugely larger mass of the Sun). Physics in inertial reference frames has the simplest form. For instance the motion of planets around the Sun is described along ellipses with the Sun as one of the center, with a good approximation. The ultimate reason of this fact (assuming the Newtonian form of the gravitational law) is that I pointed out: If referring to another reference frame one has to include so-called, in a sense unphysical, inertial forces in addition to the gravitational one to explain the complicated motion of planets. All this reasoning makes sense if disregarding cosmological issues where general relativity plays a crucial role, and instead adopting the Newtonian paradigm.

People who are studying something something generally use a frame of reference which is reasonably close to the things of interest. While it might in theory be possible to measure the stature of a man by very accurately determining the distance from the center of the Earth to the bottoms of his feet, as well as the distance from the center of the earth to the top of his head, and subtracting the first from the second, it is both easier and more accurate to measure the height of the top of the person's head relative to that of a surface upon which the person is standing.

The distance from the Earth to the Sun is so much greater than the diameter of the earth that when reporting the locations of terrestrial objects, it makes sense to describe locations relative to other terrestrial objects. Only if one is regarding everything on Earth as a single point does it make sense to use the Sun as a reference point. Going the other way, the distance between the Sun and the nearest star is so much greater than the distance between the Sun and the most distant known orbiting body that it only makes sense to use any reference point outside the solar system if the Sun and everything orbiting it are regarded as a single point.

Because of GPS and similar technologies to determine the locations of terrestrial objects, determining a person's stature by measuring the absolute positions of the head and feet would almost be practical from an astronomical perspective, however, trying to use any sort of solar or galactic coordinate system to plot the locations of terrestrial objects would be like trying to use a barometer to measure stature. A barometer may allow rough determinations of altitude, but the uncertainty in the altitude measurements of the person's head and feet would likely exceed the distance between them by orders of magnitude, making any stature determinations meaningless.

## The Reference Frame

Some days ago, we had interesting discussions about the special theory of relativity, its main message, the way of thinking, the essence of Einstein's genius and his paradigm shift, and the good and bad ways how relativity is presented to the kids and others.

Newton has introduced mathematics to the thinking about the physical phenomena including the accelerated motion of objects. This mathematics was compatible with the common sense and it allowed the people to think as reductionists. I think that most people who can pronounce "relativity" understand this viewpoint.

The world is composed of various objects – particles, solid objects, fields – and they obey some differential equations with time as the independent variable. These equations may be written down, solved, and exploited. The intuition is that the world is composed of many things, each works in some way, and we are learning how they work one by one.

So Newton has introduced some reductionism as a basis for science – and the world could be divided to objects and pieces that evolved according to some differential equations. The differential equations are a bit hard and most people aren't good at them – but they sort of understand the intuition behind them.

In this whole framework, it was assumed – because it really seemed obvious – that there were objective values of the relevant quantities describing the location and shape of "things" that were a function of time (t) and all the objects were embedded in the three-dimensional flat Euclidean space (RR^3). A copy of that space – with objects at some locations – existed at each moment of time. Details weren't known from the beginning but the basic framework seemed clear forever. You could only change the precise shape of the differential equations – including the forces – and you could construct larger objects from more elementary ones (which I will later describe as the invention of "constructivist" theories).

The elementary objects could have been understood and the understanding of these objects or "stuff" wasn't terribly different from the work of inventors such as Edison – that's why I embedded the diagram of the light bulb. Because the speed of light is so tightly incorporated into special relativity, many people end up thinking that Einstein was similar to Edison. Just like Edison grabbed a light bulb and optimized it, Einstein played with another object, light, and theoretically understood what it does and how it moves.

But that's a wrong lesson. Special relativity isn't about light itself. It's about the amazing role of the speed called the speed of light – and the speed of light isn't the speed of light only. Instead, it is also the speed of light, aside from other things.

