View Full Version : The Peripatetic Albert, Round 3
...And so, I was driving north from McPherson toward Salina, explaining Special Relativity to my wife and oldest daughter (and however many of the other children were actually listening). As I did so, I used our Suburban as an example, explaining how that, in the absence of any absolute coordinate system, there was no real way to tell whether the Suburban was moving over the road, or the road was moving under the Suburban.
About that time, we turned onto the highway - and I realized that, I had either used the steering wheel to turn the car in relation to the earth, or I had used the steering wheel to turn the earth in relation to the car - and that, motion being purely relative, either could be as true as the other.
Now, here was a remarkable fact: Assuming the car to be at rest (which Special Relativity requires me to be able to do), it seems that I was actually able to change the orientation of the entire earth simply by turning the steering wheel!
Now, that's power steering!
How does Special Relativity explain this curiousity?
humanino
Sep16-04, 03:59 PM
That does not seem to be a paradox to me : when you turn, you are not an inertial observer anymore ! You have been accelerated.
humanino
Sep16-04, 04:14 PM
Sometimes when I walk, I like to think I am having to Earth roll under my feet :shy:
geometer
Sep16-04, 09:26 PM
...And so, I was driving north from McPherson toward Salina, explaining Special Relativity to my wife and oldest daughter (and however many of the other children were actually listening). As I did so, I used our Suburban as an example, explaining how that, in the absence of any absolute coordinate system, there was no real way to tell whether the Suburban was moving over the road, or the road was moving under the Suburban.
Actually, you left out a critical detail. If you were undergoing completely unaccelerated motion, there is no experiment that will tell you whether you are moving or the earth is moving in your example. However, in a car, it's just about impossible to be completely unacclerated; bumps are acclerations, the swaying of the car is an acceleration, obviously, even minute changes in your speed are accelerations.
Okay, then...
How does GR explain this?
(I can't help but think that we've missed the point, though. Essentially, we see what appears to be a blatant abrogation of fundamental laws - the energy required to change the earth's direction is many orders of magnitude greater than the energy required to change the car's direction - so how can we say that the principle of relativity is upheld in this scenario? I don't think that promoting the problem to a GR question helps this observation. Further, I have heard several board members, much more knowledgeable than me, make SR analyses of non-linear circumstances not unlike this. But if we are going to say that "SR only applies to straight-line motion," then fine. In that case, I welcome a GR explanation.)
humanino
Sep16-04, 10:36 PM
when you turn, you are not an inertial observer anymore ! You have been accelerated.
What is wrong with this ? :confused:
I don't think bumps are acclerations, the swaying of the car is an acceleration, obviously, even minute changes in your speed are accelerations
has any relevance for the problem. However, the whole thing looks solved to me by the previous one.
humanino
Sep16-04, 10:44 PM
the energy required to change the earth's direction
Contrary to you, the Earth has not been accelerated ! Besides, you would have to change the direction of the entire Universe :surprised
Contrary to you, the Earth has not been accelerated ! Besides, you would have to change the direction of the entire Universe :surprised
But this is exactly my point: What reason have I to believe that it is I, not the earth, which has been accelerated - other than resorting to classical mechanics? Observationally, by the principle of relativity, neither idea should have any advantage over the other. Is it me moving, or the earth, or the entire universe? Why would one observational perspective have any advantage over another?
humanino
Sep16-04, 11:07 PM
No, you can measure a force. There was no force on the earth.
Well, strictly speaking, there was the exact same and opposite force, and it did move. But its inertia or mass is so huge, that it did not really affect it much.
well i suggest u perform this thought experiment..keep a glass of water i n ur car and on earth beside and turn ur car...u will easily see which body is being accelerated by observing the movement in the water in the glass...
so it is u who is accelerating since a device to measure force records one in ur frame(accelerated that is) and not in the frame of reference of the earth
humanino
Sep16-04, 11:21 PM
Welcome a1_phy ! Very good argument.
One-eye, relativity applies to velocity not acceleration. Acceleration is not relative.
No, you can measure a force. There was no force on the earth.
Well, strictly speaking, there was the exact same and opposite force, and it did move. But its inertia or mass is so huge, that it did not really affect it much.
Very good. So, then, we have a principle, related to mass and force, which mitigates the principle of relativity: Where force can be calculated, the principle of relativity no longer applies: One can tell with certainty which object is moving when one is able to calculate the force.
Right?
One-eye, relativity applies to velocity not acceleration. Acceleration is not relative.
I don't believe that this is quite right. I believe that the correct statement is, "Special Relativity applies only to velocity; you must use General Relativity to evaluate questions of acceleration."
selfAdjoint
Sep17-04, 10:44 AM
I don't believe that this is quite right. I believe that the correct statement is, "Special Relativity applies only to velocity; you must use General Relativity to evaluate questions of acceleration."
No, this is an urban legend. You can treat accleration in SR, and people have done it in other threads on this board; look up "relativistic rocket". What is more true is that GR is a complete theory of forces and accelerations whereas SR is a special case. It is correct that accelerations are not Lorentz-invariant or covariant. They follow a different change-of-frame law.
humanino
Sep17-04, 11:05 AM
Very good. So, then, we have a principle, related to mass and force, which mitigates the principle of relativity: Where force can be calculated, the principle of relativity no longer applies: One can tell with certainty which object is moving when one is able to calculate the force.
Right?
Wrong. Let us sum up what has been collected here : there is an inertial reference frame for the system Car/Earth. In this frame, the acceleration is undergone by the car. The acceleration of the Earth is negligible. If you had a very precise mean of measurement, you could in theory notice the force on Earth, but such an accuracy would probably require to take into account the whole solar system.
You can locally make acceleration disappear by changing the referential. Only locally. The free-fall observer not noticing the Earth gravitational field has a limited spave around him, otherwise he would notice the spherical shape.
You raised the question of energy. Let us assume now that you want to turn very fast. Very very fast. Let us say there is no limit on the energy you can spend for this turn. If you turn too fast, you will really be able to produce a serious force on Earth !
No, this is an urban legend. You can treat accleration in SR, and people have done it in other threads on this board; look up "relativistic rocket". What is more true is that GR is a complete theory of forces and accelerations whereas SR is a special case. It is correct that accelerations are not Lorentz-invariant or covariant. They follow a different change-of-frame law.
selfAdjoint: Thank you for weighing in on this. But let me be sure that I understand what you are saying:
You are saying that SR does apply in the case I originally posited; that the fact that I "accelerated" (not necessarily true, but we will say that it is) or moved in a non-linear fashion does not disallow an analysis of the situation using SR. Is that correct?
