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Thread: Jerk or impulse limits

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    Jerk or impulse limits

    I am starting this thread because of a question in my mind arising from relativity and acceleration which has been explored in another thread. I have come across jerk and impulse in engineering contexts where unexpected things happen. Jerk is the name for rate Of change of acceleration.

    Impulse is force times time and, like jerk, has engineering applications in impacts and explosions. Both the speed of sound in a material and the speed of shockwaves in a material become relevant in engineering applications.

    But are there interesting limits to the size of a jerk or the time of an impulse which are more fundamental at the atomic or fundamental particle level. when a nuclear fission ejects a neutron, for example, it is accelerated for a very short time. Is there a theoretical limit to that acceleration And jerk just as there is a limit to the speed of light?

    I asked this question because I still have in mind the recent experiments where quantum interactions were shown to take place over a finite time, which was news, But perhaps should not have been any surprise.

    Then perhaps it’s a naive question?
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Quote Originally Posted by profloater View Post
    I am starting this thread because of a question in my mind arising from relativity and acceleration which has been explored in another thread. I have come across jerk and impulse in engineering contexts where unexpected things happen. Jerk is the name for rate Of change of acceleration.

    Impulse is force times time and, like jerk, has engineering applications in impacts and explosions. Both the speed of sound in a material and the speed of shockwaves in a material become relevant in engineering applications.

    But are there interesting limits to the size of a jerk or the time of an impulse which are more fundamental at the atomic or fundamental particle level. when a nuclear fission ejects a neutron, for example, it is accelerated for a very short time. Is there a theoretical limit to that acceleration And jerk just as there is a limit to the speed of light?

    I asked this question because I still have in mind the recent experiments where quantum interactions were shown to take place over a finite time, which was news, But perhaps should not have been any surprise.

    Then perhaps it’s a naive question?
    Profloater. Not naieve. Thoughtful. Yes there is a limit, set by SR, the acceleration cannot produce a superluminal velocity. It can produce a large velocity. The fission ejection of a neutron does not produce superlumonal neutrons. The binding energy in Mev, accelerates the nuclear fragments, ( usually isotopes like Ba and I ) in uranium, and some energetic neutrons. The gross kinetic energy shows up as heat in a nuclear reactor, producing steam, and electricity, and does work in expanding gases, ionizing atoms, generating a blast wave in a weapon.
    Nothing exceeds c in velocity. The neutrons not engaged in further chain reactions disintegrate by half lives of about 10 minutes, and decay by weak interactions involving W bosons, to produce protons, electrons, and electron type antineutrinos. The energy in that decay is the mass difference between the neutron and the three particles generated. The jerk involved can again not be making superlumonal particles..... ( except for theorists positing tachyons, for which, like monopoles, and supersymmetry, no experimental evidence for them exists).
    So, for scientists, yep there is a limit. For a big boost, you park your spaceship in orbit little further out than an AU, around a precursor to a supernova, and the radiation will zap anything alive from the prompt burst, and then the expanding eject will sweep up the remains of the craft at about c/ 10 max. Ouch.
    pete

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    Interestingly, in my perusing thru ArXiv, in the last few days, there was a paper, by a gentleman who suggested that the kinematic orbits of satellite galaxies to larger central galaxies ( Milky Way type), could be explained by SR, in that the gravitational attraction that held them in their seemingly non-Keplerian orbits, was generated long ago from a larger central mass, that had inexplicably been annihilated, and that the propagation of the new gravitational field, which no longer could hold those satellites bound was in the process of traveling outward at c throughout the galaxy to get to the halo.
    For the Milky Way, some 150,000 lightyear across, that would leave our scientists viewing a kinematic velocity curve requiring a non-existent dark matter. Unfortunately, his name eludes me, but he skipped no.steps in SR and GR expectations, though I read not his methodology for eliminating the hub mass a long time ago.
    His point did eliminate the velocity/radius issue brought up by Zwicky and Rubin.. it was very recent, last 3 days in arXIv.
    pete

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    Quote Originally Posted by trinitree88 View Post
    So, for scientists, yep there is a limit. For a big boost, you park your spaceship in orbit little further out than an AU, around a precursor to a supernova, and the radiation will zap anything alive from the prompt burst, and then the expanding eject will sweep up the remains of the craft at about c/ 10 max. Ouch.
    pete
    I was reading the same thread as Profloater.

