# Energy = mass * c^2 where c=speed of light

1. Mar 25, 2004

### expscv

energy = mass * c^2 where c=speed of light.

every mass (build up with atoms) when trying to reach the speed of light
and the energy put in will converted to mass. so is it convey into the same mass? depends on atom reaction i guess. but for light it self. does it means light do not have a mass or any energy?

2. Mar 25, 2004

### expscv

wait i should post this to somewhere else?

3. Mar 25, 2004

### Janitor

If you are suggesting that a little clump of iron atoms that number 10,439 in the rest frame appears to have 11,342 iron atoms in it to an observer whizzing by at some fraction of the speed of light, you are incorrect. But maybe that is not what you are saying?

Light does have energy, and momentum as well.

4. Mar 26, 2004

### Integral

Staff Emeritus
Could you re-express this in an understandable form. I really can only guess at the meaning of your words.

5. Mar 26, 2004

### expscv

sorry i was in a rash

1.does light have a mass or energy?

2.since by the law conservation of mass/energy work on all object

how come it have nothing to do with light.

3. i was told that if a object trying to reach the speed of light is impossible
and nothing can go faster than light. because once you put energy in push the obejct that energy will converted into mass and therefore harder to push.
and more energy reqired so on. (is it true?)

4. the energy is converted into mass, what kinda mass is it?

related
qualitatively and quantitatively the consequence of special relativity in relation to:
– the relativity of simultaneity
– the equivalence between mass and energy
– length contraction
– time dilation
– mass dilation

The relativity of simultaneity

If two events in different places are judged by one observer to be simultaneous then they will not generally be judged to be simultaneous by another observer in a different reference frame in relative motion. In other words, whether or not two events are seen by you to be simultaneous depends upon where you are standing.

Try this thought experiment offered by Einstein:
A train is fitted with light operated doors. The light fitting is in the centre of the roof, and is operated by a train traveller standing in the middle of the floor. When the train is travelling at half the speed of light, the train traveller turns on the light. The light travels forwards and backwards with equal speed and reaches both doors at the same time. The doors then open, and the train traveller sees them opening simultaneously. An observer standing outside the train watches this happen, but sees the back door opening before the front. This is because the back door is advancing on the light waves coming from the light, while the front door is moving away from the light waves.

The equivalence between mass and energy
The rest mass of an object is equivalent to a certain quantity of energy. Mass can be converted into energy under extraordinary circumstances and, conversely, energy can be converted into mass. For example, part of the mass is converted into energy in nuclear fission reactions. When a particle and its anti-particle collide, the entire mass is converted into energy.
Einstein’s famous equation expresses the equivalence between energy, E and mass, m: E = mc2. The amount of energy given off in a nuclear transmutation is related by this equation to the amount of mass “lost”.

In Special Relativity, the Law of Conservation of Energy and the Law of Conservation of Mass have been replaced by the Law of Conservation of Mass-Energy.
Length contraction

The length of an object measured within its rest frame is called its proper length (Lo). Observers in different reference frames in relative motion will always measure the length (Lv) to be shorter.

The equation that expresses this is L(v)= L(o) * sqrt( 1- (v^2)/(c^2))

For example: A train that is measured to be 100 metres long when at rest, travels at 80% of the speed of light (0.8 c). A person inside the train will measure the length of the train to be 100 m. A person standing by the side of the track will observe the train to be just 60 metres long.

Time dilation

The time taken for an event to occur within its rest frame is called the proper time (to). Observers in different reference frames in relative motion will always judge the time taken (tv) to be longer.

The equation that expresses this is T(v)= T(o)/( sqrt( 1- (v^2)/(c^2)))

For example: A traveller on a train with a speed of 0.8 c, picks up and opens a newspaper. The event takes 1.0 second as measured by the train traveller. As observed by a person standing by the side of the track the event takes 1.7 seconds.
Mass dilation

Another consequence of the theory of Special Relativity is that the mass of a moving object increases as its velocity increases. This is the phenomenon of mass dilation. It is another expression of the mass-energy equivalence and is represented mathematically as:

M(v)= M(o)/( sqrt( 1- (v^2)/(c^2)))

where

m = relativistic mass of particle,
m0 = rest mass of particle,
v is the velocity of the particle relative to a stationary observer and
c = speed of light.

This effect is noticeable only at relativistic speeds. As an object is accelerated close to the speed of light its mass increases. The more massive it becomes, the more energy that has to be used to give it the same acceleration, making further accelerations more and more difficult. The energy that is put into attempted acceleration is instead converted into mass. The total energy of an object is then its kinetic energy plus the energy embodied in its mass.

To accelerate even the smallest body to the speed of light would require an infinite amount of energy, all the energy of the universe, plus a whole lot “more”. Thus material objects are limited to speeds less than the speed of light.

6. Mar 26, 2004

### gta-maloy]

Light is always at a constant speed unless slowed by another object depending on the density, it has it's own momentum and energie. If it had a mass it would not be able to travel at a given speed, slow through a field, and exit at the speed it first entered. Although an object that has a momentum, once slowed by an object, needs a force to speed it up again, this is what confuses me the most about light. [?]

7. Mar 26, 2004

### pmb_phy

Proper mass? No.
Inertial (aka Relativistic) mass? Yes.
Yes. It's true that the faster a body goes the greater its inertial mass is.
Inertial mass.

