General Relativity- the Sun revolves around the Earth?

[espen180]

If you want to express Newtonian gravity as a spacetime theory, in order to compare it to GR, there is nothing stopping you from doing that. You'll get the same kind of matter->space and space->matter coupling as in GR, but the field equations will look different.

 

[Dale]

The Sun is more massive than the Earth; that is the decisive factor.
The Sun/Earth mass ratio and convenience of models are two distinct subjects.
...

What does their relative mass have to do with the possible coordinate charts that can be used?

 

[K^2]

The Sun is more massive than the Earth; that is the decisive factor.
The Sun/Earth mass ratio and convenience of models are two distinct subjects.

Sun is more massive. Yes. Why does that make any difference? Tell me a way to measure which one is actually moving, and then you have a point. Saying that the heaviest thing ought to be in the center is on the same shelf as Aristotelian Mechanics. Seems intuitively correct, but otherwise meaningless.

 

[Cleonis]

Tell me a way to measure which one is actually moving, and then you have a point.

Once again I will move to a wider context.

A comparison:
If you ask a particle physicist whether neutrino's have mass, what will he answer? He will answer that the weight of evidence is towards neutrino's having mass. The accumulated evidence is that the rates at which the various flavors of neutrinos are detected are consistent with the theoretically predicted phenomenon of neutrino oscillation. Neutrino oscillation will occur if and only if the neutrino's have non-zero mass.

OK, my point is that neutrino mass has not been measured directly. The existence of neutrino mass is inferred from the neutrino oscillation. In turn the neutrino oscillation is inferred from neutrino detection rates (starting with the observation of the solar neutrino deficit.)

Growth of knowledge

There is rarely - if ever - a direct measurement. The growth of knowledge is in the form of an intricate web of inferences. Scientists do not demand absolute proof; the criterium is that the evidence settles the issue beyond reasonable doubt.

For the motion of the Earth and the Sun: it is unwarrented and unrealistic to insist on direct measurement for that case. It is sufficient to argue the case on general considerations. Rephrasing the question by the original poster:
"Is the motion of the Earth and the Sun relative to each other just as relative as the motion of the magnet and the coil of the SR-inspiring magnet-and-coil case?"

- For the magnet-and-coil case SR asserts as a matter of principle that no experiment will indicate such a thing as the velocity of either the magnet or the coil with respect to some absolute reference of motion. As a scientist you must gather all the information that you can, but no matter how much information you gather, you won't be able to infer such a thing as a velocity vector for either the coil or the magnet with respect to some absolute referene of motion.

- For orbital motion (a planet orbiting a sun) information is abundant. And around the time of the Copernican revolution it was inferred that the Earth is orbiting the Sun.

It's the difference between no existence of information in the magnet-and-coil case, and abundant information in the case of orbital motion.Summerizing:
There is rarely - if ever - a direct measurement.
For the motion of the Earth and the Sun: it is unwarrented and unrealistic to insist on direct measurement for that case. It is sufficient to argue the case on general considerations.

 

[K^2]

You are missing the point. Any kind of measurement, even an indirect one, would be a violation of GR postulates. If you say that you can tell that Earth revolves around the Sun, you are saying that General Relativity does not work. It is as simple as that.

 

[Cleonis]

You are missing the point. Any kind of measurement, even an indirect one, would be a violation of GR postulates.

So let's examine the principle that is unique to GR.

There is no experiment, under any circumstance, that will indicate a difference between inertial mass and gravitational mass. The distinction inertial/gravitational mass is not inherent to the phenomena. .

I will refer to this principle by its usual name, the Principle of Equivalence.


http://physics.bu.edu/people/show/stachel" , a physicist and historian of physics, has written a story to illustrate the nature of the transition between SR and GR. It's called 'The story of Newstein'. In this story history takes another course, and the principle of equivalence is implemented before the year 1900. Stachel argues that many of the elements necessary for such a development were available by that time, and that the principle of equivalence being implemented first is in fact a plausible course of events. The fictional physicist developing that theory is called 'Newstein'.

