Implications of the statement Acceleration is not relative

[GregAshmore]

The modern way of thinking about it is that a position, such as a location on Earth, is absolute. The top of the Eiffel Tower is a definite spot; there is no ambiguity, or relativism involved. But there are infinitely many coordinate systems that can be used to specify a position.

In relativity, the primary thing is not a position, but an event, a point in space and time. So "the top of the Eiffel tower when Michelle Obama went up it" is an event, and it's absolute. But if I try to describe it using 4 numbers, for example, (latitude, longitude, altitude in meters, time in seconds since 1900), its description is relative to a coordinate system.

A spacetime path, giving the events that a traveler passes through, as a function of the time on his watch, is an absolute thing, because each event is absolute. But to describe the path as a set of 4 functions x(\tau), y(\tau), z(\tau), t(\tau) is relative to a choice of a coordinate system.

I agree in principle with what you've said, but I question its practical utility. I read it this way: "A spacetime event (position and time) has a real existence apart from any coordinate system, yet can only be described in terms of some coordinate system." It would seem that the absoluteness of a spacetime event is metaphysical, because it cannot be verified empirically.

Furthermore, I believe that the rocket twin will deny what you say about "path", and all that follows from it. See below.

The proper velocity of a path is again an absolute thing, while the components of the proper velocity are relative to a coordinate system. Proper acceleration is an absolute thing, while its components are relative to a coordinate system.

I assume that you develop the absolute path of a particle in this way. An arbitrary coordinate system whose origin is at the object under scrutiny is chosen. Using myself as an example, X is to my right, Y is straight ahead, Z is out the "top" of my head. My path through spacetime is marked by placing a monument in space at regular time intervals (by my clock).

At each iteration of my clock, I place a monument. I inscribe on the monument the time as read from my clock. I also consult my accelerometer to determine (some calculation is necessary) the change in my orientation since the previous iteration. I inscribe the differential change in orientation on the monument that was placed at the previous iteration. The change in orientation is necessarily expressed as rotations about the axes of the arbitrarily chosen coordinate system. Finally, I take my measuring rod and place its end against the previously placed monument; I then read directly the distance traveled since the previous iteration. I write that distance on the previous monument. Thus, my friend can follow my path without a map (coordinate system) if he starts at the first monument, adjusts his orientation as directed, and travels the distance indicated. At each monument, he repeats the process.

All of that is well and good, if one accepts the premise that I am moving through space. But, if you will recall, I am that very obstinate occupant of the rocket who insists that he is not moving at all. In my world, there is only one monument, and my orientation does not change.

 

[stevendaryl]

I agree in principle with what you've said, but I question its practical utility. I read it this way: "A spacetime event (position and time) has a real existence apart from any coordinate system, yet can only be described in terms of some coordinate system." It would seem that the absoluteness of a spacetime event is metaphysical, because it cannot be verified empirically.

There's nothing metaphysical about it--it's very concrete. A meteor crashes to the Earth. That marks a unique event. You don't need to have coordinates for it. George Washington is born. That marks a unique event. A star goes supernova. That's a unique event.

On a piece of paper, you draw a dot. That dot is a unique location on the piece of paper. You don't need coordinates to know that it's unique. You don't need coordinates to know whether the dot is at the same location as the X that someone else drew on the paper.

I assume that you develop the absolute path of a particle in this way. An arbitrary coordinate system whose origin is at the object under scrutiny is chosen. Using myself as an example, X is to my right, Y is straight ahead, Z is out the "top" of my head. My path through spacetime is marked by placing a monument in space at regular time intervals (by my clock).

At each iteration of my clock, I place a monument.

Specifying the initial location of the monument isn't good enough. You have to also specify it's initial velocity.

A path through spacetime is a 4D analogue of a curve drawn a piece of paper. An event in spacetime corresponds to a point on the paper. A velocity of a path corresponds to the slope of the tangent line drawn through a curve.

I inscribe on the monument the time as read from my clock. I also consult my accelerometer to determine (some calculation is necessary) the change in my orientation since the previous iteration. I inscribe the differential change in orientation on the monument that was placed at the previous iteration. The change in orientation is necessarily expressed as rotations about the axes of the arbitrarily chosen coordinate system. Finally, I take my measuring rod and place its end against the previously placed monument;

Once again, an event is a single moment. You can't place a monument at a single moment, and you can't return to an earlier moment. The monument is going to follow its own path through spacetime, and when and if you get back to the same monument, it's not the same point in spacetime. Both you and the monument have moved since then.

All of that is well and good, if one accepts the premise that I am moving through space. But, if you will recall, I am that very obstinate occupant of the rocket who insists that he is not moving at all.

EVERYONE moves at all times. If you look at your watch, then wait a while and look at your watch again, the second look is a different event from the first event. You've traveled from one event to another. You've "moved" through spacetime.

Now, you can certainly choose a coordinate system so that the spatial coordinates of the second event are the same as the spatial coordinates of the first event. But there is no way to choose coordinates so that all coordinates are the same. There is no way to avoid having motion in spacetime.

 

[GregAshmore]

Really? When you, standing on the surface of the Earth, throw a ball upward, its motion is determined purely by its mass and the force you apply? Then why does it come back down?

I perhaps should have been even more careful in my wording. The "gravity" under discussion here is not the gravity of Earth or any massive body. For the purposes of the twin paradox problem, the gravitational field due to the mass of the Earth is ignored. The gravity under discussion is the gravity of unspecified origin that Einstein posits to explain the motion of the Earth when the rocket engine is fired. This gravity is purely the result of the choice of coordinate system, as I understand DaleSpam.

When I throw a ball in SR, its motion is indeed determined purely by its mass and the force I apply. It does not return. It continues to move forever at some constant speed.

The ball changes its kinetic energy with respect to you even though you didn't exert any additional force on it; at some point in its trajectory, it is momentarily motionless with respect to you (up in the air at the instant it stops rising and starts falling back). Where did the kinetic energy you gave the ball go?

This paragraph does not apply; the ball does not reverse in SR.

You give away the problem with the position you are trying to take when you say "not exactly the same law". That's just the point: if you want "the laws of physics" to be "the same" in all reference frames, so that you can always view yourself "at rest", then the laws of physics have to include counterintuitive things like the Earth and the stars changing direction and speed just because you fired your rocket engine. If you want the laws of physics to always look simple, then you have to restrict yourself to frames in which they look simple (because all the counterintuitive stuff cancels out in those frames). You can't have it both ways; you can't have both simple-looking laws *and* a free choice of frames; your choice of frames determines how simple the laws look in the frames you choose.

The problem is not that the law of physics proposed by DaleSpam to explain the sudden movement of the Earth and stars at the firing of the rocket is not simple, or is not intuitive. The problem is that he has not proposed any law at all. Or at least, I do not recognize the statement "the movement of the Earth and stars was not caused by the firing of the rocket; it was caused by my choice of a certain set of coordinates" as a law of physics; certainly no other law of physics that I have learned looks like that. Furthermore, the statement borders on the delusional (I tried to find a neutral word; I could not; sorry) in that it denies the obvious causal connection between the firing of the rocket and the movement of the Earth and stars (which I made bold in the quote of your post).

That is how it seems to me. I don't really have the right to speak on the matter because I do not know anything about Christoffel symbols, and therefore cannot understand the line of reasoning taken by DaleSpam. It is much better for me to leave this alone for the time being. I only mentioned it in my summary because it is an outstanding issue that must eventually be addressed.

 

[PeterDonis]

The gravity under discussion is the gravity of unspecified origin that Einstein posits to explain the motion of the Earth when the rocket engine is fired.

Ah, ok, so the rocket is floating in flat spacetime. That clarifies things. But my comments still apply. See below.

This gravity is purely the result of the choice of coordinate system, as I understand DaleSpam.

If spacetime is flat, yes.

The problem is not that the law of physics proposed by DaleSpam to explain the sudden movement of the Earth and stars at the firing of the rocket is not simple, or is not intuitive. The problem is that he has not proposed any law at all.

