Mass= energy,how we know this.

[Asimov]

I had difficulty visualizing how mass and energy are the very same thing. This is basic relativity according to Einstein and all good physicists. Calder explains it well:

 

At 1/10 C the energy of an approaching star is increased by 10.55% If receding it loses 9.55% of its energy.This is an average gain of .5%.

This only depends on the relative speeds of observer and star.Since C doesn't vary,mass and energy are equivalent. Einstein intuited E=M before putting it to math . Paraphrased from "Einstein's World' Nigel Calder

 

Calder stated additionally, "The rest-energy is the energy required to create matter." Matter is made of energy.

[ajb]

Matter is made of energy is not the way to think of it. Energy is a property of a physical configuration; it is basically some number we can associate with a given arrangement of particles and fields.

 

What Einstein really tells us is that when we want to look at the total energy of a system you need to include the mass.

 

Examples of how we know this is true include the nuclear binding energy and the mass defect.

[Sensei]

See radioactive isotope decay energy calculation

http://www.scienceforums.net/topic/83451-radioactive-decay-and-information-split-from-what-is-real-in-physics/?p=808149

Before event, we have sample with mass at rest,

after decay, "debris" newly made particles are often accelerated to relativistic velocities (they have large kinetic energy)..

Edited July 31, 2015 by Sensei

[Nicholas Kang]

Both mass and energy should be considered when one needs to solve relativistic equations and problems.

 

According to Einstein`s Theory of Relativity, for an object with rest mass m, its energy is given by the equation E=mc².

 

Although E=mc² is the World's Most Famous Equation, there is one point noteworthy. When an object moves, its mass will increase (though by a minuscule amount at insignificant speeds). The increase in mass can be determined by the following equation:

 

E=mc² times gamma factor OR E=mc²/square root (1-v²/c²)

 

The gamma factor or Lorentz factor determines the values of energy and mass.

If you express the speed in question in the form of a fraction of c, the constant c drops out of the equation, thus the formula becomes:

 

E=m/square root (1-v²)

 

This "modified" equation facilitates calculation.

For an object travelling at some 87% of the maximum speed of light in vacuum or c, the gamma factor is 0.5.

You get twice the mass for an object travelling at 87% of c.

 

You can also calculate relativistic kinetic energy from this equation.

Kinetic Energy=Total energy-Rest Energy or

 

E_k=mc²/square root (1-v²/c²) - mc²

 

Now, I would like to talk a little about the mass-energy equation's history. According to Ira Mark Egdall's book, Einstein Relatively Simple, the equation E=mc² actually comes from the classical Newtonian Kinetic Energy Equation. Please kindly refer to Egdall's book.

 

Here is the historic paper we will never forget. Try to follow his thought experiment and Enjoy Physics.

 

https://www.fourmilab.ch/etexts/einstein/E_mc2/e_mc2.pdf

Edited July 31, 2015 by Nicholas Kang

[swansont]

Both mass and energy should be considered when one needs to solve relativistic equations and problems.

 

According to Einstein`s Theory of Relativity, for an object with rest mass m, its energy is given by the equation E=mc².

 

Although E=mc² is the World's Most Famous Equation, there is one point noteworthy. When an object moves, its mass will increase (though by a minuscule amount at insignificant speeds). The increase in mass can be determined by the following equation:

 

 

Well, no, not really. Mass is a form of energy, so to say you have to consider mass and energy isn't really correct. It's when you consider energy, mass has to be part of that consideration.

 

E=mc² was derived by Einstein for an object at rest. That's when the equation applies. It was not derived for an object that is moving. For an object that's moving, the equation is E² = p²c² + m²c⁴ There's a mass term and a kinetic term. The mass is the rest mass — it doesn't change. This is useful because it's taken from a of a four-vector and includes an invariant term: m².

 

To use E = mc² for a system in motion requires you to redefine mass, which some do but most physicists don't. It requires you to keep track of which definition of mass you are using, and it's frame-dependent. It's just a proxy for total energy, so why not just use total energy?

[Nicholas Kang]

As a high school student still in the process of learning, I, Nicholas Kang would like to express my utmost gratitude to Dr. Tom Swanson for his meticulous teaching.

 

Thank you Dr. Tom Swanson. You make my day.

 

Anyway, I don' think the above post was a bad one. You see, I have studied painstakingly to comprehend Relativity, at least to some degree. (No, I am not asking for praise or anything in return, just a statement)

 

Not all high school students can study modern physics and classical physics at the same time, especially when they need to go through the hardships of choosing either fields when answering high school exam questions. You would feel the pain of "betraying yourself" when writing wrong or "inaccurate" answers, as some might argue that classical physics isn't the big blunder of physics after all.

 

Well, Dr. Swanson, is there any more errors in my post? Feel free to correct it.

 

It's nice to have a teacher like you.

 

Thank you.

 

Your mentee,

 

Nicholas Kang

Edited August 1, 2015 by Nicholas Kang

[michel123456]

I had difficulty visualizing how mass and energy are the very same thing. This is basic relativity according to Einstein and all good physicists. Calder explains it well:

 

At 1/10 C the energy of an approaching star is increased by 10.55% If receding it loses 9.55% of its energy.This is an average gain of .5%.