Four theoretical framework can be arranged on four corners of a square.
- From left to right the transition is the introduction of the (-,-,-,+) signature metric
- From top to bottom the transition is the implementation of the principle of equivalence


Classical dynamics | Special relativity
--------------------------------------------
Newstein theory | General Relativity


This diagram illustrates that the two transitions are independent. Neither is an extension of the other.

The purpose of the Newstein story is to illustrate that the transition from SR to GR is unrelated to any relativity concept. The principle of equivalence could have been implemented without any awareness of the (-,-,-,+) signature metric.

 

[K^2]

What the hell are you talking about? What does any of that have to do with the discussion?

Again, can you produce an experiment that would detect Earth's rotation around the Sun? No, because that would violate GR. Not JUST the equivalence principle, but it's one of the possible violations. I don't know in what way you propose to make a measurement, so I don't know specifically which principle you are going to violate.

 

[D H]

Again, can you produce an experiment that would detect Earth's rotation around the Sun?

http://improbable.com/airchives/paperair/volume7/v7i3/angels-7-3.htm

I would agree with you K^2 if the Sun and Earth were the only things in the universe. They aren't. We can see other planets, other stars, quasars, ... Observations of these objects coupled with parsimony says that the Earth orbits the Sun rather than the other way around.

 

[espen180]

Taking the risk of entering a semantical debate, the two are, strictly speaking, orbiting each other. The centre of mass, and the point about which the planet and star orbit just happens to be inside the sun.

If you want to say that "one orbits the other", you have to define explisitly what this means. Once a mathematical definition is in place, you can talk about measuring whether one orbits the other or vice versa according to that definition.

 

[D H]

Taking the risk of entering a semantical debate, the two are, strictly speaking, orbiting each other. The centre of mass, and the point about which the planet and star orbit just happens to be inside the sun.

If you want to say that "one orbits the other", you have to define explisitly what this means. Once a mathematical definition is in place, you can talk about measuring whether one orbits the other or vice versa according to that definition.

I'll propose one, although slightly problematic: Is the center of mass inside of one of the objects or between them? The IAU considered but rejected this back in 2006 to determine whether a pair of co-orbiting objects are a planet and moon versus a double planet. A couple of issues with this definition: (1) In a few billion years, our Moon will magically become our Double Planet. (2) The Sun-Jupiter barycenter is outside of the Sun. Everyone still thinks of Jupiter as a planet and Jupiter as orbiting the Sun (more or less).

Note that the Sun-Earth barycenter is so deep inside the Sun that neither of these concerns is in play.

 

[Dale]

I would agree with you K^2 if the Sun and Earth were the only things in the universe. They aren't. We can see other planets, other stars, quasars, ... Observations of these objects coupled with parsimony says that the Earth orbits the Sun rather than the other way around.

As I mentioned above, you can describe the distant star's and planet's motions in an earth-centered coordinate system also. If by "parsimony" you mean that the metric in such a coordinate system is unnecessarily complicated then you are certainly right, but that doesn't make the coordinate system invalid.

 

[1MileCrash]

Part of my thinking here, is that just because the sun is more massive doesn't make it the stationary one and Earth the moving one, because that entire part of the galaxy is also moving, and, our galaxy is moving, etc etc.

Neither is stationary. They are both all over the place. To debate which one orbits which is utterly meaningless, and we can attribute a coordinate system to either and they are equally valid.

 

[D H]

As I mentioned above, you can describe the distant star's and planet's motions in an earth-centered coordinate system also.

By this I am assuming you mean an Earth-centered, Earth-fixed system in which the Sun appears to orbit the Earth once per day and traces an analemma over the course of a year.

First, let me answer this question you raised a while ago:

What does their relative mass have to do with the possible coordinate charts that can be used?