No, the "problem" is that you have picked a scenario with a particular kind of simplicity, but then you want to choose a frame that doesn't match up with that simplicity. You have set your scenario in flat spacetime; in flat spacetime the laws of physics looks simplest in a global inertial frame. If you pick a non-inertial frame, like your "rest frame" when you fire your rocket, the laws of physics won't look as simple; they will have counterintuitive stuff in them like the Earth and the stars moving just because you fired your rocket engine. Once again, you can't have it both ways.

Or at least, I do not recognize the statement "the movement of the Earth and stars was not caused by the firing of the rocket; it was caused by my choice of a certain set of coordinates" as a law of physics; certainly no other law of physics that I have learned looks like that.

How about "you picked a reference frame that doesn't match up with the special properties of the spacetime you are in". Does that help?

The laws in question are the simple laws of flat spacetime. You already know them in an inertial frame. The talk about a "gravitational field" that appears when you choose non-inertial coordinates, or about the movement of the Earth and stars being caused by the choice of coordinates, is just a way of describing the fact that non-inertial coordinates make the laws look more complicated.

Furthermore, the statement borders on the delusional (I tried to find a neutral word; I could not; sorry) in that it denies the obvious causal connection between the firing of the rocket and the movement of the Earth and stars (which I made bold in the quote of your post).

What is this causal connection? How does the firing of your rocket make stars that are light years away suddenly move? It doesn't. It can't. Causal influences can only propagate at the speed of light; there's no way your firing your rocket engine here and now can make a star that is light years away move "right now".

This is one way that trying to choose a frame in which you are always at rest, when your motion is non-inertial, makes the laws of physics look more complicated: the laws of physics now have to include the possibility of "motions" that violate the usual rules of causality. The example Einstein used was rotation: if I consider myself, sitting here on the surface of the Earth, to be "at rest", then the stars must be moving around me faster than the speed of light.

But nothing can move faster than light! you say. Correct: but the "motion" of the stars due to my rotation is not a "real motion" that is subject to that law. The complete laws of physics in my "rest frame" now have to include the possibility of "fictitious motions" like the motion of the stars around me, or the motion of the stars in response to you firing your rocket engine, which can be faster than the speed of light and which can stop and start "instantly" if I change my state of motion, even though that "violates" causality.

Once more, you can't have it both ways. If you want simple, intuitive laws of physics, where there are no "fictitious motions" or "fictitious forces", you have to pick a reference frame that allows the laws to look that simple. If you insist on picking a frame where you are always at rest, even when you move non-inertially, the laws will not look simple in that frame. You can't avoid that trade-off.

 

[Dale]

Fair enough. But this may also lead to problems. For example, if proper time is measured by a clock, what is the proper time for the life of an individual particle? What clock do we read to measure its proper life span? This is of particular importance with regard to SR, as experiments with high speed particles are offered as evidence in support of the theory. We do not send a clock to accompany the particle on its journey in the accelerator. It seems to me that one is reduced to claiming that the particle is itself the clock. But if the particle is itself the clock, then there is no independent measure of the proper time that the particle existed, and thus no verification of the theory. There is no question that high speed particles live longer, as measured from our perspective. The question would be whether time in the rest frame of the particle is the same regardless of the speed of the particle measured in some other inertial frame, as the theory of SR requires. (I need to think about this some more; perhaps my logic is not entirely sound.)

This is merely a current technological limitation, not an in-principle limitation. In principle you could accelerate a regular clock up to .9999c and use it to measure the lifetime of particles that we shoot alongside it as it passes by. There will always be experiments that we would like to do but cannot currently accomplish.

However, what we can do with current tecnhology is to take modern clocks and make them so incredibly stable and accurate that we can measure relativistic effects with ordinary velocities. I.e. whether or not a velocity is "relativistic" or not depends on your sensitivity, and modern clocks are so exquisitely sensitive that we can measure relativistic effects at walking speeds.

Nonsense. I'm sitting at rest in my rocket the whole time. Don't tell me about choosing coordinate frames--there is only one coordinate frame that matters: mine.

This is the nonsense statement. It is nonsense for two reasons. First, because it uses an undefined concept. "Your frame" is non-inertial and there is no standard definition of a non-inertial object's frame. Second, because it is false. All coordinate systems have equal validity and yours is not particularly important and doesn't "matter" any more than any other coordinates.

When I throw a ball, its acceleration (with respect to the only coordinate system that matters) is determined by its mass and the magnitude of the applied force.

This statement is wrong. The acceleration in that frame is not only determined by the mass and magnitude of the applied force, but also by the fictitious force (gravity) acting on it in that frame.

When the Earth and the stars move, the same law should apply.

The same laws do apply to both, you just made a mistake in the case of the ball.

{Edit: Not exactly the same law. I realize that gravity will cause coordinate acceleration without applied force. But the moving Earth and stars have acquired kinetic energy with respect to the rocket. That energy must have come from somewhere.}

Actually, according to Noether's theorem, energy is NOT conserved in a non-inertial frame like that of the rocket. Energy is also frame variant.

A secondary (and less emotional) reaction is to ask the original question in a more precise way. What causes the spatial displacement between the rocket and the Earth to change?

What do you mean by "spacial displacement"? Do you just mean the coordinate displacement or are you thinking of some physical measure of displacement? If the latter, then exactly what measure are you thinking of?

 

[Dale]

The problem is that he has not proposed any law at all. Or at least ... no other law of physics that I have learned looks like that.

I can make it look more like a standard law of physics quite easily:\frac{d p^{\mu}}{d\tau} = f^{\mu} - {\Gamma^{\mu}}_{\nu\lambda} u^{\nu} p^{\lambda}Where f is the sum of the real four-forces acting on the particle, p is the four-momentum, u is the four-velocity, τ is the proper time along the particle's worldline, and \Gamma is the Christoffel symbols in the coordinate system in question.

Furthermore, the statement borders on the delusional (I tried to find a neutral word; I could not; sorry) in that it denies the obvious causal connection between the firing of the rocket and the movement of the Earth and stars (which I made bold in the quote of your post).

It may be an obvious connection, but it is not a causal connection, as I clearly demonstrated earlier. If you would like to actually address the points that I made instead of making a blatantly fallacious rebuttal then I would be glad to discuss it.

 

[stevendaryl]

The problem is not that the law of physics proposed by DaleSpam to explain the sudden movement of the Earth and stars at the firing of the rocket is not simple, or is not intuitive. The problem is that he has not proposed any law at all. Or at least, I do not recognize the statement "the movement of the Earth and stars was not caused by the firing of the rocket; it was caused by my choice of a certain set of coordinates" as a law of physics; certainly no other law of physics that I have learned looks like that.

That's because you probably have used inertial Cartesian coordinates in physics. With inertial Cartesian coordinates, the relationship between applied force and coordinate acceleration is, as Newton wrote:

m \dfrac{dV^\mu}{d \tau} = F^\mu

where V^\mu is the 4-velocity.

When you use noninertial or curvilinear coordinates, the relationship between applied force and coordinate acceleration is more complicated:

m \dfrac{dV^\mu}{d \tau} +fictitious force terms = F^\mu

So even when the applied force F^\mu is zero, the coordinate acceleration \dfrac{dV^\mu}{d \tau} can be nonzero due to "fictitious force" terms. Examples of such fictitious forces are the "g forces" due to acceleration, the "centrifugal force" and the "coriolis force". These "forces" are not due to any kind of physical interaction, but are artifacts of your choice of coordinate systems.

 

[harrylin]

That's done just to simplify the example. It's not a fundamental assumption of the explanation.

With instantaneous turnarounds, the proper distance along each leg is just algebra: \sqrt{\Delta t^2-\Delta x^2}. If we don't assume instantaneous turnarounds, we have to evaluate some sort of line integral. It's fairly easy to prove that in the limit as the turnaround time approaches zero, the line integral reduces to the simple algebraic calculation, so we use the latter when the details of the turnaround aren't important to the problem at hand.

In order to get a point through, simplification is fundamental to explanations...

 

[harrylin]

As you make your \delta \tau small the SR predicted accelerometer reading becomes large while the actual accelerometer reading remains 0. [..]

[..]SR predicts a very large accelerometer reading during the turnaround, and real free falling accelerometers read 0.

SR doesn't predict that an accelerometer in free fall will indicate a large acceleration. If you insist in this thread instead of starting it as a topic, I'll start that topic for you.