Light is a casual name for some electromagnetic waves – or photons – but the speed of light is also the speed of gravitational waves – and gravitons – and, in principle, other things (I think that photons and gravitons are the only massless particles in Nature – gluons are massless as well but they're confined). Well, it's the speed that all massless objects move by and all massive objects may approach arbitrarily closely from below. The speed (v), energy (E), and rest mass (m_0) obey:[

] For massless objects such as photons and gravitons, (m_0=0) and the left hand side is infinity whenever (E eq 0) which means that the right hand side must be infinite, too. That's the case when (v=c). Massless objects simply must move by the speed of light. On the other hand, when (m_0gt 0), the ratio (E / m_0 c^2) may also be arbitrarily high if you pump up the kinetic energy. Then (v) goes up and approaches (v o c) from below – but it can never quite reach it, let alone surpass it.

Those who understand this rather basic stuff know that special relativity isn't exclusively about light. It's really about the space and time – which must be unified into the spacetime. Space, time, and spacetime affect everything that can live or move within them – which really means everything (as well as every thing) in our real lives.

The postulates become the "beginning", not the "end"

1. the laws of physics have the same form in all inertial frames (that are moving by a constant velocity relatively to each other)
2. the speed of light is measured to be the same constant, (c=299,792,458,< m m/s>), in all inertial frames

If you interpret this statement in a strong way – so that even the measurement of the light that comes outside cannot help you to determine the speed of the train – then the second postulate follows from the first one as a special example.

In Newton's physics, the first postulate (the principle of relativity) was true – because Newtonian mechanics respected the so-called Galilean relativity. You could change all the velocities of all objects by (vec V), a constant:[

vec v_i o vec v_i + vec V

] and everything obeyed the laws of physics just like before. The simple additive shift of all the velocities corresponded to a simple change of the vantage point – if things seemed to obey the laws of physics in one inertial frame, they had to obey the laws of physics in another frame as well.

However, Newton assumed that the light was made of particles, the curpusles, when the inertial frame was switched, those had to change their speed additively as well. So if light were emitted from a source to have a speed (|vec v_< m light>| = c), then the speed had to look different in generic, other reference frames. (Even those who believed that light was made of waves thought that the speed of those waves looked different to observers in motion.)

Well, the simple Galilean transformation didn't touch the time at all, (t o t). You know that the Galilean group was replaced by the Lorentz group (SO(3,1)) or the Poincaré group – which also allows spacetime translations. The Galilean group is a "contraction" of the Lorentz group the Lorentz group is a "deformation" of the Galilean group.

I think that people who have been sufficiently exposed to relativity – at least a few successful hours, if I try to quantify it in some way – understand these statements about group theory. There exists some Lorentz group that mixes the space and time and Newton's space and time didn't mix in this way. But I think that even most of the people in the world who would claim that they understand this statement still misunderstand relativity. And it boils to the title of the blog post.

My experience is that most laymen and amateur physicists still think about the constancy of the speed of light and the Lorentz transformation as about some derived facts, some properties of objects such as light bulbs and the light itself. They think that physicists "grab stuff", like the light, look at it, and they determine that the stuff has some properties and moves so that it's compatible with the relativistic formulae and symmetry.

With this (wrong) perspective, Einstein's postulates and the Lorentz symmetry remain permanently unnatural and eternally challenged. These people tend to think: So far it's worked but it's really a coincidence and when physicists look at new things or they look more closely, the formulae will be found to be inaccurate and the symmetry will be seen to be approximate. It will probably break down at some point.

But that's not the conclusion that Einstein – or anyone who really understands modern physics – would make.

In reality, it's extremely likely that all tests of special relativity (within freely falling frames or locally, so that I get rid of gravity in some way) will confirm this theory of Einstein's in the rest of this century and the next one and many others. Why? Because Einstein has found new principles that seem to agree with all the tests so far nontrivially and incredibly accurately, yet a priori surprisingly, and that's quite some evidence that these principles are perfectly true.

Most quantitative statements about Nature are approximate. When we say that the Sun is 150 million kilometers away, it's not surprising that a precise measurement yields a slightly different figure – in fact, the right figure oscillates with seasons and depends on the treatment of the Sun's and Earth's nonzero size, too. Indeed, it's a good habit to expect some error margin in most of such statements.

