The basic meaning of E=mc2

[randylowther]

I think I would like to hear from you(collectively that is) reguarding the basic consept of that most famous of Equations...My limted understanding tells me that among many things,It (the equation that is) states that Matter and Energy are fundmentaly the Same and are interchangable.....But I also understand that there must be more...So what am I missing....

 

[nailpounder]

I think I would like to hear from you(collectively that is) reguarding the basic consept of that most famous of Equations...My limted understanding tells me that among many things,It (the equation that is) states that Matter and Energy are fundmentaly the Same and are interchangable.....But I also understand that there must be more...So what am I missing....

Yup! You got it pretty straight there. You can also relate it to F=MA (Newton). Einstein's was just a bit more refined!

.................Al

 

[Shpaget]

You can also relate it to F=MA (Newton). Einstein's was just a bit more refined!

Could you relate if for me please?

 

[MeteorWayne]

I heard there's a new book out called Why Does E=MC2 and Why Should We Care. I'll try and find a link, and the book to read One of the authors (Brian Cox) was on The Colbert Report.

Here's a synopsis:

http://www.powells.com/biblio/9780306817588

Professor Brian Cox and Professor Jeff Forshaw go on a journey to the frontier of 21st century science to consider the real meaning behind the iconic sequence of symbols that make up Einstein's most famous equation, E=mc2. Breaking down the symbols themselves, they pose a series of questions: What is energy? What is mass? What has the speed of light got to do with energy and mass? In answering these questions, they take us to the site of one of the largest scientific experiments ever conducted. Lying beneath the city of Geneva, straddling the Franco-Swiss boarder, is a 27 km particle accelerator, known as the Large Hadron Collider. Using this gigantic machine--which can recreate conditions in the early Universe fractions of a second after the Big Bang--Cox and Forshaw will describe the current theory behind the origin of mass.

 

[origin]

I think I would like to hear from you(collectively that is) reguarding the basic consept of that most famous of Equations...My limted understanding tells me that among many things,It (the equation that is) states that Matter and Energy are fundmentaly the Same and are interchangable.....But I also understand that there must be more...So what am I missing....

It is not so much that they are interchangable. Matter is not energy and energy is not matter. The equation is the equivilancy of matter and energy. So matter can be converted to energy and energy can be converted to matter relative the equation.

The importance of this is far reaching, some of the everyday results of this is:

Nuclear reactors - A uranium atom is split and the mass of the parts are less than the mass of the original atom the mass loss was converted to energy following the equation E=mc^2. The energy released is in the form of KE of the fission products and EM radiation.

The Sun converts hydrogen to helium the mass of the parts are more than the mass of the fused atoms, the missing mass was converted to energy again following the equation E=mc^2. The majority of the energy is in the form of EM radiation.

 

[drwayne]

I think of it as representing an exchange rate, much like a currency exchange rate.

Wayne

 

[randylowther]

Thanks to all you out there for feilding that question......Not to worry I'll most likely have more as times goes on....Like this one.....Is Gravity is Force all it's own....Or is just a property of Mass.....Secondly Tachyon(this is misspelled so pardon my lack of English skills) I have heard that these particals travel seemingly backwards in time...Is this Truth?Also I have Heard that Space itself travels faster than light...ala "The Red Shift"..If that is so..What does that mean for The Idea of FTL travel???

 

[MeteorWayne]

Tachyons are purely theoretical constructs, there is NO evidence that they exist.

 

[vividasday]

Geez, upon your question...go back. Disregard the meaning and appreciate the definition.

 

[mabus]

t is not so much that they are interchangable. Matter is not energy and energy is not matter. The equation is the equivilancy of matter and energy. So matter can be converted to energy and energy can be converted to matter relative the equation.

I think you are mistaken here.... matter IS energy in a contained form. Think of the difference between water and ice. Ice IS water in a contained form but it is still water, so is steam. In a similar fashion, the components of "matter" and energy are exactly the same.