 

[harrylin]

[..] But this much I believe to be undeniably true of a purely SR treatment of a scenario in which two bodies, one inertial and the other non-inertial, separate from each other and then approach to reunion: the non-inertial body must experience unbalanced force at the transition from separation to approach. [..]

SR uses the inertial frames of classical mechanics. If you know classical mechanics, then you certainly understand that if you accelerate freely in a gravitational field, your accelerometer will read approximately zero. If you don't know that, we can discuss this in the classical forum.

 

[harrylin]

[..] The problem is not that the law of physics proposed by DaleSpam to explain the sudden movement of the Earth and stars at the firing of the rocket is not simple, or is not intuitive. The problem is that he has not proposed any law at all. Or at least, I do not recognize the statement "the movement of the Earth and stars was not caused by the firing of the rocket; it was caused by my choice of a certain set of coordinates" as a law of physics; certainly no other law of physics that I have learned looks like that. Furthermore, the statement borders on the delusional (I tried to find a neutral word; I could not; sorry) in that it denies the obvious causal connection between the firing of the rocket and the movement of the Earth and stars (which I made bold in the quote of your post). [..]

You evidently understand the question that Einstein attempted to address in 1918. Regretfully, few people who try to answer you understand the question. But in any case, nobody here gave support for the answer that Einstein gave, and neither does the physics FAQ.

 

[Dale]

SR doesn't predict that an accelerometer in free fall will indicate a large acceleration. If you insist in this thread instead of starting it as a topic, I'll start that topic for you.

The entire Langevin scenario is off-topic, but at this point it would take too much effort to split off and it doesn't make sense to do so, IMO.

Yes, SR does predict that. According to SR the proper acceleration is:a^{\mu}=\frac{d^2x^{\mu}}{d\tau^2}Where x is the worldline in an inertial frame and τ is the proper time along that worldline. That quantity is non-zero.

 

[Dale]

You evidently understand the question that Einstein attempted to address in 1918. Regretfully, few people who try to answer you understand the question. But in any case, nobody here gave support for the answer that Einstein gave, and neither does the physics FAQ.

It is hard to see how you can believe that there was any definite answer since you don't even know what he meant by the term "gravitational field".

 

[harrylin]

It is hard to see how you can believe that there was any definite answer since you don't even know what he meant by the term "gravitational field".

I even cited his answer several times.

 

[Dale]

I even cited his answer several times.

Yes, you did. But you never were able to identify what you thought he meant. Seems strange to claim that a quote is an answer when you don't claim to know what the quote is even referring to.

 

[harrylin]

[..] at this point it would take too much effort to split off [..]

A misunderstanding of something so basic and simple surely requires discussing - much more than the topic of this thread.
Promised thread started here: https://www.physicsforums.com/showthread.php?p=4284966

 

[harrylin]

Yes, you did. But you never were able to identify what you thought he meant. Seems strange to claim that a quote is an answer when you don't claim to know what the quote is even referring to.

Instead I claimed to know what he was referring to; however I don't try hard anymore to explain other people's explanations - that is usually futile.

 

[Dale]

I claimed to know what he was referring to

So, according to you, what exactly was he referring to with the term "gravitational field"? I believe it was the Christoffel symbols. You believe he was referring to _______.?

 

[Alain2.7183]

See this topic

https://www.physicsforums.com/showthread.php?t=490163

Thanks for that link. Very interesting. Lots of good stuff.

 

[harrylin]

So, according to you, what exactly was he referring to with the term "gravitational field"? I believe it was the Christoffel symbols. You believe he was referring to _______.?

Einstein definitely referred to a field of force that possesses the property of imparting the same acceleration to all bodies; according to his theory, the gravitation-field generates the accelerated motion.
- http://en.wikisource.org/wiki/The_F...in_the_extension_of_the_relativity-postulate.

 

[stevendaryl]

Einstein definitely referred to a field of force that possesses the property of imparting the same acceleration to all bodies; according to his theory, the gravitation-field generates the accelerated motion.
- http://en.wikisource.org/wiki/The_F...in_the_extension_of_the_relativity-postulate.

Yes, in Einstein's original discussion of the twin paradox, with elevators and all that, the way he put it was something like this: (paraphrased)

If an elevator in outer space accelerates downward, the people in the elevator will feel an apparent upward force lifting them toward the ceiling. This is the inertial force due to being at rest in an accelerated frame.

If you have the same elevator falling in a gravitational field, it's accelerating downward, but the people feel no forces, because the upward inertial force is exactly canceled by the downward gravitational force.
​

I can't find an online reference to the original argument, but I remember reading it once, and it seemed that Einstein talked about freefall as not the absence of any forces, but as an exact balance between gravitational forces and inertial forces so that they cancel. From the standpoint of today, that seems like a convoluted way of describing it.

 

[PeterDonis]

Yes, in Einstein's original discussion of the twin paradox, with elevators and all that, the way he put it was something like this: (paraphrased)

I don't think this is right. The argument as he puts it in the popular book Relativity: A Clear Explanation That Anyone Can Understand goes like this: suppose we have an "elevator" in empty space, and some kind of "being" attaches a rope to one end (there happens to be a hook on that end) and starts pulling on it. A man inside the elevator will be able to stand on its "floor" (the end opposite the hook) just as if the elevator were at rest in a gravitational field, and if he drops a rock, it will appear to him to accelerate downward just as if he were at rest in a gravitational field. Finally, the man wonders how the elevator can be at rest in a gravitational field when it's in the middle of empty space, but then he discovers the hook in the roof with the rope attached to it; the elevator is hanging at rest in the field.

There's no argument about "forces" or "balance of forces" at all; the argument is purely about the man's observations and how they can be accounted for equally well by the "being" pulling on the rope in free space or by the rope suspending the elevator at rest in a gravitational field.

This wasn't a discussion of the twin paradox, it was a discussion of the equivalence principle, so I don't know if you were thinking of some other discussion of his; but what you paraphrased doesn't seem like a discussion of the twin paradox either.

 

[ghwellsjr]

I can't find an online reference to the original argument, but I remember reading it once, and it seemed that Einstein talked about freefall as not the absence of any forces, but as an exact balance between gravitational forces and inertial forces so that they cancel.

The argument as he puts it in the popular book Relativity: A Clear Explanation That Anyone Can Understand goes like this...

I don't know if Einstein's 1920 book, Relativity: The Special and General Theory is the same one you just mentioned but it has an identical explanation as you can read in this online reference.

 

[stevendaryl]

I don't think this is right. The argument as he puts it in the popular book Relativity: A Clear Explanation That Anyone Can Understand goes like this: suppose we have an "elevator" in empty space, and some kind of "being" attaches a rope to one end (there happens to be a hook on that end) and starts pulling on it. A man inside the elevator will be able to stand on its "floor" (the end opposite the hook) just as if the elevator were at rest in a gravitational field, and if he drops a rock, it will appear to him to accelerate downward just as if he were at rest in a gravitational field. Finally, the man wonders how the elevator can be at rest in a gravitational field when it's in the middle of empty space, but then he discovers the hook in the roof with the rope attached to it; the elevator is hanging at rest in the field.

There's no argument about "forces" or "balance of forces" at all; the argument is purely about the man's observations and how they can be accounted for equally well by the "being" pulling on the rope in free space or by the rope suspending the elevator at rest in a gravitational field.

I certainly prefer that way of looking at the equivalence principle, but years ago, someone pointed me to something written by Einstein that took the (in my opinion, convoluted) approach of saying that for an elevator in freefall, the gravitational force canceled the "fictitious force due to acceleration". I will continue to search for this passage from Einstein.

 

[Samshorn]

In Langevin's "twin" example the accelerator reading is zero during turn-around; in early SR there was no "twin paradox". http://en.wikisource.org/wiki/The_Evolution_of_Space_and_Time

Could you point to (or quote) the specific passage in that reference where Langevin describes using gravity to give a turn-around with zero accelerometer reading?

 

[PeterDonis]

I don't know if Einstein's 1920 book, Relativity: The Special and General Theory is the same one you just mentioned

Looks like it, yes. I think the subtitle "A Clear Explanation That Anyone Can Understand" was added in a later edition.

