The Opposite Of E=Mc2?.......sort Of

[layman]

energy is equal to mass accelerated to the speed of light x the speed of light.

 

so if we took a particle, say an electron and accelerated it to c(the speed of light) it would hit the light speed barrier, we then keep dumping in energy

until we reach the equivalent energy of c2, at that point the particle would transform into pure energy.

 

as it's accelerating it's gaining mass,  just prior to becoming pure energy it would be very large.

what material could represent the "largeness"? the electron can't just keep swelling up, there has to be matter forming there.

 

if there is matter forming there, then that means matter gets created above the energy level of a photon, yet matter is much less energetic than photons,

 

if we slowed down energy to the square root of c2, we would then get a photon.

if we then subtract the speed of light from the photon, we get absolute zero.

 

where does matter come in? at what "speed" does energy become matter?

[sanctus]

E=mc² means it always is not that it becomes. The main problem in your reasoning is though that the energy needed to accelerate your massive electron to almost the speed of light is huge ("huge" depending on the definition of "almost" ;-)), but the energy needed to accelerate from almost c to really close to c is even bigger and to get even closer it is even bigger again, etc.: the formulas show that to actually reach c you need infinity of energy s you never reach c.

[layman]

there are definitely problems in my reasoning. i can understand it superficially like most everyone else and there by not sound so dumb. but i'd rather admit to myself i don't quite understand the underlying principles even if it means making myself look stupid.

 

 

i know in reality we can't accelerate a particle to that speed but on paper we can.  matter is energy but it's not energy in it's native state.

E=mc² is saying matter at that speed is equal to energy's pure state. at least that's how i think of it, energy has to have a native state for it to have variant states.

 

if you have to increase matter's energy to get it to equal native energy, that says that whatever the energy matter has, it is less energetic than pure energy.

 

but from what i understand, how matter is created is when energy vibrates at a very high frequency and a particle pops into existence, along with an anti-particle. most times they recombine but sometimes a particle escapes it's anti counter part and it remains in existence, thus we have an accumulation of matter.

 

if i got that right, then that says matter is produced when energy's own energetic state is increased. increased energy produces matter............which we then would have to add energy to to make it equal to the energy it came from?

 

there's seems to be a conflict there, in other words.

if you have to increase the energy of the thing on the right to make it equal to the thing on the left, than basic math says that you can also decrease the energy of the thing on the left to make it equal the thing on the right.

 

I know it's got to me, I'm sure I haven't discovered a bug in the system, but it's something i'm have trouble putting together in my head.

Edited August 26, 2015 by layman

[layman]

lets say:

 

1 unit of matter equals 1G

1 unit of pure energy equals 100Gs

c² equals 100Gs

 

1 unit of matter plus 99Gs = pure energy.

 

thus:

100Gs of pure energy minus 99Gs = matter.

 

 

i don't understand why that doesn't make sense.

 

[HydrogenBond]

E=MC2 was used to calculate the energy output from nuclear reactions. Fission of atoms larger than iron and fusion of atoms smaller than iron, will burn mass and will give off energy. The equation allows one to know how much special material you need to get a certain size boom; kilotons or megatons of TNT. Ir was not about energy and mass being the same thing, since energy stays at C and mass can't reach C. 

[CraigD]

lets say:

1 unit of matter equals 1G

1 unit of pure energy equals 100Gs

c² equals 100Gs

 

1 unit of matter plus 99Gs = pure energy.

 

thus:

100Gs of pure energy minus 99Gs = matter.

 

i don't understand why that doesn't make sense.

It doesn’t make sense because you convert from a quantity with units of mass, such as the kilogram, to one with units of energy, such as the joule (1 kg m²/s², using subtraction. You must multiply the mass quantity by a quantity with units of length² divided by time², such as speed² ((L/T)²), or length time acceleration (L * L/T²).

 

You also can’t use the same unit for both mass and energy. You shouldn’t use a unit like the “G” you use in you post for both energy and mass. Instead, use units with which everyone is familiar, such as the kg and J.

