Highest velocity possible

Originally posted by wormwood
isn't the heart of all this confusion that mass actually doesn't change at all when an object accelerates?

M = sqrt( m/(1-v­²/c² ) ) does grow, but m doesn't. which means an apple approaching light speed won't become a black hole, it'll just have a huge energy. and that energy would be equal to the energy of a co ...[text shortened]... n the mass actually grows to M.

the amount of energy changes, the mass doesn't.

Actually in the old days physicists loved that notion of mass increase while velocity increases. But nowadays they shun that notion and use the one you are talking about. When I was still in college I did some research and discussed the issue with a teacher and didn't reach any conclusion. I like to think in mass increase terms cause that means you'd have an infinite inertia to overcome to top c but I don't know if that's the final word.

Originally posted by adam warlock
Actually in the old days physicists loved that notion of mass increase while velocity increases. But nowadays they shun that notion and use the one you are talking about. When I was still in college I did some research and discussed the issue with a teacher and didn't reach any conclusion. I like to think in mass increase terms cause that means you'd have an infinite inertia to overcome to top c but I don't know if that's the final word.

There may be some mileage in the old idea that inertial mass and gravitational mass are not the same thing. In which case increasing speed would increase inertial mass but leave the gravitational mass alone. That actually makes sense since if gravitational mass increases with speed then some high speed cosmic particles ought to be able to perturb the paths of planets and stars.

Originally posted by adam warlock
Why so then? I don't see any reason for that to happen.

Its simply the opposite of the requirement for infinite energy to accelerate a mass to light speed. The deceleration is the reverse process, and for any deceleration whatsoever an infinite amount of energy will be released.

Originally posted by Kepler
There may be some mileage in the old idea that inertial mass and gravitational mass are not the same thing. In which case increasing speed would increase inertial mass but leave the gravitational mass alone. That actually makes sense since if gravitational mass increases with speed then some high speed cosmic particles ought to be able to perturb the paths of planets and stars.

But with general relativity we already know that gravitational mass and inertial mass are equivalent. And we also have lots of experiment that show that they both are equal to great accuracy. Of course this isn't the end of the road and knowledge is evolving all the time.

But those high speed cosmic particles had rest masses (this too is becoming a dated concept) very small to start with and even with speeds near c they aren't that massive so I don't think their gravitational mass would be great enough to overpower massive stars and palnets.

I think that your argument can be a very strong argument for the no increase mass scenario though.

Originally posted by twhitehead
Its simply the opposite of the requirement for infinite energy to accelerate a mass to light speed. The deceleration is the reverse process, and for any deceleration whatsoever an infinite amount of energy will be released.

I still don't follow your argument. Let's assume that you start in a non-moving state,then you accelerate till you reach 50 J of kinetic energy. You go on for that kinetic energy for a while. At any given time you can decelerate and only lose 20 or any other fraction of the 50 J. So I why if do you have to lose an infinite amount of energy to decelerate if you start with an infinite amount?

This discussion is severely flawed though. We are using some very dubious (read wrong) mathematical reasoning.

Originally posted by twhitehead
Its simply the opposite of the requirement for infinite energy to accelerate a mass to light speed. The deceleration is the reverse process, and for any deceleration whatsoever an infinite amount of energy will be released.

Deceleration is just an everyday word for acceleration that makes things go slower. In mathematical terms acceleration and deceleration are equivalent. Both will require a force to cause them and both will require energy so deceleration will not release any energy any energy.

Originally posted by Kepler
Deceleration is just an everyday word for acceleration that makes things go slower. In mathematical terms acceleration and deceleration are equivalent. Both will require a force to cause them and both will require energy so deceleration will not release any energy any energy.

I think he's meaning decceleration via a collision process. So that's why he's mentioning energy release.

Originally posted by adam warlock
I still don't follow your argument. Let's assume that you start in a non-moving state,then you accelerate till you reach 50 J of kinetic energy. You go on for that kinetic energy for a while. At any given time you can decelerate and only lose 20 or any other fraction of the 50 J. So I why if do you have to lose an infinite amount of energy to decelerate ...[text shortened]... is severely flawed though. We are using some very dubious (read wrong) mathematical reasoning.

