E=mc^2

[CraigD]

One question: is there a chance that any mass could travel faster than light?

 

I mean, sure Einstein's theory says that not, but is it definite?

Pretty definite, I think.

 

On the other hand, Relativity only prohibits physically real particles from exceeding the speed of light. Changes in time regarding one or more particle’s quantum wave function are not so constrained, rather occur instantaneously over a distance. Some speculate that it might be possible to exploit this to move information in excess of the speed of light, though to date, theoretical explorations have found no way to “cheat” Relativity – although such things as quantum entangled particles can be thought of as “communicating” instantaneously at a distance, no one appears to have been able to imagine a theoretical scheme that would allow any usable information to be transmitted this way.

 

To a very advanced civilization, matter is only a means of carrying information, so being able to communicate faster than light would be equivalent to being able to travel faster than it. Whether a very advanced civilization would be able to accomplish

FTL communication is an open question. Personally, I don’t believe so, but when speaking about arbitrarily advanced science, it’s difficult to be certain.

[learnin to learn]

What would happen if one could travel at the speed of light? Would'nt they be weightless???

[Edge]

What would happen if one could travel at the speed of light? Would'nt they be weightless???

Yep, they transform into energy. Cool, isn't it?

[CraigD]

What would happen if one could travel at the speed of light? Would'nt they be weightless???

Yep, they transform into energy. Cool, isn't it?

According to current most widely accepted theory, an object with non-zero mass can’t travel at the speed of light relative to any observer.

 

There are many popular explanations of this claim. The most common uses the famous equation for which this thread is named (E=M*c^2), and the relativistic formula for mass (M=Mrest/((1-(V/c)^2)^.5)) to show that, for any non-zero mass M, the amount of energy required to accelerate it to V approaches infinity as V approaches c. Since there’s a finite amount of mass and energy in the accessible universe, there’s not enough energy to accelerate any non-zero mass to the speed of light.

 

A similar argument can be made that no object with non-zero mass traveling at c relative to any observer already exists, using the above formula and the universal gravity formula (F=g*M1*M2/(R^2)) to show that if such an object with mass M1 exists, the gravitational force it exerts on any observer with non-zero mass M2 would be infinite, regardless of the distance R between them.

 

I think this claim does not imply that an object with non-zero mass, such as a spacecraft, cannot travel a distance D in less time (as measured on the spacecraft) than D/c. Relativistic time dilation and length contraction predicts that, with sufficient energy, and solving many other engineering demands of spaceflight (no easy task!), a spacecraft can be made to go anywhere in effectively as little time (as measured on the spacecraft) as one wishes. Only an observer stationary with respect to the spacecraft’s initial velocity would measure the voyage to require at least more than the time D/c.

[Edge]

According to current most widely accepted theory, an object with non-zero mass can’t travel at the speed of light relative to any observer.

 

There are many popular explanations of this claim. The most common uses the famous equation for which this thread is named (E=M*c^2), and the relativistic formula for mass (M=Mrest/((1-(V/c)^2)^.5)) to show that, for any non-zero mass M, the amount of energy required to accelerate it to V approaches infinity as V approaches c. Since there’s a finite amount of mass and energy in the accessible universe, there’s not enough energy to accelerate any non-zero mass to the speed of light.

 

A similar argument can be made that no object with non-zero mass traveling at c relative to any observer already exists, using the above formula and the universal gravity formula (F=g*M1*M2/(R^2)) to show that if such an object with mass M1 exists, the gravitational force it exerts on any observer with non-zero mass M2 would be infinite, regardless of the distance R between them.

 

I think this claim does not imply that an object with non-zero mass, such as a spacecraft, cannot travel a distance D in less time (as measured on the spacecraft) than D/c. Relativistic time dilation and length contraction predicts that, with sufficient energy, and solving many other engineering demands of spaceflight (no easy task!), a spacecraft can be made to go anywhere in effectively as little time (as measured on the spacecraft) as one wishes. Only an observer stationary with respect to the spacecraft’s initial velocity would measure the voyage to require at least more than the time D/c.

Woa, interesting. Then I stand corrected.

 

However, I have heard that mass can be made energy and otherwise. (Something like that) I dunno if this is true...

 

Damn, this Einstein theories are not my best...

[CraigD]

However, I have heard that mass can be made energy and otherwise. (Something like that) I dunno if this is true...

It's true. High velocities aren’t necessary for this to be observed - we see mass converted into energy all the time – the sun’s nuclear fusion energy comes from the slight mass difference between 4 atoms of Hydrogen and one of Helium. Energy from nuclear fission, both the natural kind suspected of occurring deep with in the Earth, and the artificial kind from powers commercial and military nuclear reactors, is due to a slight mass difference between the fissionable fuel and the end products.

 

Conversion of energy into mass on a detectable scale is much less commonplace. I can’t think of any examples one can actually observe with the naked eye – most require a high-energy particle accelerator, and/or particle trap, and create only miniscule quantities of mass at very low efficiencies.

[learnin to learn]

that is awsome!!!

[Tormod]

It's true. High velocities aren’t necessary for this to be observed - we see mass converted into energy all the time – the sun’s nuclear fusion energy comes from the slight mass difference between 4 atoms of Hydrogen and one of Helium.

 

Or even more commonly in cars where gas is ignited to produce energy. :friday:

[learnin to learn]

but can we recreate nuclear fusion on earth?

[CraigD]

but can we recreate nuclear fusion on earth?

Not only can we, we have, in the form of fusion bomb tests, on 11/1/1952, and may times since then.

 

Using fusion for practical electrical power generation has thus far not been achieved.

[cwes99_03]

Not exactly, the bond energy of gasoline between the molecules is being turned into free energy. Is there mass associated with the bond energy between two molecules? I was under the impression that there wasn't.

[CraigD]

Not exactly, the bond energy of gasoline between the molecules is being turned into free energy. Is there mass associated with the bond energy between two molecules? I was under the impression that there wasn't.

I believe that yes, in fact, the energy of chemical bonds such as you describe are associated with very small mass changes, because the increase in electromagnetic interaction between its nuclear quarks and electrons produce increase in weak nuclear interaction among the quarks. Bosons of weak nuclear force are much more massive (~80 vs. .006 Gev/c^2), so this increased interaction results in increased mass.

 

I’m perilously close to my edge of understanding of the Standard Model with this sort of talk, so please consider it very tentative.