 

[Dale]

Einstein definitely referred to a field of force that possesses the property of imparting the same acceleration to all bodies; according to his theory, the gravitation-field generates the accelerated motion.

The Christoffel symbols do that.

 

[GregAshmore]

I can make it look more like a standard law of physics quite easily:\frac{d p^{\mu}}{d\tau} = f^{\mu} - {\Gamma^{\mu}}_{\nu\lambda} u^{\nu} p^{\lambda}Where f is the sum of the real four-forces acting on the particle, p is the four-momentum, u is the four-velocity, τ is the proper time along the particle's worldline, and \Gamma is the Christoffel symbols in the coordinate system in question.

I see it.

It may be an obvious connection, but it is not a causal connection, as I clearly demonstrated earlier. If you would like to actually address the points that I made instead of making a blatantly fallacious rebuttal then I would be glad to discuss it.

I went back to read the points you made. Here they are:

As I explained to harrylin, it doesn't. If you say "A causes B" then that means that the presence of A implies B. So, if we say that "a force applied to the rocket causes the Earth and all the stars to move" that means that a force applied to the rocket implies that the Earth and all the stars must move. In an inertial frame, there may be a force on the rocket without movement of the Earth, so the force on the rocket does not imply movement of the Earth. Therefore the force on the rocket does not cause the Earth to move.

Agreed that the force on the rocket does not cause the Earth to move.

So what does cause the Earth to move? The answer is that specific choice of non-inertial coordinates. That choice of coordinates implies that the Earth moves, regardless of the presence or absence of any rockets with any forces. Every time you use that choice of coordinates the Earth moves. So the choice of coordinates causes the Earth to move, not the rocket.

The text in bold is false. Prior to the firing of the rocket, selection and use of the rocket coordinates does not cause the Earth and stars to move. By the very same logic you used to prove that the force on the rocket does not cause the Earth to move, it is shown that the selection of coordinates does not cause the Earth to move. There may be a selection of the rocket coordinates without movement of the Earth; therefore the selection of rocket coordinates does not cause movement of the Earth.

In the following I elaborate on why the selection of coordinates cannot cause the Earth and stars to move. In the process, I will have something to say about the premise at which you started your chain of logic.

We are discussing one and the same incident viewed by two observers, at rest on two bodies, Earth and rocket. (I need not repeat that all mass-induced gravity is ignored.) The two bodies have been separated for some time by the constant distance X. The rocket engine is fired. Coincidentally, the distance between the two bodies begins to increase. What is the cause of the change in distance between the two bodies?

First, an axiom and a postulate:

Axiom: Whatever the cause, it must be physical. This is self-evident in a discussion of physics.

Postulate: Whatever the physical cause, it must be the same for both observers. I think that this follows from the premise that there is one physical reality for all observers. However, I am not entirely confident that it is self-evident, as an axiom must be...as I understand the meaning of the terms axiom and postulate.


The cause according to the observer on Earth.
The observer on the Earth begins by claiming that the change in distance between the Earth and rocket is in fact the movement of the rocket. This follows from the claim of the observer on Earth that he is "anchored in place".

[Note: In my summary I said that, according to the principle of relativity, every observer may legitimately claim that he is at rest; anchored in place, as it were. It is the anchoring in place, the reckoning of the observer that his position is absolute, that makes the observer's coordinate system the only one that matters. His coordinate system is the only one that matters because it is the only one that is traceable to an absolute position. All other coordinate systems are derived in some way from his coordinate system. At this point in the discussion, it is a mistake to say that all coordinate systems are equally valid, for that is precisely the issue that is in question when discussing the validity of the principle of relativity.]

The observer on Earth goes on to claim that the movement of the rocket was caused by the force that was applied to the rocket. In support of the claim, he submits this evidence: the force is a physical phenomenon that was applied to the rocket only; only the rocket moved; the form of the motion correlates in a definite way with the force on the rocket and the mass of the rocket.

This is also the premise at which you started your chain of logic: "if we say that 'a force applied to the rocket causes the Earth and all the stars to move' that means..." (I'm sure that I have also said many times that the cause of the rocket's movement is the force on the rocket.)

Though the weight of evidence is great, the claim cannot be valid. It has been shown (by you) that the force on the rocket cannot be the cause of the movement of the Earth, as seen in the rocket frame. Therefore, expressed in relative terms, the force on the rocket cannot be the cause of the increasing distance between Earth and the rocket.

What can be the cause is the firing of the rocket. The firing of the rocket is a physical phenomenon. The force is the direct result of the firing of the rocket, so the rest of the case made by the observer on the Earth is valid.


The cause according to the observer on the rocket.
The observer on the rocket begins by claiming that the change in distance between the Earth and rocket is in fact the movement of the Earth and all the stars. This follows from the claim of the observer on the rocket that he is "anchored in place".

It might be questioned whether the stars move with the Earth, given that the distances between the rocket and the various stars have not been measured to verify that they are changing. However, it must be assumed that the stars move with the Earth, unless some cause for them to change their positions in relation to the Earth can be adduced.

What will the observer on the rocket consider as candidates for the cause of the movement of the Earth and stars?

It has been suggested that the choice of coordinates is the cause. This suggestion must be rejected, for the following reasons.

1. As noted above, the rocket coordinates may be chosen without resulting in the movement of the Earth and stars. Selection of the rocket coordinate system does not imply movement of the Earth and stars; therefore the selection of the rocket frame cannot be the cause of the movement of the Earth and stars.

2. A coordinate system is an abstraction, a mere convention used to identify a position in space. A coordinate system is not a physical entity, and therefore cannot be the cause of any physical phenomenon. (By the axiom.)

3. If in the rocket frame the selection of the coordinate system is the cause of the increasing distance between Earth and rocket, it must also be the cause in the Earth frame. (By the postulate.) No one has suggested that the choice of coordinates is the cause in the Earth frame.

4. If the selection of the coordinate system is the cause, then the firing of the rocket cannot be the cause in the Earth frame. (By the postulate.) But there is strong evidence that the firing of the rocket is the cause in the Earth frame.

The observer on the rocket will look for a physical cause. The only physical candidate is the firing of the rocket. There is strong evidence to support the candidate, and it satisfies both the axiom and the postulate.


It is now left to the rocket observer to derive the law of physics for the motion of the Earth and stars at the firing of the rocket...

Here I note that Einstein proposes a gravitational field which comes into existence when the rocket is fired. He suggests induction from the distant stars (and in the process rules out the coordinate systems as the cause):

To be sure, the accelerated coordinate systems cannot be called upon as real causes for the field, an opinion that a jocular critic saw fit to attribute to me on one occasion. But all the stars that are in the universe, can be conceived as taking part in bringing forth the gravitational field; because during the accelerated phases of the coordinate system K' they are accelerated relative to the latter and thereby can induce a gravitational field, similar to how electric charges in accelerated motion can induce an electric field.

http://en.wikisource.org/wiki/Dialog_about_objections_against_the_theory_of_relativity

In my view, a strong case can be made that such an induction cannot bring into being the required gravitational field because, as was pointed out by another, no causal signal can move faster than the speed of light.

 

[Dale]

The text in bold is false.

The text in bold is correct. You are confusing the rocket with a set of coordinates where the rocket is at rest. Or perhaps you are confusing the broad class of coordinate systems where the rocket is at rest with a specific choice of one such coordinate system.

The coordinates simply map events in spacetime to points in R4. If you use a mapping where the Chistoffel symbols at Earth are non zero then Earth accelerates, regardless of whether or not the rocket is firing it's engines or even whether or not the rocket exists. The choice of coordinates determines the Christoffel symbols and therefore the acceleration, not the rocket.

You are correct that there are multiple different coordinate systems which have legitimate claim to be the rockets coordinates. So the term is ambiguous, which is the reason I said "that specific choice of non inertial coordinates". Once you define it by identifying a specific mapping, then that mapping gives a unique prediction for Earth's motion.

The rest of your post is too long to digest. Please be more concise.

 

[PeterDonis]

Postulate: Whatever the physical cause, it must be the same for both observers. I think that this follows from the premise that there is one physical reality for all observers.

But it also requires you to define a "physical cause" as something that meets this requirement. See further comments below.

All other coordinate systems are derived in some way from his coordinate system. At this point in the discussion, it is a mistake to say that all coordinate systems are equally valid, for that is precisely the issue that is in question when discussing the validity of the principle of relativity.