I would really like to nail this down, since I have had several questions answered in like manner: "Your scenario does not apply, since you are accelerating, and SR is not useful to consider acceleration." But I have seen other posters who seem to indicate that SR is as useful for non-linear motion (e.g., rotary/orbital motion) as it is for linear motion - and my original case seems to be reducible using the theorem of the addition of velocities from SR. So, I have always doubted the "SR is only for linear velocity" disqualifications which I have heard.
Am I right to doubt?
humanino
Sep17-04, 11:40 AM
Always right to doubt.
At least I did not tell you SR does apply when acceleration is here. I only wanted to point that there are two inertial frames, before and after the turn, but the interesting moment is in the middle.
geometer
Sep17-04, 12:35 PM
What is wrong with this ? :confused:
I don't think
has any relevance for the problem. However, the whole thing looks solved to me by the previous one.
Nothing wrong with your answer, I was agreeing with you and showing that even if you are moving in a straight line in a car, you are probably not even then an inertial observer.
geometer
Sep17-04, 12:51 PM
You can locally make acceleration disappear by changing the referential. Only locally. The free-fall observer not noticing the Earth gravitational field has a limited spave around him, otherwise he would notice the spherical shape.
I have to disagree humanino, an observer in an isolated laboratory can detect an acceleration. You can't transform accelerations away.
humanino
Sep17-04, 01:13 PM
Now I am even more confused. The free falling observer is accelerated, and this is the very important initial idea of Einstein : he would locally not notice this acceleration because the lab falls with him, hence gravity ~ change of ref.
Why might have a misunderstanding here ! If something is accelerated inside the free falling lab, then he would notice it. You cannot make tidal forces disapear, but this is due to different accelerations in different points. This is non-local.
geometer
Sep17-04, 03:12 PM
Let's assume we are riding on a train and looking out the window at the scenery. Further, let's assume that this train is a perfectly inertial system right now - strictly unacclerated, straight line motion. In this case, there is no way I can tell whether I am moving or the world outside is moving.
But, now, let's assume the train takes a corner. Now I am accelerated, and in fact, I will feel the acceleration and it is possible for me to determine whether I am moving or the world is moving. Since I feel the acceleration, I must be moving. And even I choose myself as the origin of my reference frame, I still feel the acceleration. No matter what coordinate system I choose, I still feel the accleration.
geometer
Sep17-04, 03:22 PM
Actually, Einstein's great insight was that the person in the freely falling lab couldn't tell whether any acceleration that was imposed on him was due to a gravitational field or some artificial source such as a rocket engine. This argued that gravity wasn't some intrinsic characteristic of a mass itself, but a secondary effect.
pervect
Sep17-04, 03:36 PM
Now, here was a remarkable fact: Assuming the car to be at rest (which Special Relativity requires me to be able to do), it seems that I was actually able to change the orientation of the entire earth simply by turning the steering wheel!
Now, that's power steering!
How does Special Relativity explain this curiousity?
Back in the old days, life was simple. You weren't allowed to change the orientation of the Earth by turning your steering wheel, nor were you allowed to change the orientation of the entire universe by turning your head (or swiveling in your swivel chair). You were told, in no uncertain terms, to pick an inertial frame of reference, and stick with it.
Back in the old, simple days, physics was simple, too - bodies at rest remained at rest, bodies in motion remained in motion.
Now, it turns out to be convenient, sometimes, to be able to change the orientation of the Earth, or the universe, with the turn of a head, or the stroke of a pen. You can do physics in such a coordinate system, but don't expect Newton's laws to apply.
If you've internalized the concept of Newton's laws, you might say that changing the orientation of the universe with the stroke of a pen isn't really a "physical" change, it's just a change of coordinates.
If you start focusing on what you calculate, I think a lot of the confusion will disappear. You can calculate what will happen next when you turn the steering wheel - it's just a matter of viewpoint, of how you describe what happens next.
humanino
Sep17-04, 04:02 PM
But, now, let's assume the train takes a corner.
Non-uniform acceleration ! We are agreeing, I am almost certain of this. The non-uniform acceleration is locally uniform. There is a local change of coordinate making the acceleration vanish at one instant. Even here.
So, then, I am driving down the road... or the road is rolling under me... whichever. Both are equally true, relativistically speaking. I am at liberty to consider the case either way, and neither view has any advantage over the other. In any case, the earth is turning under me at 100 kph, but I am perfectly still. The sun is shining; the birds are singing; all is right in the world.
And, because I insist on a perfect inertial frame of reference, I do not touch the steering wheel. I lashed it tightly with a bungie cord as soon as the highway got up to 100 kph underneath me.
Unfortunately, geography interferes with my progress: The road curves to the left, and I do not. The road rolls out from under me, and a bridge abutment plows right into the nose of my perfectly stationary vehicle.
How do I calculate the energy of collision?
geometer
Sep18-04, 10:37 AM
Non-uniform acceleration ! We are agreeing, I am almost certain of this. The non-uniform acceleration is locally uniform. There is a local change of coordinate making the acceleration vanish at one instant. Even here.
I'm afraid not. Inertial coordinate systems are coordinate systems moving at constant velocity with respect to each other. If one system is accelerating, even uniformly, with respect to another system it is no longer an inertial system, and you should be able to detect acclerations and thereby determine who is really moving.
A coordinate system which is in free-fall with respect to the earth say, is undergoing acceleration and is therefore not an inertial system.
HallsofIvy
Sep18-04, 11:12 AM
Yes, you can treat acceleration in both SR and GR. The point everyone has been trying to make to OneEye is that acceleration is NOT relative. There is no experiment you make in a completely selfcontained room that will determine uniform velocity. You can determine acceleration. OneEye's original question was about turning which involves acceleration even if done at a constant speed.
pervect
Sep18-04, 11:12 AM
Unfortunately, geography interferes with my progress: The road curves to the left, and I do not. The road rolls out from under me, and a bridge abutment plows right into the nose of my perfectly stationary vehicle.
How do I calculate the energy of collision?
