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Mass Equalivant To Energy?


hazelm

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Yesterday, in John Barrow's "Origin of the Universe",  I read a statement that Energy and Mass are equivalent.  He then gave E=mc^2 as evidence.  I was stopped for a while, knowing that "equivalent" means equal to.  Reading Einstein's formula literally,  the measurement of a given mass does not equal the measurement of a given  energy - not until you multiply the mass times the speed of light squared.  So?

 

But, am I mis-interpreting?  If we reverse the formula, maybe it says that measuring mass time speed of light squared will tell us how much energy that particular mass contains?  mass time speed of light squared = its energy. 

 

Can someone please clarify?  Thank you. 

 

 

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Hi Hazel yes, loosely speaking, mass is equivalent to energy with a conversion factor (which is just c^2) and it intends to show that you get a lot of energy from a small piece of mass. Better put, mass is a concentrated energy and energy is a diffused mass. 

So, his statement was over-simplified?  The big picture takes in the light source?  Hoping I have it, thanks.

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Hi Hazel yes, loosely speaking, mass is equivalent to energy with a conversion factor (which is just c^2) and it intends to show that you get a lot of energy from a small piece of mass. Better put, mass is a concentrated energy and energy is a diffused mass. 

In doing the arithmetic for the graphical behavior in my proof of the Josephson Constant (frame-dragging of the gravitational pilot-fluid sphere inversions that govern quantum electro-dynamics) the equations did this naturally as the photon aether system tended toward compression/ negative entropy (locally) .

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E=MCis a very basic form of mass and energy equivalence to truly understand this you must begin to understand the Strong Nuclear Force.

 

 

 

This is incorrect. You do not need to consider the nuclear strong force at all to understand E=mc². 

 

The expression is completely general to all forms of energy conversion and is far from specific to nuclear reactions. If you charge a chemical battery it gets heavier, just not by enough to measure in practice. 

 

The common misunderstanding that it applies only to nuclear reactions is because this is one area in which the mass differences before and after the release of energy are easy to measure, because of the very large amounts of energy released from very tiny objects and the consequently large proportionate change in mass that takes place. 

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This is incorrect. You do not need to consider the nuclear strong force at all to understand E=mc². 

 

The expression is completely general to all forms of energy conversion and is far from specific to nuclear reactions. If you charge a chemical battery it gets heavier, just not by enough to measure in practice. 

 

The common misunderstanding that it applies only to nuclear reactions is because this is one area in which the mass differences before and after the release of energy are easy to measure, because of the very large amounts of energy released from very tiny objects and the consequently large proportionate change in mass that takes place. 

 

 

You know I was trying to make this simple but I suppose I cannot and Yes you are right. Alright in any region where energy is stored in a form called "Potential Energy" there is a increase in the density of the energy because of this stored energy via forces trapping it. What we consider to be mass is actually just energy at a higher density in that space formed by energy trapped by forces with a much higher density than normal, thus energy and mass are actually the same-thing just one is the form not trapped by a force, mass is the energy trapped by forces which increase the energy of objects usually this energy is trapped in the Strong Nuclear Force which is considered to be mass. Other Forces can trap energy too which would be considered to be "Mass" too, but generally the amount of energy trapped by these forces is much less than the Strong Nuclear Force and not in such a small volume of space, thus the energy release is much less noticeable when broken like exchemist said, but usually mass is considered to be Strong Nuclear Force bonds but any bonds could be said to have mass rather than energy because mass is just energy at a higher density which all bonds cause energy to be at a higher density in the volume they inhabit.

 

Edited by VictorMedvil
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So, his statement was over-simplified?  The big picture takes in the light source?  Hoping I have it, thanks.

No Hazel you don't need light to be involved. It is just that the rest mass in an object represents a certain amount of contained energy and if you want to know how much you take the mass and multiply by the square of the speed of light. 

 

You can sort of see the units stack up: 

 

The amount of energy done in mechanical work is W= Force x distance i.e. F x d. But from Newton we know F=ma, so the energy expended in mechanical work is ma x d. This has units of mass x distance /time² x distance, i.e. mass x distance²/time². All forms of potential energy  (signifying work done against a force through a distance) are of this kind.

 

 Similarly for kinetic energy we have E=1/2 mv², which has units of mass x (distance/time)² i.e. once again mass x distance²/time².

 

The total energy of a system is the sum of these two type of energy, potential and kinetic.  

 

And now we have E=mc², which has again units of mass x (distance/time)². So the units check out. 

 

Specifically, if E is measured in Joules, mass in kilograms and speed in metres/second, then joules = kg x (3x10⁸m/sec)² , i.e. mass in kg x 9 x 10¹⁶ - almost a conversion factor of mass to energy of 10¹⁷.   That is a lot of energy in one kilogram!

 

Needless to say we can't in practice release anything like this amount from a kilo of matter. But if you were to let half a kilo of matter collide with half a kilo of antimatter that is what would be given off when the two annihilated each other. 

