Implications of the statement "Acceleration is not relative"

DaleSpam

I can make it look more like a standard law of physics quite easily:[tex]\frac{d p^{\mu}}{d\tau} = f^{\mu} - {\Gamma^{\mu}}_{\nu\lambda} u^{\nu} p^{\lambda} [/tex]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 [itex]\Gamma[/itex] is the Christoffel symbols in the coordinate system in question.

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

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:

[itex]m \dfrac{dV^\mu}{d \tau} = F^\mu[/itex]

where [itex]V^\mu[/itex] is the 4-velocity.

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

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

So even when the applied force [itex]F^\mu[/itex] is zero, the coordinate acceleration [itex]\dfrac{dV^\mu}{d \tau}[/itex] 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

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

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.

harrylin

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

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.

DaleSpam

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:[tex]a^{\mu}=\frac{d^2x^{\mu}}{d\tau^2}[/tex]Where x is the worldline in an inertial frame and τ is the proper time along that worldline. That quantity is non-zero.

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".

harrylin

I even cited his answer several times.

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.

harrylin

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

harrylin

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.

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 _______.?

Alain2.7183

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

harrylin

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.

stevendaryl

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

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.