Gravity - an accelerating frame paradox

[Dale]

This is nice but completely misses the point of why there is a need for those EM interaction to take place in the first place. An astronaut on the ISS can comfortably levitate above his chair for a long time and hardly interact with it at all. While the same astronaut on the ground cannot do this (unless he does work to compensate for the now present fictitious force) and he will feel the contact force.

You are completely misapplying the equivalence principle. The equivalence principle does NOT state that an astronaut on the ground (at rest in a gravitational field) is equivalent to an astronaut in orbit (free-falling in a gravitational field). It says that the astronaut on the ground (at rest in a gravitational field) is equivalent to an astronaut far from any source of gravity in an accelerating rocket (accelerating in the absence of gravity). The astronaut in orbit (free-falling in a gravitational field) is equivalent to an astronaut far from any source of gravity in a non-accelerating rocket (not accelerating in the absence of gravity). The contact forces are the same in the equivalent scenarios whether the fictitious force is due to gravitation or inertia.

Wow, you interpret the Newton's 3rd law quite rigidly. While it is in fact a disguised law of conservation of energy.

It is not a matter of interpretation, that is simply what it says. And it is conservation of momentum, not conservation of energy, although the two are closely related in relativity.

The fictitious force of acceleration and the contact force have both the same direction and magnitude

This is simply wrong. The fictitious force is gravity and gravity points down by definition. If the contact force were also pointing downwards then instead of sitting on the floor we would accelerate into the floor at 2g. Since we do not observe that happening it is clear that the contact force points upwards. And since the accelerometer reads 1g upwards it is clear that it does not detect the fictitious force of gravity.

See Figure 4 here
http://eta.physics.uoguelph.ca/tutorials/fbd/intro.html

and paragraphs a and c here:
http://a-s.clayton.edu/campbell/physics/phys1112/Supplements/phys1111fb.htm

and example 1 here:
http://hrsbstaff.ednet.ns.ca/pvickers/normal_force_and_freebody_d.htm

 

[ZirkMan]

There is only one way to interpret Newton's third law: the forces involved are exactly equal but opposite, they arise from the same interaction, and they act on different bodies.


This is completely wrong. You started with a wrong premise and went off on a tangent from that incorrect premise. Newton's third law can be viewed as a consequence of conservation of momentum, not energy. What results from this derivation is that the interactions between particles must comprises paired equal but opposite forces -- Newton's third law. Construing the gravitational force and the normal force acting on some body as a third law interaction is erroneous.

If it is wrong or not totally depends on the definition of energy and its conservation and you seem to use a different one than me. Otherwise you wouldn't say the conservation of momentum is different to conservation of energy.

What conservation law would apply to a situation where a running steam engine train would hit a stationary train and move it away?
Is it only the law of conservation of momentum together with Newton's 3rd law? Or some other combination of various partial conservation laws?

Or can I say that the chemical energy released by the burning coal in the moving train's engine was translated into the final motion of the energy (and momentum) of the (before) stationary train?
I think I can say that and I'm sure that if you calculate how much energy was released by burning coal in the train's engine minus losses due to friction etc. you would get the exact energy (and momentum) the stationary train had after the impact. Because the law of conservation of energy (in this broad sense) is always true there cannot be a contact force without something else that powers it. And I don't see any other predecessor for that particular case than the fictitious force.

 

[ZirkMan]

This is simply wrong. The fictitious force is gravity and gravity points down by definition.
If the contact force were also pointing downwards then instead of sitting on the floor we would accelerate into the floor at 2g. Since we do not observe that happening it is clear that the contact force points upwards. And since the accelerometer reads 1g upwards it is clear that it does not detect the fictitious force of gravity.

I was analyzing the situation from the perspective of a free falling observer where he sees only the accelerating surface which he interprets as accelerating due to the fictitious force of gravity. I also assumed that this acceleration won't stop after he hits the surface and will continue to drive him up (through the contact force). In this frame there is no need for a downward pulling fictitious force. But maybe you have to switch frames after you hit the ground. I don't know. I feel I need to study this in even greater detail to fully understand what's going on there.