    Personally, I like my "things" to be recognizable after the interaction. If you had far less energetic interaction, say a nice kinetic push with human scaled simple machines, does modeling this sort of interaction become easier to compute? Is this what modulus's (moduli?) are for?

    My dad has "a thing" for military history and he one time asked me how long it would take to knock down a stone wall with stones from a catapult. I was taking physics at the time but wisely asked, "Is this for a game?" He said "yes" and I told him to make up a number that would be "fun in a game". In the back of my mind, I suspected that the answer would be super hard to compute. There is a good chance either the rock thrown would be too small to have any effect, or so large that it would work immediately without any measure of "effectiveness" and then maybe a happy middle model where it takes some time to work. People do crazy things, including making up game mechanics which are impossible to quantify realistically. However, since I couldn't actually figure it out, it stuck in my head. Am I on the right track with what I said? Not that I want to know an exact answer, I just want to know if I was applying my knowledge correctly in assuming that you could figure it out, but it wouldn't make for a very fun game?
    Solfe

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    Quote Originally Posted by Solfe View Post
    I was reading the same thread as Profloater.

    Personally, I like my "things" to be recognizable after the interaction. If you had far less energetic interaction, say a nice kinetic push with human scaled simple machines, does modeling this sort of interaction become easier to compute? Is this what modulus's (moduli?) are for?

    My dad has "a thing" for military history and he one time asked me how long it would take to knock down a stone wall with stones from a catapult. I was taking physics at the time but wisely asked, "Is this for a game?" He said "yes" and I told him to make up a number that would be "fun in a game". In the back of my mind, I suspected that the answer would be super hard to compute. There is a good chance either the rock thrown would be too small to have any effect, or so large that it would work immediately without any measure of "effectiveness" and then maybe a happy middle model where it takes some time to work. People do crazy things, including making up game mechanics which are impossible to quantify realistically. However, since I couldn't actually figure it out, it stuck in my head. Am I on the right track with what I said? Not that I want to know an exact answer, I just want to know if I was applying my knowledge correctly in assuming that you could figure it out, but it wouldn't make for a very fun game?
    In both macro and micro examples there are jerk limits, like your stone wall. If I use snooker, pool, balls As an example, playing the game normally the balls move on impact and survive undamaged for years. but at a certain impact spalling will occur where the forces under the skin of the ball exceed the strength of the material and lumps get ejected. To jump an electron into a higher orbit also has a threshold of energy. Both of these thresholds have limits which can be calculated from quite simple models. My question relates to how fundamental limits are imposed. trinitree88 Helpfully says A nuclear force cannot produce a super luminal ejection speed But if the force comes before the speed, there is implied a force limit which must be fundamental, and so the impulse and the jerk have fundamental limits. But I have not noticed those kind of limits being mentioned in physics explanations.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Quote Originally Posted by trinitree88 View Post
    Profloater. Not naieve. Thoughtful. Yes there is a limit, set by SR, the acceleration cannot produce a superluminal velocity. It can produce a large velocity. The fission ejection of a neutron does not produce superlumonal neutrons. The binding energy in Mev, accelerates the nuclear fragments, ( usually isotopes like Ba and I ) in uranium, and some energetic neutrons. The gross kinetic energy shows up as heat in a nuclear reactor, producing steam, and electricity, and does work in expanding gases, ionizing atoms, generating a blast wave in a weapon.
    Nothing exceeds c in velocity. The neutrons not engaged in further chain reactions disintegrate by half lives of about 10 minutes, and decay by weak interactions involving W bosons, to produce protons, electrons, and electron type antineutrinos. The energy in that decay is the mass difference between the neutron and the three particles generated. The jerk involved can again not be making superlumonal particles..... ( except for theorists positing tachyons, for which, like monopoles, and supersymmetry, no experimental evidence for them exists).
    So, for scientists, yep there is a limit. For a big boost, you park your spaceship in orbit little further out than an AU, around a precursor to a supernova, and the radiation will zap anything alive from the prompt burst, and then the expanding eject will sweep up the remains of the craft at about c/ 10 max. Ouch.
    pete
    Thank you for that. Is the limit implied by E =MC^2 ?
    The acceleration cannot be instantaneous if the particle has mass, and the force must be one of the fundamental forces in each case of an impulse, so in effect the time must be limited during which the force “happens” . An interesting example is with ionisation of a gas. The atoms change from snooker balls to “damaged” Atoms we call ions. There must be a time involved, surely?
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    What I am getting at is that using Newton we have velocity increment equals impulse v=ft but we know we cannot use the speed of light for v because according to Einstein, that would imply an infinite impulse. Or indeed an instantaneous zero time. For the same reason the jerk cannot be infinite. So I am wondering what is the expression that limits impulse at a fundamental level? Added, I did not mean ft, will revise.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Impulse = force x time, and = change in momentum , mass x velocity. Giving velocity increment = acceleration x time. That’s what I meant. But relativity limits the possible impulse. How?
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Profloater. You must remember that the force applied initially accelerates the rest mass, but as soon as it gets going in that reference frame, it acquires kinetic energy. That too, energy, also has inertia, and it increases relativistically. So initially, you only have to accelerate the rest mass, but almost instantaneously, that devolves into the more complex issue of SR. m= E / c squared. See Prof. FOWLER, see:

