Documentairy

[William Gaatjes]

Because of this ongoing cold/flu i finally had some time watching this documentary.

E=mc2 -Einstein and the World's Most Famous Equation


Fun to watch and amazing to realise how long the search is been going on.

People the documentairy is about :

Micheal Faraday

James Maxwell

Antoine Lavosier and Marie-Anne Pierrette Paulze

Emilie du Chatelet

Albert Einstein and Mileva Maric

EDIT : lise Meitner

EDIT : Otto Hahn


I think Robert Boyle is mentioned very briefly as well.

 

[Cogman]

I haven't finished it yet, but I loved the piece on Michel Faraday. He is definitely the man.

 

[Nathelion]

Michael Faraday = I can see electric fields! Hurp derp!

 

[William Gaatjes]

He sure was/is.

He could just imagine it. See it in his mind.

I feel that Faraday for example was a real explorer with a pitbull mentality and a gut feeling. Einstein in mine opinion was more of a man who could find the missing links between seemingly unrelated phenomena. He was at his place in that patent office. He could read about all the discoveries and unite them when appropriate.

When i read and watch about history, i realize how good we have it nowadays. That we all can be faraday's when we are young. Imagine there is no way that you could educate yourself by means of school or being autodidact or a combination of both. If faraday did not received that ticket to meet Davy, he would maybe never have met him and discovered what he discovered. On the other hand, as the documentary shows he was not the only researcher at that time researching electric and magnetic fields. The difference is that Faraday was a true explorer from the heart, not driven by greed but by the desire to know and understand. Greed is a downfall, that's for sure. We in the west have come so far, we should not let our educational system be destroyed( at least that is how i feel about it in my country ).

 

[William Gaatjes]

I must be interpreting this wrong or my information is wrong.

Gottfried Leibniz came up wit the formula E=mc2 To describe the energy of a moving object.


And it was Emilie du Chatelet who proved Newton wrong and that Leibniz was right.

At the age of 23, du Chatelet discovered a talent for advanced mathematics which she relished. So much so that she began to formulate ideas of her own; ideas that challenged the great physicists, including Sir Isaac Newton. Newton stated that the energy (or force) of a moving object could simply be expressed as its mass multiplied by its velocity. But while corresponding with a German scientist called Gottfried Leibniz, du Chatelet learned that Leibniz considered the energy of a moving object is better described if its velocity is squared. But how to test this? Du Chatelet tried an experiment that would prove her point ? dropping lead balls into clay.

Du Chatelet conducted her lead ball experiment and sure enough, doubling the velocity of the ball (by dropping it from twice the height) resulted in the ball travelling four times further into the clay. This simple but brilliant experiment proved that when calculating the energy of moving objects, the velocity at which they travel must be squared. The energy of an object is a function of its velocity squared ? it is for this reason that the speed of light in Einstein's equation must be squared.

E=mc2


Einstein used it to formulate mass energy equivalence in his 1905 paper.
But du Chatelet lived from 1706 to 1749 and Leibniz from 1646 to 1706.
It has been approximately 200 years before the knowledge from Leibniz was put to good use...

 

[Born2bwire]

Originally posted by: William Gaatjes
I must be interpreting this wrong or my information is wrong.

Gottfried Leibniz came up wit the formula E=mc2 To describe the energy of a moving object.


And it was Emilie du Chatelet who proved Newton wrong and that Leibniz was right.

At the age of 23, du Chatelet discovered a talent for advanced mathematics which she relished. So much so that she began to formulate ideas of her own; ideas that challenged the great physicists, including Sir Isaac Newton. Newton stated that the energy (or force) of a moving object could simply be expressed as its mass multiplied by its velocity. But while corresponding with a German scientist called Gottfried Leibniz, du Chatelet learned that Leibniz considered the energy of a moving object is better described if its velocity is squared. But how to test this? Du Chatelet tried an experiment that would prove her point ? dropping lead balls into clay.

Du Chatelet conducted her lead ball experiment and sure enough, doubling the velocity of the ball (by dropping it from twice the height) resulted in the ball travelling four times further into the clay. This simple but brilliant experiment proved that when calculating the energy of moving objects, the velocity at which they travel must be squared. The energy of an object is a function of its velocity squared ? it is for this reason that the speed of light in Einstein's equation must be squared.

E=mc2


Einstein used it to formulate mass energy equivalence in his 1905 paper.
But du Chatelet lived from 1706 to 1749 and Leibniz from 1646 to 1706.
It has been approximately 200 years before the knowledge from Leibniz was put to good use...

