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1) The increase in heat of the water is equivalent to the loss of mass. So presumably you are referring to the equivalence principle E=mc^{2}. The ^{2} in c^{2} represents acceleration.

2) The energy produced is unknown until it is measured which involves obliterating the photons making them give up their energy as momentum and re-radiating some photons at a lower energy level. The increase in momentum of the target is acceleration.

3) Presumably this relies upon knowing initially both the volume and mass of 1 molecule.Knowing the mass of 1 molecule relies upon counting the total number of protons and neutrons and knowing the weight of a proton.“Because atoms are exceptionally small, scientists typically work with atoms in larger quantities called moles. A mole is the amount of a substance with as many atoms as there would be in 12 grams of the isotope carbon-12. This number is roughly 600 sextillion (6 times 10 to the 23rd power) atoms, and is known as Avogadro's number for the scientist who defined it.”...sorry, you cannot view external links. To see them, please REGISTER or LOGINThis method of calculating the mass depends upon initially knowing the atomic weight of one molecule and that requires ‘weighing’ it. Weighing it requires a non-inertial (accelerating) reference frame. It’s a calculation based upon a measurement taken in an accelerating reference frame.

4) Is essentially the same answer as 3 but substituting atom for molecule.

Quote from: Geezer on 10/06/2012 19:48:54Quote from: MikeS on 10/06/2012 11:38:07It's not arbitrary as it is comparing an unknown mass with a known mass.All three cases involve acceleration and acceleration costs energy. In the case of the spring and triple balance the energy comes from gravitational potential energy. It makes little difference where the energy comes from it still causes acceleration and gives "some idea of the relationship between mass and energy".As Evan points out, the known mass is completely arbitrary, so the compared mass is also completely arbitrary. Consequently, any form of balance isn't really telling you anything about the mass.If you use a spring type scale, or an accelerometer, you are determining weight, not mass. You could use a "known mass" to determine the intensity of a gravitational field by this method then do a comparison to determine the relative mass of another object, but then you are back to only establishing a comparitive arbitrary mass.On the other hand, if you actually alter the momentum of an object, there are methods of directly quantifying the energy conversion.I agree it does not tell you anything about mass itself but it is not really arbitrary if you do the comparison with a known mass. Anyway that argument is beside the point. The question was “Do we need acceleration to define the concept of mass?"How do you propose to "alter the momentum of an object" without accelerating it?If you accept that it accelerates then presumably you accept that you "Do .. need acceleration to define the concept of mass?" Which is what I said in the first place and repeated in post #40 of this thread."For example imagine a big rock floating in space. Give it a slap with a calibrated hand so you know exactly how much energy you gave it. Now measure how fast the rock is moving."...sorry, you cannot view external links. To see them, please REGISTER or LOGIN"That's one way of measuring the mass and it involved acceleration of the mass."

Quote from: MikeS on 10/06/2012 11:38:07It's not arbitrary as it is comparing an unknown mass with a known mass.All three cases involve acceleration and acceleration costs energy. In the case of the spring and triple balance the energy comes from gravitational potential energy. It makes little difference where the energy comes from it still causes acceleration and gives "some idea of the relationship between mass and energy".As Evan points out, the known mass is completely arbitrary, so the compared mass is also completely arbitrary. Consequently, any form of balance isn't really telling you anything about the mass.If you use a spring type scale, or an accelerometer, you are determining weight, not mass. You could use a "known mass" to determine the intensity of a gravitational field by this method then do a comparison to determine the relative mass of another object, but then you are back to only establishing a comparitive arbitrary mass.On the other hand, if you actually alter the momentum of an object, there are methods of directly quantifying the energy conversion.

It's not arbitrary as it is comparing an unknown mass with a known mass.All three cases involve acceleration and acceleration costs energy. In the case of the spring and triple balance the energy comes from gravitational potential energy. It makes little difference where the energy comes from it still causes acceleration and gives "some idea of the relationship between mass and energy".

The Earth pushes the scale. The scale pushes the mass. This results in a change of momentum for the mass. This is acceleration.

A tripple balance compares an unknown mass with a known mass and the difference in gravity (acceleration) on different planets is compensated for by affecting both the known and unknown mass in the same proportion. The mass remains the same but the weight changes.

Whether you apply acceleration to the mass by the Earth pushing it or anything else pushing it, its the same thing, acceleration.

There is no difference between accelerating a mass by applying a force to it and the Earth accelerating the same mass by applying a pseudo-force to it (gravity). They are equivalent.

There is no difference in measuring a force applied to a mass and the distance it travels than measuring the pseudo-force the Earth applies to the same mass and the distance it travels.

