Implications of the statement "Acceleration is not relative"

by GregAshmore
Tags: implications, statement
 P: 2,863 Addressing the OP more specifically, maybe he is finding difficult to understand why if there is no two notions of velocity coexisting (an absolute and a relative velocity) in relativity, one does have both absolute and relative acceleration. While one justifies easily the first case because in relativity we have a spacetime rather than separate space and time and therefore one doesn't have any absolute space wrt wich define an absolute velocity, this doesn't work in the case of acceleration and ultimately it seems one has to settle with "because this is just the way it is". This isn't something that is very often clarified.
P: 1,618
 Quote by TrickyDicky Addressing the OP more specifically, maybe he is finding difficult to understand why if there is no two notions of velocity coexisting (an absolute and a relative velocity) in relativity, one does have both absolute and relative acceleration. While one justifies easily the first case because in relativity we have a spacetime rather than separate space and time and therefore one doesn't have any absolute space wrt wich define an absolute velocity, this doesn't work in the case of acceleration and ultimately it seems one has to settle with "because this is just the way it is". This isn't something that is very often clarified.
I don't think that things are that dissimilar when it comes to velocity and acceleration.

You can define a 4-velocity $V^\mu$ by $V^\mu = \dfrac{d}{d \tau} x^\mu$ and you can similarly define a 4-acceleration $A^\mu$. Neither is more absolute than the other. However, you can always choose coordinates so that the spatial components of $V^\mu$ are all zero, but you can't always do that for the spatial components of $A^\mu$
P: 2,863
 Quote by stevendaryl However, you can always choose coordinates so that the spatial components of $V^\mu$ are all zero, but you can't always do that for the spatial components of $A^\mu$
Right there, that's what I mean. This is the asymetry that is not so easy to explain. And maybe the OP naively thinks that if there is an absolute acceleration it would imply a rate of change of absolute velocity but that can't be because there is no such a thing as absolute velocity in relativity.
At this point I guess I should wait for the OP to confirm if this gets any close to his line of thought.
P: 3,178
 Quote by DaleSpam [..] My point remains, that the "gravitational field" he refers to by "A gravitational field appears, that is directed towards the negative x-axis. Clock U1 is accelerated in free fall, until it has reached velocity v. An external force acts upon clock U2, preventing it from being set in motion by the gravitational field. When the clock U1 has reached velocity v the gravitational field disappears" is the field from the Christoffel symbols and it is entirely determined by the choice of coordinates. [..]
Once more, Einstein's comment related to your point was:
"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."
 please be explicit about what mathematical term you think he intends and why.
I think that Einstein was clear enough, and I was explicit in my clarification - he gave a physical explanation which I don't copy and to which you turned a blind eye. That shows that you also don't copy it; please stop trying to turn your agreement with me in an argument about something else.
P: 3,178
 Quote by GregAshmore [..] In my previous post, I asked for a SR solution of the problem in which the non-inertial rocket is always at rest. I don't recall anyone presenting such a solution. My sense is that my calls for such a solution have been rebuffed. [..] The article discussing acceleration in special relativity also speaks of the accelerating object as in motion.
Indeed, SR presents solutions for the physical consideration of a traveler who changes velocity; SR isn't made for the view of a traveler who is constantly at rest, such that the universe is bouncing around while the traveler doesn't accelerate.
 I, in my rocket, claim that I am not in motion. I have been sitting in my rocket in the same position throughout the episode. You claim that I will be younger than my twin at the end of the episode. As proof, you present to me a diagram that shows me in motion. I reject it. I categorically deny that the diagram applies to me. The diagram shows me in motion; I have not moved. [..]
An SR diagram does not address your issue. Einstein's 1918 paper does; however few people accept his Machian solution.
 I would like to see a SR solution which has me in one position throughout the episode.
A non-moving traveler isn't addressed in SR. SR can only provide a mapping to rocket, such that the description is from the view of the accelerating rocket.
Mentor
P: 16,298
 Quote by harrylin I think that Einstein was clear enough, and I was explicit in my clarification - he gave a physical explanation which I don't copy and to which you turned a blind eye.
I wasn't asking for a physical explanation, I was asking for clarification about its definition. What is meant by the term "gravitational field"? Until it is known what is meant by the term it is nonsense to even talk about providing a physical explanation for it. If I give you a physical explanation for a flubnubitz without defining the term, have I actually told you anything? E.g. "All the stars that are in the universe, can be conceived as taking part in bringing forth the flubnubitz."