Are we discussing the validity of the principle of relativity? I thought we were discussing how the (assumed to be valid) principle of relativity is applied to non-inertial observers. That is, I thought you were looking for "laws of physics" that could be applied by *any* observer who assumes himself to be at rest always. I didn't think you were questioning that such laws can exist.

What can be the cause is the firing of the rocket. The firing of the rocket is a physical phenomenon. The force is the direct result of the firing of the rocket, so the rest of the case made by the observer on the Earth is valid.

I don't necessarily disagree with this, but the only reason I can see for drawing a distinction between the firing of the rocket as "cause" and the force as "result" is that the force is frame-dependent; more precisely, the coordinate acceleration that results from the force is frame-dependent. In other words, you are maintaining that the firing of the rocket is an event that all observers must agree on, but the force is not.

But if there is a frame-independent way of measuring force, or acceleration, this argument fails. And there *is* a frame-independent way of measuring *proper* acceleration (but not coordinate acceleration), as you know. If that's the case, then on what basis do we distinguish the firing of the rocket as "cause" from the proper acceleration as "result"?

Note, again, that I'm not necessarily disagreeing; I'm pointing out what I think is a gap in your argument that needs to be filled. But this question also comes up in relation to "motion"; see further comments below.

However, it must be assumed that the stars move with the Earth, unless some cause for them to change their positions in relation to the Earth can be adduced.

The way you are stating this, along with the way you are stating your argument as a whole, presupposes that "motion" is something definite and absolute. It's not; it's frame-dependent. What you really should say here is that the stars and the Earth are not moving *relative to each other* (to the approximation we are working with here, anyway).

Similarly, before the rocket fires, Earth and the rocket are not moving *relative to each other*; but after the rocket fires, they are. It is the *relative* motion that needs to be explained; that is the thing that isn't frame-dependent. But your argument tries to explain the "motion of the rocket" or the "motion of the Earth", as if they were absolute. They're not.

In short, if you are going to take as an axiom that the cause must be "physical", then you should also take as an axiom that the *effect* must be physical as well. And since "physical", from the above, basically means "frame-independent", neither the motion of the Earth by itself, nor the motion of the rocket by itself, qualify as "effects" that need to be explained. Only the *relative* motion of the Earth and the rocket qualifies. The whole thing just boils down to: the firing of the rocket causes relative motion of the rocket and the Earth. That's all that's needed.

It is now left to the rocket observer to derive the law of physics for the motion of the Earth and stars at the firing of the rocket...

Same comment here: the laws of physics don't talk about the motion of the Earth, or the stars, or the rocket by themselves; they only talk about the *relative* motion of these things with respect to each other.

In my view, a strong case can be made that such an induction cannot bring into being the required gravitational field because, as was pointed out by another, no causal signal can move faster than the speed of light.

I'm not saying I necessarily prefer the "gravitational field" explanation, but the fact that causal signals can't move faster than light (which I brought up before) does not rule out "induction" as a source for the "gravitational field" Einstein talks about. Such an argument, if it were valid, would prove too much: it would prove that ordinary magnetic induction can't exist either. Obviously that's not true.

Consider the analogy with ordinary magnetic induction further. If you try to push a magnet that's in the field of another magnet, the first magnet feels an instant reaction force pushing back; it doesn't have to wait until a light signal has made a round trip to the other magnet. Why not? Because what causes the instant reaction force is not the field produced by the second magnet "right now", but the field produced by the second magnet one light-travel time ago. (For example, if the second magnet is 1 meter away, then the reaction force comes from the field emitted by the second magnet 3.3 nanoseconds ago.)

Similarly, if I am floating in free space and I fire a rocket, I feel a force, normally said to be due to "inertia". But it could also be attributed to the fact that I am in a "gravitational field" produced by the distant stars, just with a time delay; the contribution to the field from Alpha Centauri, say, is from Alpha Centauri as it was 4.3 years ago. The distant stars don't immediately feel any effect from my rocket firing, but I feel an immediate effect because the field at my location has already had plenty of time to propagate from the distant stars.

 

[harrylin]

Could you point to (or quote) the specific passage in that reference where Langevin describes using gravity to give a turn-around with zero accelerometer reading?

Sorry for the misunderstanding, I was not clear. It was well known at the time that in free fall all parts of an instrument fall at the same speed, without relative displacement between the parts. That topic is now discussed here: https://www.physicsforums.com/showthread.php?t=674336

 

[harrylin]

The Christoffel symbols do that.

Symbols can't move a body
Compare: http://en.wikipedia.org/wiki/The_Treachery_of_Images

 

[Dale]

Symbols can't move a body

Don't get distracted by the name. The Christoffel symbols are a set of fields. The Christoffel symbols meet all of the requirements you have identified for the "gravitational field".

 

[Dale]

First, an axiom and a postulate:

Physics forums is for discussing mainstream theories only. Personal theories are not permitted. You cannot propose your own axioms or postulates here.

1. As noted above, the rocket coordinates may be chosen without resulting in the movement of the Earth and stars. Selection of the rocket coordinate system does not imply movement of the Earth and stars; therefore the selection of the rocket frame cannot be the cause of the movement of the Earth and stars.

Selection of any specific coordinate system does. I am sorry that you missed the word "specific" in my original statement.

2. A coordinate system is an abstraction, a mere convention used to identify a position in space. A coordinate system is not a physical entity, and therefore cannot be the cause of any physical phenomenon.

Then motion is not a physical phenomenon by this classification. This should not be terribly surprising.

3. If in the rocket frame the selection of the coordinate system is the cause of the increasing distance between Earth and rocket

I was talking about movement, not increasing distance. They are two different things. Movement is a change in position, this is different from a change in distance.

4. If the selection of the coordinate system is the cause, then the firing of the rocket cannot be the cause in the Earth frame.

I think you are still confusing change in position with change in distance.

 

[A.T.]

In my view, a strong case can be made that such an induction cannot bring into being the required gravitational field because, as was pointed out by another, no causal signal can move faster than the speed of light.

If I understand the gravitational field explanation correctly, it boils down to an inertial force that acts in the accelerated frame. In this case the propagation speed argument doesn't apply. Inertial forces are not propagating from A to B, they appear everywhere. And propagation speed limits don't apply to non-inertial frames anyway. For example: When you start rotating, the distant stars quickly reach speeds beyond c in your frame, and they are immediately subject to inertial centrifugal and Coriolis forces.

 

[nitsuj]

Symbols can't move a body
Compare: http://en.wikipedia.org/wiki/The_Treachery_of_Images

lol that's funny.

It's little tough for me to accept Dalespam's wording. But imo it's accurate.

From which perspective is physics described? I would say it is from the perspective of modeling.

And from that perspective I'd say that's a perfect looking pipe.

Pretty sure Dalespam doesn't feel he can power his commute to work with equations. (although indirectly I'd guess he does )

Pretty sure Dalespam could model that commute (and from different observer perspectives) physically.

And if the model is experimentally accurate, what is the difference between the model & what it describes.

 

[Dale]

Einstein definitely referred to a field of force that possesses the property of imparting the same acceleration to all bodies; according to his theory, the gravitation-field generates the accelerated motion.

Just to go back to this statement. Mathematically you can see that the Christoffel symbols is the field which does this. Starting with the previous equation:
\frac{d p^{\mu}}{d\tau} = f^{\mu} - {\Gamma^{\mu}}_{\nu\lambda} u^{\nu} p^{\lambda}

Dividing through by the mass we get
a^{\mu}=\frac{d u^{\mu}}{d\tau} = \frac{1}{m}f^{\mu} - {\Gamma^{\mu}}_{\nu\lambda} u^{\nu} u^{\lambda}

The acceleration imparted by the term with f depends on m, but the acceleration imparted by the term with the Christoffel symbols is the same for all bodies regardless of mass.

 

[GregAshmore]

The text in bold is correct. You are confusing the rocket with a set of coordinates where the rocket is at rest. Or perhaps you are confusing the broad class of coordinate systems where the rocket is at rest with a specific choice of one such coordinate system.