One answer is time. Because the Earth's orbit is not circular, one second as measured on the surface of the Earth in January versus one second in July are not quite the same from the perspective of an observer at the solar system barycenter (or an observer well outside the solar system). Failure to incorporate that the Earth's orbit about the Sun is not circular will impact the accuracy of your results.
Now to answer your main question, time is but a small part of your problem. To have any chance of describing things with anything close to a modern degree of accuracy/precision for anything but a short interval of time you will need

• A precise model of apparent motion. To obtain this you will need to at least temporarily pretend that the Earth does indeed orbit the Sun. Even then, I suspect you won't be able to do so with the precision needed by modern milliarcsecond (and moving toward microarcsecond) astronomy. 'Tis much easier to suspend your disbelief and model the Earth as orbiting the Sun. Model the behavior in ICRS coordinates and only at the end transform to GCRF coordinates.
• A precise model of Earth's rotation. To obtain this you will need to at least temporarily pretend that the Earth does rotate about its axis. The IAU 2006 precession model and IAU 2006A nutation model have over a thousand terms. You will need to incorporate each and every one into your metric. Four words: Good luck with that.
• Ooops. Even then you don't have a good enough model. There are some terms in the Earth's rotation that we just don't know how to model yet. These unmodeled variations in the direction (polar motion) and magnitude (length of day) of the Earth's angular velocity are determined after-the-fact and are reported daily via IERS Bulletin A and monthly via IERS Bulletin B. Those unmodeled terms are going to play havoc with predictions using a ITRF-based chart. Those errors will only appear at the very end if you do things rationally.

If by "parsimony" you mean that the metric in such a coordinate system is unnecessarily complicated then you are certainly right, but that doesn't make the coordinate system invalid.

No, it doesn't make it invalid. It just makes it a stupid choice.

 

[Cleonis]

Taking the risk of entering a semantical debate, [...]

As you point out: this overlong thread is not a technical discussion.

For instance, the way I understand the statements by K^2 his underlying reasoning is as follows:
"The Earth has no odometer. In a car we can see the numbers moving in the display, counting the miles you're travelling. For the Earth no such display exists. We can say that the circumference of the Earth's orbit is so-and-so many million kilometers, but that's not a direct measurement. The circumference of the Earth's orbit is inferred from the Earth-Sun distance, and the period of the Earth's orbit."

The way I understand K^2 is that his reasoning then proceeds as follows:
"Since there is no Earth odometer, we have zero information as to the question whether the Earth moves or not."
More generally, K^2 seems to take as starting point "If you can't measure it directly then you have no knowledge of it."

As I understand it K^2 insists that his reasoning is the only valid reasoning.


The purpose of physicsforums is to discuss physics technicalities. This thread has shifted away from that. In this thread the tugging has been about the question What is valid reasoning?

 

[ElTaco]

What if a force on an object doesn't cause the object to move but in fact causes the "agent" of the force to change its velocity?

I've been reading this thread, and it seems to me that's the only explanation that works in K^2's favor. Since we technically describe changes in velocity based on the mass of the other object when considering gravity, an object with a larger mass will have a smaller acceleration due to the force of gravity from the smaller object than vice versa (which is basically what Cleonis is pointing out, correct me if I'm wrong).

Before reading this thread, I thought that relativity only works in an inertial frame of motion. If we decide to apply relativity out of these boundaries (because an orbit is in no way an inertial frame of motion), don't we have to completely change our conception of physics?

 

[1MileCrash]

What if a force on an object doesn't cause the object to move but in fact causes the "agent" of the force to change its velocity?

I've been reading this thread, and it seems to me that's the only explanation that works in K^2's favor.

Both are the case depending on the frame of reference. In other words, they are two different descriptions for the same event.

Force "causing an object to move" and "causing the agent to change it's velocity" are the same thing. It simply depends on whether or not we are attributing the reference frame or coordinate system to the object that is being acted upon, or the agent (and neither is more valid than the other.)

If you're in space, floating around, with your best friend, and you push him, did the force cause the object (your friend) to move, or did it cause you (the agent) to have a change in velocity?

From your reference frame, the former.
From your friend's reference frame, the latter.
From any other reference frame, both, or either, in varying degrees of anywhere in-between.

I've also been reading this thread and according to my limited knowledge, most of relativity and physics in general works in K^2's favor.