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You know I was trying to make this simple but I suppose I cannot and Yes you are right. Alright in any region where energy is stored in a form called "Potential Energy" there is a increase in the density of the energy because of this stored energy via forces trapping it. What we consider to be mass is actually just energy at a higher density in that space formed by energy trapped by forces with a much higher density than normal, thus energy and mass are actually the same-thing just one is the form not trapped by a force, mass is the energy trapped by forces which increase the energy of objects usually this energy is trapped in the Strong Nuclear Force which is considered to be mass. Other Forces can trap energy too which would be considered to be "Mass" too, but generally the amount of energy trapped by these forces is much less than the Strong Nuclear Force and not in such a small volume of space, thus the energy release is much less noticeable when broken like exchemist said, but usually mass is considered to be Strong Nuclear Force bonds but any bonds could be said to have mass rather than energy because mass is just energy at a higher density which all bonds cause energy to be at a higher density in the volume they inhabit.

 

 

Look, you don't need any of this stuff about forces. It is simply a true relation for any situation. Like F=ma. 

Edited by exchemist
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Look, you don't need any of this stuff about forces. It is simply a true relation for any situation. Like F=ma. 

 

Yes but that doesn't explain why it is that way. Which basically is due to the energy being trapped in that system, you must move the energy within those bonds with the object which increases the amount of force required to move that object being that the energy stored as mass weighs the object down, when the energy is no longer trapped being that the bond is broken, it decreases in density then becomes energy that is untrapped again which is called "Energy" and not "Mass".

 

energy13.gif

 

Edited by VictorMedvil
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Yes but that doesn't explain why it is that way. Which basically is due to the energy being trapped in that system, you must move the energy within those bonds with the object which increases the amount of force required to move that object being that the energy stored as mass weighs the object down, when the energy is no longer trapped being that the bond is broken, it decreases in density then becomes energy that is untrapped again which is called "Energy" and not "Mass".

 

 

What explains why it is that way is Special Relativity, nothing to do with ball and stick models and arrows showing forces.

 

Your models purport to show one way that potential energy arises, that's all, though they get it wrong*. They do not explain E=mc². 

 

*They are wrong because they suggest that a bond stores energy. The opposite is true. It takes energy to break a bond.

 

Energy is released when bonds form. That is why bound states stay bound: they are at a lower potential energy level.

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What explains why it is that way is Special Relativity, nothing to do with ball and stick models and arrows showing forces.

 

Your models purport to show one way that potential energy arises, that's all, though they get it wrong*. They do not explain E=mc². 

 

*They are wrong because they suggest that a bond stores energy. The opposite is true. It takes energy to break a bond.

 

Energy is released when bonds form. That is why bound states stay bound: they are at a lower potential energy level.

 

It is the opposite for chemical bonds then the other forces. The Reason for that in chemical bonds is it takes less energy sustain that state of being bonded in chemical bonds, unbounded chemicals are more unstable but in the other forces it is opposite.

Edited by VictorMedvil
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It is the opposite for chemical bonds then the other forces. The Reason for that in chemical bonds is it takes less energy sustain that state of being bonded in chemical bonds, unbounded chemicals are more unstable but in the other forces it is opposite.

No it isn't. It is true of all bonds and all binding.

 

There is quite a good if long article about it all here: https://en.wikipedia.org/wiki/Binding_energy

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No it isn't. It is true of all bonds and all binding.

 

There is quite a good if long article about it all here: https://en.wikipedia.org/wiki/Binding_energy

 

Yes and when the bond is broken the binding energy and mass defect of the bond is released. When I was speaking about the potential energy of the bond I was talking about the Potential energy and the "Mass" of the bond or "Mass Defect" as Potential energy if you don't include the "Mass Defect" as potential energy it is lower, but since both mass and energy are the same-thing I was speaking of them both as potential energy of the bond. The Term I guess I should have used to stop confusion was "Total Bond Energy" and not Potential Energy as that would get confused with binding energy.

Edited by VictorMedvil
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Yes and when the bond is broken the binding energy and mass defect of the bond is released. When I was speaking about the potential energy of the bond I was talking about the Potential energy and the "Mass" of the bond or "Mass Defect" as Potential energy if you don't include the "Mass Defect" as potential energy it is lower, but since both mass and energy are the same-thing I was speaking of them both as potential energy of the bond. The Term I guess I should have used to stop confusion was "Total Bond Energy" and not Potential Energy as that would get confused with binding energy.

No, I repeat, it takes energy input to break the bond. You do not "release" energy by breaking a bond. 

 

That is why the mass of nucleons is always less than the mass of their constituent protons and neutrons. The nucleon contains less energy than the protons and neutrons do when separated. You must put energy in to separate them. More here: http://hyperphysics.phy-astr.gsu.edu/hbase/NucEne/nucbin.html

 

The reason why fission yields energy is because the fission products have less energy than the starting material. So you have a certain energy input to split the nucleus but an energy release greater than the input, when the bits combine to form new nuclei.

 

So the overall effect is that stronger bonds are formed than the ones that are broken and the total energy of the system goes down, i.e. the products are more stable than the starting material. 

Edited by exchemist
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