You certainly were not explicit at all about what you believe he means by the term "gravitational field" even when directly asked for clarification, and you seem to disagree with Einstein's use of the term although you quote him. If you wish to clarify what specifically you believe Einsetin refers to by the term "gravitational field" then we can continue the discussion.

I don't understand your reluctance to clarify your position. Surely by now you realize how easily misunderstandings can arise in online forums. A request for clarification should always be taken seriously and complied with willingly.
P: 1,618
 Quote by harrylin Once more, Einstein's comment related to your point was: "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."
I would say that there are several aspects of gravity:
1. For each point in spacetime, and for each possible initial velocity, there is a unique inertial path, the freefall path, or geodesic. These geodesics are physical, and are affected by the presence of matter and energy.
2. In general, geodesics that start close together and parallel do not remain close together and parallel as you follow them. This is a manifestation of spacetime curvature.
3. If one takes a path through spacetime that does not follow a geodesic, there will be resistance--it requires the application of a physical force to depart from geodesic motion.
4. If one uses a coordinate system in which coordinate axes are not geodesics, then the path of an object with no physical forces acting on it will appear "curved", meaning that the components of velocity in this coordinate system are not constant.

The first 3 aspects of gravity don't involve coordinates at all, and only mention physical forces, not fictitious forces. The 4th aspect to me is what the meaning of "fictitious forces" are, which is that the coordinate flows are not geodesics. The terminology "coordinate flow" is made up by me; I'm not sure what the technical term is, or if there is one. But in a similar way that specifying an initial point in spacetime, together with an initial velocity, determines a path through spacetime--the geodesic, specifying an initial point in spacetime, together with an initial velocity, determines a different path through spacetime, the coordinate flow, which is the solution to the component equation:

$\dfrac{dV^\mu}{d\lambda} = 0$

(where $\lambda$ is the affine parameter for the path).

This would be a geodesic, if it were flat spacetime and inertial cartesian coordinates were used.

 I think that Einstein was clear enough
Actually, I don't think he was very clear, mainly because he is using the words "gravitational field" (or something in German, more likely) without giving a precise definition of what it means.
Mentor
P: 16,298
 Quote by stevendaryl The 4th aspect to me is what the meaning of "fictitious forces" are, which is that the coordinate flows are not geodesics. The terminology "coordinate flow" is made up by me; I'm not sure what the technical term is, or if there is one.
I think that the technical term would be "integral curves of the coordinate basis", but it certainly isn't a commonly used term. "Coordinate flows" sounds nice.
Mentor
P: 16,298
 Quote by my_wan If one hits the gas to speed up, not only does the occupant feel the force, but no matter which coordinates you choose every observer will agree that its speed is changing.
Just a point of clarification. This should be "no matter which inertial coordinates you choose".
P: 863
 Quote by DaleSpam Just a point of clarification. This should be "no matter which inertial coordinates you choose".
Yep, it even looks awkward stated the way I did now that you pointed it out.
P: 3,178
 Quote by my_wan I just wanted to add a few words for GregAshmore [..] Note the force felt when accelerating. When on the surface of a gravitational mass, like Earth, the principle of equivalence tells us this weight we feel is the same force we feel when accelerating. Now if you jump off a roof then while accelerating toward the ground you feel no force, effectively weightless. Hence, in your frame of reference you are at rest, i.e., not accelerating, but the Earth is accelerating toward you. Yet everybody in the Universe can agree that your speed is changing, even if not by how much. [..] So in this case gravity is absolute, but the coordinate acceleration due to gravity is relative.
Thanks for bringing that up, as it is exactly that modern argument that 1916GR denies; and I had the impression that GregAshmore noticed that point, that it's basically that issue that he discovered. Einstein tried to relativise acceleration by relativising gravitation, so that it's a matter of free opinion if a rocket accelerates or not. Nowadays few people accept that view.
 Now reconsider the twin paradox. If two observers experience the same amount of acceleration X time, then neither one will age any faster than the other.
That argument fails in the first version by Langevin, see my earlier remarks as well as elaborations by others.
PF Gold
P: 4,786
 Quote by my_wan Gravity turns this relationship on its head. Note the force felt when accelerating. When on the surface of a gravitational mass, like Earth, the principle of equivalence tells us this weight we feel is the same force we feel when accelerating. Now if you jump off a roof then while accelerating toward the ground you feel no force, effectively weightless. Hence, in your frame of reference you are at rest, i.e., not accelerating, but the Earth is accelerating toward you. Yet everybody in the Universe can agree that your speed is changing, even if not by how much. In this case proper gravity is absolute, while how much gravity and coordinate paths are relative. So in this case gravity is absolute, but the coordinate acceleration due to gravity is relative.
Not quite everyone in the universe: someone who jumped off the roof next to you would not agree. As for someone far away, in GR, the whole concept of relative velocity at a distance is fundamentally ambiguous because you can't compare vectors at a distance in curved spacetime. So this argument is not so clear cut.