The energy of collision is frame dependent, unfortunately. So what you typically do is go to the center of mass frame between you and the bridge abutment.
You can compute the energy in other frames, but if you want to cmpute how much your care will crumple by the equation
energy = crumple_force * crumple_distance
you want to use the center-of-mass frame energy.
In the case of a car and a bridge abutment, typically this frame is almost exactly the same as the frame of the bridge abutment. And the energy of the bridge abutment in this frame is very close to zero, so the total energy is very close to .5*m_car*v_car^2.
Now, if you were running into a duck, the situation would be different. You would be more massive than the duck, and you'd get a good estimate of the energy of collision by using the car frame as a reference. in this case the energy would be just .5*m_duck*v_duck^2. Here v_duck is measured from the car frame, so it's the total relative velocity of the duck.
Intermediate cases are intermediate. If you were running into a stationary car of the same mass as yourself, you'd wind up with a center of mass frame that was exactly midway between your frame and the stationary car's frame.
This would "waste" about half the energy, which is good when you are colliding cars. Each car has an energy of .5*m*(v/2)^2, i.e. m*v^2/8, so the total energy of both cars in the center-of-mass frame is only m*v^2/4.
But if you were colliding particles, and wanted the energy to be as high as possible, because you spent a lot of money to build your tevatron, this would be bad. Here you'd want to arrange a head-on collision between two particles.
geometer
Sep18-04, 12:14 PM
Yes, you can treat acceleration in both SR and GR. The point everyone has been trying to make to OneEye is that acceleration is NOT relative. There is no experiment you make in a completely selfcontained room that will determine uniform velocity. You can determine acceleration. OneEye's original question was about turning which involves acceleration even if done at a constant speed.
Exactly! Thanks Halls, obviously I wasn't being too clear!
humanino
Sep18-04, 09:29 PM
Yes, thank you HallsofIvy. I was probably even less clear that you geometer. I was saying that, in the free fall referential coordinates, there is apparently no acceleration, and in any case, even non-uniform acceleration, the proper referential always make the acceleration disappear. That was really confusing in the context of this discussion, because of course this is not an inertial frame.
In the case of non-uniform acceleration, one can even find an inertial frame in which the acceleration disappear at a single point in spacetime. That was linked to an earlier discussion I had with Pete on GR, curvature and the (speculative but interesting) possibility that curvature does not encompass all gravitational effects, especially when topological defect play in the game. I should have been more careful in keeping my preoccupations out of the current discussion.
Thanks again every one.
... If one system is accelerating, even uniformly, with respect to another system it is no longer an inertial system, and you should be able to detect acclerations and thereby determine who is really moving. ...
I think not. Even though a thrusting event produces a sensation in the seat of the pilot's pants, it cannot be differentiated from a gravitational thing and so you are still technically unable to conclude "who is really moving". I find relativity easiest to understand when the observatory is always considered at rest. What power made the Earth and cosmos twist under your car? maybe just some fictitious force, especially considering that GR is full of such forces.
humanino
Sep19-04, 12:36 AM
Welcome in PF ostren !
It depends ! I agree with you, but we had several misunderstanding during the discussion !
I think geometer was answering the initial question in the context of SR, without gravitational phenomena.
russ_watters
Sep20-04, 09:55 AM
I think not. Even though a thrusting event produces a sensation in the seat of the pilot's pants, it cannot be differentiated from a gravitational thing and so you are still technically unable to conclude "who is really moving". Since you can correlate the sensation in your pants (eh....I'll let that one go) with the turning of the steering wheel and the front wheels of the car, you can certainly conclude you are the one accelerating. Same goes for a rocket - you push the "fire" button, hear the engine start, see the flame, and feel the acceleration, you know you are the one accelerating.
Well, you might know it's you who is accelerating, or you might equally presume you have encountered a gravitational field; but in either case, you will not be able to make the unequivocal determination that you are "truly in motion". That last was the only conclusion that I was countering.
geometer
Sep21-04, 09:56 AM
Well, you might know it's you who is accelerating, or you might equally presume you have encountered a gravitational field; but in either case, you will not be able to make the unequivocal determination that you are "truly in motion". That last was the only conclusion that I was countering.
That seems like a contradiction in terms - if you are accelerating, you must be moving. Can you give me an example of where you might be accelerating and not be moving?
That seems like a contradiction in terms - if you are accelerating, you must be moving. Can you give me an example of where you might be accelerating and not be moving?
Well, there is of course the obvious case of you being in deep intergalactic space and you feel a tug of acceleration, but it could just as readily be DEceleration that you are feeling... which leaves you stopped. But that doesn't answer the challenge well enough. The truth is that no object can categorically be deemed to be in absolute motion; only relative motion makes sense, for absolute motion implies an absolute preferred frame of reference, which has been shown to be pure myth. The relativistic explanation holds: any tug of acceleration felt could just as easily be a passing gravitational field, for no astute study of the behavior of light can betray otherwise.
geometer
Sep21-04, 12:35 PM
Well, there is of course the obvious case of you being in deep intergalactic space and you feel a tug of acceleration, but it could just as readily be DEceleration that you are feeling... which leaves you stopped. But that doesn't answer the challenge well enough. The truth is that no object can categorically be deemed to be in absolute motion; only relative motion makes sense, for absolute motion implies an absolute preferred frame of reference, which has been shown to be pure myth. The relativistic explanation holds: any tug of acceleration felt could just as easily be a passing gravitational field, for no astute study of the behavior of light can betray otherwise.
But, when I feel the tug of acceleration, I can now say I know I am moving. I am either speeding up or slowing down, but I am moving.
But, when I feel the tug of acceleration, I can now say I know I am moving. I am either speeding up or slowing down, but I am moving.
Are you? I think not. With respect to what reference are you moving? Unanswerable! The only answer is the relativistic one: there's no such thing as unequivocal motion. This is verified by light's behavior.
russ_watters
Sep21-04, 03:14 PM
Are you? I think not. With respect to what reference are you moving? Unanswerable! Wrong. If you feel acceleration that you know you caused (by hitting your engine fire button or turning your steering wheel), you can measure that acceleration and use it to calculate a change in velocity based on the assumption that you were at rest prior to the acceleration. Arbitary rest frame? Certainly, but thats Relativity!
humanino
Sep21-04, 04:31 PM
Wrong. If you feel acceleration that you know you caused (by hitting your engine fire button or turning your steering wheel), you can measure that acceleration and use it to calculate a change in velocity based on the assumption that you were at rest prior to the acceleration. Arbitary rest frame? Certainly, but thats Relativity!