The coordinates simply map events in spacetime to points in R4. If you use a mapping where the Chistoffel symbols at Earth are non zero then Earth accelerates, regardless of whether or not the rocket is firing it's engines or even whether or not the rocket exists. The choice of coordinates determines the Christoffel symbols and therefore the acceleration, not the rocket.

Does this mean that we can put an engine-less pod in space (without gravity due to mass, per the scenario) and then select the appropriate mapping, at will and as needed, to accelerate the Earth and stars until the star of our choice meets up with the pod?

 

[GregAshmore]

[]Are we discussing the validity of the principle of relativity? I thought we were discussing how the (assumed to be valid) principle of relativity is applied to non-inertial observers. That is, I thought you were looking for "laws of physics" that could be applied by *any* observer who assumes himself to be at rest always. I didn't think you were questioning that such laws can exist.

We began by discussing the absoluteness of proper acceleration in the context of the twin paradox. We proceeded to discuss why certain objectors (the one in Taylor & Wheeler, and myself) believe that their objection has not been dealt with. I ended by saying that I am satisfied that the twin paradox is resolved with respect to kinematics, but I am not able to form an opinion with respect to dynamics. So, no, I do not assume that relativity is valid. Specifically, I do not assume that the non-inertial observer in the rocket can legitimately claim that he is at rest throughout. That must be proven.

So what makes a claim to be at rest "legitimate"? If the only requirement is the development of one set of equations that can be used by all at-rest observers to correctly predict the behavior of physical systems, then I don't think I have any quarrel with relativity. (I'm past worrying about whether time can vary with velocity.) But if the requirement is that the observed universe be "real" to every at-rest observer, then I'm not so sure.

As I read the posts in this thread regarding what the observer in the resting rocket observes, I saw the word "fictitious" many times. I'm fine with fictitious quantities if they allow me to correctly calculate what is going to happen. (I'm an engineer, not a theoretician.) But if the proceedings seen by the observer in the resting rocket are fictitious, I am not comfortable affirming the statement that all coordinate systems are equally valid. It seems to me that a coordinate system that has the stars violating a law of physics--traveling faster than light speed--has a lesser validity than a coordinate system that has the stars behaving within the laws of physics. The two coordinate systems may be equally useful, depending on circumstances, but they are not equally valid: one of them is telling a lie about the stars.

I don't necessarily disagree with this, but the only reason I can see for drawing a distinction between the firing of the rocket as "cause" and the force as "result" is that the force is frame-dependent; more precisely, the coordinate acceleration that results from the force is frame-dependent. In other words, you are maintaining that the firing of the rocket is an event that all observers must agree on, but the force is not.

But if there is a frame-independent way of measuring force, or acceleration, this argument fails. And there *is* a frame-independent way of measuring *proper* acceleration (but not coordinate acceleration), as you know. If that's the case, then on what basis do we distinguish the firing of the rocket as "cause" from the proper acceleration as "result"?

Note, again, that I'm not necessarily disagreeing; I'm pointing out what I think is a gap in your argument that needs to be filled. But this question also comes up in relation to "motion"; see further comments below.

I don't know how proper acceleration is calculated. If the calculation has the rocket moving, then the observer in the at-rest rocket will dispute the definition. His claim is that he is absolutely at rest, as explained below.

The way you are stating this, along with the way you are stating your argument as a whole, presupposes that "motion" is something definite and absolute. It's not; it's frame-dependent. What you really should say here is that the stars and the Earth are not moving *relative to each other* (to the approximation we are working with here, anyway).

Similarly, before the rocket fires, Earth and the rocket are not moving *relative to each other*; but after the rocket fires, they are. It is the *relative* motion that needs to be explained; that is the thing that isn't frame-dependent. But your argument tries to explain the "motion of the rocket" or the "motion of the Earth", as if they were absolute. They're not.

It is claimed that motions are not absolute. That must be proven. You know it is true. I do not. I am not required to accept the premise until it is proven. Indeed, I ought not to accept it until it is proven. I am attempting to prove the premise.

The premise is that every observer may legitimately consider himself to be at rest. For the premise to have any meaning at all, "at rest" must mean "absolutely at rest". (Einstein says, "permanently at rest".) Every observer develops the laws of physics on the assumption that he is at rest in absolute space.

If all such observers are able to agree on one set of physical laws ("of the same form"), then the premise that motion is not absolute is proven to be true. If all observers are absolutely at rest, none are. But if just one observer can show that in his circumstances the laws of physics are unique, then the premise is falsified.

In short, if you are going to take as an axiom that the cause must be "physical", then you should also take as an axiom that the *effect* must be physical as well. And since "physical", from the above, basically means "frame-independent"

Your definition of physical assumes the truth of the premise that is to be proven.

neither the motion of the Earth by itself, nor the motion of the rocket by itself, qualify as "effects" that need to be explained. Only the *relative* motion of the Earth and the rocket qualifies.

I disagree. The task is for every resting observer to explain what he sees, expressed as laws of physics. The observer in the resting rocket sees the Earth moving by itself; that is an effect which must be explained.

The whole thing just boils down to: the firing of the rocket causes relative motion of the rocket and the Earth. That's all that's needed.

Not so. The principle of relativity requires the rocket observer to explain how it is that the Earth moves while he remains at rest.

Same comment here: the laws of physics don't talk about the motion of the Earth, or the stars, or the rocket by themselves; they only talk about the *relative* motion of these things with respect to each other.

No again. The principle of relativity requires that the rocket be at rest, which implies that the Earth is moving by itself. The laws of physics must explain the motion of the Earth by itself, and the rocket by itself, if the principle of relativity is true.

If all we need to do is explain the relative motion of the rocket and Earth, I'm good with the force applied to the rocket. There is no reason at all to deal with the headache of induced gravitational fields in flat spacetime. But if the rocket must be allowed to rest, then the Earth must be moving by itself, and the headache must be endured.

I'm not saying I necessarily prefer the "gravitational field" explanation, but the fact that causal signals can't move faster than light (which I brought up before) does not rule out "induction" as a source for the "gravitational field" Einstein talks about. Such an argument, if it were valid, would prove too much: it would prove that ordinary magnetic induction can't exist either. Obviously that's not true.

Consider the analogy with ordinary magnetic induction further. If you try to push a magnet that's in the field of another magnet, the first magnet feels an instant reaction force pushing back; it doesn't have to wait until a light signal has made a round trip to the other magnet. Why not? Because what causes the instant reaction force is not the field produced by the second magnet "right now", but the field produced by the second magnet one light-travel time ago. (For example, if the second magnet is 1 meter away, then the reaction force comes from the field emitted by the second magnet 3.3 nanoseconds ago.)

Similarly, if I am floating in free space and I fire a rocket, I feel a force, normally said to be due to "inertia". But it could also be attributed to the fact that I am in a "gravitational field" produced by the distant stars, just with a time delay; the contribution to the field from Alpha Centauri, say, is from Alpha Centauri as it was 4.3 years ago. The distant stars don't immediately feel any effect from my rocket firing, but I feel an immediate effect because the field at my location has already had plenty of time to propagate from the distant stars.

Einstein says that "a gravitational field appears" when the rocket is fired. Then, "when the clock U1 has reached velocity v the gravitational field disappears."

 

[PeterDonis]

I do not assume that the non-inertial observer in the rocket can legitimately claim that he is at rest throughout. That must be proven.

Do you assume that an *inertial* observer can legitimately claim that he is at rest? If so, what's the difference? What makes an inertial observer special?

So what makes a claim to be at rest "legitimate"?

To me the answer is "mu": the question itself presupposes that "at rest" has some absolute meaning. It doesn't; "at rest" is relative. That means the only requirement is indeed this:

If the only requirement is the development of one set of equations that can be used by all at-rest observers to correctly predict the behavior of physical systems, then I don't think I have any quarrel with relativity.

if the requirement is that the observed universe be "real" to every at-rest observer, then I'm not so sure.

"Real" is too vague a term to be useful here, IMO. Perhaps the term "fictitious" has given a wrong impression:

I'm fine with fictitious quantities if they allow me to correctly calculate what is going to happen. (I'm an engineer, not a theoretician.) But if the proceedings seen by the observer in the resting rocket are fictitious, I am not comfortable affirming the statement that all coordinate systems are equally valid.