Before reading this thread, I thought that relativity only works in an inertial frame of motion. If we decide to apply relativity out of these boundaries (because an orbit is in no way an inertial frame of motion), don't we have to completely change our conception of physics?

No

That is special relativity. We are talking about general relativity.

 

[Cleonis]

If you're in space, floating around, with your best friend, and you push him, did the force cause the object (your friend) to move, or did it cause you (the agent) to have a change in velocity?

I would like to submit the following setup to you.

You are in a big spaceship, your best friend is in small shuttle. The two crafts are connected by the equivalent of a bungee chord, a very long one. You push your friend's shuttle, the distance between the two of you increases, the bungee chord is stretched, the two of you are pulled closer again, you push off again, etc, for as many cycles as you want.

Both you and your friend have clocks onboard, and these clocks count elapsed time with enough precision that over time the two of you observe that for your friend less proper time is elapsing.

Of course this difference in elapsed proper time is what you expect to happen. Since your vessel is much heavier it is your friends shuttle that is traveling a larger spatial distance as the bouncing cycles proceed. Larger spatial distance traveled corresponds to less elapsed proper time.

The bottom line: size matters.
If a large mass and a small mass push off against each other then the small mass undergoes a proportionally larger change of velocity. This is not relative.

(Well, you don't know your own absolute mass; what you can infer from the measurements is the mass ratio between the big spaceship and the small shuttle.)

[later edit]
GR subsumes SR, and for the above setup (which does not involve spacetime curvature) GR upholds the SR description of the physics taking place.
[/later edit]

 

[1MileCrash]

I disagree with your example.

Think about the twin paradox. It's settled because the change in direction of the ship invalidates its reference frame, but until that occurs, there is no way to know whether the Earth or the ship has covered more absolute spatial distance, or which experiences absolute greater time dilation, or which is absolutely moving faster, even though the ship has much less mass than the earth.

Larger spatial distance traveled corresponds to less elapsed time, relative to whatever reference frame we are measuring from. A "larger spatial distance" has to be measured from something, and from my frame of reference I traveled no spatial distance, and from my friend's frame of reference he traveled no spatial distance. We would see each other's clock moving more slowly. Time dilation is relative, and spatial distance covered is relative. If my friend and I move in opposite directions from one another, our net, combined speed is absolute, but there is no way of knowing who's time is absolutely dilating, who is absolutely moving faster, and who absolutely covered more spatial distance.

The bottom line: size matters.
If a large mass and a small mass push off against each other then the small mass undergoes a proportionally larger change of velocity. This is not relative.

If we measure this from an inertial frame of reference that has the system in this example moving, we could infer that the small mass ceases to move once the masses push from one another. You're right, it's change in velocity or net velocity is not relative, but which one is "moving" and which one "isn't" is relative.

In other words, since we cannot measure the absolute speed or direction of the entire system itself (both the small mass, and the larger mass, and the space they occupy) nor can we measure the absolute motion of whatever is in it. We can say the smaller mass changed speed more than the large mass, but we can't say whether it slowed down, sped up, stopped, started moving, etc. because of that force.

 

[Cleonis]

We could use a coordinate system that shows that my friends shuttle ceases to move when pushed (he starts moving with the frame of reference we are using) and clocks measured from our new frame of reference would show time passing "normally" in the smaller ship.

Your response gives the impression that you are unaware of the http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html" .In any setup both in the main ship and in the shuttle time is elapsing normally. For any clock time elapses normally. There is no such thing as abnormal time, or "abnormal" time.

The thing is, using the word abnormal, even when cushioning it with "", is unhelpful. What must be avoided is any suggestion that Newtonian time is normal time, and that SR time is abnormal time.

The shuttle travels a longer distance, hence for the shuttle less proper time elapses than for the main ship.

[later edit]
This response of mine is to a post that no longer exists.
This can happen because here on physicsforums it's possible to edit existing posts.
I suppose it's better to allow more time to elapse before starting a reply.
[/later edit]

 

[1MileCrash]

In the twin scenario, the shuttle observes that less time has elapsed because it turns around. Not because it "travels a longer distance." Up until the point it turns around, the ship reckons clocks on Earth are running slow, and the Earth reckons the clocks on the ship are running slow.