However, in physics and science, there may also be statements that are true exactly, some ultimate principles, postulates, axioms, or theorems of Mother Nature or God. They are meant to be perfectly true – exactly like religious dogmas. When someone believes in statements that are perfectly true, doesn't it mean that he's religious – and what he pretends to be science is therefore a kind of faith, a religion?

Well, not necessarily. The real difference between the "scientific dogmas" and the "religious dogmas" is that the "scientific dogmas" have passed some empirical tests that were nontrivial to start with. But the dogmas have succeeded. The religious dogmas – such as the virginity of Mary – haven't really passed empirical tests, at least not tests that you (an independent scientist who isn't satisfied with the brainwashing by others) could reproduce in your lab (your lab shouldn't be in your bedroom because the virginity test would then be negative, anyway).

OK, so Einstein found some postulates which imply the mixing of space with time, Lorentz transformations as symmetries, and he wanted us to believe that these claims are exact. Is it good science that we're supposed to believe in some "new scientific dogmas"? Yes, it is. The point is that these "new dogmas" aren't a completely new, unprecedented creation. If you look carefully, you will see that they're just competitors to – and because they work very well, replacement for – some other "scientific dogmas" that people had believed before Einstein.

Einstein has articulated those postulates – "scientific dogmas" – and derive lots of implications which have the same truth value and reliability – "derived scientific dogmas". Did he make science more faith-based? Not at all. It's actually great that he articulated those dogmas and other propositions – and looked at the evidence that tells us something on their validity (yes, they seem true) – because it's more scientific to clearly articulate propositions and to judge them than to remain silent or assume that everything is clear!

If you think about special relativity rationally, you must understand that (SO(3,1)) was just proposed as a replacement for the Galilean group, the spacetime was proposed as a replacement for the space and time that didn't mix, the maximum cosmic speed became a replacement for the belief that the speed of an object may always be increased towards infinity, and all other statements of relativity replace some non-relativistic statements. The point of special relativity is the "reform" of all these qualitative statements – and then the measurement of the key parameter, (c), becomes just a subsequent small task for experimenters.

A funny fact is that many of these non-relativistic statements that were replaced by their relativistic counterparts hadn't even been clearly articulated before Einstein – but they were believed, anyway. For example, Einstein found out that the simultaneity of events is relative: it depends on the inertial system. That "dogma" is clearly a replacement of the opposite non-relativistic dogma: the simultaneity of events is absolute.

Did the physicists before Einstein spend their days by screaming that the simultaneity of events is absolute? They didn't. It was an assumption that they were making all the time. All of science totally depended on it. But it seemed to obvious that they didn't even articulate that they were making this assumption. When they were describing the switch to another inertial system, they needed to use the Galilean transformation and at that moment, it became clear that they were assuming something. But everyone instinctively thought that one shouldn't question such an assumption. No one has even had the idea to question it. And that's why they couldn't find relativity before Einstein.

Einstein has figured out that some of these assumptions were just wrong and he replaced them with "new scientific dogmas". He ate the apple in the Garden of Eden. The clearly articulated alternatives – Einstein's and the silently believed predecessor of Einstein's dogmas – could have been compared and be sure that Einstein's dogmas were found to be right and the non-relativistic ones were found to be wrong. The difference becomes really obvious when speeds of object become comparable (or even very close) to the speed of light.

Once again, Einstein has replaced the "old scientific dogmas" that looked so obvious that they weren't even discussed by "new scientific dogmas" that are a little bit more abstract, must be abstract, and may be empirically shown to be superior. Now, if you're rational, you see that Einstein clearly won a match against Newton. So if you were certain about Newton's dogmas, you should simply replace them by Einstein's dogmas and be equally certain about them as you were previously about Newton's dogmas. That surely improves your understanding of the Universe because Einstein's dogmas may be proven to be strictly better than Newton's dogmas! If you question Einstein's postulates much more than you questioned Newton's axioms, it means that you have an irrational preference for theories that don't seem to work too well empirically and it's bad.