Events are real to all observers. Does that help? For example, if two twins meet up and find that one's clock has less elapsed time than the other's, that's not a "fictitious proceeding". But if one twin says "well, your clock had more elapsed time because you were higher up than me in a gravitational field while my rocket was firing", the gravitational field could be termed "fictitious". But that's more a matter of terminology or interpretation than physics; the traveling twin wants to interpret everything in his "rest frame", but that frame is non-inertial, so physics doesn't look as simple. "Gravitational field" is just a label he puts on the lack of simplicity; but the lack of simplicity is there because of the coordinates he chose. Nothing forces him to use coordinates in which he is always at rest.

It seems to me that a coordinate system that has the stars violating a law of physics--traveling faster than light speed--has a lesser validity than a coordinate system that has the stars behaving within the laws of physics.

The stars aren't violating any laws of physics. The actual law is not "things can't travel faster than light"; it is "things can't move outside the local light cones". All of the stars' worldlines are within their local light cones.

Once again, you appear to want to have it both ways; you want the "laws of physics" to look simple, but you want to be able to choose any coordinates you like. You can't have both of those things.

I don't know how proper acceleration is calculated.

You calculate the path curvature of the rocket's worldline. That can be done in any coordinates, including ones in which the rocket is at rest.

It is claimed that motions are not absolute. That must be proven.

How do you want it proven? It has already been shown that "motion" depends on the coordinates you choose. What more do you need?

The premise is that every observer may legitimately consider himself to be at rest. For the premise to have any meaning at all, "at rest" must mean "absolutely at rest".

I disagree; you can't call anything "absolute" if it depends on the coordinates you adopt.

Every observer develops the laws of physics on the assumption that he is at rest in absolute space.

Really? When you're driving your car, do you intuit its physics based on the assumption that you are at rest in absolute space and everything else is moving? If you do, you're pretty unusual; most people talk about "going somewhere" in their car (or walking or bicycling or any other way, for that matter), not "making the grocery store come to me using my car".

If all such observers are able to agree on one set of physical laws ("of the same form"), then the premise that motion is not absolute is proven to be true.

Then it's proven; GR provides just such a set of laws. But in some coordinates, a bunch of the terms in the equations become zero, so the laws look simpler in those coordinates.

Your definition of physical assumes the truth of the premise that is to be proven.

Then give an alternative definition that doesn't make any assumptions relevant to the argument.

The task is for every resting observer to explain what he sees, expressed as laws of physics.

I agree with this. But that doesn't imply this:

The observer in the resting rocket sees the Earth moving by itself; that is an effect which must be explained.

No, the observer in the rocket sees the Earth moving *relative to him*. That's how the laws work. You don't get to declare by fiat that the laws *must* take a certain form, or *must* deal with "absolute rest" or "absolute motion". You have to find out whether they do by finding out what the laws are. It turns out that the actual laws--the laws of GR--do *not* talk about absolute rest or absolute motion; they talk only about relative rest and relative motion. If you want laws that talk about absolute rest and absolute motion, you're going to be disappointed, because there aren't any.

The laws of physics must explain the motion of the Earth by itself, and the rocket by itself, if the principle of relativity is true.

No, the principle of relativity says that *relative* motion is what matters; it says that there is no such thing as absolute motion or absolute rest.

Einstein says that "a gravitational field appears" when the rocket is fired. Then, "when the clock U1 has reached velocity v the gravitational field disappears."

Yes, but he's using the term "gravitational field" in different ways (possibly without realizing it). When he talks about the field being produced by "induction", there *has* to be a time delay involved; but that means there has to be *something* propagating even when the rocket is not firing. That something is the "gravitational field" that is produced by "induction", with the distant stars as the source. When he talks about the field appearing and disappearing, he's using "gravitational field" to mean the force that is felt only when the rocket is firing; but the "field" (the underlying whatever-it-is that produces the induction effect) is there whether or not the rocket is firing.

 

[Dale]

Does this mean that we can put an engine-less pod in space (without gravity due to mass, per the scenario) and then select the appropriate mapping, at will and as needed, to accelerate the Earth and stars until the star of our choice meets up with the pod?

The meeting of worldlines is a frame-invariant geometric fact which cannot be changed through a choice of coordinates.

 

[PAllen]

Specifically, I do not assume that the non-inertial observer in the rocket can legitimately claim that he is at rest throughout. That must be proven.

What do you think of the following:
- The rocket cannot consider themselves inertial. This means that the simplest form of laws of physics cannot be used. A more complex way of expressing laws, that is also true (by natural vanishing of extra terms) for inertial motion, can be used. Thus, if you choose the more complex expression, laws are the same for all motion; however, this in no way changes that inertial and non-inertial motions are in-equivalent.
- The rocket is clearly at rest relative relative to itself. There is no escaping this, so it is clearly a legitimate thing to recognize.

...
But if the requirement is that the observed universe be "real" to every at-rest observer, then I'm not so sure.

What can you possibly mean by this? How can the universe become less real because you are in a rocket firing thrust? I assume this isn't really what you mean, but I am at a loss for what you possibly could mean.

As I read the posts in this thread regarding what the observer in the resting rocket observes, I saw the word "fictitious" many times. I'm fine with fictitious quantities if they allow me to correctly calculate what is going to happen. (I'm an engineer, not a theoretician.) But if the proceedings seen by the observer in the resting rocket are fictitious, I am not comfortable affirming the statement that all coordinate systems are equally valid. It seems to me that a coordinate system that has the stars violating a law of physics--traveling faster than light speed--has a lesser validity than a coordinate system that has the stars behaving within the laws of physics. The two coordinate systems may be equally useful, depending on circumstances, but they are not equally valid: one of them is telling a lie about the stars.

I can sympathize with this. Normally, you do not picture that distant mountains move rapidly when you turn your head. However, what would lead to a real problem is trying to apply the simplest form of laws to the 'turning head' frame. The simplest form of laws (only valid in inertial frames) says no matter can travel faster than the speed c. In the turning head frame, there are no limits on coordinate speed; but this law remains in a different way: no matter catches a pulse of light.

I don't know how proper acceleration is calculated. If the calculation has the rocket moving, then the observer in the at-rest rocket will dispute the definition. His claim is that he is absolutely at rest, as explained below.

Proper acceleration calculation has been explained a few times in this thread. I will not repeat. However, I stress that proper acceleration can easily be non-zero for an observer at rest in non-inertial coordinates. As I tried to express it above, the rocket is indisputably at rest relative to itself. However, it is also indisputably non-inertial, which allows proper acceleration to be nonzero for an observer at coordinate rest.

I am not going to address the rest of your post because I am curious to your reaction to the above, first.

 

[stevendaryl]

As I read the posts in this thread regarding what the observer in the resting rocket observes, I saw the word "fictitious" many times. I'm fine with fictitious quantities if they allow me to correctly calculate what is going to happen. (I'm an engineer, not a theoretician.) But if the proceedings seen by the observer in the resting rocket are fictitious, I am not comfortable affirming the statement that all coordinate systems are equally valid. It seems to me that a coordinate system that has the stars violating a law of physics--traveling faster than light speed--has a lesser validity than a coordinate system that has the stars behaving within the laws of physics. The two coordinate systems may be equally useful, depending on circumstances, but they are not equally valid: one of them is telling a lie about the stars.

The laws of physics are not violated by noninertial coordinates, it's just that they have a different form when they are expressed in noninertial coordinates.

For example, Newton's laws of motion, when described using inertial Cartesian coordinates x and y, look like this:

\dfrac{d^2 x}{dt^2} = \dfrac{1}{m} F^x
\dfrac{d^2 y}{dt^2} = \dfrac{1}{m} F^y

If we change to a new coordinate system
r = \sqrt{x^2 + y^2}
\theta = arctan(\dfrac{y}{x})

then the same equations of motion look like this:

\dfrac{d^2 r}{dt^2} - r (\dfrac{d\theta}{dt})^2 = \dfrac{1}{m} F^{r}
\dfrac{d^2 \theta}{dt^2} + \dfrac{2}{r} \dfrac{dr}{dt} \dfrac{d \theta}{dt} = \dfrac{1}{m} F^{\theta}

They're the same laws of motion, except written in different coordinates. The form of the laws change in different coordinates, but the physical content does not.