This only depends on the relative speeds of observer and star.Since C doesn't vary,mass and energy are equivalent. Einstein intuited E=M before putting it to math . Paraphrased from "Einstein's World' Nigel Calder

 

Calder stated additionally, "The rest-energy is the energy required to create matter." Matter is made of energy.

Mass is not equal to energy. Because c^2 has units.

 

One could say that the amount of mass is directly proportional to the amount of energy. Because c^2 is a constant.

 

If mass were equal to energy, then c^2 should be a simple number without units, and units of mass would be the same as units of energy multiplied by a number. But that is not the case.

Edited August 1, 2015 by michel123456

[studiot]

 

swansont

the equation is E² = p²c² + m²c⁴

 

Hi Nick, I didn't see a definition of p from swansont - p is momentum.

 

(Special) relativity is accessible to those in upper high school who have studied enough mechanics and calculus to know what momentum and a derivative is.

Advanced mathematics is not necessary (Einstein was a physicist not a mathematician and argued as such).

 

A good little book to understand the physics from is

 

Relativity Physics

 

by R E Turner

 

It is one of the Routledge 'Student Physics' series for first and second year undergraduates.

 

 

Michel123456

Mass is not equal to energy. Because c^2 has units.

 

One could say that the amount of mass is directly proportional to the amount of energy. Because c^2 is a constant.

 

If mass were equal to energy, then c^2 should be a simple number without units, and units of mass would be the same as units of energy multiplied by a number. But that is not the case.

 

 

Yes indeed.

A pedantic point perhaps but a true one nonetheless.

In fact the c² (L² S^-2) can be regarded as the necessary units of conversion between mass (M) and energy (M L² S^-2)

 

You can use the fact that momentum = mass (M) times velocity (L² S^-2) to verify the dimensional correctness of swansont's equation above.

Edited August 1, 2015 by studiot

[Asimov]

Thank you for your perspective.

 

I see Calder's thought experiment fell mostly on deaf ears. What Einstein REALLY said is that energy and mass are one and the same. E=M. Not just a way of thinking about it or a metaphor or analogy. Hard to visualize. Energy can manifest itself in different ways but is fundamentally the ability to do work or make change .Also it is mass Not some number. That famous equation E=mc*2 on sweat shirts everywhere serves to convert units of mass to units of energy and back regardless of the units used. It works.It appiies to moving objects as well.

 

Adding 25 kilowatt hours of ANY form of energy to a mass increases it's mass by 1 microgram. Any form of energy. Period. { see Wikipedia, Mass energy equivalence } Energy is mass. Visa versa.

 

More astonishing still, relativistic mass is also energy. Right, the mass-energy total depends on the relative motion of the observer! Not some theory of mine Old stuff. I've presented it as well as I can. That famous equation is literal.. I wont try to defend this most basic and important of relativity's tenets any further. Calder said additionally{and literally}:

 

High-speed motion changes the apparent energy of objects.

 

A moving luminous object seems to shed energy of motion.

 

Einstein inferred light must be heavy.

 

Mass and energy are equivalent: E=mc*2

 

Matter is frozen energy.

[studiot]

 

What Einstein REALLY said is that energy and mass are one and the same

 

Can you offer the exact quote (from Einstein) that makes you think this?

[Asimov]

Studiot: " Matter is energy." Albert Einstein Special Theory of Relativity

 

 

" Matter is frozen energy. This was revealed in what must be the worlds most famous equation, e=mc*2: energy equals mass times the velocity of light squared."

 

Timothy Ferris "The Whole Shebang" page 104,

 

We dont have to agree, just keep on learning .

[ajb]

The correct way to think of energy and mass is as I said in my post #2. You have to be careful with loose statements made in popular science books.

[Asimov]

ABJ: Direct quotes from Einstein's paper, Timothy Ferris and Wikipedia. Loose? Add 25 kilowatt hours of ANY energy to a mass and you add 1 microgram mass. Loose?

 

25kilowatthours= 1 microgram mass ----- Loose?

 

We must agree to disagree. All of us. Das wirt alles, danke.

[studiot]

 

Asimov

just keep on learning

 

 

I've had quite enough of comtemptuous comments thank you.

 

They add nothing to a scientific discussion.

[Asimov]

Studiout: I have no contempt for you or anyone on this forum This upsets me and is totally unexpected..The comment was intended to apply to you, me and anyone else in general that is following this thread. I have learned while disagreeing with others and hope they learn too.My intent was palliative, not to offend anyone.

 

Time flys like the wind,

 

Fruit flys like the bananas

[J.C.MacSwell]

ABJ: Direct quotes from Einstein's paper, Timothy Ferris and Wikipedia. Loose? Add 25 kilowatt hours of ANY energy to a mass and you add 1 microgram mass. Loose?

 

25kilowatthours= 1 microgram mass ----- Loose?

 

We must agree to disagree. All of us. Das wirt alles, danke.

These statements are not equivalent.