I would agree that gravity is absolute for a different reason: tidal 'forces', physically; curvature geometrically. Tidal forces are detectable in a small region.
PF Gold
P: 4,436
 Quote by GregAshmore Answers to questions: Q1. Both the Earth and the rocket claim to be at rest throughout the episode. Can both make good on this claim? Yes, kinematically. Earth and rocket X coordinates are 0.0 throughout. Whether this makes physical sense dynamically is unknown, given limited knowledge noted above.
The Earth can claim to be at rest in an inertial frame. The rocket can claim to be at rest in a non-inertial frame.

 Quote by GregAshmore Q2. What are the clock readings on Earth and rocket at G6? The Earth clock reads 25.0. The rocket clock reads 15.0.
Correct.

 Quote by GregAshmore Q3. Are the clock readings calculated for Q2 unambiguously unique? Yes.
Correct.
 Quote by GregAshmore There is only one way to construct the spacetime diagram, due to the unique non-inertial behavior of the rocket.
I don't know why you would say this. Are you referring to the Earth's inertial rest frame? There are an infinite number of ways to construct spacetime diagrams for your scenario, all with different velocities with respect to each other and all just as valid and all producing the same final clock readings and the same things that each observer actually sees.

 Quote by GregAshmore Visually, the Earth and rocket experiences are symmetric. Each sees the other move away and return. Nevertheless, the rocket is unambiguously younger than the Earth at reunion.
No, they are not symmetric. The rocket sees the Earth move away at 0.8c for a distance of 3.333 units and then remain at that distance for some time and then come back to the rocket. But the Earth sees the rocket move away at 0.8c to a distance of 10 units and then immediately start coming back. It doesn't matter what spacetime diagram you use to depict your scenario, they are all just as valid and produce the same results. The only thing that is different in them are the values of the coordinates (and the geometric shapes of the worldlines).
P: 863
 Quote by harrylin Einstein tried to relativise acceleration by relativising gravitation, so that it's a matter of free opinion if a rocket accelerates or not. Nowadays few people accept that view.
In a sense I would say Einstein succeeded via the principle of equivalence, with caveats. The first problem is as PAllen stated in his objection to my use of the term "everyone". A gravitational field cannot be globally transformed away unless it is itself globally uniform. The second problem is that, even if you could, any time two inertial observers are accelerated with respect to each other a gravitational field must be involved, such that these two observer cannot be at rest with respect to each other and still be inertial. Everyone can agree that a gravitational field exist even if they may not agree on where the gravitational field is located, its geometry, etc. This issue is the reason energy conservation became so controversial in GR, but it's really more a localization issue than a conservation issue.

The break in the symmetry under both special and general relativity occurs whenever an observer enters a non-inertial state. Sitting motionless on the surface of the Earth is a non-inertial state, which is why you feel weight. By the principle of equivalence you feel this same g-force when you accelerate under special relativity, which breaks the symmetry GregAshmore is wanting to absolutely maintain, leading to his difficulties.