 

[mabus]

Secondly Tachyon(this is misspelled so pardon my lack of English skills) I have heard that these particals travel seemingly backwards in time...Is this Truth?Also I have Heard that Space itself travels faster than light...ala "The Red Shift"..If that is so..What does that mean for The Idea of FTL travel???

As for Tachyons, they do not exist. You will not find them referenced in any modern papers really other than some fringe stuff, and of course star trek.

The red shift has to do with how the universe is expanding. As it expands light gets shifted towards the red end of the spectrum. Your second question relates to the speed of light. People often ask this question so you are not alone. The idea of light travelling at C, and that nothing can go faster than C only applies to matter inside the universe, and not to space-time itself, just matter inside the universe. Because of this, the red shift has absolutely nothing at all to do with the idea of faster than light travel.

 

[Kessy]

I think the best way to explain the relationship between matter and energy is to look at the history of the idea of energy itself. Early scientists noticed that certain things always interact in a certain predictable way - speed, weight, height, temperature, pressure, electric charge, and so on. They all seemed to be working on some common principle, so they came up with an abstract idea, energy, to describe how they all interact. What we've discovered is that mass itself is also part of that common principle, too.

Another way to think about it is that when you measure mass and energy, you're measuring slightly different aspects of the same thing, like voltage and amperage. You can't have one without the other.

A side note about nuclear reactions - it's only true that the mass of the reactants is greater then the mass of the products if you're talking about their rest masses. If a distant observer were to measure the total apparent mass of the entire system, including all the photons involved, it would be the same both before and after the reaction.

 

[SpeedFreek]

This is how I sum it up:

A compressed spring weighs more than an uncompressed spring.

 

[weeman]

I think I would like to hear from you(collectively that is) reguarding the basic consept of that most famous of Equations...My limted understanding tells me that among many things,It (the equation that is) states that Matter and Energy are fundmentaly the Same and are interchangable.....But I also understand that there must be more...So what am I missing....

E=mc^2 represents the idea that: given the mass, we can determine the amount of energy, and vice versa. It also tells us that the closer an object travels to the speed of light, the more its mass increases. Since mass and energy are two versions of the same thing, when an object moves faster and faster towards lightspeed it exerts more energy, therefore increasing its mass. The mass of an object moving towards light speed will continue to grow, exponentially. An object traveling at 99.9% the speed of light will weigh less than itself when it's traveling at 99.999999% the speed of light. This would mean that it requires an infinite amount of energy to propel an infinite amount of mass, which of course is impossible.

It was because of this equation that Einstein discovered that nothing can travel faster than light.

 

[benbald]

Well this is only part of the equation. The full equation is E^2 = (pc)^2 + (mc^2)^2. This is Einstein's relativistic energy-momentum equation and what you notice is that in the special case where velocity is zero, it reduces to the more familiar E=mc^2. Which basically states that in a closed system, even when something is not moving, it has some minimum amount of energy by virtue of the fact that it has mass, which is called it's "rest energy".

As has been previously stated in this thread, that relation will allow you to calculate the energy of the photons released when a chunk of mass is converted to photons, however I think it is indeed a mistake to say that mass and energy are the same thing. They are not. The water and ice comparison is completely irrelevant as this is not a phase change at all. When you get into particle physics what you find is that particles like to decay from one kind to another, of different masses, but the thing that is always conserved is energy and this equation correctly describes the mass to energy conversion so that before and after any given process, the total energy is always conserved.

Its quite an interesting argument whether energy is a completely mathematical way to track the numbers, or whether there is a more physical aspect to it but either way, conservation of energy really is one of the most fundamental (if not THE most fundamental) tools that we have in science.

 

[yevaud]

This is how I sum it up:

A compressed spring weighs more than an uncompressed spring.

Er, no it doesn't. Not even a picogram.

 

[darkmatter4brains]

This is how I sum it up:

A compressed spring weighs more than an uncompressed spring.

Er, no it doesn't. Not even a picogram.