No, Chatelet did nothing but prove Newtonian physics was correct, that the energy of an object is directly proportional to the square of its velocity. Einstein's equation, E=mc^2, does not affect kinematics. E=mc^2 is the rest mass contribution to the energy, it is a constant offset and we can add a constant offset to the energy without affecting the observed kinetic energy (otherwise Newtonian force and energy laws would not follow observation). If you do the proper expansion of E=\gamma m_0 c^2 for a moving object, then you do regain Newton's equations.

E = m_0 c^2 + 0.5m_0v^2 + ...

We can see that the first term is the rest mass energy, the second term is the classical kinetic energy, and the rest are higher order corrections of order (m_0 c^2 (v^3/c^3) = m_0v^3/c). So the first order approximation of the energy in terms of v^2/c^2 agrees with Newtonian physics.

Neither Leibnitz, Chatelet, or anyone at that time could come up with E=mc^2 since there was no idea of the finite-speed of light. What would they choose c^2 as? Not to mention that statement just hurts my brain. Force and energy are different things. Newtonian physics says that energy is related to the square of the velocity and force is related to the acceleration. Newtonian physics does not say that force and energy are directly proportional to the velocity.

 

[William Gaatjes]

Originally posted by: Born2bwire

Originally posted by: William Gaatjes
I must be interpreting this wrong or my information is wrong.

Gottfried Leibniz came up wit the formula E=mc2 To describe the energy of a moving object.


And it was Emilie du Chatelet who proved Newton wrong and that Leibniz was right.

At the age of 23, du Chatelet discovered a talent for advanced mathematics which she relished. So much so that she began to formulate ideas of her own; ideas that challenged the great physicists, including Sir Isaac Newton. Newton stated that the energy (or force) of a moving object could simply be expressed as its mass multiplied by its velocity. But while corresponding with a German scientist called Gottfried Leibniz, du Chatelet learned that Leibniz considered the energy of a moving object is better described if its velocity is squared. But how to test this? Du Chatelet tried an experiment that would prove her point ? dropping lead balls into clay.

Du Chatelet conducted her lead ball experiment and sure enough, doubling the velocity of the ball (by dropping it from twice the height) resulted in the ball travelling four times further into the clay. This simple but brilliant experiment proved that when calculating the energy of moving objects, the velocity at which they travel must be squared. The energy of an object is a function of its velocity squared ? it is for this reason that the speed of light in Einstein's equation must be squared.

E=mc2


Einstein used it to formulate mass energy equivalence in his 1905 paper.
But du Chatelet lived from 1706 to 1749 and Leibniz from 1646 to 1706.
It has been approximately 200 years before the knowledge from Leibniz was put to good use...

No, Chatelet did nothing but prove Newtonian physics was correct, that the energy of an object is directly proportional to the square of its velocity. Einstein's equation, E=mc^2, does not affect kinematics. E=mc^2 is the rest mass contribution to the energy, it is a constant offset and we can add a constant offset to the energy without affecting the observed kinetic energy (otherwise Newtonian force and energy laws would not follow observation). If you do the proper expansion of E=\gamma m_0 c^2 for a moving object, then you do regain Newton's equations.

E = m_0 c^2 + 0.5m_0v^2 + ...

We can see that the first term is the rest mass energy, the second term is the classical kinetic energy, and the rest are higher order corrections of order (m_0 c^2 (v^3/c^3) = m_0v^3/c). So the first order approximation of the energy in terms of v^2/c^2 agrees with Newtonian physics.

Neither Leibnitz, Chatelet, or anyone at that time could come up with E=mc^2 since there was no idea of the finite-speed of light. What would they choose c^2 as? Not to mention that statement just hurts my brain. Force and energy are different things. Newtonian physics says that energy is related to the square of the velocity and force is related to the acceleration. Newtonian physics does not say that force and energy are directly proportional to the velocity.

If you say so...
The Bold text above states otherwise. But in all honesty it might be Newton had the same idea but it was interpreted wrong.
The history i read and seen so far say Leibniz came up with the idea of velocity squared and not Newton. Can you please explain what you mean ?




pbs.org

 

[Born2bwire]

Originally posted by: William Gaatjes

Originally posted by: Born2bwire

Originally posted by: William Gaatjes
I must be interpreting this wrong or my information is wrong.

Gottfried Leibniz came up wit the formula E=mc2 To describe the energy of a moving object.


And it was Emilie du Chatelet who proved Newton wrong and that Leibniz was right.

At the age of 23, du Chatelet discovered a talent for advanced mathematics which she relished. So much so that she began to formulate ideas of her own; ideas that challenged the great physicists, including Sir Isaac Newton. Newton stated that the energy (or force) of a moving object could simply be expressed as its mass multiplied by its velocity. But while corresponding with a German scientist called Gottfried Leibniz, du Chatelet learned that Leibniz considered the energy of a moving object is better described if its velocity is squared. But how to test this? Du Chatelet tried an experiment that would prove her point ? dropping lead balls into clay.