 

[nismaratwork]

If it is wrong or not totally depends on the definition of energy and its conservation and you seem to use a different one than me. Otherwise you wouldn't say the conservation of momentum is different to conservation of energy.

What conservation law would apply to a situation where a running steam engine train would hit a stationary train and move it away?
Is it only the law of conservation of momentum together with Newton's 3rd law? Or some other combination of various partial conservation laws?

Or can I say that the chemical energy released by the burning coal in the moving train's engine was translated into the final motion of the energy (and momentum) of the (before) stationary train?
I think I can say that and I'm sure that if you calculate how much energy was released by burning coal in the train's engine minus losses due to friction etc. you would get the exact energy (and momentum) the stationary train had after the impact. Because the law of conservation of energy (in this broad sense) is always true there cannot be a contact force without something else that powers it. And I don't see any other predecessor for that particular case than the fictitious force.

re bold: I think it's clear that you have your own special definitions to encompass most of physics. Maybe you should take a chance on less opposition for its own sake, and actually make use of the information already given to you in this thread.

 

[D H]

If it is wrong or not totally depends on the definition of energy and its conservation and you seem to use a different one than me. Otherwise you wouldn't say the conservation of momentum is different to conservation of energy.

I suggest you read some more / take some more physics classes. What you wrote makes no sense. Newton's third law is equivalent to conservation of momentum, not energy. Conservation of momentum follows from Newton's third law, and Newton's third law follows from conservation of momentum. The derivation is in practically every text for the sophomore/junior level class classical mechanics taken by almost all physics majors.

Regarding your earlier notion that the normal force is equal but opposite to the gravitational force: It isn't. From the perspective of an inertial observer, the forces acting on a person standing still on the surface of the Earth are the normal force and gravitation. Except at the poles, these forces cannot and do not sum to zero. The person is after all undergoing uniform circular motion about the Earth's rotation axis, so there must necessarily be some non-zero net force acting on the person.

Regarding your interpretation of the equivalence principle: Please re-read post #43.

 

[Dale]

I was analyzing the situation from the perspective of a free falling observer where he sees only the accelerating surface which he interprets as accelerating due to the fictitious force of gravity.

A free-falling frame is inertial. There are no fictitious forces in it, only the real forces. Specifically, in the free falling frame the astronaut on the ground is accelerating upwards at g due to the unbalanced upwards-pointing real contact force. There is no fictitious force pointing down to prevent his acceleration, and his coordinate acceleration matches the proper acceleration measured by an accelerometer as you would expect in an inertial frame.

 

[Dale]

Regarding conservation of momentum vs conservation of energy and Newton's 3rd law.

Let us imagine a world where Newton's 3rd law is replaced by a law where for every action there is an equal and perpendicular reaction. Consider a perfectly elastic collision between a ball moving towards the origin along the x-axis and a ball of equal mass at rest at the origin. The moving ball feels a force in the -x direction which stops it. By the modified 3rd law the resting ball feels a force in the y direction. It moves away with the same speed as the original ball and therefore energy is conserved. However, it is moving in a different direction (y instead of x) and therefore momentum is not conserved.

So, in a world where Newton's 3rd law is violated momentum is not conserved even if energy is. Newton's 3rd law is most definitely associated with conservation of momentum rather than conservation of energy.

 

[ZirkMan]

Specifically, in the free falling frame the astronaut on the ground is accelerating upwards at g due to the unbalanced upwards-pointing real contact force. There is no fictitious force pointing down to prevent his acceleration, and his coordinate acceleration matches the proper acceleration measured by an accelerometer as you would expect in an inertial frame.

This is exactly the situation I have a problem to understand. Where does this "unbalanced upwards-pointing real contact force" come from? Does it arise as a "barrier force" preventing me following a geodesic motion?

 

[ZirkMan]

Regarding conservation of momentum vs conservation of energy and Newton's 3rd law.

