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B How can we tell that "fictitious forces" are not real?

  1. Apr 25, 2016 #1
    Earlier today I was reading through this entire thread:
    And I remained confused about one thing in particular. The original poster made a statement (bolded below) on page 1 that seemed intuitive to me, and it seemed like the other posters never did sufficiently engage with it and explain why it was mistaken:


    >"An accelerometer is a device that measures proper acceleration."
    >>"This is an inference."

    >"Conceptually, an accelerometer behaves as a damped mass on a spring. When the accelerometer experiences an acceleration, the mass is displaced to the point that the spring is able to accelerate the mass at the same rate as the casing. The displacement is then measured to give the acceleration."
    >>"Again, the bold text is an inference. Einstein interprets the behavior of the instrument in two ways. Observed from the inertial reference frame, it is indeed acceleration that causes the displacement and counteracting force. Observed from the non-inertial frame, it is a gravitational field and the forcible restraint from acceleration that displaces the mechanism. There is no acceleration in the non-inertial frame, according to Einstein's interpretation."


    Basically, my question is this: how do we know that an accelerometer is measuring proper acceleration? How do we know that fictitious forces are not real forces? This is not meant to try to debunk relativity. I am just having a hard time grasping how we can be so confident about detecting absolute acceleration.

    Imagine that you have lived in a windowless space station your entire life (with internal power sources to provide lighting to grow plants, etc.). For all of your life, you have freely floated with the space station. Any relative motion with the walls of the space station had to come from the work of your limbs against the walls of the space station, in your experience. That's all you know so far.

    Imagine that, one day, you notice the entire space station shift in relative motion with respect to you after you were just freely floating in mid-air, and you feel yourself pushed against one side of the interior of the space station for one minute. Then, after that minute, the apparent "force" stops, and you feel yourself freely floating again.

    You are just a lowly space station janitor, so you know nothing about any sort of rocket propulsion with which the space station might be equipped. All you know is, one minute there was this change in relative motion and, even after this relative motion stopped once you made contact with the side of the space station, this apparent "force" that continued to push you against one of the sides of the space station with considerable force, and then the next minute it stopped.

    In this scenario, should such a person be able to deduce with the information on hand that the apparent force was a fictitious force and that, in reality, it was the space station that was undergoing proper acceleration? Could such a person be able to rule out the idea that they themselves were the ones that initiated the relative motion, and the space station was merely resisting their progress? Would the person need any more information in order to figure this out? If the latter, then what additional information would that person need?

    Does the person need to know about the rocket engine? Does the person need to be able to look at the fixed stars and measure a change in relative velocity with the fixed stars in order to deduce that it was the space station undergoing proper acceleration, and not the person themselves? To be sure, an accelerometer attached to the space station would show tension in the springs. However, how do we know that it is not the springs themselves that are flexing and moving the internal bits of the accelerometer (or however an accelerometer works), rather than a force acting on the accelerometer?
  2. jcsd
  3. Apr 25, 2016 #2


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    Per definition.

    Also per definition.
  4. Apr 25, 2016 #3


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    By definition. Proper acceleration is what an accelerometer measures. But "accelerometer" might seem too abstract, so let me substitute a more concrete word: weight. Proper acceleration means you feel weight.

    Because objects that are subjected only to fictitious forces are weightless. And in GR, we treat the force of gravity as a fictitious force, because objects moving solely under gravity are weightless.

    No, because the apparent force was not a fictitious force. For the minute that the wall of the station was pushing on the janitor, he felt weight; he was not weightless. So he was undergoing proper acceleration.

    Yes, because he only felt weight while the station wall was pushing on him. If he had initiated the motion--say he had his own rocket pack strapped to his back for example--he would feel weight as soon as he initiated the motion himself (as soon as he turned on the rocket pack).

    No. See above.