Admittedly, my GR is real rusty as usual but, as I understand it, Speedfreeks statement is essentially correct. You can sorta see this from Einstein's GR equation:

G_subscripts = 8*pi*T_subscripts (2 subscripts on each of those tensors, T and G)

G is the Einstein tensor, and the curvature of spacetime (gravitional effects) is contained within it. T is the stress energy tensor and contains more than just mass - it has indices that cover energy and pressure.

So, if SFs compressed spring is in a higher energy state than an umcompresses spring, it will have a greater gravitational effect on the spacetime around it. Also, the infamous saying a hot potato is heavier than a cold potato. Although, you're probably right - it might only be by a picogram :lol:

Another consequence of the stress energy tensor, is if space is filled with negative pressure, gravity will become a repulsive force - a condition that has been hypothesized for the early Unvierse.

Anyhow, hopefully, I got all that mostly straight. Ramparts, where are you?

 

[Saiph]

Darkmatter...that is also my understanding of GR.

Of course, I'm uncertain if it's a true increase in 'mass' or just an increased resistance to acceleration (and increased gravitational effect). I.e. the rest mass vs relativistic 'mass' issue.

 

[Jerromy]

Would that relate to string theory as well? Would a compressed string "weigh" more than a relaxed string? Or is that only in another parallel universe that the energy of the string would be contained in while the string itself would be contained in our universe? Perhaps a 26 dimension string would weigh the same in any potential energy state?

 

[Kessy]

I think some of the confusion is because we normally think of mass as an inherent property of objects, a fundamental measure of how much stuff there is in something. At least in this context, that's not a very good way to think of it.

Mass is not weight, and mass is not matter. Mass is a particular property of matter, formally defined by Newton's second law, F = ma. (The force applied to an object is equal to its mass multiplied by the acceleration caused by that force.) So what Saiph said is correct - from the perspective of physics, mass *is* an object's resistance to acceleration.

The really strange thing is that relativity says that a particular object's mass is not the same for all observers. So, for example, if one person on Earth were to measure the mass of an object, let's say an asteroid, and another person on a spaceship traveling past Earth at near the speed of light were to measure the mass of the same asteroid, they would get different answers. Because of this, we often need to specify what frame of reference we're using when talking about mass, and the most common distinction is between apparent mass - the mass of something from a particular observer's point of view - and rest mass - the mass of something from the point of view of an observer at the same energy as the object. So, a compressed spring has a greater apparent mass then an uncompressed spring, but the same rest mass, and a hot potato has a larger apparent mass then a cold potato, but the same rest mass. In fact, adding energy to a system in any form will always increase that system's apparent mass.

Now, we don't see this effect in everyday life because the changes in apparent mass caused by changes of energy of the scale we normally deal with is very very small. Remember that in E = mc^2 that c is a really really big number.

Apparent mass and rest mass are a bit like the apparent magnitude and absolute magnitude of stars in astronomy. Apparent magnitude is how bright a particular star looks from our point of view here on Earth, and absolute magnitude is what a star's apparent magnitude would be under particular conditions, specifically if you were looking at the star from a specified distance.


One small technical side note - in classical physics, there were actually two different definitions of mass. Inertial mass, which I described above, and gravitational mass. For centuries it was a great mystery why inertial and gravitational mass are the same, it wasn't until Einstein's geometric interpretation of gravity in general relativity that was explained.

 

[magikmal@gmail.com]

:idea: e = mc^2

energy = mass * square of the speed of light...
so the energy possessd depends on the mass and speed of an object... an object with higher mass and higher speed has higher energy... light has the maximum speed but the least mass... so acc the string theory and all tht there,
there are two memberans like things floating in space... when those two memberanes hit each other the tremendous energy outburst was converted into mass and energy... in 1 memberane the mass is more and in the other the speed is more... ultimately goin along wid the einsteins theory... we happen to be in the memberans where there is mass, and less speed... otherwise the world wldve been moving in the speed of light... thus moving away from the plae of the bang... so we are all a part of the energy whch was changed into mass...
i think its irrelavent in this question, but i liked this theory and thought of sharing it...