OK, Einstein found the right new principles or postulates or axioms or dogmas. And this very methodology – the search for the "new and better dogmas" – is one of Einstein's more general contributions to science. A physicist should really question things because even some of the assumptions that seem so obvious that no one even articulates them may be wrong and may be replaced by much deeper and more accurate replacements. The quantum mechanical revolution has applied Einstein's general philosophical strategy and found something even deeper than relativity.

Einstein was very aware of this change of methodology – by which he really started modern physics. As a teenager, I liked to read a book of his essays ("Mein Weltbild") many times. He was rather modest about this change of the perspective, too. Because of the focus on the "search for correct axioms and derivations starting with these axioms", he considered relativity to be a "principled theory" of physics. The other class of physical theories were "constructive theories". I basically started with them – it's the reductionism where things are made of pieces.

In this classification, relativity was an example of a principled theory but Einstein pointed out that he wasn't really the first physicist who made this change of the perspective. Thermodynamics did it before relativity. Like relativity, thermodynamics was also built around some basic laws – the laws of thermodynamics.

It sounds simple and logical. Just to remind you, the perpetuum mobile of the first kind produces energy and never stops the perpetuum mobile of the second kind spontaneously transmits heat from a colder object to a hotter one.

Like in relativity, these basic laws of thermodynamics may be interpreted as general axioms – "scientific dogmas" – and physicists are invited to behave as mathematicians who try to derive interesting "theorems" out of these "axioms" (which may be applied to more specific situations).

Even in the case of thermodynamics, a too "constructivist" person may fail to understand the power of the "valid principles" and the methodology based on the "scientific dogmas". Well, if you don't get that the principles above are almost certainly general – and there is quite some evidence that they're true – you are at risk of spending your life by trying to construct the perpetuum mobile! The men who have spent years with this futile exercise don't see the forest through the trees. They're not capable of thinking in terms of big statements – like the "scientific dogmas". Whenever they add a new building block to their candidate machines (a metallic handle, water, electricity, and lots of other things), they believe to have a much higher chance to succeed although they have failed so far. They don't get discouraged because they're blind to the main negative arguments against their hopes – and they're blind because these statements are too "big", too "general" for them. The constructors of the perpetuum mobile don't understand or don't believe general statements and principles. If you close your eyes and overlook universal laws and big-picture statements, the perpetuum mobile may look like a matter of patience.

We know e.g. the first law of thermodynamics – the energy conservation. It holds for some laws of physics (e.g. the Standard Model) whose equations may be written down. But the energy conservation doesn't really depend on the Standard Model Lagrangian too much. It's not some derived property of more detailed, constructed laws of physics. Instead, you should think of the Standard Model as a set of equations – a theory of a certain kind – that obeys the energy conservation and lots of other, stronger principles.

What's going on? As I promised you, we're really changing the starting point. The little pieces and point masses and the differential equations that they "possess" are no longer the starting point. Instead, you start with some well-chosen principles – you must be a good enough physicist to find the laws of thermodynamics or the postulates of relativity – and then you guess the right microscopic equations from a list of candidates that obeys the principles. Can you see the difference? The thermodynamic founding fathers and Albert Einstein added a fundamental step at the very beginning – the guessing of the right "new scientific dogmas". And the next work for scientists actually follows after those!

This extra step at the beginning has made the work of theoretical physicists deeper and more philosophical. When this new principled perspective was born, many deep theoretical physicists have been switched

The postulates of relativity, the laws of thermodynamics, and similar principles are deeper and more far-reaching than any single particular statement about the behavior of any particular elementary particle or another object. In some sense, Einstein became a boss of all the people who later constructed relativistic (classical or quantum) field theories. He wrote the general laws of relativity that define the general framework – what is allowed and what is not – and the constructivist physicists may only invent or change "relative details".

It's not a perfect analogy but I must mention it: the role of physicists such as Einstein was changed to the role of America's founding fathers who needed to write and enforce some foundational documents for Edison to succeed later.