Similarly, the rule of light-speed is, in differential form: If an object travels a distance \delta x in time \delta t, then

(c \delta t)^2 - (\delta x)^2 \geq 0

That's what the law looks like in Cartesian coordinates. In general coordinates, the same law looks like this:

g_{\mu \nu}\ \delta x^\mu\ \delta x^\nu \geq 0 (summed over all indices \mu and \nu)

where g_{\mu \nu} are the components of the metric tensor in the new coordinate system. In an inertial Cartesian coordinate system, the metric tensor has the simple form

g_{tt} = c^2
g_{xx} = g_{yy} = g_{zz} = -1
(with all other components zero).

The laws of physics look different in noninertial or curvilinear coordinates, but they have the same physical content.

 

[harrylin]

lol that's funny.

It's little tough for me to accept Dalespam's wording. But imo it's accurate.

From which perspective is physics described? I would say it is from the perspective of modeling. [..]

Somewhat yes; but a physicist never looses sight of the things that he is modelling - in the context of the topic here Einstein also didn't. Never confound physical entities with their mathematical representation.

 

[Dale]

Somewhat yes; but a physicist never looses sight of the things that he is modelling - in the context of the topic here Einstein also didn't. Never confound physical entities with their mathematical representation.

Nobody here is doing that either.

 

[A.T.]

The two coordinate systems may be equally useful, depending on circumstances, but they are not equally valid: one of them is telling a lie about the stars.

You've got it backwards. Frames are preferred based on usefulness, not because some are more valid. For example, if you find it useful to use conservation of momentum, you prefer to use inertial frames, where conservation of momentum applies. But if you don't need conservation of momentum for your calculations, you might prefer some non-inertial frame. The fact that total momentum is not conserved in the non-inertial frame doesn’t make it less valid, just less practical in some cases. Nobody is lying here. Velocity is simply frame dependent.

 

[GregAshmore]

The meeting of worldlines is a frame-invariant geometric fact which cannot be changed through a choice of coordinates.

I'd like a yes or no answer.

After the resting rocket twin fires his engine and sees the Earth accelerate away, he eventually sees his target star approach. He can measure the distance to the star at intervals and verify that it is indeed getting closer. You have said repeatedly that the motion of the Earth is caused by the choice of coordinates, independent of the firing of the rocket. I give you the very same scenario, except without an engine in the rocket. Can you make the very same events happen? Can you cause the Earth and stars to move by selecting a certain coordinate system?

 

[PeterDonis]

I'd like a yes or no answer.

But you've asked two different questions. This actually illustrates well the difference between "motion" and relative motion.

I give you the very same scenario, except without an engine in the rocket. Can you make the very same events happen?

This is question 1. The answer is no: you can't make the very same events happen because you can't change the relative motion of the Earth and the rocket (or the target star and the rocket) without a rocket engine. (We're assuming no other possibilities, i.e., no gravity, no aliens with tractor beams, etc. )

Can you cause the Earth and stars to move by selecting a certain coordinate system?

This is question 2, and is *not* the same as question 1. The answer is yes, of course; just take the coordinate system in which the Earth, the rocket, and the target star are all at rest (since there's no rocket engine, they will always be at rest in this coordinate system), and boost it in some random direction. You now have a coordinate system in which all three are moving, at the same velocity.

What you can't do is get them moving at *different* velocities just by changing coordinate systems. But nobody was claiming that you could; that is, nobody was claiming that you could change their *relative* velocities just by changing coordinates. That's what takes the rocket engine; which is why relative motion is "physical" in a way that "motion" by itself is not.

 

[Mentz114]

Can you cause the Earth and stars to move by selecting a certain coordinate system?

Yes. Any observer moving relative to the Earth and stars will see them moving relative to himself. Velocity is relative.

 

[GregAshmore]

Do you assume that an *inertial* observer can legitimately claim that he is at rest? If so, what's the difference? What makes an inertial observer special?

I don't assume anything with regard to which kind of observer can consider himself at rest. The concept was never of more than passing interest until I read Einstein's book Relativity. I didn't have any pre-conceived ideas going in.

To me the answer is "mu": the question itself presupposes that "at rest" has some absolute meaning. It doesn't; "at rest" is relative. That means the only requirement is indeed this:

I don't think that is true, as a matter of logic. "At rest" must have an absolute meaning for the observer who claims it. Einstein's stated goal was to show that acceleration does not have any absolute quality. Absolute acceleration (as Einstein used the term acceleration in the book referenced above) implies absolute motion. The charge is, "You are accelerating; therefore I am certain that you are in absolute motion." Einstein counters the charge with, "No. I am permanently at rest." For that statement to have any effectiveness against the charge of absolute motion, the rest spoken of must be absolute. If the rest is not absolute, then the observer must admit that he is moving, or at least might be moving. The observer must believe that he is absolutely at rest; he must evaluate all the evidence on the presumption that he is absolutely at rest. You will note that I have not said that any observer is absolutely at rest in actual fact, only that he evaluates what he observes on that basis. So for the resting rocket twin, the Earth moves by itself; the Earth moves absolutely.

I'm going to skip replying to some of your responses. I need more time, and probably more study, to give a good answer.

Events are real to all observers. Does that help? For example, if two twins meet up and find that one's clock has less elapsed time than the other's, that's not a "fictitious proceeding". But if one twin says "well, your clock had more elapsed time because you were higher up than me in a gravitational field while my rocket was firing", the gravitational field could be termed "fictitious". But that's more a matter of terminology or interpretation than physics; the traveling twin wants to interpret everything in his "rest frame", but that frame is non-inertial, so physics doesn't look as simple. "Gravitational field" is just a label he puts on the lack of simplicity; but the lack of simplicity is there because of the coordinates he chose. Nothing forces him to use coordinates in which he is always at rest.

The difference in elapsed clock times is not the issue--not any longer. The issue is whether the rocket twin is moving in some absolute sense, or can legitimately claim to be at rest.

As to why the rocket twin insists on claiming that he is at rest, I guess you'ld have to ask Einstein. I certainly never thought to make an issue of it until I read his book.

Once again, you appear to want to have it both ways; you want the "laws of physics" to look simple, but you want to be able to choose any coordinates you like. You can't have both of those things.

Again, the issue for me is not the simplicity or complexity of the equations. The issue is whether the claim to be at rest makes physical sense. See the end of this post.

You calculate the path curvature of the rocket's worldline. That can be done in any coordinates, including ones in which the rocket is at rest.

Ok. I don't recall seeing this definition before. If it was in this thread, I missed it.

Really? When you're driving your car, do you intuit its physics based on the assumption that you are at rest in absolute space and everything else is moving? If you do, you're pretty unusual; most people talk about "going somewhere" in their car (or walking or bicycling or any other way, for that matter), not "making the grocery store come to me using my car".

In the context, I thought it was clear that I meant every resting observer.

Yes, but he's using the term "gravitational field" in different ways (possibly without realizing it). When he talks about the field being produced by "induction", there *has* to be a time delay involved; but that means there has to be *something* propagating even when the rocket is not firing. That something is the "gravitational field" that is produced by "induction", with the distant stars as the source. When he talks about the field appearing and disappearing, he's using "gravitational field" to mean the force that is felt only when the rocket is firing; but the "field" (the underlying whatever-it-is that produces the induction effect) is there whether or not the rocket is firing.

Prompted by the above, I read this again:

But all the stars that are in the universe, can be conceived as taking part in bringing forth the gravitational field; because during the accelerated phases of the coordinate system K' they are accelerated relative to the latter and thereby can induce a gravitational field, similar to how electric charges in accelerated motion can induce an electric field.

This is consistent with the idea that the field is present all the time. But there seems to be a causal conundrum here. The effect of the field is not felt until the Earth accelerates. But the Earth only accelerates due to the effect of the field.

If no plausible explanation for the workings of the gravitational field can be given, the field must be considered a pure fiction; ad-hoc hand-waving. In that case, the absoluteness of acceleration is not removed, at least with respect to SR.

Personally, I have no stake in the argument. I don't care if there is an absoluteness to acceleration. But the issue was important to Einstein, and having come this far, I'd like to be able to evaluate whether he succeeded in eliminating the problem.