The special-relativistic relation connecting energy with (rest) mass, $ E^2 - (m c^2)^2= (pc)^2 $. May be used to provide accounting constraints in energy and momentum, both conserved in total, even in reactions where m is not. Use for all manifestations or consequences of the relation.

learn more… | top users | synonyms

69
votes
1answer
2k views

Does the 4/3 problem of classical electromagnetism remain in quantum mechanics?

In Volume II Chapter 28 of the Feymann Lectures on Physics, Feynman discusses the infamous 4/3 problem of classical electromagnetism. Suppose you have a charged particle of radius $a$ and charge $q$ (...
44
votes
6answers
3k views

What keeps mass from turning into energy?

I understand the energy and mass can change back and forth according to Einstein. It is fluid; it can go from one to the other. So, what keeps mass from just turning into energy? Is there some force ...
41
votes
6answers
9k views

Why do lasers cut? Is this a case of light acting as matter?

All I found in Google was very broad. From a physics models perspective, why can photons emitted from a laser cut? Does this cut mean that the photons are acting like matter?
33
votes
4answers
6k views

If a 1kg mass was accelerated close to the speed of light would it turn into a black hole?

I'm a big fan of the podcast Astronomy Cast and a while back I was listening to a Q&A episode they did. A listener sent in a question that I found fascinating and have been wondering about ever ...
28
votes
5answers
5k views

Why is there a controversy on whether mass increases with speed?

Some people say that mass increases with speed, some people say that the mass of an object is independent of its speed. I understand how some (though not many) things in physics are a matter of ...
25
votes
3answers
6k views

Why can't I do this to get infinite energy?

I know that I cannot do this because of conservation of energy, so I am looking for an answer as to why this will not work. So by my understanding of Einstein's whole famous $E=mc^2$ thing it is ...
22
votes
1answer
19k views

Does the mass of a battery's change when charged/discharged?

... and if so, how much? Is it possible to detect it, or is it beyond any measurement? I'd say there are two possible scenarios (depending on the battery type) and both seem interesting: The battery ...
19
votes
3answers
1k views

Why can't a nucleus become a black hole?

A nucleus is very small and very dense. Its density is approximately $2.3 \times 10^{17}~\mathrm{kg/m^3}.$ So why can't a nucleus itself become a black hole?
19
votes
6answers
2k views

Why does matter/antimatter only produce gamma rays?

According to wikipedia, all antimatter annihilation produces gamma rays (along with potentially other elements). Why specifically Gamma rays? Why not electromagnetic waves of other wavelength?
18
votes
4answers
2k views

Does a box containing photons have more inertia than an empty box?

A box containing photons gravitates more strongly than an empty box, and thus the equivalence principle dictates that a box containing photons has more inertia than an empty box. The inescapable ...
18
votes
2answers
2k views

Do chemical bonds have mass?

When an exothermic reaction occurs, the energy in the chemical bonds of the reactants is partially transferred to the chemical bonds of the products. The remaining energy is released as heat. For ...
18
votes
3answers
466 views

Comparing predictions and reality for the gravitational attraction due to light beams

While doing some on-the-side reading, I stumbled across this question: Do two beams of light attract each other in general theory of relativity?. Great question and a great, easily understandable ...
17
votes
4answers
3k views

Does the mass of an electron change with its “energy state”?

When an electron absorbs a photon, it gets into a higher energy state and goes into the upper orbit/shell. Does (rather should) this absorption of energy also have an impact on its mass (although ...
17
votes
2answers
4k views

Does $E = mc^2$ apply to photons?

Photons are massless, but if $m = 0$ and $E=mc^2$, then $E = 0c^2 = 0$. This would say that photons have no energy, which is not true. However, given the formula $E = ℎf$, a photon does have energy ...
16
votes
3answers
6k views

How does rest mass become energy?

I know that there's a difference between relativistic rest mass. Relativistic mass is "acquired" when an object is moving at speeds comparable to the speed of light.Rest mass is the inherent mass that ...
15
votes
6answers
2k views

Is there any way to annihilate matter without the use of anti-matter?

Is there any way to annihilate matter without the use of anti-matter? And vice versa? I mean, for example is it possible to totally convert the mass of a proton into "pure energy" without use an anti-...
13
votes
2answers
1k views

An atomic bomb explodes inside of an “unbreakable” container which is on a scale. Does the “weight” of the container change?

