Fail

Why would the amount of energy required to accelerate a constant rate grow at all, much less geometrically? Accelerating at a constant rate requires a constant amount of energy.

Right, that's why, since you trust in relativity you have to accept this, in a relativistic situation, as, say, a ship accelerates and gets closer and closer to the speed of light, it increases it's mass as well, requiring more energy to propel it?

Silly relativity, let's just throw some of it out and forget about it! :wink:

Might as well, you RE'ers just keep making up 'how relativity works' anyway.

Yeah buddy, keep telling yourself that.

Try "E=mcc"

And please, please, please! Read these.

http://www.astro.ucla.edu/~wright/relatvty.htm
http://en.wikipedia.org/wiki/General_relativity
http://nobelprize.org/educational_games/physics/relativity/
http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html#7

Quote from: "dys"

Why would the amount of energy required to accelerate a constant rate grow at all, much less geometrically? Accelerating at a constant rate requires a constant amount of energy.

Right, that's why, since you trust in relativity you have to accept this, in a relativistic situation, as, say, a ship accelerates and gets closer and closer to the speed of light, it increases it's mass as well, requiring more energy to propel it?

The Earth is only approaching the speed of light relative to some observers; therefore its mass is only increasing relative to some observers.

No, mass does not become relative. It's a constant, and the closer it gets to appreaching c, the more it's mass increases. Mass will always be a constant.

Hara, maybe I miss-understood your last post but mass is not a constant.  Rest mass is a constant under a lorentz transformation but total mass, in the since of gamma*M(r), where M(r) is rest mass and gamma is 1/sqrt(1-(v/c)^2), where v is mag of velocity, is clearly not maintained under a lorentz transformation.  With that in mind, most physicists now a days use mass to refer only to the rest mass of an object, in which case you are correct.  The total mass, or more appropriatly the total energy, on the other hand is in no way constant under a transformation.

Can you explain how it would work (detailed if possible) with relativity?

Yea, for sure...do you want me to explain the whole mass/energy thing?  I'll type up a quick summary...

Yes please, I am very curious now.

of course no response

These definitions will prove useful:    and B=v/c.  v is the magnitude of the velocity of an object with respect to the observers refrence frame and c is the speed of  light.  Energy in relativity is defined as  .  m is called the rest mass.  It is the mass measured in a refrence frame where the object is at rest.  Depending on one’s refrence frame, different values of v will be observed.  Thus, total energy is dependent on your refrence frame.  However, there are quantities that are independent of the observor’s refrence frame.  These are called concerved quantities.  For example, in euclidean geometry, length is a concerved quantity (think about it for a second).  In relativity, we have this famous equation WHICH ALWAYS HOLDS:  .  P is momentum, and equal to m*v.  Now, suppose we are at rest, then p = 0 and  we are left with the famous equation E=mc^2.  m is a concerved quantity, like electric charge.  It does not change from refrence frame to refrence frame.  Now, lets see what happens  whe v -> c.  In this case, B ->1 and gamma -> infinity.  This meens  that the total energy also goes to infinity.  Sometimes people define a relative mass as M=gamma*m.  So, M also goes to infinity.  The result is that nothing with mass can ever reach the speed of light because otherwise it would have infinite energy.  But, what about light?  For light, gamma = infinity but we know that photons have finite energy.  Well, look at the equation for E again and note that while gamma = infinity, we  also have m = 0 … the two cancel each other out to give finite energies.  Now, here are some mathematical details.  The  laurence  transformation: Those vectors are called four vectors and the matrix is called the laurence transformation matrix, or also the Minkowski Metric for flat space time.  This tells you how to go from one refrence frame to another.  It should be clear from observation that under such a  transformation length is always contracted and time is dialated.  These equations can be derived easily.  Simply remember that the speed of light is constant and think about the geometry of a laser beem on a space ship, as observed from both the ship and earth.  The momentum four-vector, which also transforms as above, is given by  .  From here it is easy to see that the total momentum squared is invariant.  This then implies that  .  Ok, that’s as much as  I feel like wrighting, for more info see http://en.wikipedia.org/wiki/Special_relativity or get a book on special rel.

Oh no! The equations did not coppy.  I'm soory, there should be equations in there.  Umm.... i don't know what to do about that, soory...

How about this, go the wikipedia article and read starting from "Reference frames, coordinates and the Lorentz transformation".  Let me know if you have any questions on the physics, the math, or the notation.  I am a physics grad student and I have been a TA (teaching assistant) in special relativity classes.

Quote from: "Hara Taiki"

Quote from: "dys"

Why would the amount of energy required to accelerate a constant rate grow at all, much less geometrically? Accelerating at a constant rate requires a constant amount of energy.

Right, that's why, since you trust in relativity you have to accept this, in a relativistic situation, as, say, a ship accelerates and gets closer and closer to the speed of light, it increases it's mass as well, requiring more energy to propel it?

The Earth is only approaching the speed of light relative to some observers; therefore its mass is only increasing relative to some observers.

!!!!

Relative mass?? What are you talking about? Man FE is reaching new heigts.

Would you care to explain how mass can be relative to observers? ( let alone how you can tell mass by simple observation)

!!!!

Relative mass?? What are you talking about? Man FE is reaching new heigts.

Would you care to explain how mass can be relative to observers? ( let alone how you can tell mass by simple observation)

The mass of particles are given as "rest mass."  Why would that be?  

Anti-matter explains it very well in his post above:  

. . when v -> c. In this case, B ->1 and gamma -> infinity. This meens that the total energy also goes to infinity. Sometimes people define a relative mass as M=gamma*m. So, M also goes to infinity.

No, mass does not become relative. It's a constant, and the closer it gets to appreaching c, the more it's mass increases. Mass will always be a constant.

I never thought I'd see the day when somebody, in one post, touts himself as a scientific authority, and in the next, talks about constants that increase.

My standards for REers are too high by far.  TOO HIGH BY FAR.

I stood corrected by someone who knows more physics than me. FTL. :roll:

Jesus, boy, you're supposed to be their leader, you should have better observational and reading skills than that.

Hara Taiki, you're the one attending college at a diploma mill...

Not really. I left. I am contemplating on going back. Because of this, I still claim myself as a Student.

But my college education has nothing to do with things like my powers of observation and reading comprehension.

So Tom, bite it, k?  :wink:

Quote from: "Hara Taiki"

No, mass does not become relative. It's a constant, and the closer it gets to appreaching c, the more it's mass increases. Mass will always be a constant.

I never thought I'd see the day when somebody, in one post, touts himself as a scientific authority, and in the next, talks about constants that increase.

My standards for REers are too high by far.  TOO HIGH BY FAR.

You don't know what kind of mass he was talking about; he might have been talking about rest mass.