 

The famous mass-energy equivalence formula Energy = Mass c² has valid units because c, the speed of light, is a speed, so its units are of type L/T.

 

Physicists don’t usually use the phrases, but there is a physics concept that roughly divides the universe into “matter” and “pure energy”: fermions and bosons.

 

Fermions are particles that have non-zero invariant (or “rest”) mass, can never move as or faster than light, and “follow Fermi-Dirac statistics”, which, simplified, means you can’t pack an unlimited number of them in a finite volume”. They correspond to the intuitive concept of “matter”, and include ordinary matter particles like protons, neutrons, and electrons.

 

Bosons can have zero rest mass, move at exactly the speed of light, and “follow Bose-Einstein statistics”, meaning you can pack an unlimited number of them in a finite volume. They correspond to the intuitive concept of “pure energy”, and include the photon, which carries visible and invisible light energy, and the gluon, which holds the quarks that make up protons and neutrons together, and accounts for about 99% of the mass of a proton or neutron.

 

Bosons are commonly called “force carriers” or “interaction carriers”. They are what allow Fermions to interact with one another.

 

Once you have the concept of fermions and bosons, and how they interact, you can answer your original questions:

where does matter come in? at what "speed" does energy become matter?

Bosons – energy – are “absorbed” and “emitted” by Fermions – matter. When a fermion absorbs a boson, its mass increases – you could say energy becomes matter. When a fermion emits a poson, its mass decreases – you could say matter becomes energy.

 

Here’s a simple example:

An electron at rest (mass about 9.10938 x 10⁻³¹ kg) absorbs a photon of visible red light (energy 3 x 10^-29).

The electron’s mass increases by about 2.42514 x 10^-49 kg.

Since the electron’s mass is now greater than its rest mass, it’s no longer at rest, but moving at a speed about 8.11103 m/s (about running speed), in the direction the photon it absorbed was moving.

 

Here’re the equations/concepts you need to work out the above:

Energy of a photon: E = h v

Mass energy equivalence: E = m c²

Relativistic mass: [math]m = \frac{m_0}{\sqrt{1-\left(\frac{v}{c}\right)^2}}[/math]

 

So, answering

at what "speed" does energy become matter?

There’s no special speed that energy becomes matter, or matter energy. It happens constantly, all around us – it’s what keeps electrons bound to atoms, atoms apart in ordinary materials, and your fingers from passing through your keyboard when you type.

[sanctus]

I think you might also have a too "romantic" science-fiction-style interpretation of Energy. Energy is an abstract thing you don't have such a thing as pure energy. Take some high-school physics as an example: move a rock to the tenth floor and it will have a given potential energy and if you hold it at rest no kinetic energy, let it fall to the ground and just before impact it will have no potential energy but a kinetic energy with the same value as the potential energy it had on the tenth floor. All fine so far, but what if I were to consider the basement floor and not the ground floor as the reference from were to compute the potential energy? Then suddenly on the 10. floor the rock has higher potential energy and just before landing on the ground it has the same kinetic energy as before but also some extra potential energy left.

 

I also do not understand your whole reasoning, to me an equation like A=B just says that A and B are the same, not that some point A becomes B.

[layman]

It doesn’t make sense because you convert from a quantity with units of mass, such as the kilogram, to one with units of energy, such as the joule (1 kg m²/s², using subtraction. You must multiply the mass quantity by a quantity with units of length² divided by time², such as speed² ((L/T)²), or length time acceleration (L * L/T²).

 

You also can’t use the same unit for both mass and energy. You shouldn’t use a unit like the “G” you use in you post for both energy and mass. Instead, use units with which everyone is familiar, such as the kg and J.

 

The famous mass-energy equivalence formula Energy = Mass c² has valid units because c, the speed of light, is a speed, so its units are of type L/T.

 

Physicists don’t usually use the phrases, but there is a physics concept that roughly divides the universe into “matter” and “pure energy”: fermions and bosons.