The reason why it's called the twin paradox is because if we forget about the acceleration of the ship (it turning around) then relativity says that each twin should see the other twin younger than themselves upon their reunion, which proves my point. The twin that was on the ship is the younger one when he returns to earth, but not because he traveled more distance. He is the younger one because he turned around in his space ship. There are three reference frames, the twin on earth, the twin leaving earth, and the twin returning to earth.

We cannot say who traveled the longer distance. Answer me this, if we cannot measure our direction, or speed, relative to space, how can we possibly determine who traveled the more "spacial distance?"

Put it this way, say that hypothetically, we found an absolute reference frame. Relative to space, Earth is moving 800 MPH in direction Q. A ship takes off from Earth in direction P (opposite of direction Q) at 700 MPH. Since we now have an absolute reference frame, we now can say that Earth is moving 800 MPH in direction Q, and the ship is moving in 100 MPH in direction Q. So therefore, in any given amount of time, Earth is covering more "spacial distance" than the ship.

The ship absolutely had a greater change in velocity than the earth, but a change in velocity doesn't mean an increase in velocity. We can say that the change in velocity for the smaller mass is greater, but we can't say whether or not that change in velocity made it start moving, slow down, speed up, or stop moving. This is what I meant in my initial response to ElTaco. The object starting to move, and the agent having a change in velocity, are two descriptions of the same physical event,

Of course, we have no absolute reference frame. All motion, distance, direction, and speed is measured from something else. Therefore it is impossible to say who covered more "spacial distance."

In any setup both in the main ship and in the shuttle time is elapsing normally. For any clock time elapses normally. There is no such thing as abnormal time, or "abnormal" time.

The thing is, using the word abnormal, even when cushioning it with "", is unhelpful. What must be avoided is any suggestion that Newtonian time is normal time, and that SR time is abnormal time.

I'm sorry, what I meant by "normally" is that the clocks would run at the same speed between our hypothetical reference frame and the smaller ship.

 

[Dale]

By this I am assuming you mean an Earth-centered, Earth-fixed system in which the Sun appears to orbit the Earth once per day and traces an analemma over the course of a year.

Yes, either that or an Earth-centered, non-rotating reference frame where the stars are fixed, or any other absurd coordinate system you might choose. The point is that GR works fine regardless of your coordinates, which is what the OP was asking.

No, it doesn't make it invalid. It just makes it a stupid choice.

Exactly.

 

[Dale]

The bottom line: size matters.
If a large mass and a small mass push off against each other then the small mass undergoes a proportionally larger change of velocity. This is not relative.

You have to be careful here. There are two separate concepts which embody the idea of a "change in velocity". One is called "proper acceleration" and is a coordinate independent concept (the covariant derivative of the tangent vector), it is the acceleration measured by an accelerometer. The other is called "coordinate acceleration" and is a coordinate dependent concept (the second time derivative of the position). Those two measures of acceleration need not be equal and, in fact, they are unequal in the presence of gravity.

In your scenario the small mass will have a greater proper acceleration, this is the acceleration which is not relative and it will be greater regardless of the coordinate system used. But it may have a smaller coordinate acceleration or even no coordinate acceleration, depending on the coordinate system chosen. There is no requirement that the coordinate system be such that a given object is at rest.

 

[Cleonis]

[...] if we cannot measure our direction, or speed, relative to space, how can we possibly determine who traveled the more "spatial distance?"

All motion, distance, direction, and speed is measured from something else. Therefore it is impossible to say who covered more "spatial distance."

I have selected these statements to quote, because I think they capture the core of your questions.

Note that your questions are very distant from the origin of this thread, which is about GR. Your questions are about first introduction to SR.

I will discuss SR only in this message. I intend it to be my final message in this thread. In retrospect I realize I needed to be reminded why it's not a good idea to discuss relativistic physics on internet.I have uploaded three images to physicsforums. Three spacetime diagrams representing the twin scenario. The three diagrams are for three respective coordinate systems.

