Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: jeffreyH on 18/03/2017 19:33:07
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If we have a particle freely falling in a gravitational field would it experience an increase in relativistic mass as it accelerates? If not why not?
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On a planet with different gravity to earth an object will weigh more if the gravity is at the surface is greater. If we consider this to be a non inertial frame are we justified in attributing this to a gain in relativistic mass. If not why not?
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If we have a particle freely falling in a gravitational field would it experience an increase in relativistic mass as it accelerates? If not why not?
No, because of conservation of energy, and because gravity is not a force in the Newtonian sense. When you drop a brick, gravity converts potential energy into kinetic energy. Then when the brick hits the ground the kinetic energy is dissipated, and you're left with a mass deficit (https://en.wikipedia.org/wiki/Binding_energy#Mass-energy_relation). The point to note here is that the potential energy was not stored in the gravitational field, it was stored in the brick, as mass-energy. This mass-energy is actually internal kinetic energy, which is why a radiating body loses mass. See Einstein's E=mc² paper (https://www.fourmilab.ch/etexts/einstein/E_mc2/www/). So when the brick is falling all that was happening is that internal kinetic energy is being converted into external kinetic energy. The sum total energy does not change, so the relativistic mass does not change either, because relativistic mass is really total energy. Instead the rest mass is decreasing as the brick falls.
On a planet with different gravity to earth an object will weigh more if the gravity is at the surface is greater. If we consider this to be a non inertial frame are we justified in attributing this to a gain in relativistic mass. If not why not?
No, because the relativistic mass doesn't change, and because the mass deficit depends on gravitational potential rather than gravitational force.
* conservation of momentum p=mv means the Earth is also affected. But there's no discernible motion of the Earth. The kinetic energy KE=½mv² is not equally shared. The brick gets all bar an infinitesimal portion of the kinetic energy.
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John the second question I asked was intentionally wrong. Can you understand why?
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BTW John I'm intentionally ignoring the rubbish you typed in response to the first question. Just in case you thought otherwise.
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On a planet with different gravity to earth an object will weigh more if the gravity is at the surface is greater.
In what sense can this be considered as an increase in mass, of any kind?
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On a planet with different gravity to earth an object will weigh more if the gravity is at the surface is greater.
In what sense can this be considered as an increase in mass, of any kind?
That is a topic I am investigating. I am having to invent some new mathematical tools to do so.
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BTW John I'm intentionally ignoring the rubbish you typed in response to the first question. Just in case you thought otherwise.
Your response is abusive and ignorant, and it brings Naked Scientists into disrepute. My answer contained appropriate references, and was correct.
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Relativistic mass doesn't change? The rest mass is decreasing as the brick falls? And that is just two of your misconceptions. You could always go back to physics.stackexchange.com if you don't like it here. Oh sorry no you can't.
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Before one ask Jeffrey.
Is relativistic mass something belonging to a object, or would it be a result of circumstances?
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It is as a result of the circumstance of velocity. More precisely a change in velocity. That is acceleration. However it persist when the force is removed. So that it can be considered to be inertial.
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so, in a empty space, how would you measure it?
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You can't since there would be no mass present. When you ask if relativistic mass belongs to an object it is the wrong question. The change in relativistic mass is continuous and not quantised as far as I know so you cannot separate it from rest mass. Since you would have to define which part of the mass in the local frame is at rest. Usually all of it in its own inertial frame.
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Yea, but how would you measure a relativistic mass?
Where I get stuck is when I think of it locally.
I don't see any way to measure it.
It's in a way resembling the the problem I have with 'potential energy'. It needs a 'universe' to be defined.
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The problem is 'direct measurements' relative 'indirect measurements'.
If I define a 'direct measurements'' to be a result of me measuring in a 'black box'.
Then a gravitational acceleration doesn't exist.
If that doesn't exist, where does 'potential energy' exist?
The whole question makes me think of Mach universe.
If I move 'outside' then the guy in the box have to be lying, from the frame of me observing him 'gravitationally accelerating'.
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Well it is good to be thinking about it. That way new insights are gained.
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Relativistic mass doesn't change? The rest mass is decreasing as the brick falls? And that is just two of your misconceptions. You could always go back to physics.stackexchange.com if you don't like it here. Oh sorry no you can't.
You can read about stack exchange here: Dishonest moderation on Physics Stack Exchange (http://www.physicsdiscussionforum.org/dishonest-moderation-on-physics-stack-exchange-t1073.html). And you can read about the mass deficit here: Wikipedia: binding energy (https://en.wikipedia.org/wiki/Binding_energy#Mass-energy_relation):
"Classically, a bound system is at a lower energy level than its unbound constituents. Its mass must be less than the total mass of its unbound constituents. For systems with low binding energies, this "lost" mass after binding may be fractionally small. For systems with high binding energies, however, the missing mass may be an easily measurable fraction. This missing mass may be lost during the process of binding as energy in the form of heat or light, with the removed energy corresponding to removed mass through Einstein's equation E = mc²".
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Reading that shows how justified the moderators were to challenge your assertions. To suggest that Paul Dirac had no idea about the electron is pretty embarrassing for you I'm sure. If not then you are beyond help.
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You have a strange idea about the relationship between binding energy and gravity. Please explain how this 'mass deficit' comes about in your own words. So we can actually tell whether or not you actually understand the concept.
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I've told you already. See Einstein's E=mc² paper (https://www.fourmilab.ch/etexts/einstein/E_mc2/www/). A radiating body loses mass because mass-energy is internal kinetic energy. This is demonstrated in extremis by electron-positron annihilation. Each is a radiating body that loses mass. All of it. When you drop an electron, it falls down because some of the internal kinetic energy is converted into external kinetic energy. Then when it hits the ground this external kinetic energy is typically radiated away. The electron mass is then less than what it was. There is a mass deficit. There's also a mass deficit when an electron is attracted to a proton to form a hydrogen atom. The hydrogen atom mass is circa 13.7ev less than the mass of a free proton plus the mass of a free electron.