 

You can consider yourself loosely correct if it makes you feel better. You are only wrong in a more rigorous sense…one that is used by most physicists.

[Asimov]

J.C.MacSwell: Thank you for your input but dont worry about my feelings. Truth is what makes me feel good.I prefer to be entirely and rigorously correct Calder., Ferris and Einstein.,were they speaking loosely when they stated energy and mass are equivalent? If it it has been discovered that there are some instances in which energy-mass equivalence is not correct please let me know. I have found this nowhere. My mind is open. I think one may find energy-mass equivalence hard to visualize but intrpreting it with a grain of salt.?

I think not. Basically I want to know this more rigorous sense that I am wrong in regarding mass-energy equivalence. I dont deny what you are saying but I need to know.

 

While I have your attention, doesnt conservation of energy apply? Energy cant be created or destroyed we know. If mass is not energy, then energy cant just become mass, it must BE mass. Right? Conservation. Also, if mass is not equvalent to energy, just what is mass? 25kilowatts of only energy adds 1 microgram mass to an object. Where does this microgram of mass come from if not solely from said energy which must be mass.? Thank you for your time and input.

 

"Why stay we on the Earth if not to Grow ?" Robert Browning

[Strange]

J.C.MacSwell: Thank you for your input but dont worry about my feelings. Truth is what makes me feel good.I prefer to be entirely and rigorously correct Calder., Ferris and Einstein.,were they speaking loosely when they stated energy and mass are equivalent?

 

They may be equivalent. They are not equal. Mass can be converted to energy and vice versa. But they are not the same thing.

[ajb]

ABJ: Direct quotes from Einstein's paper, Timothy Ferris and Wikipedia. Loose? Add 25 kilowatt hours of ANY energy to a mass and you add 1 microgram mass. Loose?

This is okay. If you add energy to an isolated system then the mass of that system increases by that change in energy divided by c squared. But that does not exactly tell us that mass and energy are the same thing nor that matter is frozen energy.

 

You should again look at binding energy and mass defect.

[swansont]

Direct quotes from Einstein's paper,

 

Which paper?

Timothy Ferris and Wikipedia. Loose?

 

Ferris in what looks to be a popular work, and … Wikipedia?

 

Your calculation shows what ajb said: mass is a form of energy. Nothing more fanciful than that.

 

They may be equivalent. They are not equal. Mass can be converted to energy and vice versa. But they are not the same thing.

 

I prefer "converted to another form of energy" rather than "converted to energy". Energy is the overall property. Mass is one form of it, rather than being separate.

[Asimov]

Swansont: Actually at least 4 papers. Why bother to look? This is known by just about everyone that studies relativity.Yes, mass is energy. What I have been saying !

 

No you cant change energy to anything other than energy, another form of energy, like mass which IS energy.Mass and energy are one and the same thing.Call it different forms if you like. Conservation of energy denies changeing or converting or transfering energy to anything but another form of energy, like mass! Duh, double duh. Some have disagreed with this possibly accidently!. Read all the posts. My original tread was intended to help others visualize this sameness of energy and mass not to have to debate it.. We could dwell on basics we basically agree on by splitting hairs indefinately! Beats drinking beer at the beech.

 

MacSwell said I am loosely correct but wrong in a more vigorous sense used by most physicists. If so I can maybe learn from him. His instruction is I hope pending. As to MASS= frozen energy, that is a popular expression by physicists. Literal? Metaphor? Analogy? Nice to met you all.

 

http://www.classle.net/book/mass-energy-equivalence Re: Einstein's 4+ papers Most know about these so I wouldnt bother.

[Strange]

As to MASS= frozen energy, that is a popular expression by physicists. Literal? Metaphor? Analogy?

 

At best, an analogy. More like a fairly meaningless soundbite to sell a book.

[swansont]

Swansont: Actually at least 4 papers. Why bother to look? This is known by just about everyone that studies relativity.Yes, mass is energy. What I have been saying !

 

That doesn't answer the question. Which paper were you quoting, where you found "matter is energy"? Einstein's 1905 paper in which he derives E=mc² does not mention matter at all, and says "The mass of a body is a measure of its energy-content" (nor does he use "matter" in this context in the original SR paper)

[Sorcerer]

 

That doesn't answer the question. Which paper were you quoting, where you found "matter is energy"? Einstein's 1905 paper in which he derives E=mc² does not mention matter at all, and says "The mass of a body is a measure of its energy-content" (nor does he use "matter" in this context in the original SR paper)

If we're doing semantics, what else are bodies composed of?

 

 

 

In physics, a physical body or physical object (sometimes simply called a body or object) is an identifiable collection of matter, which may be more or less constrained to move together by translation or rotation, in 3-dimensional space.

 

I might not be good at the math, but I know words.

[Strange]

If we're doing semantics, what else are bodies composed of?

 

 

 

I might not be good at the math, but I know words.

 

And where does that say "matter [or a body] is energy"?

 

And in what way is energy "an identifiable collection of matter, which may be more or less constrained to move together by translation or rotation, in 3-dimensional space"?

Edited August 3, 2015 by Strange