1. co-moving with the stationary twin
2. co-moving with the away journey of the traveling twin
3. co-moving with the return journey of the traveling twin.

Of course the scenario can be diagrammed in any member of the equivalence class of inertial coordinate systems.

For special relativity the idea is to identify the things that are common to all diagrams. A lot of things, such as coordinate velocity, are frame dependent: on transformation they transform to another value.
But crucially some things are common to all diagrams, these aspects are thought of as inherent in the phenomena.

What is common to all diagrams is that the traveler covers more spatial distance than the stay-at-home twin. (The precise value in coordinate distance will be different from diagram to diagram, but it's always more for the traveler.)
You can map the twin scenario in any member of the equivalence class of inertial coordinate systems. When you evaluate how much difference in amount of elapsed proper time there will be from parting to rejoining everyone of those mappings will yield the same answer.
There is no individual assessment of distance traveled, you can only say something in comparison.

[...] if we cannot measure our direction, or speed, relative to space, how can we possibly determine who traveled the more "spatial distance?"

Specifically to your question:
Before special relativity the assumption was that it is possible to assign an absolute velocity vector to objects, a velocity with respect to the luminiferous ether. Obviously it was also assumed that the luminiferous ether is uniform, since any erratic thing cannot be a background reference.

Special relativity asserts that there is no such thing as assigning a velocity vector of motion with respect to space: the principle of relativity of inertial motion. However, special relativity does have the underlying assumption that space is uniform. Or, saying the same thing with other words, special relativity depends on the underlying assumption that when an object is in inertial motion it covers equal distances in equal intervals of time.

You have to separate those two concepts:
- You cannot assign a velocity vector representing motion with respect to space.
- Space is uniform: in inertial motion you cover equal distances in equal intervals of time.

(Of course, since SR works with spacetime rather than with space and time separately it's better to say that SR has as underlying assumption that spacetime is uniform.)

Without the underlying assumption of the uniformity of spacetime it would be impossible to formulate the invariance of the spacetime interval. Given the assumption that spacetime is uniform it is possible to make statements about the twins traveling different spatial distance from parting to rejoining. When the twins rejoin they may find that for one of them a smaller amount of proper time has elapsed. According to SR the twin with the least amount of elapsed proper time has traveled more spatial distance.About acceleration:

I often notice the differential aging of the twins being attributed to the acceleration. While the acceleration is necessary, thinking of it as the cause of the differential aging doesn't hold up: it leads to self-contradiction.

Some time ago I came across the following diagram that was uploaded in 2008:

https://www.physicsforums.com/attachment.php?attachmentid=14191&d=1212060478
This is from the thread https://www.physicsforums.com/showpost.php?p=1747855&postcount=4"

It's a triplet this time. C stays at home, A and B go on a journey. In the worldlines the red sections represent a phase of acceleration. A and B both experience the same acceleration for the same time, but A's total elapsed time is shorter than B's.

.

 

[Dale]

What is common to all diagrams is that the traveler covers more spatial distance than the stay-at-home twin.

Look at your diagrams. This is only true in the first diagram. In the 2nd and 3rd the spatial distance traveled by the two twins is equal.

 

[Cleonis]

In the 2nd and 3rd the spatial distance traveled by the two twins is equal.

Yeah.

I was completely focused on the aspect that in all diagrams the stay-at-home worldline is a continuous straight line, whereas the traveler's worldline always consists of multiple sections that are at an angle to each other.

Ah well.

 

[Dale]

I was completely focused on the aspect that in all diagrams the stay-at-home worldline is a continuous straight line, whereas the traveler's worldline always consists of multiple sections that are at an angle to each other.

That is indeed a correct observation. One twin's worldline forms two sides of a triangle and the other twin's worldline is a single side of the triangle. This observation analogous to the triangle inequality.

In Euclidean geometry the sum of the lengths of two sides of a triangle is always longer than the length of the third side. In Minkowski geometry the sum of the time of two sides of a timelike triangle is always shorter than the time of the third side.