    file:http://galileo.phys.virginia.edu/cla...stic_mass.html
    Last edited by trinitree88; 2020-May-07 at 02:15 AM. Reason: Link

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    Profloater. It's easier to see graphically. At low velocity, the classical increase is near identical to the relativistic one....add some joules of kinetic energy....woo hoo! But you can see as you approach c....more and more of the work done by your engine, in Joules, goes into causing your object to become more massive, and less and less goes into mske the velocity increase. Asymptotically, it becomes impossible to reach c. Nice graph see:
    Last edited by trinitree88; 2020-May-07 at 03:39 PM. Reason: link

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    It's important to keep your reference frames straight here, and do the appropriate coordinate transformations. The concept of relativistic mass isn't necessary, and some would say it's unhelpful, because it distracts from the coordinates.
    So although a spacecraft accelerating towards the speed of light appears to undergo a progressive decrease in its acceleration as it approaches the speed of light, this is a coordinate effect, arising from a disagreement about measures of time and length between the rest frame and the spacecraft frame. Aboard the spacecraft, the crew experience exactly the same accelerative force from their engines throughout their flight, even as their acceleration in the rest frame coordinates is decreasing.

    Grant Hutchison

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    Yes I understand those points. I am wondering if the impulse is limited in order that the speed of light limit is not broken.
    When we see a neutron radiated, or an electron, we know it cannot be superluminal but it was accelerated by impulse, its jerk was huge, and we assume elastic. The Neutron does not shatter like a billiard ball. But the jerk is still finite. It takes time. The relativistic mass of the neutron does not explain the jerk limit.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Quote Originally Posted by profloater View Post
    Yes I understand those points. I am wondering if the impulse is limited in order that the speed of light limit is not broken.
    When we see a neutron radiated, or an electron, we know it cannot be superluminal but it was accelerated by impulse, its jerk was huge, and we assume elastic. The Neutron does not shatter like a billiard ball. But the jerk is still finite. It takes time. The relativistic mass of the neutron does not explain the jerk limit.
    I was reponding to trinitree88, but forgot to use the quote function to make that clear.
    This thread seems to start with the assumption that there are limits to jerk and impulse, but I don't know where those assumptions come from. I do think that if there are relativistic velocities involved, we need to look in the frame of the accelerating object. And perhaps that thinking of subatomic particles as little hard balls with definite instantaneous locations might give a misleading picture.

    Grant Hutchison

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    Quote Originally Posted by grant hutchison View Post
    I was reponding to trinitree88, but forgot to use the quote function to make that clear.
    This thread seems to start with the assumption that there are limits to jerk and impulse, but I don't know where those assumptions come from. I do think that if there are relativistic velocities involved, we need to look in the frame of the accelerating object. And perhaps that thinking of subatomic particles as little hard balls with definite instantaneous locations might give a misleading picture.