I read that most of the "mass" in the proton was actually energy from the quarks and gluons, as opposed to the actual mass which was coupled to the Higgs field. This made me start thinking about ...
12
votes
2answers
3k views

Higgs Boson mass in Electron volts?

Im no physics genius here, I was just interested in the Higgs Boson so I was reading this article : How the Discovery of the Higgs Boson Could Break Physics I came across this Furthermore, ...
12
votes
3answers
36k views

When does 'energy' turn to matter?

I always hear about matter converting to 'energy' - fusion, fission. When does it go the other way around? What conditions lead to it? Are there reproducible experiments on this topic?
11
votes
12answers
2k views

Is the distance between the Sun and the Earth increasing?

M = mass of the Sun m = mass of the Earth r = distance between the Earth and the Sun The sun is converting mass into energy by nuclear fusion. $F = \frac{GMm}{r^2} = \frac{mv^2}{r} \rightarrow r =...
11
votes
2answers
6k views

What was Albert Einstein's proof for $E=mc^2$?

Most people know the famous equation: $$E=mc^2$$ What were his steps of thinking for this equation that helped us discover so much about our world?
10
votes
6answers
2k views

Potential energy in $E_f^2=(mc^2)^2+(pc)^2$?

Let's consider $$E_f^2=(mc^2)^2+(pc)^2$$ where the $mc^2$ is the rest energy due to the rest mass -- in Finnish "lepomassa". $$ \sqrt{(mc^2)^2+(pc)^2} - mc^2~=~(\gamma-1)mc^2$$ is the kinetic ...
10
votes
3answers
6k views

When an atom is split, what form of energy is released?

When an atom is split, what form of energy is released? All of the websites I have looked at say there is a lot of energy released when an atom is split, but it never says what form of energy it is in....
10
votes
3answers
1k views

What happens to gravity after matter-antimatter annihilation?

Both matter and antimatter have mass and thus gravity, but since energy from annihilation has no mass what happens to the force of gravity that was previously present? What about conservation of ...
10
votes
6answers
1k views

Energy and its physical significance

What does it exactly mean when we say that energy has moved from one body to another, what has physically been transferred? The concept of energy is very confusing, please help. And if gravitational ...
10
votes
4answers
642 views

How does $E=mc^2$ put an upper limit to velocity of a body?

How does $E=mc^2$ put a upper limit to velocity of a body? I have read some articles on speed of light and they just tell me that it is the maximum velocity that can be acquired by any particle. How ...
10
votes
3answers
381 views

What's the purpose of the arbitary additive constants in Einstein's Inertia of Energy Paper?

In Einstein's paper: Does the Inertia of a Body Depend upon its Energy content? he introduces arbitary additive constants whose purpose I'm confused about. The paper has a frame $(x,y,z)$ where a ...
9
votes
3answers
3k views

Could any object have zero mass? [duplicate]

Energy and mass are interrelated. As everything has energy could any object be massless? For example a photon is a packet of energy but still it is considered to be a massless particle. Why is it so?
9
votes
2answers
980 views

Is everything made of massless particles?

Photons have no mass. Yet they interact gravitationally, as all energy does, with other energetic and massive particles. This means that if you put multiple photons in a system, you get something that ...
8
votes
2answers
2k views

Does a cooling mass lose mass as it radiates?

Assume we have a red hot cannonball in space. It starts off with mass M at 1000K. Later it has cooled by radiation to 100K. Has the mass decreased?
8
votes
5answers
449 views

How to derive $E=mc^{2}$?

Is there some way to derive $E=mc^{2}$? I can understand that energy in something is proportional to its mass, but the $c^{2}$ part. I have no idea. It seems like the way the units are going it would ...
8
votes
4answers
10k views

What is “pure energy” in matter-antimatter annihilation made of?

I used to read the term "pure energy" in the context of matter-antimatter annihilation. Is the "pure energy" spoken of photons? Is it some form of heat? Some kind of particles with mass? Basically,...
8
votes
4answers
468 views

A question about $E=pc$ for massless particles

Since photon has no (rest)mass and $$E^2=(pc)^2+(mc^2)^2$$ we derive that $E=pc$ for particle with no (rest)mass. However, if we transform the non-relativistic formula for kinetic energy $$E_k=\...
8
votes
4answers
3k views

What matter in the original atom bomb is converted to energy?