 

Fermions are particles that have non-zero invariant (or “rest”) mass, can never move as or faster than light, and “follow Fermi-Dirac statistics”, which, simplified, means you can’t pack an unlimited number of them in a finite volume”. They correspond to the intuitive concept of “matter”, and include ordinary matter particles like protons, neutrons, and electrons.

 

Bosons can have zero rest mass, move at exactly the speed of light, and “follow Bose-Einstein statistics”, meaning you can pack an unlimited number of them in a finite volume. They correspond to the intuitive concept of “pure energy”, and include the photon, which carries visible and invisible light energy, and the gluon, which holds the quarks that make up protons and neutrons together, and accounts for about 99% of the mass of a proton or neutron.

 

Bosons are commonly called “force carriers” or “interaction carriers”. They are what allow Fermions to interact with one another.

 

Once you have the concept of fermions and bosons, and how they interact, you can answer your original questions:

Bosons – energy – are “absorbed” and “emitted” by Fermions – matter. When a fermion absorbs a boson, its mass increases – you could say energy becomes matter. When a fermion emits a poson, its mass decreases – you could say matter becomes energy.

 

Here’s a simple example:

An electron at rest (mass about 9.10938 x 10⁻³¹ kg) absorbs a photon of visible red light (energy 3 x 10^-29).

The electron’s mass increases by about 2.42514 x 10^-49 kg.

Since the electron’s mass is now greater than its rest mass, it’s no longer at rest, but moving at a speed about 8.11103 m/s (about running speed), in the direction the photon it absorbed was moving.

 

Here’re the equations/concepts you need to work out the above:

Energy of a photon: E = h v

Mass energy equivalence: E = m c²

Relativistic mass: [math]m = \frac{m_0}{\sqrt{1-\left(\frac{v}{c}\right)^2}}[/math]

 

So, answering

There’s no special speed that energy becomes matter, or matter energy. It happens constantly, all around us – it’s what keeps electrons bound to atoms, atoms apart in ordinary materials, and your fingers from passing through your keyboard when you type.

 

thank you for a really informative and comprehensive reply.

 

 

i was thinking the units of measure weren't important in such a simple example because i was thinking of matter and energy as being

different forms of the same thing, such as water and ice. but if i'm understanding, you're saying an inch of wood is not the same as an inch

of water. they each have to be measured in units relative to their own properties and then find a way to equivocate the two.

 

 

I really appreciate you breaking down matter and energy. I didn't know the difference between a boson and fermion and how the particles you mentioned fit together. you explained it very well.

it gives me a good road map.

 

let me see if i'm getting some of this down.

 

a class of particles are boson and they have no mass so they can move at light speed and can be considered pure energy.

 

then there is a class called fermions and they do have mass so they can't move at light speed.

 

a gluon, which is a boson, facilitates the strong force interaction between quarks, which are fermions and already have mass,

making them stay bound together. when a fermion absorbs a boson like a gluon, it gains mass, quarks bind together and we get a proton.

 

when a fermion emits a boson, it decreases in mass and be considered energy(though it still has mass?).

 

 

if fermions have a rest mass and they are an elemental particle, wouldn't that imply that matter is elemental?

 

I'm unclear on whether anything with mass can be considered matter.

 

obviously i have a lot of reading to do.

[layman]

I think you might also have a too "romantic" science-fiction-style interpretation of Energy. Energy is an abstract thing you don't have such a thing as pure energy. Take some high-school physics as an example: move a rock to the tenth floor and it will have a given potential energy and if you hold it at rest no kinetic energy, let it fall to the ground and just before impact it will have no potential energy but a kinetic energy with the same value as the potential energy it had on the tenth floor. All fine so far, but what if I were to consider the basement floor and not the ground floor as the reference from were to compute the potential energy? Then suddenly on the 10. floor the rock has higher potential energy and just before landing on the ground it has the same kinetic energy as before but also some extra potential energy left.

 

I also do not understand your whole reasoning, to me an equation like A=B just says that A and B are the same, not that some point A becomes B.