Do you get my point? When modern physics began, physics became much more philosophical. Philosophers used to look for the "right dogmas" as well except that it hasn't ever led to anything that would be useful to understand Nature. Modern physicists have actually found general principles that do apply to Nature and that seems to work. Modern physicists are the only successful philosophers in this very sense.

Ironically enough, the amateur physicists who love to present themselves as "philosophers" – a "philosopher" is basically a self-described physicist who is ignorant of physics according to all actual physicists, so a "philosopher" is basically synonymous with a "crackpot" – usually misunderstand this point (that physics has become more philosophical). The Czech crackpot and "reformer of relativity" named Jan Fikáček – an ex-boss of Mensa Czechoslovakia – is an excellent example of that.

All these people love to immediately jump into some technicalities. They never really think about their starting point too deeply because they think that the right starting points are obvious. But that's completely wrong. The search for (and selection of) the right principles that define the rough rules of the game for all the subsequent dirty work has become the most important part of theoretical physics. It's a work that philosophers had wanted to do – but only modern physicists could do it well. And the contemporary "philosophers" i.e. self-confident crackpots are the group of people who maximally misunderstand the need to pick the right principles in physics.

Bonus: there is a related point I want to make. Brian Greene posted an innocent comment about dark matter and prizes:

Dark matter will remain hypothetical until we finally capture a particle of dark matter in one of the many detectors searching for them worldwide. That's when the prizes will flow. https://t.co/7QVvjsREei

&mdash Brian Greene (@bgreene) July 24, 2018

Someone disagreed with that:

Mmm. I couldn't disagree more. There should be a Nobel prize for flat rotation curves, not for dark matter. Like there is a Nobel prize for the accelerated expansion of the Universe, not for dark energy. We must keep observational evidence and interpretations well separated. https://t.co/lLHwXjOyuX

&mdash Federico Lelli (@lellifede) July 24, 2018

Keeping them separated doesn't mean rewarding mindless observations only. The discoveries that had some meaning - some interpretations - have always been more important and they were also rightfully rewarded by prizes. A discovery that has no clear implications is a weak one.

&mdash Luboš Motl (@lumidek) July 25, 2018

Even if I decide to agree that one of these two directly follows, it was nontrivial to find it and the people who found these two possible interpretations might deserve more fame than those who saw the flat galaxy rotation curves. However, at most one of these two is right. -)

&mdash Luboš Motl (@lumidek) July 25, 2018

You know, some of the people want to keep theory and experiments separated, and all stuff like that. It's bizarre because the whole point of the scientific method is that theories and experiments intensely interact with each other. But you can see what drives Federico Lelli, Peter Yoachim, and a majority of similar "empirical activists". They just want to praise some dull, obedient observations, even in the absence of any interpretation, and say that the interpretations and theories don't matter.

But science could never work like that. The viable interpretations are actually the ultimate goal of the experiments and only when viable interpretations appear, the experiments become important and truly trustworthy. In this sense, the people who find the correct interpretations – probably some theorists – are more important and their work is essential for making the experimenters important, too.

An ally gave a good example:

Exactly, a popular example would be the Pioneer anomaly.

&mdash Hélvio Vairinhos (@hvairinhos) July 25, 2018

The Pioneer anomaly was just some artifact of some instrumental mess. I have already forgotten what caused it. It's known and there was no new physics behind it. But that's a textbook example of a surprising observation without an impressive interpretation – without a new theory that naturally explains the observation. When you have surprising observations without good theories, it usually means that the observation is rubbish. You just shouldn't mindlessly believe isolated surprising observations. It's a part of the scientific attitude to reality that you realize that lots of isolated surprising claims may be rubbish and only when there's some synergy between them which is consistent with some theory, they may be really trusted.

The belief in isolated, very surprising empirical or experimental statements is basically synonymous with the belief in miracles and – even though the "empirical activists" think that such a belief is maximally scientific – that's actually very unscientific.