    When we talk about the station as a whole, it is initiating its own motion--when the station's rocket engine turns on, the accelerometer reads nonzero; when the engine turns off, the accelerometer reads zero again. So it can't be something in the springs, because then it wouldn't be correlated with the state of the rocket engine.
  5. Apr 25, 2016 #4
    Ah, so it has to do with weight. Thanks for the explanations, it makes sense!

    So, in the twin paradox experiment, the twins start out inertial, which relative motion between each other of 0 km/sec. When the experiment begins and one is on a non-firing rocket and the other is on a rocket that is firing, both twins can agree on which twin was the accelerating twin and which was not by seeing which twin felt weight. So, both twins can agree on which twin, in effect, "caused" the relative motion between them to change from 0km/sec to 10,000 km/sec or whatever it is. One twin can honestly say, "My relative motion is now different from yours, but it is not because of anything I did. I have not changed my rate of movement. Our increased relative motion between us is because YOU started increasing the relative motion between us with the firing of your rocket. How can I tell? You reported feeling weight, and I did not. Your accelerometer detected weight, and mine did not."

    Let's think about another thought experiment: what if some alien civilization had (improbably) managed to outfit every detectable piece of matter in our observable universe with rockets all pointing in the same direction, and they activated these rockets at such a time in the past that information of their activation would converge upon our twins at just the moment when the one twin chose to fire his rocket.

    Even in this case, where it appears that the twin with the non-firing rocket is the "odd man out" in the universe (where everything else seems to be changing its relative motion compared to him—the distant masses in one direction, and their rocket exhaust in the other direction), he could still say, "Everything else is accelerating. I am not accelerating because I do not feel any weight. You other twin, even though it might look like you are just drifting with the rest of the universe, are in fact accelerating."

    I don't see, then, why the "fixed stars" would have anything to do with defining proper acceleration, as Ernst Mach (as I understand it) seemed to think. You could give the whole rest of the observable universe (aside from all of the combined rocket exhaust, which would be traveling in the opposite direction) a certain preferential direction, and it would not change the conditions under which a person would feel proper acceleration.

    Instead, it sounds like the "need" for proper acceleration falls right out of the fact that inertia as a thing exists. Inertia is pretty weird. It's like mass kind of "remembers" (I know I'm anthropomorphizing, but I can't help it) its motion from one moment to the next. Or rather, the universe "keeps track" of how much motion a mass has from one moment to the next. And any change in this motion registers as proper acceleration. And this change in motion has to be a proper change in motion, not just a relative change in motion, because everything else in the universe accelerating with respect to something will still not make that thing feel a weight and undergo a proper acceleration.

    So, in order to have inertia and proper acceleration, you also need a concept of proper motion? That is, for each thing in its own reference frame, there is a physically real (not just coordinate-dependent) measure of motion that is not relative, but rather is absolutely defined against its current motion? Wait, WHAT? Have I gone astray somewhere?

    Edit: Maybe the concept of "proper motion" that I'm searching for is actually "proper velocity" or "celerity"? I'm reading up on it now to see if this is same thing as I was talking about.
  6. Apr 25, 2016 #5


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    Yes, that whole thought is incorrect. There is no such thing as a measure of motion that is not relative, but you don't need such to explain acceleration (I've never heard the term "proper acceleration"), as has been explained to you already.
    Last edited: Apr 25, 2016
  7. Apr 25, 2016 #6
    If the entire universe were to accelerate rotationally, with you at the center of rotation, you would feel the effects the same as if your spaceship were spinning around. You and everything inside would be pushed to the walls by a “fictitious” force, and hence you would feel proper acceleration due to Mach’s principle.

    I think it's alright to think of it that way.

    Not really. You can change your inertia/motion without proper acceleration. For example if your spaceship is in space and gets a gravitational slingshot while passing by a planet.
  8. Apr 25, 2016 #7


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    Yes. But note that the general rule this leads you to, that the twin that felt weight is the one that will end up aging less, only works for sure in flat spacetime, i.e., with no gravity present. In the presence of gravity, that rule no longer works all the time; there are scenarios where the twin that feels weight ends up aging more, not less. And there are also scenarios where neither twin ever feels weight, but they end up aging differently.