    Grant Hutchison
    Well I do not assume a limit, but my question may be better put in the frame of the Neutron, say, pushed out, or created, or collapsed, when fission or indeed fusion occurs. At a short interval afterwards there is a massive no charge particle at high speed. If we interpret its acceleration and rate of acceleration classically, it may beg the question, because it just cannot be classical. It also cannot be faster than light but does that have an understood meaning if we consider the neutron’s frame? It is not just an accelerating frame, it is a jerked frame. I admit I have no answer which is why I asked the question because there clearly is a limit there, but the interpretation is not clear, to me.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Quote Originally Posted by trinitree88 View Post
    Profloater. You must remember that the force applied initially accelerates the rest mass, but as soon as it gets going in that reference frame, it acquires kinetic energy. That too, energy, also has inertia, and it increases relativistically. So initially, you only have to accelerate the rest mass, but almost instantaneously, that devolves into the more complex issue of SR. m= E / c squared. See Prof. FOWLER, see:

    file:http://galileo.phys.virginia.edu/cla...stic_mass.html
    Thanks, I read through and now must read through more slowly! I can see Einstein took a bold move and put conservation law above classical Newtonian , so conservation of momentum is the answer And inertia is more important than mass in that answer.

    The corollary that even kinetic energy has inertia, which is actually easier to visualise than mass being speed dependent, for me anyway, is another Einstein light bulb moment.

    It does leave me with a hazy understanding of how momentum conservation leads to C because it still seems difficult to understand c during the Newtonian jerk interpretation. Which is why I will read that reference again, slowly. There is a kind of “understanding jerk“ which I have not experienced yet.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    The neutron is a wavefunction at the time it is emitted, so I don't think there's much enlightenment to be had from relativity there.
    But it seems your general problem is perhaps something like the "train and tunnel paradox" in reverse. A train, shortened in the rest frame by its relativistic length contraction, is just shorter than the tunnel it passes through. So it is possible, in the rest frame, to briefly, simultaneously, close doors at both ends of the tunnel with the train completely inside. But in the train's frame, the tunnel is shorter than the train. However, the simultaneous closure of the doors in the rest frame is not simultaneous for an observer on the train--the front door closes and reopens just before the train hits it, and then, some time later, the back door closes just after the rear of the train has cleared it.
    So now we replace the door at the far end of the tunnel with a wall. The train smashes into the wall and comes quickly to rest inside the tunnel. Does its rear end protrude from the near end of the tunnel or not?
    The answer lies in the fact that the train cannot be entirely rigid under relativity, because a compression wave from the collision cannot propagate down the train faster than light. In the train frame, the train compresses sequentially as it slams into the wall, observers aboard the train see the tunnel increase in length as their velocity falls with the passage of the compression wave, and the wreckage of the train lies entirely within the tunnel when it comes to rest.
    The external observer in the rest frame sees a compression wave pass very rapidly (but still slower than light) down the shortened length of the train as it slams into the wall, and this compression wave causes the destruction necessary to make the train debris fit into the tunnel even when it has come to rest.

    If we time reverse this scenario, replacing the train with a spring that is initially compressed within the tunnel but released by opening a door at one end, I think it approximates the problem you're wrestling with. As with almost all apparent paradoxes in relativity, the solution lies in understanding that signals cannot propagate faster than a light through a material object, and that observers in relative motion will see compression signals propagate through an accelerating object for different distances and over different time periods before a new state of motion is achieved.

    Grant Hutchison

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    Thank you for that. The train paradox is like the two rockets and string thought experiment discussed earlier and elsewhere. The limit of compressive waves is also familiar, as I mentioned inthe OP but I can see the combination of momentum conservation and the wave function interpretation makes the original question too Newtonian. Those experiments where the wave function collapse take finite time were part of the thought experiment and perhaps my clinging on to cause (impulse) and effect (subluminal ejection). In conservation of momentum, as with billiard balls in macro examples, we have to accept it just is the rule in quantum events.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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