Let us imagine a world where Newton's 3rd law is replaced by a law where for every action there is an equal and perpendicular reaction. Consider a perfectly elastic collision between a ball moving towards the origin along the x-axis and a ball of equal mass at rest at the origin. The moving ball feels a force in the -x direction which stops it. By the modified 3rd law the resting ball feels a force in the y direction. It moves away with the same speed as the original ball and therefore energy is conserved. However, it is moving in a different direction (y instead of x) and therefore momentum is not conserved.

So, in a world where Newton's 3rd law is violated momentum is not conserved even if energy is. Newton's 3rd law is most definitely associated with conservation of momentum rather than conservation of energy.

Thanks for a clarification. I have regarded the momentum only as mass x velocity not as a vector unit. If you ignore the vector dimension then really the conservation of momentum vers. conservation of energy should make no difference because from this perspective it's all and only energy that's being transfered. Of course the vector dimension and distinction between energy and momentum has its practical use for direction calculations etc. but one should not forget that at the end of the day it is only energy that is being transferred (momentum being just a specific expression of it).

 

[D H]

Thanks for a clarification. I have regarded the momentum only as mass x velocity not as a vector unit.

And you had the gall to accuse me of using non-standard definitions of the conservation laws?

The problem here is that you are trying to learn to run (general relativity) when you can't even crawl (non-calculus Newtonian mechanics).

 

[ZirkMan]

I suggest you read some more / take some more physics classes. What you wrote makes no sense. Newton's third law is equivalent to conservation of momentum, not energy. Conservation of momentum follows from Newton's third law, and Newton's third law follows from conservation of momentum. The derivation is in practically every text for the sophomore/junior level class classical mechanics taken by almost all physics majors.

See my #59 reply to DaleSpam.

Regarding your earlier notion that the normal force is equal but opposite to the gravitational force: It isn't. From the perspective of an inertial observer, the forces acting on a person standing still on the surface of the Earth are the normal force and gravitation.

So is there a gravitation force for the inertial observer? I believe what DaleSpam says here is correct (and I was wrong when I thought there is a fictitious force in that frame):

A free-falling frame is inertial. There are no fictitious forces in it, only the real forces.

Regarding your interpretation of the equivalence principle: Please re-read post #43.

I tried to sum up of how I understood it in post #44. You haven't replied on that so I am not sure if I understood it correctly.

 

[D H]

See my #59 reply to DaleSpam.

Already discussed in post #60.

[QUOTE}So is there a gravitation force for the inertial observer? I believe what DaleSpam says here is correct (and I was wrong when I thought there is a fictitious force in that frame)[/QUOTE]
I should have been clearer that the inertial observer in post #55 was looking at things from a Newtonian rather than relativistic perspective.

 

[ZirkMan]

And you had the gall to accuse me of using non-standard definitions of the conservation laws?

I didn't say they are non-standard! I was just trying to say that for that particular illustration the distinction between energy and momentum conservation is not necessary.

The problem here is that you are trying to learn to run (general relativity) when you can't even crawl (non-calculus Newtonian mechanics).

Sorry this will be a little bit metaphysical but we have come to this point.

I know I still have to learn a lot even more about the very basic notions and their relations. Because what I often see is that lot of people don't see that there are way too many basic physics notions that are defined for a very specific purpose to illustrate some aspect of a well known and physically real phenomenon in a special situation. And once that definition is done the special aspect is often forced to apply on situations where this aspect is not important at all and what is worse it takes an independent life and many proclaim its existence independent from the real phenomenon from which it was derived (because it has a definition of its own). Don't get me wrong, exact definitions are necessary for a rigorous debate when we know what we are talking about (I don't deny that!). Even worse than "independent aspects"are definitions of "virtual notions" that are part of models that explain some aspect of the physical world but don't have a connection to any physically real entity (such as speed or maybe even spacetime). So you see, yeah, I have to learn a lot. But it seems to me I have to unlearn a lot as well in order to understand what is this physical theory really trying to say.

 

[nismaratwork]

I didn't say they are non-standard! I was just trying to say that for that particular illustration the distinction between energy and momentum conservation is not necessary.