    As long as you assume that the rest of the matter in the universe has no mass, and therefore no gravity, this reasoning works. But of course the assumption is not valid. See below.

    Because the matter in the universe has mass (more precisely, stress-energy), and therefore it affects the spacetime geometry of the universe. And the spacetime geometry of the universe determines what the free-falling, weightless states of motion are. To put it another way, the spacetime geometry of the universe determines how you will move if you do nothing to give yourself weight--no rocket firing, no pushing off of anything, just floating in free fall. But that is equivalent to determining which states of motion will cause you to feel weight.

    Yes, it would, because it would change the spacetime geometry of the universe. See above.

    This is one way of thinking of the effect of spacetime geometry, yes.

    But this part is not correct. See above.

    No. Motion is still relative. More precisely, at any given point in spacetime, there are an infinite number of possible states of motion that are weightless. These states form a six-parameter group: the six parameters of a local Lorentz transformation (roughly, three parameters to choose a direction in space, and three parameters to choose a relative velocity). All of these states of weightless motion are equivalent--at any given instant, there is no way to tell that one observer is "really moving" while another is "really at rest". The only thing that is absolute is proper acceleration, i.e., weight; but if one observer feels weight and another does not, that only means the first is changing his state of motion; it doesn't say whether the change is "starting to move from rest" or "coming to rest from moving". The motion itself is still relative.

    It isn't. It's a concept worth learning about, but it isn't "absolute motion" or anything like it. It's still relative.
  9. Apr 25, 2016 #8


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    This is not a "change in motion" by the definition we are using in this discussion (which is also the definition used in GR). Objects moving solely under gravity are weightless, and follow geodesic paths in spacetime. These are the paths of "unchanging motion" in a curved spacetime geometry.
  10. Apr 26, 2016 #9
    Let’s say a spaceship is heading from the earth towards the star Procyon. What I meant was that we can introduce a gravitational effect such that the ship's path will be changed to head towards Aldebaran instead of Procyon, without proper acceleration. What would be a better way to say this rather than a change in motion/inertia?
  11. Apr 26, 2016 #10


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    Change in global direction through space.
  12. Apr 26, 2016 #11
    "If the entire universe were to accelerate rotationally, with you at the center of rotation, you would feel the effects the same as if your spaceship were spinning around. You and everything inside would be pushed to the walls by a “fictitious” force, and hence you would feel proper acceleration due to Mach’s principle."

    But I thought that the previous example I used established exactly the opposite—that I would still not feel a proper acceleration, even if the entire universe started rotating around me. That's what I meant by my surprise at the fact that proper acceleration is absolute rather than relative. It intuitively clashes with the rest of relativity. Mach's principle would seem to intuitively follow from the rest of relativity, but apparently it is wrong. (What I mean by Mach's principle is that that proper acceleration and the experience of weight would be determined by relative acceleration—a sort of "majority vote" on whether you were changing your motion based on how everything else in the universe was on average changing its motion). But the previous posters shot that down and reaffirmed that proper acceleration is absolute. It has nothing to do with comparison with how anything else is moving. It depends on a force acting to move something from a free-falling geodesic, which will produce an experience of weight on that object. Therefore, that observer or object requires no information about what the rest of the universe is doing to determine whether that observer or object will undergo proper acceleration and feel a weight. In other words, Mach's principle (as I understand it) is wrong. That's what the windowless space station established, I thought.

    "The only thing that is absolute is proper acceleration, i.e., weight; but if one observer feels weight and another does not, that only means the first is changing his state of motion; it doesn't say whether the change is "starting to move from rest" or "coming to rest from moving". The motion itself is still relative."