Devil advocate :
Someone fastidious could say : how do you know this is not also due to a gravitational wave ? Not solely due to your engine ? Imagine you have been fooled all your life by a deamon sending the right gravitational wave at the right instant you turn the engine, so that you never noticed anything wrong in the calculations of fuel consumption...
geometer said, "If one system is accelerating, even uniformly, with respect to another system it is no longer an inertial system, and you should be able to detect acclerations and thereby determine who is really moving."
The word "really" in the above citation is all that I was countering. There's never much dispute about relative motion. :rolleyes:
geometer
Sep21-04, 10:11 PM
Devil advocate :
Someone fastidious could say : how do you know this is not also due to a gravitational wave ? Not solely due to your engine ? Imagine you have been fooled all your life by a deamon sending the right gravitational wave at the right instant you turn the engine, so that you never noticed anything wrong in the calculations of fuel consumption...
If the demon's acceleration is in the same direction as the engine, you just go faster, but if you burn the engine, you consume fuel. If the demon's acceleration is exactly equal to, but opposite that of the engine, you don't accelerate so the question is moot (but you still burn the fuel).
But, looking at the bigger picture, who cares what causes the acceleration? In fact, the whole point behind general relativity is that you can't differentiate between the accleration caused by a gravitational field and that created by any other mechanism.
If you are accelerating with respect to any other system you are no longer an inertial system and therefore you can in principle determine that you are moving.
..If you are accelerating with respect to any other system you are no longer an inertial system and therefore you can in principle determine that you are moving.
Moving with respect to what? You don't have to be a non-inertial system to determine that you are moving relative to another frame. So the felt tug of acceleration provides no qualitative enhancement to one's assumptions.
russ_watters
Sep22-04, 07:26 AM
Moving with respect to what? You don't have to be a non-inertial system to determine that you are moving relative to another frame. So the felt tug of acceleration provides no qualitative enhancement to one's assumptions. Haven't you ever heard of inertial navigation? A submarine keeps an accurate fix on its position by measuring acceleration alone. All that is needed is a starting point. For a submarine, the starting point is provided by GPS right before the sub surfaces, but it doesn't need to be. In open water maneuvering, it can simply be "where I was 5 minutes ago relative to where I am now." On the spaceship, you can throw an obect overboard right before you start accelerating to mark your position, but you don't need to - and even if you do throw an obect out, you don't ever need to look at it to come back to it later - you don't have to have a physical marker for your position to use it as a reference point.
Also, when doing collision avoidance, maneuvering, doing dead reckoning, etc. ships use a "where I started from" reference frame that isn't necessarily fixed to a position on earth. Its simply not necessary.
I read all of the last post and am unimpressed. Acceleration is not an unequivocal guarantee of motion, and certainly not absolute motion (ie. "through space") because there's no such thing. The topic is relativity, and how one navigates through a body of water is hardly on point.
So you toss something out of a spacecraft and then accelerate away and return to find your "landmark". NO WAY is that any indication that you actually and unequivocally moved "through space". It's a moot point. Maybe you and the landmark were already in motion, and the engine thrust merely decelerated your craft to a standstill while the landmark continued on its merry way by momentum. But it's all made academic by Relativity anyway, because there's no such thing as unequivocal motion "through space", because "space" is not a medium -- space is the absence of any medium.
humanino
Sep22-04, 10:04 AM
Russ-waters' argument does not really need any medium : as long as the gravitational field around is uniform, that would do.
russ_watters
Sep22-04, 10:14 AM
Nor do I say anything about "absolute motion." I agree there is no such thing. So what is the problem? It almost seems like you are saying that since motion is absolute, motion doesn't exist. But thats a contradiction. It does exist, and it is relative. So you toss something out of a spacecraft and then accelerate away and return to find your "landmark". NO WAY is that any indication that you actually and unequivocally moved "through space". You moved relative to your arbitrary landmark. No one is saying anything here about the implications for absolute motion - because there are none. All motion is relative - relative to whatever you choose. If I choose an arbitrary landmark, choose to call it "stationary" and then observe my distance to it to be increasing, then I am moving.
Nor do I say anything about "absolute motion." ... No one is saying anything here about the implications for absolute motion..
Please have a look at my post #42, this thread, wherein that is answered. YOU may not have been trying to assert anything about absolute motion, but in geometer's original post, there was that clear implication.
You may need to review more of the thread to get a handle on this: one can discern relative motion without dispute, but I refuted geometer's claim that acceleration leads one to conclude "who is really in motion".
russ_watters
Sep22-04, 11:28 AM
Please have a look at my post #42, this thread, wherein that is answered. YOU may not have been trying to assert anything about absolute motion, but in geometer's original post, there was that clear implication. This quote: geometer said, "If one system is accelerating, even uniformly, with respect to another system it is no longer an inertial system, and you should be able to detect acclerations and thereby determine who is really moving." This does not imply anything about absolute motion. "who is really moving" is talking about which of two objects is moving with respect to the other, not whether either is "moving" absolutely. I think you misunderstood.
Ie, if a spaceship tosses a marker over the side, then fires its engines, you can't say its the marker that's "really moving" (with respect to the spaceship) because its the spaceship, not the marker, thats undergoing acceleration.
You can't even say both were moving and the ship decelerated and is now stopped because you then need a 3rd reference point from which to declare the ship moving at the beginning.
... I think you misunderstood. ...you can't say its the marker that's "really moving" (with respect to the spaceship) because its the spaceship, not the marker, thats undergoing acceleration..
I misunderstood nothing. When geometer said, "If one system is accelerating, even uniformly, with respect to another system it is no longer an inertial system, and you should be able to detect acclerations and thereby determine who is really moving." But acceleration does nothing to differentiate "who is really moving". There's no such determination. There's no preferred frame! If one pilot fires his thrusters and thence feels a G-force, that's no indication what*so*ever as to which of two arbitrary frames "is really moving". They are each moving relative to one another and acceleration cannot qualify that any better.
geometer
Sep22-04, 12:22 PM
I misunderstood nothing. When geometer said, "If one system is accelerating, even uniformly, with respect to another system it is no longer an inertial system, and you should be able to detect acclerations and thereby determine who is really moving." But acceleration does nothing to differentiate "who is really moving". There's no such determination. There's no preferred frame! If one pilot fires his thrusters and thence feels a G-force, that's no indication what*so*ever as to which of two arbitrary frames "is really moving". They are each moving relative to one another and acceleration cannot qualify that any better.