 

i know what you mean, like if we increase the mass of an Orange to the same as a bowling ball, the Orange doesn't become a bowling ball, it's just equal to a bowling ball. however i distinctly recall hearing physicists say during lectures that energy can be "transmuted" into matter and vice versa and that was one of the profound implications of E=Mc².

 

I've always been under the impression that a tiny fraction after the big bang, there was nothing but pure energy and that all matter was created in the ensuing time.

 

is it more correct to think of the universe as having native fields, that were just there at the moment of the big bang and view "energy" as merely the conditions of those fields?

 

[layman]

 from wikipedia

 

 

Matter should not be confused with mass, as the two are not quite the same in modern physics.^[7] For example, mass is a conserved quantity, which means that its value is unchanging through time, within closed systems. However, matter is not conserved in such systems, although this is not obvious in ordinary conditions on Earth, where matter is approximately conserved. Still, special relativity shows that matter may disappear by conversion into energy, even inside closed systems, and it can also be created from energy, within such systems. However, because mass (like energy) can neither be created nor destroyed, the quantity of mass and the quantity of energy remain the same during a transformation of matter (which represents a certain amount of energy) into non-material (i.e., non-matter) energy. This is also true in the reverse transformation of energy into matter.

Different fields of science use the term matter in different, and sometimes incompatible, ways. Some of these ways are based on loose historical meanings, from a time when there was no reason to distinguish mass and matter. As such, there is no single universally agreed scientific meaning of the word "matter". Scientifically, the term "mass" is well-defined, but "matter" is not. Sometimes in the field of physics "matter" is simply equated with particles that exhibit rest mass (i.e., that cannot travel at the speed of light), such as quarks and leptons. However, in both physics and chemistry, matter exhibits both wave-like and particle-like properties, the so-called wave–particle duality.^[8][9][10]

 

so by some definitions matter is anything with a rest mass and volume. And energy and matter are interchangeable.

 

if "equivalent" means that I can do anything with 2+2 that I can with 4. then why wouldn't the "=" sign in E=Mc² mean the same thing? to me is says that if a mass had the same amount of energy equal to the amount of c² you could do anything with it you could do with plain old E. conversely if you could remove the same amount of energy from energy(i know what that sounds like, but there isn't another word) you'd have matter.

 

 

 

 

 

 

 

[Pmb]

 

energy is equal to mass accelerated to the speed of light x the speed of light.

That is incorrect. First off the E in that expression only pertains to the sum of rest energy and kinetic energy. I myself refer to this as Inertial Energy. I say this so that nobody makes the mistake of thinking that E includes potential energy of position. The only potential energy that it pertains to is the internal potential energy of the interaction of particles that make up the rest energy of the body whose mass is m.

 

What E = mc² does mean is that it a body having mass m then there is an internal energy E associated with it. For example; if you have a body at rest having an initial mass M in the inertial frame S and it emits two pulses of radiation of equal amounts in opposite directions where the total amount of energy is E then the mass of the body will decrease by the amount E/c².

 

 

... at that point the particle would transform into pure energy.

There's no such thing as "pure energy." I recommend reading a webpage I wrote on what energy is. It's on my personal website at:

http://home.comcast.net/~peter.m.brown/mech/what_is_energy.htm

Then watch the video that I took of Alan Guth (creator of the theory of inflation) explaining why there's no such thing as "pure energy." It's on my companies' website at: http://newenglandphysics.org/common_misconceptions/DSC_0004.MOV

 

I also recommend reading The Meaning of E = mc² by Mendel Sachs, Int. Theo. Physics, 8 (1973). It too is online at my companies' website at: http://www.newenglandphysics.org/science _literature/Journal_articles/International_Journal_of_Theoretical_Physics/Sachs_M_Int_Theor_Phys_8_5_1973_.pdf

 

I worked out an example of how to apply E = mc² to nuclear fusion at http://home.comcast.net/~peter.m.brown/nuclear _fission.htm

 