Sorry this will be a little bit metaphysical but we have come to this point.

I know I still have to learn a lot even more about the very basic notions and their relations. Because what I often see is that lot of people don't see that there are way too many basic physics notions that are defined for a very specific purpose to illustrate some aspect of a well known and physically real phenomenon in a special situation. And once that definition is done the special aspect is often forced to apply on situations where this aspect is not important at all and what is worse it takes an independent life and many proclaim its existence independent from the real phenomenon from which it was derived (because it has a definition of its own). Don't get me wrong, exact definitions are necessary for a rigorous debate when we know what we are talking about (I don't deny that!). Even worse than "independent aspects"are definitions of "virtual notions" that are part of models that explain some aspect of the physical world but don't have a connection to any physically real entity (such as speed or maybe even spacetime). So you see, yeah, I have to learn a lot. But it seems to me I have to unlearn a lot as well in order to understand what is this physical theory really trying to say.

You have enough to learn that what you just said is a meaningless rant. Stop typing... Start reading.

 

[Dale]

This is exactly the situation I have a problem to understand. Where does this "unbalanced upwards-pointing real contact force" come from? Does it arise as a "barrier force" preventing me following a geodesic motion?

Do you understand where it comes from in the situation where the astronaut is on a rocket accelerating in deep space? By the equivalence principle it comes from the same thing here, the ground is accelerating upwards and carries the astronaut upwards with it, accelerating him upwards via the EM contact force.

 

[Dale]

one should not forget that at the end of the day it is only energy that is being transferred (momentum being just a specific expression of it).

This is simply incorrect, as I have already shown. Please stop repeating this erroneous assertion or any variations thereof, you simply need to let go of this incorrect concept. You cannot replace a vector conservation law (momentum) with a scalar conservation law (energy). It is logically and mathematically impossible.

 

[D H]

But it seems to me I have to unlearn a lot as well in order to understand what is this physical theory really trying to say.

I would say that you have a lot of basic physics to learn before you should even start delving into general relativity. For example,

Thanks for a clarification. I have regarded the momentum only as mass x velocity not as a vector unit.

Mass times velocity is a conserved quantity -- but only if you interpret velocity as a vectorial quantity. Mass times speed is not a conserved quantity.

 

[nismaratwork]

I don't see why you two (DaleSpam and D H) should waste your time this way. He has 3-4 solid pages of links and explanations to peruse, and before that he has basic NM to learn. I honestly think you've gone beyond polite and kind; does this thread continuing serve any purpose except to frustrate you?

 

[D H]

Please don't tell me it's wrong

You got it wrong.

You are missing the main point of Einstein's thought experiment. There is no way that a person inside the windowless elevator car ( spacecraft in modern parlance) using local experiments can distinguish between a quiescent (thrusters not firing) spacecraft in deep space versus a quiescent spacecraft in orbit about some planet. Yet Newtonian mechanics says a frame fixed with respect to the spacecraft is an inertial frame in the first case but is not inertial in the second. There similarly is no way via local experiments to distinguish between the spacecraft being deep space, this time with thrusters firing, versus being in a quiescent sitting still on the ground. Yet once again Newtonian mechanics says these are very different conditions. This suggested to Einstein that something was remiss with the Newtonian concept of an inertial frame. One shouldn't have to look outside the window or rely on reports by an external observer to determine whether or not the local environment is behaving inertially.

 

[ZirkMan]

You got it wrong.

Alas, premature joy. That insight fails to explain other many important aspect that I have not included. Sorry, I really don't want to frustrate you anymore (enjoy nismaratwork), I heed your advice and will report back only after I have learned everything that you have recommended or mentioned.

 

[nismaratwork]

Alas, premature joy. That insight fails to explain other many important aspect that I have not included. Sorry, I really don't want to frustrate you anymore (enjoy nismaratwork), I heed your advice and will report back only after I have learned everything that you have recommended or mentioned.

A wise choice...

[PLAIN]http://www.smileyshut.com/smileys/new/emot67.gif