    Yes, I get that the object's motion with respect to everything else is still relative. But how could its motion still be relative compared to what it was before if there was a change in motion? By definition, a change in motion means that there is an absolute difference between its prior motion and its new motion. So, you still couldn't assign that new motion an "absolute magnitude" in a universal sense, but you should be able to say that, whatever it is, it is different from the prior motion, right? So, if you assign your coordinates such that the prior motion registers as 0 km/sec, the new motion of that thing after proper acceleration will be non-zero km/sec in those same coordinates, right? In other words, there has been an absolute change. From what I gather, the principle of relativity DOESN'T mean that you could, using a consistent set of coordinates, say that an object was at rest (inertia), then had a proper acceleration, and then is later on still at rest (inertial). Using a consistent set of coordinates, you have to conclude that at one time or the other, the object that experienced proper acceleration is not really moving with the same motion as before, right?
  13. Apr 26, 2016 #12


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    @Comradez, please learn to use the quote button
  14. Apr 26, 2016 #13


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    I can't answer all your questions, not least because I don't really understand them. But, I'll make one point: you need to be careful interpreting "all motion is relative" or "there's no such thing as absolute motion". What it really means is that you cannot assign an absolute, definitive value to an object's velocity. If an object is at rest in one reference frame, it is automatically moving in another reference frame, and moving with a different velocity in yet another frame.

    If an object starts at rest (in an inertial reference frame), accelerates and is then moving at 10m/s, say, in that reference frame, then (in any inertial reference frame) it must have been moving at some stage. In that sense, a period of acceleration represents "absolute" motion. But, at no time can you assign an absolute value to its velocity. At no time can you say that the object was absolutely at rest.

    All this about the rest of the universe rotating and Mach's principle is just making things more complicated than need be.
  15. Apr 26, 2016 #14


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    This is a mlsleading way of putting it, unless you are talking about moving planets and stars around.

    Change in the geometry of spacetime.
  16. Apr 26, 2016 #15


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    No, that's not what we said. The spacetime geometry in your vicinity determines what states of motion are weightless and what states of motion are not. And the spacetime geometry in your vicinity is determined by the distribution of stress-energy in the rest of the universe. So information about the spacetime geometry in your vicinity is information about what the rest of the universe is doing. This is how GR implements Mach's Principle.

    I didn't say changes in motion--proper acceleration--were relative. I only said motion was relative. If you read my post further, you will see that I said:

    In other words, if you change your state of motion by undergoing proper acceleration, there is no way to say whether you were "at rest" first and then started moving, or were "moving" first and then came to rest. Both of your states of motion, before and after the proper acceleration, are relative since neither one can be said to be "moving" or "at rest" in any absolute sense. But you can say that you changed your state of motion in an absolute sense, because you felt weight, and the feeling of weight is not relative.
  17. Apr 26, 2016 #16
    Okay, yes, this makes sense to me.
  18. Apr 26, 2016 #17
    This is a long running misconception. The twin paradox in principle has nothing whatsoever to do with the twins' relative motion (search the forum for "differential aging"). The "twins" could equally well complete their journeys (or lack of!) a week apart.
  19. Apr 27, 2016 #18
    Nothing I said was meant to be misleading.

    No, unless you mean in addition to moving planets and stars around you also include moons, asteroids with rockets attached to them, very large rocks, Saturn V rockets with very heavy payloads, anything with mass, and Lake Baikal.
  20. Apr 27, 2016 #19


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    I didn't say you meant to be misleading; one can be misleading without meaning to. See below.

    I'm not sure whether you are missing my point or not. My point was that you can't "introduce a gravitational effect" without changing the arrangement of gravitational sources, and changing the arrangement of gravitational sources changes the geometry of spacetime. So you aren't changing the motion/inertia of the test object; it is still moving on a geodesic path. But you changed the geometry of spacetime, so you changed which paths are geodesic paths and which are not.
  21. Apr 28, 2016 #20
    This is incomplete. Change in global direction of what through space, velocity?
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