There's also Einstein's derivation where he showed that radiation has an equivalent amount of mass associated with it's energy. See:

http://home.comecast.net/~peter.m.brown/sr/einsteins/_box.htm

 

There's an article in the  American Journal of Physics called Does nature convert mass into energy? by Ralph Raierlein, Am. J. Phys, 75(4), Apr. (2007). It too is on my personal website at : http://home.comcast.net/~peter.m.brown/ref/baierlein.pdf

 

I have the following articles on my computer. If anybody wants to read one or more of them then please let me know and I'll make them available to read. They are:

 

Energy Transformations and Conservation of Energy by E.F. Barker, Am. J. Phys., 14(5), Sep. (1946).

Example of mass-energy-relation: Classical hydrogen atom accelerated or supported in a gravitational field by Timothy Boyer, Am. J. Phys., 66(10), Oct. (1998).

Photons and Doppler shifts in Einstein's derivation of mass energy by Thomas F. Jordan, Am. J. Phys., 50(4), Apr. (1990).

Einstein's first derivation of mass-energy of mass-energy equivalence by John Stachel and Roberto Torretti, Am. J., Phys., 50(8), Aug. (1982).

An elementary development of mass-energy equivalence by Daniel J. Steck and Frank Rioux, Am. J. Phys., 51(5), May. (1983).

On the Inertia of Energy Required by the Relativity Principle by A. Einstein, Ann. der Phys., 23 (1907).

The mystery of mass-energy by J.W. Warren, Phys. Educ. 11(7), Jan. (1976)

 

 

Physicists don't usually use the phrases, but there is a physics concept that roughly divides the universe into "matter" and "pure energy": fermions and bosons.

I don't understand what you mean here. Why don't you think that the universe is divided into matter and "pure energy." First of all, as I explained above, there's no such thing as "pure energy." What do you mean by that term? I'm going to assume that you're talking about particles that have zero rest mass or they don't where those that don't have rest mass is what you refer to as "pure energy." Is that what you mean? 

 

 

Fermions are particles that have non-zero invariant (or "rest") mass ...

That isn't part of the definition of what a fermion is. E.g. the Weyl fermion has zero proper mass. See: http://www.livescience.com/51584-weyl-fermions-created-lab.html

 

 

Bosons are commonly called "force carriers" or "interaction carriers."

Not all force carriers are bosons. There are several types of fermions which are force carriers. For example; fermionic field is a quantum field whose quanta are fermions. See: https://en.wikipedia.org/wiki/Fermionic _field

 

 

Here's a simple example:

An electron at rest (mass about 9.10938x10³¹ kg) absorbs a photon of visible red light (energy 3x10^-29).

The electron's mass increases by about 2.42514x10^-49 kg).

If I understand you correctly then this is an error. But first let me ask you a few questions. Do you mean the following? Suppose an electron is at rest in the inertial frame S. The electron is the struck by a photon whereupon it's absorbed and the rest mass of the electron increases. Then by "absorbed" do you mean that this results in an increase in its rest mass? If so then this is an error because an electron cannot increase its rest mass. At least not in the way you describe it. Griffiths text on particle physics explains why. It's quite easy to understand. I can scan it in and post a link to it if you'd like to read it?

 

One last comment: You wrote the definition of relativistic mass incorrectly. I.e. m(v) = m_0/sqrt[1 - v²/c²] is an equality, not an identity. That means that it's the value you obtain for the mass as a function of speed when you derive an expression of the relativistic mass for a tardyon (i.e. particles which move at speeds less than c). However if the particle is a luxon (v = c) then all you can do is express m in other terms such as m = hf/c²  or E/c². The correct definition of the relativistic mass of a particle is the m in p = mv. That is an identity, not an equality. By this I mean that m = p/v is the definition of mass. Another way to put it is to say that mass is defined so that mv is conserved. This was defined in 1907 by Richard C. Tolman.

[industry7]

Even just on paper, no we can't.  It would take an infinite amount of energy.

 

 

i know in reality we can't accelerate a particle to that speed but on paper we can