Du Chatelet conducted her lead ball experiment and sure enough, doubling the velocity of the ball (by dropping it from twice the height) resulted in the ball travelling four times further into the clay. This simple but brilliant experiment proved that when calculating the energy of moving objects, the velocity at which they travel must be squared. The energy of an object is a function of its velocity squared ? it is for this reason that the speed of light in Einstein's equation must be squared.

E=mc2


Einstein used it to formulate mass energy equivalence in his 1905 paper.
But du Chatelet lived from 1706 to 1749 and Leibniz from 1646 to 1706.
It has been approximately 200 years before the knowledge from Leibniz was put to good use...

No, Chatelet did nothing but prove Newtonian physics was correct, that the energy of an object is directly proportional to the square of its velocity. Einstein's equation, E=mc^2, does not affect kinematics. E=mc^2 is the rest mass contribution to the energy, it is a constant offset and we can add a constant offset to the energy without affecting the observed kinetic energy (otherwise Newtonian force and energy laws would not follow observation). If you do the proper expansion of E=\gamma m_0 c^2 for a moving object, then you do regain Newton's equations.

E = m_0 c^2 + 0.5m_0v^2 + ...

We can see that the first term is the rest mass energy, the second term is the classical kinetic energy, and the rest are higher order corrections of order (m_0 c^2 (v^3/c^3) = m_0v^3/c). So the first order approximation of the energy in terms of v^2/c^2 agrees with Newtonian physics.

Neither Leibnitz, Chatelet, or anyone at that time could come up with E=mc^2 since there was no idea of the finite-speed of light. What would they choose c^2 as? Not to mention that statement just hurts my brain. Force and energy are different things. Newtonian physics says that energy is related to the square of the velocity and force is related to the acceleration. Newtonian physics does not say that force and energy are directly proportional to the velocity.

If you say so...
The Bold text above states otherwise. But in all honesty it might be Newton had the same idea but it was interpreted wrong.
The history i read and seen so far say Leibniz came up with the idea of velocity squared and not Newton. Can you please explain what you mean ?




pbs.org

The problem is that the above bolded is a bunch of crap. The main offenders being the equivalence between force and energy and the supposition that 0.5mv^2 somehow means that people were on the right track to get mc^2. It ignores the fact that the relationship between kinetic energy and the square of velocity has been standard mechanics for centuries and that the relationship of mc^2 is completely different. E=mc^2 is the rest energy and is not part of the kinematics, as a constant offset it does not affect any classical mechanics. If we take the energy relation for a moving object, we can get the Newtonian physics energy relationship back out by a simple Taylor's expansion. The first term is the rest energy and the second is the classical kinetic energy.

So for classical kinematics, relativity does not change anything, in fact, it just reaffirms the original equations.

Looking at what they said about Newton's statement, I just got my requested copy of the Principia and while I am still going through the notes I believe that the statement is more of a misinterpretation. The Principia suffers from two problems. The first is that it is in Latin, the second is that it is largely devoid of equations, Newton talked out the relationships and both of these aspects can introduce gross misinterpretations. For example, the Cohen and Whitman translations specifies Newton's Second Law (Book 1 Law 2) as

A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.

If some force generates any motion, twice the force will generate twice the motion, and three times the force will generate three times the motion, whether the force is impressed all at once or successively by degrees.

This is open to a lot of interpretation even after its translation into English. What is meant by motion? An incorrect interpretation would think that it is velocity, thus Newton is saying that a force generates a velocity (ignoring his stipulation of change in motion in the heading for the law). Twice the force will generate twice the velocity and so on. Add in the incorrect assumption that force and energy are the same (which I do not think Newton supposed) and you get that Newton stated Force is proportional to Velocity. However, Newton is talking about a change in motion being proportional to the force. Newton's "motion" here is momentum. He is saying that the change in momentum (because he is talking about an impulse force here, not a continuous foce) is proportional to the impulse force that is applied. In addition, if we apply twice the impulse force, we get twice the change in momentum. Or, if we successively apply an impulse force we will successively add up the change in momentum. This is true and agrees with modern classical mechanics. Newton is saying that Force is proportional to the change in Mass*Velocity.

Another point is that the Principia was originally written around the idea of explaining the motion of the heavenly bodies, to put it poetically. The concept of kinetic energy was not developed here. So it is certainly correct to say that Leibnitz and others developed the idea of energy. However, the translators of my copy note that Newton did derive a value that would be equivalent to energy and his relationship is that it is equal to 0.5mv^2.

