# Implications of the statement "Acceleration is not relative"

by GregAshmore
Tags: implications, statement
P: 221
 Quote by PeterDonis 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.

 Quote by PeterDonis 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.

 Quote by PeterDonis 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.
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P: 5,507
 Quote by GregAshmore 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.

 Quote by GregAshmore This gravity is purely the result of the choice of coordinate system, as I understand DaleSpam.
If spacetime is flat, yes.

 Quote by GregAshmore 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.

 Quote by GregAshmore 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.

 Quote by GregAshmore 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.
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P: 16,476
 Quote by GregAshmore 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.

 Quote by GregAshmore 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.

 Quote by GregAshmore 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.

 Quote by GregAshmore 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.

 Quote by GregAshmore {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.

 Quote by GregAshmore A secondary (and less emotional) reaction is to ask the original question in a more precise way. What causes the spacial 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?
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P: 16,476
 Quote by GregAshmore 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.

 Quote by GregAshmore 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.
P: 1,657
 Quote by GregAshmore 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.
P: 3,178
 Quote by Nugatory 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...
P: 3,178
 Quote by DaleSpam As you make your $\delta \tau$ small the SR predicted accelerometer reading becomes large while the actual accelerometer reading remains 0. [..]
 Quote by DaleSpam [..]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.
P: 3,178
 Quote by GregAshmore [..] 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.
P: 3,178
 Quote by GregAshmore [..] 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.
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P: 16,476
 Quote by harrylin 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.
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P: 16,476
 Quote by harrylin 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".
P: 3,178
 Quote by DaleSpam 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.
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P: 16,476
 Quote by harrylin 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.
P: 3,178
 Quote by DaleSpam [..] 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.
P: 3,178
 Quote by DaleSpam 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.
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P: 16,476
 Quote by harrylin 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 _______.?
P: 24
 Quote by Mentz114 See this topic http://www.physicsforums.com/showthread.php?t=490163
Thanks for that link. Very interesting. Lots of good stuff.
P: 3,178
 Quote by DaleSpam 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_Fo...ity-postulate.

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