When an atom bomb goes off some matter is converted to energy according to $E = m c^2$. I'd like to know exactly what matter in the original atom bomb is converted to energy. Is it protons, neutrons, ...
8
votes
1answer
2k views

Does potential energy in gravitationall field increase mass?

I was just taught (comments) that any type of energy contributes to mass of the object. This must indeed include potential energy in gravitational field. But here, things cease to make sense, have a ...
7
votes
4answers
2k views

Is $E^2=(mc^2)^2+(pc)^2$ correct, or is $E=mc^2$ the correct one?

I have been having trouble distinguishing these two equations and figuring out which one is correct. I have watched a video that says that $E^2=(mc^2)^2+(pc)^2$ is correct, but I do not know why. It ...
7
votes
4answers
2k views

Am I just some energy traveled at light speed? [closed]

I don't understand $E=mc^2$ very well, and here is my question: Does this equation mean masses are just condensed energy? And does this mean that the extra energy an object has when traveling at ...
7
votes
5answers
5k views

Can one create mass from energy?

Due to $ E =m c^2 $, one can convert mass to energy. A classic example would be matter/anti-matter annihilation to produce energy (photons, etc.). Can one do the reverse? So could one do something to ...
7
votes
4answers
2k views

Can you create mass with $E=mc^2$?

If you use the equation $E=mc^2$ could you make matter by dividing the $c^2$? I'm sorry if this is a really stupid sounding question or if it shouldn't be asked here.
7
votes
4answers
10k views

Where does the energy from a nuclear bomb come from?

I'll break this down to two related questions: With a fission bomb, Uranium or Plutonium atoms are split by a high energy neutron, thus releasing energy (and more neutrons). Where does the energy ...
7
votes
3answers
2k views

Potential energy in Special Relativity

In Special Relativity, the energy of a free particle is $E^2=p^2c^2+m^2c^4$. But what would be the energy when there is potential energy? If it's something like $E=\sqrt{p^2c^2+m^2c^4}+U$, what ...
7
votes
1answer
88 views

Why is the energy of particles in accelerators much higher than the energy of the particles they are trying to find?

I have been wondering. In the LHC, or other particle accelerators for that matter, they are colliding particles with energies above TeV. The LHC is going to be 14 TeV or something like that the next ...
6
votes
3answers
294 views

$E=mc^2$ resembles kinetic energy formula?

The simplest equation expressing mass–energy equivalence is the famous $E=mc^2$ where $c$ represents the speed of light. Compare this with $E_K = \frac{1}{2}mv^2$. Since $E=mc^2$ can be applied to ...
6
votes
9answers
539 views

Why does my apple not weigh 500 tons?

Related to this question: What is potential energy truly? $E=mc^2$ - energy equals mass. So, if an object has gravitational potential energy relative to another object, it should have additional mass ...
6
votes
1answer
6k views

How to explain $E=mc^2$ mass defect in fission/fusion

What is the nature of nuclear energy? This is closely related to the correct explanation of mass defect. I did some research of that topic and cannot come to a single comprehensive and consistent ...
6
votes
2answers
2k views

Mass defect- From where mass is being lost?

As a school student, I have wondered while studying mass defect the following mysterious problem My assumption Just like a car's mass is constituted by each part of it(i.e total mass of car will be ...
6
votes
2answers
2k views

Mass converted to energy in a common fire?

In a common wood fire such as a campfire, is matter converted to energy or is it simply an exothermic chemical reaction and all the mass can be accounted for in the ash and soot?
6
votes
2answers
235 views

Does the mass lost by merging black holes depend on how they merged?

We've all heard the news about the detection by gravitational waves of two black holes, one 29 solar masses and the other 36 solar masses, spiraling into each other to create a single black hole of 62 ...
6
votes
3answers
63 views

Weight loss of a flashlight due to light emission

I watched this video. At one point, the man explains how a flashlight loses some mass due to light emission when turned on. OK, I get that. Then he talks about a different situation, where the ...
5
votes
2answers
859 views

Quarks in a hadron- where does the mass come from

We know that the sum of the masses of the quarks in a proton is approximately $9.4^{+1.9}_{-1.3}~\text{MeV}/c^2$, whereas the mass of a proton is $\approx931~\text{MeV}/c^2$. This extra mass is ...