I beg to differ ostren. You did misunderstand. Russ is right on. My point is that given two inertial coordinate systems, there is nothing you can do to tell which is moving relative to the other. However, as soon as one coordinate system experiences an acceleration, from whatever source, now you can tell who is moving with respect to whom. Accleration does differentiate which of two systems is moving with respect the other.
geometer
Sep22-04, 12:33 PM
You can locally make acceleration disappear by changing the referential. Only locally. The free-fall observer not noticing the Earth gravitational field has a limited spave around him, otherwise he would notice the spherical shape.
Jumping back a few posts, I'd like to make a comment on this post also. Acceleration is actually a tensor of order 1. One of the main properties of tensors is that if they are non-zero in any coordinate system, they are non-zero in all coordinate systems. So, you can't make acceleration disappear by changing the reference frame.
russ_watters
Sep22-04, 12:49 PM
ostren, if what you are saying were correct, there would be no possible resolution to Einstein's "twins paradox." You could accelerate a spaceship away from earth, claim earth is the one accelerating while the spaceship is stationary, have the spaceship turn around and come back to earth, and calculate that the clock on earth should have less elapsed time than the clock on the spaceship. But then you'd compare the clocks and find that its the clock on the spaceship that has less elapsed time.
And again, nothing in any of this has anything to do with absolute motion. You keep bringing it up, but it isn't what geometer meant and nothing I said implies it exists. Again, answering the question "who is really moving?" does not require an absolute frame of reference.
I have carefully read geometer's post #52 as well as Russ Watters' post #54 and I beg to differ with both. To geometer's claim that ..as soon as one coordinate system experiences an acceleration, from whatever source, now you can tell who is moving with respect to whom. Accleration does differentiate which of two systems is moving with respect the other.I say you are way wrong and I stand by my post #51 unaltered. And your latter sentence above makes no sense: because each is obviously moving with respect to the other -- it's not lop-sided.
And to Russ's claim that answering the question "who is really moving?" does not require an absolute frame of reference.I have to ask what in tarnation you mean by the qualifier "really"?? Ah! some motion is "real" and other motion "imaginary".. is that your contention?
As for violating the twin paradox, Russ, you've got it all wrong. The turnaround twin's acceleration doesn't mean that time dilation is his alone because he is the one who is 'really' moving. Ooh, there's that funny word again.
No, the twin paradox can be resolved even assuming that the astronaut twin is STOCK STILL in space the entire time! For example, at my website, Addendum IV.
kawikdx225
Sep22-04, 02:23 PM
I have carefully read geometer's post #52 as well as Russ Watters' post #54 and I beg to differ with both. To geometer's claim that I say you are way wrong and I stand by my post #51 unaltered. And your latter sentence above makes no sense: because each is obviously moving with respect to the other -- it's not lop-sided.
If you put an accelerometer on the space ship and another on earth you will find that it is "lop-sided" as the spaceship records acceleration and the earth does not.
kawikdx225: This is about "who is really moving", a phrase employed by geometer and echoed by russ_watters. This is not about who is realy experiencing a G-force.
geometer
Sep22-04, 03:36 PM
And to Russ's claim that I have to ask what in tarnation you mean by the qualifier "really"?? Ah! some motion is "real" and other motion "imaginary".. is that your contention?
I don't mean to speak for you Russ, but what I meant by "really" refers back to the post that started this thread. In that post, OneEye commented that it was equally valid to say his turning of his car's steering wheel caused the earth to turn as it was to say it caused his car to turn. He cited the equivalence prinicple from special relativity for this statement.
My comment was that by his turning of the steering wheel, he had introduced an acceleration into the picture, so the frame centered on and moving with his car was no longer an inertial frame and that the special relativity equivalence principle didn't apply any more. Further, since he felt the acceleration, it was possible for him to determine that it was actually he that was moving with respect to a frame stationary on the earth, and it was not the earth that was moving with respect to a frame centered on his car.
Thank you for the compromise, geometer, but I was only partly right, I think. The car's brakes or gas pedal would produce acceleration that can NOT be differentiated from gravitation by means of the local study of light. But any rotational motion, any spinning, that component I do believe is confirmed by light's behavior to be unambiguous.
geometer
Sep22-04, 05:43 PM
I think we still have a basic disagreement here ostren. Given a similar situation: If I am in my brand new Ferrari (hey, if we're going to pretend...) travelling down the freeway in a perfectly unaccelerated condition there is no way for me to tell whether I am moving with respect to the earth outside my window or whether the earth is moving and I am stationary. However, as soon as I step on the gas to pass Granny in her 57 Chevy I have introduced an acceleration into the picture and I can determine who is stationary with respect to whom.
It doesn't matter that I can't tell if the acceleration is due to gravity or to my pushing on the gas pedal; all accelerations produce equivalent effects. But, it does destroy my inertial status and enable me to differentiate the frame moving with me from any other inertial frame.
... as soon as I step on the gas .. I have introduced an acceleration into the picture and I can determine who is stationary with respect to whom.
.. it does destroy my inertial status and enable me to differentiate the frame moving with me from any other inertial frame.
Differentiate Ok, but NOT deduce anything of stationary (your word) versus moving. Please use scenarios in deep intergalactic space to make your point, and you'll see that it doesn't play, this "stationary" discernment of which you speak -- or that "really in motion" discernment of which you earlier spoke.
geometer says, " However, as soon as I step on the gas to pass Granny in her 57 Chevy I have introduced an acceleration into the picture and I can determine who is stationary with respect to whom."
Nothing could be further from the truth. Einstein would certainly concur. You see, the very definition of acceleration requires that if A is accelerating with respect to B, then B is accelerating with respect to A. Acceleration is, of course, the second time derivative of displacement, which is necessarily relative.
But, the asymmetry that lurks around this issue can be distrurbing. Not so ,with the car. The force that actually accelerates the 57 Chevy is equally and oppositely accelerating the earth -- no way to tell who is on a special frame.