Actually the term "convert" refers to the fact that the form of the energy has changed. The total is a constant, i.e. mass is conserved in nuclear fission etc.

8. Mar 26, 2004

### H-bar None

I used to wrongly think that a mass accelerating to c. gained the mass as # of atoms.

Robert Compton who wrote the book Design Notes: G.O.D. says this incorrect. He used a cube to demontrate the idea visually.

For exmaple:
The enegy content of mass is stacked like this:

photon mass
photon mass
rest mass
inertial mass
inertial mass

As an mass accelerates on part the stack is converted to another. The total energy of the cube remains constant.

9. Mar 26, 2004

### expscv

umm interesting i was thinking is possible for people to recyle energy

but the use of conservation energy/mass

10. Mar 26, 2004

### munky99999

1. it has no mass, a Photon has seen to have no mass, it obviously has energy, solar-cells. But think about this. Gravity only effects things with mass, blackholes are just huge gravity wells, but light with no mass is pulled into black holes. Why? Particle-wave duality explains it.

2. I have no idea how it is breaking that law. maybe you could explain that, unless it was after the einstein thing, never read past there.

3. Nothing with mass is capable to move at the speed of light even. It really doesn't mean mass is generated, and appears with. But rather the effects of mass become in existent, which is why light is effected by gravity. Then the next problem, even if humans moved at the speed of about 0.7xc almost the speed of light, time is the same for them, but for earth, time would be extremely fast relative to the craft that moves that fast. move at 0.7xc for around 12 seconds i believe it was and 450 years go by for earth. Would you sacrific your life to be someone whom has moved the fastest?

11. Mar 26, 2004

### chroot

Staff Emeritus
No. The acceleration due to gravity, even in the Newtonian theory, does not vary with the mass of a test particle. General relativity treats the situation even more clearly: spacetime is itself distorted by the presence of mass, and everything, including massless particles, is affected by the distortion. Quantum-mechanical effects have nothing to do with it, since classical general relativity is not a quantum theory!

- Warren

12. Mar 26, 2004

### munky99999

i knew someone would say that one, i personally havent got to that yet in school, so i can't explain that. What you said is basically all i know about that.

13. Mar 26, 2004

### expscv

awesome light is everywhere but so hard to explain wat it is. for me ...

14. Mar 26, 2004

### chroot

Staff Emeritus
Sometimes the simplest things turn out to be the hardest to fully explain. Believe it or not, gravity is even more difficult to explain than light. No one fully understands gravity right now.

That's what keeps physics so exciting for me, personally. :)

- Warren

15. Mar 26, 2004

### munky99999

me to, the quest to understand, is very exciting, but i rather perfer theory of things we can never do type things. Theory of everything, nature of time, and others along those lines.

16. Mar 27, 2004

### pmb_phy

When one is discussing whether light has mass or not then one should be state whether they're speaking of proper mass or inertial mass (aka relativistic mass.) Gravity acts on all things which has passive gravitational mass. Since passive gravitational mass equals inertial mass and since light has inertial mass it is attracted by gravity.

Recall the Feynman Lectures Vol -I page 7-11 on this. See the Section entitled Gravitation and Relativity

The (coordinate/spatial) acceleration due to gravity is not a function of the proper mass of the particle it is a function of the particle's velocity. This was not true in Newtonian theory but it is in Einstein's theory.
That is merely describing the phenomena in terms of differential geometry. This is made possible by the fact that inertial mass is proportional to passive gravitational mass. Einstein then took these facts and phrased them in terms of differential geometry. It is not an explanation of the facts. It is a description of them.

The presence of spacetime curvature merely indicates the presence of tidal forces. However there can be a gravitational force (which is an inertial force) on a particle even when the spacetime is flat. All this means is that there are gravitational forces and no tidal forces

Einstein wrote on this concept of light having mass since it has energy. In his and Infeld’s book The Evolution of Physics dated 1938, Einstein comments on the observation made by an observer inside an accelerating elevator. The elevator observer claims that light is ‘weightless’. Einstein then explains on page 231

17. Mar 27, 2004

### munky99999

i was talking about rest mass, not inertial which i thought i had implied, i forgot the name. like in my #3 i sorta went over inertial. did i not?

18. Mar 27, 2004

### pmb_phy

If you're trying to explain the physics to someone on this point then its best not to imply this point but to make it precisely clear. My comment on this point was merely a suggestion. Ignore it if you disagree with it. But in my experience its best to state this explicity in discussions such as this. When explaining relativity to someone it's customary to qualify what you mean on this point at least once. By "customary" I mean that almost all authors of relativity texts (E.g. Wald, Ohanian, Schutz etc.) qualify what they mean by "mass".

19. Mar 27, 2004

### munky99999

well where I usually talk about physics, Its unneccessary to explain beyond implications

20. Mar 27, 2004

### pmb_phy

What is neccessary depends on the person whom you're addressing.

I explained to the expscv that light has zero proper mass and non-zero relativistic mass. You then later told him "light has no mass" without qualifying it. From the question asked it appears as if expscv may not be aware of these different terms and different definitions. For all expscv knew, you might have been disagreeing with my statement that light has non-zero relativsitic mass.

I understand that you might think I'm being nitpicky. I don't wish to. But I recently ran into a poster in a newsgroup who thought that light has zero relativistic mass. So I don't make any assumptions regarding this point anymore.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook