E=mc^2

[Zarnaxus]

I am very new to this site. (couple minutes actually) but i am not new to the concepts of theoretical and quantum physics. I have read a couple beginning books on these topics, but have many more on their way. I have always been extremely interested in these crazy theorems and ideas. I plan on taking a physics related career in my life, and want to begin learning lots about it's expansive information.

 

Anyways, over my readings i have read over the simple equation E=mc^2 many many times. I understand its meaning well enough. E standing for energy. m for mass. and c obviously for the speed of light. This meaning that a very very large amount of energy is stored in such a small amount of mass, or maybe that mass itself is extremely condensed energy? I get this conclusion by viewing that c is a gargantuan number, and that c^2 is completely unfathamable.

 

The thing that i seem to not understand, is if Einstein was just simply stating that there is a large amount of energy in matter, or if the amount of energy in that matter is exacty equal to mc^2. So, what im trying to say is: Is the c^2 there just to represent a giant number, or is it the exact coefficient of m when mass is changing to energy. Is there exactly a c^2 amount of energy in one unit of mass? or again, sounding a little redundant, is c^2 there just to represent a giant number. If so, physicists should try to find the exact number that can be used to translate mass and energy. Maybe they already have. I am the student. Teach me.

[ydoaPs]

The equation shows that mass is a type of energy. C is not a random large number, the equation actually provides accurate results. The equation as you have put it, though, assumes that the object being studied is at rest with respect to your reference frame.

 

E²=m²c⁴+p²c² where E is energy, m is mass, c is the speed of light, and p is momentum.

[Zarnaxus]

awesome. Thanks for that. Sometimes i find these more simpler concepts to continually be getting more and more complex as i dive deeper and deeper into the physics universe.

[lemur]

The equation shows that mass is a type of energy. C is not a random large number, the equation actually provides accurate results.

 

"Accurate results" predicting what? measured how? Can you give an example, please? Thanks.

Edited December 4, 2010 by lemur

[Mr Skeptic]

"Accurate results" predicting what? measured how? Can you give an example, please? Thanks.

 

Weigh an atom. Throw protons or neutrons at it and see how much energy is released. Then weigh the results. E=mc^2 tells you how much lighter the atoms will be if you know the energy released, or if you measure how much lighter they are it tells you the energy that reaction releases.

[between3and26characterslon]

I am very new to this site. (couple minutes actually) but i am not new to the concepts of theoretical and quantum physics. I have read a couple beginning books on these topics, but have many more on their way. I have always been extremely interested in these crazy theorems and ideas. I plan on taking a physics related career in my life, and want to begin learning lots about it's expansive information.

 

Anyways, over my readings i have read over the simple equation E=mc^2 many many times. I understand its meaning well enough. E standing for energy. m for mass. and c obviously for the speed of light. This meaning that a very very large amount of energy is stored in such a small amount of mass, or maybe that mass itself is extremely condensed energy? I get this conclusion by viewing that c is a gargantuan number, and that c^2 is completely unfathamable.

 

The thing that i seem to not understand, is if Einstein was just simply stating that there is a large amount of energy in matter, or if the amount of energy in that matter is exacty equal to mc^2. So, what im trying to say is: Is the c^2 there just to represent a giant number, or is it the exact coefficient of m when mass is changing to energy. Is there exactly a c^2 amount of energy in one unit of mass? or again, sounding a little redundant, is c^2 there just to represent a giant number. If so, physicists should try to find the exact number that can be used to translate mass and energy. Maybe they already have. I am the student. Teach me.

 

 

C is the exact number not just an arbitrarily large number, E=mc² didn't just appear out of nowhere it was derived from previous knowledge.

 

Take a look here http://www.adamauton.com/warp/emc2.html

[TonyMcC]

Mr Skeptic, is your tongue very often in your cheek - or do you just like big bangs as well as big pools of water?

Edited December 4, 2010 by TonyMcC

[lemur]

Weigh an atom. Throw protons or neutrons at it and see how much energy is released. Then weigh the results. E=mc^2 tells you how much lighter the atoms will be if you know the energy released, or if you measure how much lighter they are it tells you the energy that reaction releases.

That makes sense, but how does C work since it's a speed? How do you multiply 1 gram by C^2? Does energy come out in force per unit distance (i.e. power)?

[Mr Skeptic]

That makes sense, but how does C work since it's a speed? How do you multiply 1 gram by C^2? Does energy come out in force per unit distance (i.e. power)?

 

Why don't you put it in google calculator? Or look up the units yourself? Or, compare to the units in the kinetic energy formula.

[Sisyphus]

That makes sense, but how does C work since it's a speed? How do you multiply 1 gram by C^2? Does energy come out in force per unit distance (i.e. power)?

 

Energy is in units of mass*distance^2/time^2. For example, the definition of a joule is 1 kilogram times 1 meter squared divided by 1 second squared.

 

It isn't the same as power. Power is energy per unit time, so mass*distance^2/time^3. (1 watt is 1 joule per second.)

[lemur]

Energy is in units of mass*distance^2/time^2. For example, the definition of a joule is 1 kilogram times 1 meter squared divided by 1 second squared.

 

It isn't the same as power. Power is energy per unit time, so mass*distance^2/time^3. (1 watt is 1 joule per second.)

These units confuse me. Speed = distance * time makes sense to me because it is a rate of change in distance. Likewise, momentum = mass * velocity makes sense to me because a fast moving light object can transfer its momentum to a heavier object to produce a lower speed. Power = force * distance makes sense because it makes sense to define power as continuously applied force. But how do these units for energy make any intuitive sense? Why is the distance divided by time? Are they just squared to avoid having to plug a negative number into the denominator? Is there any logic to defining what energy is in a qualitative sense? To me, energy (kinetic) is particle momentum, so it should be in mv units.

 

edit: I just remembered that force over a distance is work, not power. sorry for the mistake. no need to point out my mistake. it was just an example of an intuitively intelligible physics concept.

Edited December 4, 2010 by lemur

[Incendia]

...Lemur has hijacked the topic...

[Sisyphus]

These units confuse me. Speed = distance * time makes sense to me because it is a rate of change in distance. Likewise, momentum = mass * velocity makes sense to me because a fast moving light object can transfer its momentum to a heavier object to produce a lower speed. Power = force * distance makes sense because it makes sense to define power as continuously applied force. But how do these units for energy make any intuitive sense? Why is the distance divided by time? Are they just squared to avoid having to plug a negative number into the denominator? Is there any logic to defining what energy is in a qualitative sense? To me, energy (kinetic) is particle momentum, so it should be in mv units.

 

edit: I just remembered that force over a distance is work, not power. sorry for the mistake. no need to point out my mistake. it was just an example of an intuitively intelligible physics concept.

 

It makes intuitive sense if you work up to it.

 

Velocity is distance/time.

 

Acceleration is velocity per time, so distance/time^2.

 

Force is mass*acceleration, so mass*distance/time^2.

 

Energy is force through a distance, so mass*distance^2/time^2.

[swansont]

...Lemur has hijacked the topic...

 

!

Moderator Note

This is what the "report post" button is for, but in this case, I disagree. The OP seems to have been addressed, and this is a reasonable followup on the same topic.

[lemur]

...Lemur has hijacked the topic...

By actively attempting to clarify how the equation works and flesh-out the empirical logic of the units?

 

It makes intuitive sense if you work up to it.

 

Velocity is distance/time.

 

Acceleration is velocity per time, so distance/time^2.

 

Force is mass*acceleration, so mass*distance/time^2.

 

Energy is force through a distance, so mass*distance^2/time^2.

Ok, so I would call acceleration "rate of change of velocity where velocity is rate of change in distance." Then would force be "rate of change in momentum?" since momentum is mass * velocity? So by the same logic would energy be "rate of change in momentum through a distance?" So increasing energy means an object accelerates faster across a given distance or gains mass across a given distance of constant acceleration?

 

Would it also make sense to say that energy results in a certain amount of mass accelerating for a certain amount of distance? So, for example, if an atom fragments into pieces and the pieces accelerate, the combined force that generates acceleration in the various particles over the distance that they accelerate before reaching equilibrium is the amount of energy liberated by fission? And likewise if two hydrogens fuse into a helium, the resulting energy will exceed the input energy by an amount equivalent to the mass lost in the reaction?

 

So can you show the actual equation work with numbers plugged in so I can see it? Sorry to be babyish - if there's a link you can give me that shows it that would suffice. It seems that 300k m/s has to be first squared, making 90000k m^2/s^2 (or did I get that wrong already?). Then what mass do you use for, say, 1 gram of hydrogen? You can't just multiply 1g by 9000k m^2/s^2 and get 9000k gm^2/s^2, can you? If so, how do you convert that number into joules, btus, kwhours, etc.?

 

 

[Janus]

By actively attempting to clarify how the equation works and flesh-out the empirical logic of the units?

 

 

 

 

So can you show the actual equation work with numbers plugged in so I can see it? Sorry to be babyish - if there's a link you can give me that shows it that would suffice. It seems that 300k m/s has to be first squared, making 90000k m^2/s^2 (or did I get that wrong already?). Then what mass do you use for, say, 1 gram of hydrogen? You can't just multiply 1g by 9000k m^2/s^2 and get 9000k gm^2/s^2, can you? If so, how do you convert that number into joules, btus, kwhours, etc.?

 

The units must belong to the same system, thus if the mass is in grams, c is in cm/sec and the answer is in ergs. If the mass in kg, c is in m/sec and the answer is in joules. A joule is a watt-second, so there are 3,600,000 joules to a kwh. There are also 1055 joules to a BTU

 

If the mass is in pounds, c is in ft/sec and the energy is in ft-poundals.(the poundal being the unit of force in this system)

 

If the mass in in slugs, c is in ft/sec and the energy is in ft-lbs. (there being 778 to a BTU)

 

As will note, there are two systems that use pounds and feet; one in which the pound is a unit of force and the other where it is a unit of mass. They are often distinguished by designating them as lb(f) and lb(m). (there is also a third system that uses the lb for both force and mass, in which it is really important to keep them straight)

 

The units must belong to the same system, thus if the mass is in grams, c is in cm/sec and the answer is in ergs. If the mass in kg, c is in m/sec and the answer is in joules. A joule is a watt-second, so there are 3,600,000 joules to a kwh. There are also 1055 joules to a BTU

 

If the mass is in pounds, c is in ft/sec and the energy is in ft-poundals.(the poundal being the unit of force in this system)

 

If the mass in in slugs, c is in ft/sec and the energy is in ft-lbs. (there being 778 to a BTU)

 

As you will note, there are two systems that use pounds and feet; one in which the pound is a unit of force and the other where it is a unit of mass. They are often distinguished by designating them as lb(f) and lb(m). (there is also a third system that uses the lb for both force and mass, in which it is really important to keep them straight)

[lemur]

The units must belong to the same system, thus if the mass is in grams, c is in cm/sec and the answer is in ergs. If the mass in kg, c is in m/sec and the answer is in joules. A joule is a watt-second, so there are 3,600,000 joules to a kwh. There are also 1055 joules to a BTU

 

If the mass is in pounds, c is in ft/sec and the energy is in ft-poundals.(the poundal being the unit of force in this system)

 

If the mass in in slugs, c is in ft/sec and the energy is in ft-lbs. (there being 778 to a BTU)

 

As will note, there are two systems that use pounds and feet; one in which the pound is a unit of force and the other where it is a unit of mass. They are often distinguished by designating them as lb(f) and lb(m). (there is also a third system that uses the lb for both force and mass, in which it is really important to keep them straight)

 

Ok, thanks, I think I'm getting it. So if I use m/sec for C, which is 300k, then I should use 1/1000 for 1g. 90000k/1000=90000 joules, which would convert to kwhours by 90000/3600000, which is 0.025. That doesn't sound like much energy though. That's 25 watt-hours, which wouldn't even run a cfl lightbulb for two hours. Did I do something wrong?

[Craig Dilworth]

I am very new to this site. (couple minutes actually) but i am not new to the concepts of theoretical and quantum physics. I have read a couple beginning books on these topics, but have many more on their way. I have always been extremely interested in these crazy theorems and ideas. I plan on taking a physics related career in my life, and want to begin learning lots about it's expansive information.

 

Anyways, over my readings i have read over the simple equation E=mc^2 many many times. I understand its meaning well enough. E standing for energy. m for mass. and c obviously for the speed of light. This meaning that a very very large amount of energy is stored in such a small amount of mass, or maybe that mass itself is extremely condensed energy? I get this conclusion by viewing that c is a gargantuan number, and that c^2 is completely unfathamable.

 

The thing that i seem to not understand, is if Einstein was just simply stating that there is a large amount of energy in matter, or if the amount of energy in that matter is exacty equal to mc^2. So, what im trying to say is: Is the c^2 there just to represent a giant number, or is it the exact coefficient of m when mass is changing to energy. Is there exactly a c^2 amount of energy in one unit of mass? or again, sounding a little redundant, is c^2 there just to represent a giant number. If so, physicists should try to find the exact number that can be used to translate mass and energy. Maybe they already have. I am the student. Teach me.

 

E = mc² is from the 1880s and is derivable from Maxwell's equations. It has virtually nothing to do with Einstein. Could talk more about the equation, if you're interested.

 

Craig

[Incendia]

... E=MC² is Eisteins equations. He simplified all those long equations made by his predecessors into one short easy to understand one.

[Sisyphus]

Ok, thanks, I think I'm getting it. So if I use m/sec for C, which is 300k, then I should use 1/1000 for 1g. 90000k/1000=90000 joules, which would convert to kwhours by 90000/3600000, which is 0.025. That doesn't sound like much energy though. That's 25 watt-hours, which wouldn't even run a cfl lightbulb for two hours. Did I do something wrong?

 

Couple things. The speed of light is not 300k meters per second. It's 300 million meters per second. You also didn't square it correctly. 300k*300k is not 90000k - that's just 300k*300.

 

So, 300,000,000m/s squared is 90,000,000,000,000,000, making your answer off by a factor of 1 billion. It will run a CFL bulb for two billion hours.

[michel123456]

It makes intuitive sense if you work up to it.

 

Velocity is distance/time.

 

Acceleration is velocity per time, so distance/time^2.

 

Force is mass*acceleration, so mass*distance/time^2.

 

Energy is force through a distance, so mass*distance^2/time^2.

 

Emphasis mine.

 

If Energy = Force through Distance we shoud have

 

E= m a d

(no kidding)

 

Where E energy, m mass, a acceleration, d distance. And the product a*d happen to be equal to C^2.

 

Or to put it otherwise, we are living in a world in constant acceleration: it is the a factor in the equation.

[lemur]

Couple things. The speed of light is not 300k meters per second. It's 300 million meters per second. You also didn't square it correctly. 300k*300k is not 90000k - that's just 300k*300.

 

So, 300,000,000m/s squared is 90,000,000,000,000,000, making your answer off by a factor of 1 billion. It will run a CFL bulb for two billion hours.

 

So 1g of matter is convertible to 25,000 kwh of electricity at 100% efficiency, regardless of what type of matter it is? So a fusion reactor that would convert hydrogen to helium would only deplete 1g of mass per 25,000kwh generated? So how would you figure out how much mass is lost in the conversion? Is this also explained by E=MC^2 or does that require attention to the internal structure of the atoms in question?

[John Cuthber]

A well known search engine tells me that the mass of a proton is 1.67262158 × 10-27 kilograms

and that the mass of the helium nucleus is 6.64465620 x 10-27 Kg

So, if I fuse 4 protons together to get an alpha particle I change 4 x 1.67262158 × 10-27 i.e. 6.69048632 x 10-27 Kg into 6.64465620 X 10-27Kg

The difference

0.04583012 X 10-27 Kg is converted into energy

 

(Incidentally, I know- the charge doesn't balance and it's a bit more complicated than sticking 4 protons together but I'm just illustrating the point)

[Zarnaxus]

So, to clerify the answer to my original confusion, E=mc² might not even be the correct equation in comparing energy to mass if you take momentum into consideration. The c² is not actually a random large number in the corelation between mass and energy, but actually generates accurate results. We obtain this conclusion by viewing the meaning of energy and find that e= m a d? and that ad equals c².

 

So, proceeding forward on this topic, i am curious if you included some theoretical parts to this equation. I am aware that theoretical physics could allow the existence of negative and imaginary particles, creating negative and imaginary mass. So, completely theoretical, what is the equation that you could use to include these extra types of matter. A simple response, probably wrong, could be

E = +or- imc². Again, that is... not right probably, im just giving my own logical hypothesis. Is there an equation to show the correlation of any type of mass, be it theoretical or real, and energy considering momentum as well?

[swansont]

So, to clerify the answer to my original confusion, E=mc² might not even be the correct equation in comparing energy to mass if you take momentum into consideration.

 

An object with momentum also has kinetic energy, and you have to take that into account. E=mc^2 refers to rest energy only.