But, what about , say, a train and a car. In an observer's frame the train is in uniform motion, and the car accelerates. Clearly the car exerts no discernable force on the train. So if the car accelerates with repect to the train, where does the force come from to accelerate the train relative to the car? In fact such a force is frame dependent, much like a Corioulis(sp?) force. It's derived by using the coordinate transformation that brings the car to rest. When applied to the motion of the train, the time derivative of momentum brings in extra terms, some times called fictitious forces, which mimic the force necessary to give the train the proper acceleration in the rest frame of the car. Space invents the necessary force in order to keep the notion of motion strictly relative.
In other words, the very structure of space-time of physics completely precludes anything but pure, relative motion.
Regards,
Reilly Atkinson
geometer
Sep23-04, 09:44 AM
Differentiate Ok, but NOT deduce anything of stationary (your word) versus moving. Please use scenarios in deep intergalactic space to make your point, and you'll see that it doesn't play, this "stationary" discernment of which you speak -- or that "really in motion" discernment of which you earlier spoke.
OK. Scenario 1. Consider two spaceships in deep space alongside each other, close enough that they can see each other. Initially, they are stationary with respect to each other. We note that "stationary with respect to each other" means that with respect to a third observer, they could be not moving with respect to each other or they could be moving with the same velocity with respect to each other. In this case, observers in the spaceships will not be able to tell if any motion is occurring.
Now, let's assume one of the spaceships experiences an acceleration, say from a programmed rocket firing. Now, an observer in that spaceship could detect that acceleration and from that information deduce that he/she is now in motion with respect to the other space ship.
Scenario 2. Now we assume only one spaceship in deep space. We further assume this spaceship represents an inertial frame. Under these conditions, an observer in that spaceship will not be able to tell if she/he is in motion or is stationary with respect to any other frame of reference. Now, assume that this spaceship experiences an acceleration. Again, the observer in the spaceship will be able to detect the acceleration and can deduce that he/she is in motion with respect to some other inertial frame. The spaceship might be speeding up, slowing down or turning, I'm not sure the observer aboard that ship could tell which, but she/he can tell some kind of motion is occurring.
Note that the key to these scenarios is that an observer in an isolated lab can detect accelerations. I find support for this statement in "Concepts of Modern Physics, Fourth Edition," by Arthur Beiser, where he states "The general theory of relativity, developed by Einstein a decade later, treats problems that involve frames of reference accelerated with respect to one another. An observer in an isolated lab can detect accelerations."
The fact that you can uambiguously determine, in non-inertial conditions, the state of motion of one frame with respect to another does not imply the existence of a preferred frame. The laws of physics are the same in any frame you care to examine. (the Strong Equivalence Principle).
russ_watters
Sep23-04, 10:53 AM
Differentiate Ok, but NOT deduce anything of stationary (your word) versus moving. Please use scenarios in deep intergalactic space to make your point, and you'll see that it doesn't play, this "stationary" discernment of which you speak -- or that "really in motion" discernment of which you earlier spoke. :confused: If I fire my engine and I start to feel an acceleration, and I check an accelerometer on the marker I just dropped off my ship and see that it is not accelerating, I most certainly can deduce several things:
-There is no gravity field affecting these results (I consider it unreasonable to assume a gravity field coincidentally appeared at the instant I fired my rocket).
-I am accelerating, the marker is not.
-I am moving with respect to the marker, not the other way around.
Certainly, there are a lot of calculations that work fine assuming either to be accelerating (calculating the distance, for example), but not every one makes sense that way. I have to ask what in tarnation you mean by the qualifier "really"?? Ah! some motion is "real" and other motion "imaginary".. is that your contention? How many times do I have to say this before you accept it? All motion is relative. The words "real" and "imaginary" have nothing to do with anything.
Heck, I'm not even saying that you can't consider either stationary in your calculations, if you want to be pedantic. But it makes for much more complicated calculations since you now have to add forces that didn't exist before: to consider the marker to be moving and the spaceship stationary, you need add arbitrary forces to both. You need to add a force that cancels the force of the rocket while accelerating the marker: for example, a planet materializing out of nowhere at the exact instant the rocket started firing. Of course, if you do that, you have just added a 3rd reference frame with which to define the rocket as stationary... No, the twin paradox can be resolved even assuming that the astronaut twin is STOCK STILL in space the entire time! For example, at my website, Addendum IV. Is your explanation the same as Einstein's?The force that actually accelerates the 57 Chevy is equally and oppositely accelerating the earth -- no way to tell who is on a special frame. Minor nitpick, reilly - the force is equal and opposite, the acceleration is not. f=ma, and the Earth is a lot more "m" than that '57 chevy. Its good to bring us back to that example though: in the rocket example, the force of the engine acts on the rocket alone and a gravitational pull would act on the rocket and marker proportionally. In the car example, you have only one force and it violates f=ma to say that its the earth that is accelerated due to that force alone.
russ_watters
Sep23-04, 11:15 AM
Let me try my point another way:
If you have 2 objects and the distance between them is changing, you can reasonably say that either is "moving."
If the rate of that change in disance is changing, you can reasonably say that either is "accelerating"
If a force is measured between the two objects, it is now unreasonable to choose one of them arbitrarily and say it is accelerating and the other is not.
In the car example, a force exists and is measurable that cannot cause the measured acceleration of the earth.
humanino
Sep23-04, 11:25 AM
If you have 2 objects and the distance between them is changing, you can reasonably say that either is "moving."
Un less the space between them is expanding...
kawikdx225
Sep23-04, 12:04 PM
But, the asymmetry that lurks around this issue can be distrurbing. Not so ,with the car. The force that actually accelerates the 57 Chevy is equally and oppositely accelerating the earth -- no way to tell who is on a special frame.
You say there is no way to tell who is on a special frame. If this is true I could do a physics experiment in the accelerating car and on the earth and the results would be identical. This is not true.
Lets try another thought experiment.
Two cars are sitting at a red light.
Granny in her 57 Chevy and some punk kid in a hotrod.
Each car has a passenger that is tossing a quarter in the air then catching it.
When the light turns green the kid in the hodrod hits the throttle but granny fell asleep.
The passenger in granny's car notices no change in his physics experiment (tossing and catching the quarter) but the passenger in the hotrod must now make a correction to catch his quarter.