 

[DrPizza]

Gaatjes, that article is referring to the kinetic energy of the object, as born2bwire has pointed out. It has "nothing" to do with E=mc²


Furthermore, the article is wrong. If you drop an object from twice the height (ignoring drag), the final velocity upon reaching the ground will NOT be doubled. The velocity upon reaching the ground will be approximately 1.414 times as high. (square root of two) If you drop it from twice the height and include drag, then the velocity will be multiplied by even less than the square root of two.

 

[William Gaatjes]

Thank you for your reply born2bwire.

Great post.

 

[William Gaatjes]

Originally posted by: DrPizza
Gaatjes, that article is referring to the kinetic energy of the object, as born2bwire has pointed out. It has "nothing" to do with E=mc²


Furthermore, the article is wrong. If you drop an object from twice the height (ignoring drag), the final velocity upon reaching the ground will NOT be doubled. The velocity upon reaching the ground will be approximately 1.414 times as high. (square root of two) If you drop it from twice the height and include drag, then the velocity will be multiplied by even less than the square root of two.

Thank you for your reply, i do have a question.

How did you come to your explanation ?

I find it very interesting.

 

[Born2bwire]

Originally posted by: William Gaatjes

Originally posted by: DrPizza
Gaatjes, that article is referring to the kinetic energy of the object, as born2bwire has pointed out. It has "nothing" to do with E=mc²


Furthermore, the article is wrong. If you drop an object from twice the height (ignoring drag), the final velocity upon reaching the ground will NOT be doubled. The velocity upon reaching the ground will be approximately 1.414 times as high. (square root of two) If you drop it from twice the height and include drag, then the velocity will be multiplied by even less than the square root of two.

Thank you for your reply, i do have a question.

How did you come to your explanation ?

I find it very interesting.

The gravitational potential energy is m*g*h and the kinetic energy is 0.5*m*v^2. So doubling the height actually only increases the velocity by \sqr{2}.

 

[harobikes333]

Interesting. I'm up for the Full feature length movie. Not so sure the gf will agree with me though... :/

 

[William Gaatjes]

Originally posted by: Born2bwire

Originally posted by: William Gaatjes

Originally posted by: DrPizza
Gaatjes, that article is referring to the kinetic energy of the object, as born2bwire has pointed out. It has "nothing" to do with E=mc²


Furthermore, the article is wrong. If you drop an object from twice the height (ignoring drag), the final velocity upon reaching the ground will NOT be doubled. The velocity upon reaching the ground will be approximately 1.414 times as high. (square root of two) If you drop it from twice the height and include drag, then the velocity will be multiplied by even less than the square root of two.

Thank you for your reply, i do have a question.

How did you come to your explanation ?

I find it very interesting.

The gravitational potential energy is m*g*h and the kinetic energy is 0.5*m*v^2. So doubling the height actually only increases the velocity by \sqr{2}.

Can you now see why i doubt everything in physics unless i have done the test or mathematics myself. I have your explanation and i have the other explanation which is used in the documentairy.

From your post about the principa :

A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed. If some force generates any motion, twice the force will generate twice the motion, and three times the force will generate three times the motion, whether the force is impressed all at once or successively by degrees.

Can it be that Newton in the principa is talking about momentum ?
p = mv. Cause that seems to correspond with what you have written.


When it comes to drag... If you take a mass shaped like a droplet (good earodynamics) and of very high weight with respect to it's size, that would not negate the drag but makes the influence of drag a lot smaller, i suspect to a point that the result with or without drag calculations would still be close to the real answer. Lead would be preferred. Uranium would be ideal. Woops, i guess i now triggered some government computer program

There has been one thing that i was curious about. In the documentairy a device is used wich measures the depth with clay. The properties of the clay are important. I think the clay is much more important then the drag since the distance the object has to move is small and the object is small.

I am doing some calculations myself but translating it will take some time in order to avoid confusion. I am feeling the potentional energy and kinetic energy apply here but something need to be added.

 

[f95toli]

Yes, as far as a I remember Newton prefered to use momentum throughout his work.
This means that he instead of writing F=ma he prefered to use F=dp/dt=mdv/dt

You can easilty derive the expression Born2wire mentioned if you just conservation of energy (and he is right about the sqrt(2))

An object that is initially at rest at a height h and falls to the ground will have all of its potential energy converted to kinetic energy.
So you have potential energy at height h is equal to the kinetic energy when it hits the ground:

Wpot+Wkin=Wpot+Wkin

since v intially is zero and the height when it hits the ground is zero we have

mgh+0=0+mv^2/2

This gives
gh=v^2/2 ->2gh=v^2 ->v=sqrt(2gh)

Note that you can derive this starting from F=ma if you want as long if you use the definition of energy as force x distance (meaning you don't really need to use the "ready made" expressions for kinetic and potential energy if you don't want to)