Quote from: MikeS on 11/06/2012 11:26:16The Earth pushes the scale. The scale pushes the mass. This results in a change of momentum for the mass. This is acceleration.Sorry, but that's not right either. The only change in momentum is caused by the rotation of the Earth and the rotation of the object, and the amount of the change is very small.QuoteA tripple balance compares an unknown mass with a known mass and the difference in gravity (acceleration) on different planets is compensated for by affecting both the known and unknown mass in the same proportion. The mass remains the same but the weight changes.Yes, mass is constant, but you are ignoring the fact that gravity on Earth is not constant, so the weight of an object on Earth varies with location.QuoteWhether you apply acceleration to the mass by the Earth pushing it or anything else pushing it, its the same thing, acceleration.Pushing is NOT the same as acceleration. Acceleration requires a change in velocity. In Classical Mechanics, gravity produces an accelerative force that acts on all matter, but there is only acceleration with change in velocity, hence a change in momentum.QuoteThere is no difference between accelerating a mass by applying a force to it and the Earth accelerating the same mass by applying a pseudo-force to it (gravity). They are equivalent.But the object is not accelerating. Your argument only applies if you allow the object to free-fall, but then you will find that all objects accelerate at the same rate regardless of their mass. Treating gravity as a pseudo-force only works if you apply General Relativity. That means you have to analyze the entire problem using General Relativity.QuoteThere is no difference in measuring a force applied to a mass and the distance it travels than measuring the pseudo-force the Earth applies to the same mass and the distance it travels.Except that you don't know what the gravitational force actually is, and there isn't any "travel".

It is when talking about the acceleration of a massive body like the Earth. A steady push is the steady application of energy. The steady application of energy (as in a rocket for example) causes a steady acceleration. A 'push' changes the velocity of the object. That change in velocity is acceleration.We do know what the acceleration is it's 1 g. There must be travel as the Earth is travelling through space-time. Because we do not understand how to take the measurements does not make it any the less true.

Quote from: MikeS on 10/06/2012 11:49:001) The increase in heat of the water is equivalent to the loss of mass. So presumably you are referring to the equivalence principle E=mc^{2}. The ^{2} in c^{2} represents acceleration. velocity squared DNE accelerationQuote2) The energy produced is unknown until it is measured which involves obliterating the photons making them give up their energy as momentum and re-radiating some photons at a lower energy level. The increase in momentum of the target is acceleration.E = h.nuQuote3) Presumably this relies upon knowing initially both the volume and mass of 1 molecule.Knowing the mass of 1 molecule relies upon counting the total number of protons and neutrons and knowing the weight of a proton.“Because atoms are exceptionally small, scientists typically work with atoms in larger quantities called moles. A mole is the amount of a substance with as many atoms as there would be in 12 grams of the isotope carbon-12. This number is roughly 600 sextillion (6 times 10 to the 23rd power) atoms, and is known as Avogadro's number for the scientist who defined it.”...sorry, you cannot view external links. To see them, please REGISTER or LOGINThis method of calculating the mass depends upon initially knowing the atomic weight of one molecule and that requires ‘weighing’ it. Weighing it requires a non-inertial (accelerating) reference frame. It’s a calculation based upon a measurement taken in an accelerating reference frame. volume of molecule no need to know. mass of molecule is calculable as well as measurable Quote4) Is essentially the same answer as 3 but substituting atom for molecule. i never mentioned molecule btw. And three is easily done - whereas 4 is v difficult

Quote from: MikeS on 12/06/2012 07:39:43It is when talking about the acceleration of a massive body like the Earth. A steady push is the steady application of energy. The steady application of energy (as in a rocket for example) causes a steady acceleration. A 'push' changes the velocity of the object. That change in velocity is acceleration.We do know what the acceleration is it's 1 g. There must be travel as the Earth is travelling through space-time. Because we do not understand how to take the measurements does not make it any the less true.Mike, if you are going to argue using GR, I strongly suggest you study Classical Mechanics and basic Thermodynamics first. What you are suggesting here is that there is a continuous transfer of energy from the Earth to your backside when you are sitting in a chair. That is patently ridiculous. There is no change in energy of the Earth, you, or the chair, and even String Theory won't support the idea that there is. Standard Gravity on Earth is an approximation. It is not constant with location which is why weight varies depending on where you are on the Earth.

mass is only a function of speed (magnitude of velocity), not of acceleration.

Whether or not the Earths acceleration in space-time (gravity) involves the expenditure or energy we simply do not know. We do know that the Earth warps or bends space-time locally. Maybe the Earth extracts energy from that. I am not postulating that it does, I am simply saying it remains a possibility until proven otherwise.

How does that relate toquote lightarrow Reply #2 on: 24/05/2012 21:52:40Quote"The best way is to consider the object...still An oject's mass is its energy (divided c2) when the object is still."andThe question was not about what mass is a function of but "Do we need acceleration to define the concept of mass?"