OK. Scenario 1. Consider two spaceships in deep space alongside each other, close enough that they can see each other. Initially, they are stationary with respect to each other. We note that "stationary with respect to each other" means that with respect to a third observer, they could be not moving with respect to each other or they could be moving with the same velocity with respect to each other. In this case, observers in the spaceships will not be able to tell if any motion is occurring.
Now, let's assume one of the spaceships experiences an acceleration, say from a programmed rocket firing. Now, an observer in that spaceship could detect that acceleration and from that information deduce that he/she is now in motion with respect to the other space ship.Any such deduction is nonsequitor. Perhaps the deducer doesn't understand relativity. If he is now in motion with respect to the other ship, then the other ship is equally in motion with respect to his own. Per relativity, it is proper to attribute the G-force (of acceleration) to an unusual passing gravitational field. That may sound whacky, but it makes computations easier. You cannot ascribe relative motion to be lop-sided. The motion between the two ships is relative and utterly mutual.
2. Now we assume only one spaceship in deep space. We further assume this spaceship represents an inertial frame. Under these conditions, an observer in that spaceship will not be able to tell if she/he is in motion or is stationary with respect to any other frame of reference. Now, assume that this spaceship experiences an acceleration. Again, the observer in the spaceship will be able to detect the acceleration and can deduce that he/she is in motion with respect to some other inertial frame. The spaceship might be speeding up, slowing down or turning, I'm not sure the observer aboard that ship could tell which, but she/he can tell some kind of motion is occurring.
No he cannot determine unequivocal motion because there is no unequivocal 'background' frame with respect to which he could say he is moving. Sorry, but that's the essence of relativty.
You started all this bickering by using the phrase, "can determine who is really moving", which doesn't fly because there's no viable definition of the word "really" in that phrase.
You saw the post by Reilly Atkinson, and he seconds my opinion. He is obviously more credentialed than I am.
pervect
Sep23-04, 12:17 PM
Let me try my point another way:
If you have 2 objects and the distance between them is changing, you can reasonably say that either is "moving."
If the rate of that change in disance is changing, you can reasonably say that either is "accelerating"
If a force is measured between the two objects, it is now unreasonable to choose one of them arbitrarily and say it is accelerating and the other is not.
In the car example, a force exists and is measurable that cannot cause the measured acceleration of the earth.
The way I see it, the existence of a force between the objects isn't really the issue - the issue is the application of Newton's laws.. One is perfectly free to adopt any coordinate system one wants - but one should not expect Newton's laws to work in such an arbitrary coordinate system. Measuring a force or forces between the objects isn't the big issue here, IMO, the big issue is applying the formula f=ma.
As others have pointed out, an observer can tell whether or not f=ma "works" for them just by doing local experiments, this can be done without thinking about the forces between the two bodies.
geometer
Sep23-04, 12:18 PM
Granny in her 57 Chevy and some punk kid in a hotrod.
Are you calling me a punk kid? :biggrin:
geometer
Sep23-04, 12:23 PM
As others have pointed out, an observer can tell whether or not f=ma "works" for them just by doing local experiments, this can be done without thinking about the forces between the two bodies.
This is my point pervect. Since I can detect acclerations in my frame, I can therefore apply f=ma in my frame and conclude that I am moving. It may be difficult for me to tell if I am speeding up, or slowing down or turning depending on what other data I have available, but I can tell I am moving.
Depending on what data I have about the acceleration it may also be impossible for me to tell if I have suddenly encountered a gravitational field or the acceleration came from another source
:confused: If I fire my engine and I start to feel an acceleration, and I check an accelerometer on the marker I just dropped off my ship and see that it is not accelerating, I most certainly can deduce several things:
-There is no gravity field affecting these results (I consider it unreasonable to assume a gravity field coincidentally appeared at the instant I fired my rocket).YOU consider it "unreasonable", yet relativists consider it not only reasonable, but necessary.-I am accelerating, the marker is not.
-I am moving with respect to the marker, not the other way around.No, the motion is perfectly mutual. You are drifting back into pre-relativity recidivism.How many times do I have to say this before you accept it? All motion is relative. The words "real" and "imaginary" have nothing to do with anything. Right... so you shouldn't go around saying things like in your post #50 "who is really moving" is talking about which of two objects is moving with respect to the otherThere's no "which" to it; the motion is mutual!
And you shouldn't go around saying things like in your post #54
answering the question "who is really moving?" does not require an absolute frame of reference.There's no "really" to it; whaddya mean by that silly word?
Is your explanation the same as Einstein's?Refering to my website Addendum IV -- yes, it's the same as Einstein's.
You say there is no way to tell who is on a special frame. If this is true I could do a physics experiment in the accelerating car and on the earth and the results would be identical. This is not true.
Lets try another thought experiment.
Two cars are sitting at a red light.
Granny in her 57 Chevy and some punk kid in a hotrod.
Each car has a passenger that is tossing a quarter in the air then catching it.
When the light turns green the kid in the hodrod hits the throttle but granny fell asleep.
The passenger in granny's car notices no change in his physics experiment (tossing and catching the quarter) but the passenger in the hotrod must now make a correction to catch his quarter.In the hotrod, the quarter is tugged toward the rear. But the driver feels a tug toward the rear as well. And if you carefully examined a ray of light moving transverse to the road, it would appear to the hotrod's occupants to be tugged in that very same direction. So YES, there is asymmetry, but it is perfectly consistent with the presence of a gravitational field. Under relativity, you must ascribe the asymmetry to gravity, rather than claim someone is "really" in motion. I would have to think much too hard to tell you why... perhaps it's because a claim of unequivocal "motion" entails too too many confusing ramifications.
kawikdx225
Sep23-04, 02:44 PM
In the hotrod, the quarter is tugged toward the rear. But the driver feels a tug toward the rear as well. And if you carefully examined a ray of light moving transverse to the road, it would appear to the hotrod's occupants to be tugged in that very same direction. So YES, there is asymmetry, but it is perfectly consistent with the presence of a gravitational field. Under relativity, you must ascribe the asymmetry to gravity, rather than claim someone is "really" in motion. I would have to think much too hard to tell you why... perhaps it's because a claim of unequivocal "motion" entails too too many confusing ramifications.
hmmmm... brain hurting!