You cannot break this symmetry in either special or general relativity and pretend it is not broken. Once this symmetry, which applies only to inertial observers, is broken it is no longer "matter of free opinion" as to whether it is broken or not. GregAshmore is assuming the symmetry wasn't broken when his spaceship was accelerated. Whether this symmetry is broken by a rocket engine (SR) or a gravitational field (GR) makes no difference, though both break it in a different or inverse manner, breaking this symmetry requires one or the other.
P: 3,178
 Quote by my_wan [..] The break in the symmetry under both special and general relativity occurs whenever an observer enters a non-inertial state. [..] You cannot break this symmetry in either special or general relativity and pretend it is not broken. Once this symmetry, which applies only to inertial observers, is broken it is no longer "matter of free opinion" as to whether it is broken or not. GregAshmore is assuming the symmetry wasn't broken when his spaceship was accelerated. Whether this symmetry is broken by a rocket engine (SR) or a gravitational field (GR) makes no difference, though both break it in a different or inverse manner, breaking this symmetry requires one or the other.
That's correct of course; perhaps I read too much in GregAshmore's issues and is it only a matter of problems with the calculation methods. If so, then that should be easy to fix. So I'll also look into his last attempt.
P: 3,178
 Quote by GregAshmore [..] Here's my best shot at the Twin Paradox. Later this evening, or maybe tomorrow night, I'll see how what I did compares with your suggestions.[..] Solution of the Twin Paradox - to the degree possible knowing only the Lorentz transform and the usage of the spacetime diagram.
OK - that implies purely SR. As you seem to have solved the equations without issues, I'll skip those.
 Given: G1. Earth and rocket are both at rest at same position. Earth clock and rocket clock are synchronised. G2. At time 0.0, rocket fires a pulse. G3. Earth and rocket separate at relative velocity 0.8c. G4. At distance 10 units from Earth, as measured in Earth frame, rocket fires a pulse. G5. Earth and rocket approach at relative velocity -0.8c. G6. Upon reaching Earth, rocket fires a pulse, coming to rest on Earth. G7. Gravitational effects of mass are to be ignored. Questions: Q1. Both the Earth and the rocket claim to be at rest throughout the episode. Can both make good on this claim?
It depends on what they supposedly mean with that. In normal use of the word "in rest", in the context of SR calculations, the rocket cannot claim to be all the time in rest. This is because it's not all the time in rest in any inertial frame. Precision: "inertial frame" in SR means a set of coordinate systems that is in rectilinear uniform motion according to Newton's mechanics; also called by Einstein a "Gallilean" reference system.
 Q2. What are the clock readings on Earth and rocket at G6? Q3. Are the clock readings calculated for Q2 unambiguously unique? Solution: The questions are with regard to kinematics only: positions and times. With one exception noted later, the dynamics of the episode need not be considered.
While that is often said, it is only half true, and therefore misleading. The dynamics is inherent by the prescription of reference to inertial frames for the Lorentz transformations. If one purely considered kinematics only then the situation would be symmetrical.
 [..] Earth or rocket must change frames at velocity reversal. The reversal of velocity in G4 must be represented by a change of frame in the spacetime diagram. Without a change of frame, the worldlines of Earth and rocket can never meet. Either the Earth or the rocket, or both, must change frames. The Earth cannot change frames: No unbalanced force acts on it; it is inertial. The rocket must change frames: It is acted on by an unbalanced force; it is not inertial.
Note my earlier clarifications why such kind of reasoning does not generally hold. What matters for your SR calculation is that the rocket is not all the time at rest in an inertial frame. Also the Earth is not at rest in an inertial frame as it is in an orbit around the Sun; however the effect is small compared to the rocket. That is another simplification of the calculation.
 [..] Visually, the Earth and rocket experiences are symmetric. Each sees the other move away and return. Nevertheless, the rocket is unambiguously younger than the Earth at reunion.
Right.
[addendum: kinematically the situation looks symmetrical (which is what I supposed you meant); however next George correctly highlights that of course there are visual differences that can be observed. That is pertinent for understanding the physics. This difference in observations has also been elaborated by Langevin in the article that I linked earlier.]

 Related Discussions Computers 14 Classical Physics 2 Special & General Relativity 13 Cosmology 114 Advanced Physics Homework 4