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So you think that 'internal' kinetic energy is converted into 'external' kinetic energy. So how do you explain this 'internal' kinetic energy? What is it binding together? Since you did explicitly mention binding energy and internal kinetic energy almost in the same breath. Also how far does an object have to fall in order to lose all its rest mass and magically transform into a photon?
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So you think that 'internal' kinetic energy is converted into 'external' kinetic energy. So how do you explain this 'internal' kinetic energy? What is it binding together?
Itself. The E=hf photon is kinetic energy, and you can convert two gamma photons into an electron and a positron in gamma-gamma pair production. See two-photon physics (https://en.wikipedia.org/wiki/Two-photon_physics) on Wikipedia. As for the exact mechanism I can't give you a peer-reviewed reference I'm afraid. But I suspect it's to do with displacement current.
Also how far does an object have to fall in order to lose all its rest mass and magically transform into a photon?
It can't lose all its rest mass, it can only lose half, because E=mc² and KE=½mv².
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You do realise that rest mass is invariant don't you? It binds itself? Recursively? Up its own exhaust pipe? Why do we have the factor of 1/2 in kinetic energy. I don't mind if you google it.
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P.S. It helps if you understand calculus. Which I doubt you do John.
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You do realise that rest mass is invariant don't you?
It isn't invariant. That's why there's a mass deficit. See the Wikipedia binding energy article (https://en.wikipedia.org/wiki/Binding_energy#Mass_change): "When nucleons bind together to form a nucleus, they must lose a small amount of mass, i.e., there is a change in mass, in order to stay bound. This mass change must be released as various types of photon or other particle energy as above, according to the relation E = mc². Thus, after binding energy has been removed, binding energy = mass change × c²". Whilst you might read about "invariant mass", I'm afraid the phrase is rather misleading. Invariant mass is said to be the same thing as rest mass, but rest mass varies.
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Are you afraid of calculus then? Since you dodged the question.
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They answer the very same question on physics.stackexchange.com. I can give you the link if it helps.
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Are you afraid of calculus then? Since you dodged the question.
Not at all. I just wanted you to focus on the mass deficit. I take it you accept that now?
Yes, please do show me the stack exchange link. Meanwhile the factor of a half is present in KE=½mv² because energy equates to force x distance. Think of a gedanken cannonball in space. It's moving at 100m/s and you apply a constant braking force to stop it in ten seconds. It moves a greater distance in the first second than in the last, and you need an integral to calculate the total distance. Momentum however equates to force x time, and you're applying the force for the same time in the first second as in the last, so there's no integral. I should add that energy and momentum are not two separate things, they're two sides of the same coin, called energy-momentum. You cannot take away that cannonball's kinetic energy without taking away its momentum.
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That was all waffle. Where is the calculus.
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Right John I will give you some hints. Simply fill in the question marks. The integral of ? with respect to ? is kinetic energy. The integral is the ? under the ?. An integral is an anti-?.
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I would say as the inertia increaces then yes. ...... ..
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In free fall no force is felt. How can we tell if inertia is increasing? Does the force of gravity increase in magnitude simply because the relativistic mass is increasing? What happens as the increase in mass approaches infinity? Does the gravitational field generate free energy without bound? I would say the energy of the gravitational field is finite. I believe Mike Gale may also have come to this conclusion.
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...Does the force of gravity increase in magnitude simply because the relativistic mass is increasing? ...
It isn't increasing. Conservation of energy applies. The total energy of the falling brick doesn't change. Gravity merely converts potential energy into kinetic energy.
Right John I will give you some hints. Simply fill in the question marks. The integral of ? with respect to ? is kinetic energy.
The integral of momentum with respect to speed. Please don't try to distract from your errors with trivia.
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Wrong, it is the integral of momentum with respect to velocity. There I've written it in big so you can absorb the information. Speed is a scalar and not a vector so you wouldn't end up with a scalar but a vector. Energy is a scalar. Schoolboy error John. Still, you can write it in big for cut and paste later. Despite yourself you may actually learn some physics yet.
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Now you only have two other things to get wrong. I'll give you as long as you need to google the best guess.
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In free fall no force is felt. How can we tell if inertia is increasing? Does the force of gravity increase in magnitude simply because the relativistic mass is increasing? What happens as the increase in mass approaches infinity? Does the gravitational field generate free energy without bound? I would say the energy of the gravitational field is finite. I believe Mike Gale may also have come to this conclusion.
You affect the object off centre with another known force, track the course of both objects before and after instigation and then calculate the resistance to change
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Wrong, it is the integral of momentum with respect to velocity. There I've written it in big so you can absorb the information. Speed is a scalar and not a vector so you wouldn't end up with a scalar but a vector. Energy is a scalar. Schoolboy error John. Still, you can write it in big for cut and paste later. Despite yourself you may actually learn some physics yet.
It's speed Jeffrey. You don't end up with negative kinetic energy. Energy is a scalar. Cannonballs do not have less than zero kinetic energy.
Now, do you concede that conservation of energy applies and gravity converts potential energy into kinetic energy and so the relativistic mass of the brick does not increase? Or are you going to persist in promoting bad science?
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If you multiply speed (a scalar) with velocity (a vector) you certainly don't end up with momentum. If you don't stop posting nonsense you will be confined to new theories. If you ignore this warning your membership may be curtailed.
EDIT: I think I'm catching Duffield's disease. The above should read "If you multiply speed (a scalar) with velocity (a vector) you certainly don't end up with kinetic energy.