Well if what you say is true then (as Russ said) the twin paradox would not be a paradox and both twins would be the same age after the trip. This disagrees with Einstein. Or am I missing something.
Here's what I think I know.
"I am really moving" is a meaningless statement
"I am really moving with respect to" is valid
"I am really accelerating" is valid
motion is relative
acceleration is absolute
geometer:
lol, no. just tryin to keep it colorful.
... Well if what you say is true then (as Russ said) the twin paradox would not be a paradox and both twins would be the same age after the trip. This disagrees with Einstein. Or am I missing something.Thanks for keeping it colorful!
What you're probably missing about the Twin paradox is that the Lorentz tranform mandates more than just length contraction and time dilation (each of which is direction independent), but also a third element, that of time dissynchronicity, which is direction dependent. Actually there are a handful of adequate resolutions of the Twin Paradox, but of course none of them could be based on the astronaut twin being really*truly the one in motion. Didn't you check out my version yet?
... Minor nitpick, reilly - the force is equal and opposite, the acceleration is not. f=ma, and the Earth is a lot more "m" than that '57 chevy. Its good to bring us back to that example though: in the rocket example, the force of the engine acts on the rocket alone and a gravitational pull would act on the rocket and marker proportionally. ..
That's directed to Reilly but I wish to venture this contribution. The gravitational potential gradient that mysteriously arises is precisely of such steepness as to stall your rocket -- ie. counter the engine thrust -- and accelerate the marker just so, as it is thence perceived to travel. It may be helpful to recall that the deflections/trajectories caused by gravity acting on an object do not depend on that object's MASS. Tower of Pisa, y'know?
geometer
Sep23-04, 04:49 PM
We seem to be really hung up on the word really. What I really meant to really say was that in OneEye's original example he could conclude that he was moving with respect to the earth and not vice-versa.
Ok Ostren - let's assume we are in a totally isolated laboratory in deep space, initially in an inertial condition. This laboratory has no visual communication with the space outside, and is empty except for you, me and an acclerometer of some kind. We now experience an acceleration (let's assume it's due to a preprogrammed rocket firing just for definiteness). What can we now conclude about our state of motion?
geometer
Sep23-04, 05:31 PM
*** Nada ***
Why can I not apply f = ma and conclude that I am moving?
pervect
Sep23-04, 09:06 PM
We seem to be really hung up on the word really.
Yep. And the word "truly" too.
What I really meant to really say was that in OneEye's original example he could conclude that he was moving with respect to the earth and not vice-versa.
Really and truly? :-)
It seems to me that this thread has been about 50% arguing over semantics, and the other 50% over philosophy. I think everyone knows what happens next in all of the examples given, it's just a big argument about how to describe it.
Why can I not apply f = ma and conclude that I am moving?I think that it may be because then relativity would not be such an elegant and consummate theory of physics. Even if you apply f=ma, as I said earlier that might only indicate that you are DEcelerating (to a stop?). There is too much ambiguity and yet if you stick to the application of relativity's Equivalence Principle, then nothing is left to be ambiguous. This is my best quick reply although perhaps a bit wanting :-)
HallsofIvy
Sep24-04, 07:19 AM
Why can I not apply f = ma and conclude that I am moving?
You could apply f= ma and conclude (if f is not 0) that you are accelerating. The point is (and goes back to "Galilean Relativity") that force (which what you "feel") is proportional to acceleration, not velocity so you couldn't use that to determine your velocity- or even whether it is 0 or not.
It was the discovery that eletro-magnetic field DO depend on velocity rather than acceleration that led to the idea that we could use some sort of electro-magnetic experiments (i.e. light) to determine and "absolute" velocity. Relativity developed out of the fact that those experiments still didn't find anything!
kawikdx225
Sep24-04, 11:52 AM
I dont think anyone was saying that you could determine your absolute velocity by studying your acceleration.
The argument is that if you know for a fact that you are accelerating (by use of an accelerometer) then doesn't that imply you are moving. Since acceleration is by defination a "change in velocity with respect to time" meter/second2 ?
In other words, how can you accelerate if you are not moving? Granted you dont know how fast your velocity is or if you are speeding up or slowing down or just turning in a circle but you are moving.
selfAdjoint
Sep24-04, 05:04 PM
You stomp on the gas and feel that push in your back. Must be moving! You look out the window and the telephone poles are standing still. Whaaaat?
You're driving on an endless belt that your spinning wheels drive backwards. Or, make up your own explanation. Acceleration does not always produce motion.
geometer
Sep24-04, 06:15 PM
You stomp on the gas and feel that push in your back. Must be moving! You look out the window and the telephone poles are standing still. Whaaaat?
You're driving on an endless belt that your spinning wheels drive backwards. Or, make up your own explanation. Acceleration does not always produce motion.
Wait a minute! In this case you haven't accelerated yourself. You've acclerated the belt so you wouldn't detect the accleration. And, this acceleration did produce motion - it increased the rate at which the belt moves underneath you.
selfAdjoint
Sep24-04, 07:34 PM
But the belt is running friction free on a planetoid that JUST HAPPENS to be rotating in the opposite direction.
The point, as I indicated, isn't the particular mechanism, but the general principle that the push you feel or don't feel has nothing to do, in and of itself alone, with how you are or are not moving. You have to look at the larger picture, or make reasonable assumptions like the designers of inertial guidance systems.
kawikdx225
Sep24-04, 07:52 PM
But the belt is running friction free on a planetoid that JUST HAPPENS to be rotating in the opposite direction.
The point, as I indicated, isn't the particular mechanism, but the general principle that the push you feel or don't feel has nothing to do, in and of itself alone, with how you are or are not moving. You have to look at the larger picture, or make reasonable assumptions like the designers of inertial guidance systems.
geometer is right.
In your thought experiment an accelerometer in the car would measure 0 meters/second2 therefore you are not accelerating.
Anytime your accelerometer reads 0 m/s2you cannot say"I am in motion" you must say "I am in motion relative to".
Anytime your accelerometer reads anything other than 0 m/s2 you can say "I am in motion but I have no idea how fast or in which direction"
Kudos to geometer & kawikdx225 for finding selfAdjoint's error. The driver would NOT feel any push in his back in that scenario.
geometer
Sep26-04, 02:22 PM
Seems like we have kind of run out of steam here, but it's been a great discussion and I think, has sharpened my thinking on this. Thanks!
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