Infinites do not exist. You cannot have something with infinite energy and therefore mass cannot move with the speed of light according to the Lorenz factor.

Of course the Lorenz factor might be wrong. You want to try to prove it?

Your argument ignores the experimentally verified model used by anyone working in a field that has anything to do with very high velocities. It just assumes that the Lorenz factor does not exist. That does not fit in with experiment.

Originally posted by adam warlock
I think he's meaning decceleration via a collision process. So that's why he's mentioning energy release.

He's referring to conservation of energy. No matter how you slow it down, the energy must be conserved, and it takes infinite energy to get from less than light speed to light speed.

Originally posted by AThousandYoung
Infinites do not exist. You cannot have something with infinite energy and therefore mass cannot move with the speed of light according to the Lorenz factor.

Of course the Lorenz factor might be wrong. You want to try to prove it?

Your argument ignores the experimentally verified model used by anyone working in a field that has anything to do ...[text shortened]... . It just assumes that the Lorenz factor does not exist. That does not fit in with experiment.

nfinites do not exist. You cannot have something with infinite energy and therefore mass cannot move with the speed of light according to the Lorenz factor.

Of course the Lorenz factor might be wrong. You want to try to prove it?

Aren't you saying what I said?

Your argument ignores the experimentally verified model used by anyone working in a field that has anything to do ...[text shortened]... . It just assumes that the Lorenz factor does not exist. That does not fit in with experiment.

Please explain it.

Originally posted by AThousandYoung
He's referring to conservation of energy. No matter how you slow it down, the energy must be conserved, and it takes infinite energy to get from less than light speed to light speed.

I know energy must be conserved.
If you collide with something you'll impart some of your energy to it. That's all I said.

Originally posted by adam warlock
Actually in the old days physicists loved that notion of mass increase while velocity increases. But nowadays they shun that notion and use the one you are talking about. When I was still in college I did some research and discussed the issue with a teacher and didn't reach any conclusion. I like to think in mass increase terms cause that means you'd have an infinite inertia to overcome to top c but I don't know if that's the final word.

while googling for stuff I happened to find this einstein quote from 1948:

"It is not good to introduce the concept of the mass M = m/(1-v2/c2)1/2 of a body for which no clear definition can be given. It is better to introduce no other mass than 'the rest mass' m. Instead of introducing M, it is better to mention the expression for the momentum and energy of a body in motion."

so it looks a bit like mister e. didn't seem to be that excited about the idea. -although it might be out of context... I can't access the article to be sure. it should be from: "Does mass really depend on velocity, dad?" , Carl E Adler, American Journal of Physics 55 (1987) 739.


(oh, and I just realized I got the equation wrong, the square root...)

Originally posted by wormwood
while googling for stuff I happened to find this einstein quote from 1948:

"It is not good to introduce the concept of the mass M = m/(1-v2/c2)1/2 of a body for which no clear definition can be given. It is better to introduce no other mass than 'the rest mass' m. Instead of introducing M, it is better to mention the expression for the momentum and energ (1987) 739.


(oh, and I just realized I got the equation wrong, the square root...)

Ah! I remember seeing that article on relativity. E^2=P^2+m^2 (using natural units)is a real formula and is always right. And Einstein really put the finger on the wound on that quote. But if one looks into older books we can find proofs that mass increases with speed. I have one such book and if you want I can post the authors proof. Even Feynman liked to think on increasing mass terms but the main problem really is its fuzzyness.

And Eintein earlier on his career adopted an even shadire concept: Longitudinal mass. Maybe that's why he didn't like that much the M concept too.

Anyway premisses apart everybody agrees on what are the consequences, even though they slightly disagree on the causes, and maybe that's what important in physics.

Originally posted by adam warlock
Ah! I remember seeing that article on relativity. E^2=P^2+m^2 (using natural units)is a real formula and is always right. And Einstein really put the finger on the wound on that quote. But if one looks into older books we can find proofs that mass increases with speed. I have one such book and if you want I can post the authors proof. Even Feynma ...[text shortened]... even though they slightly disagree on the causes, and maybe that's what important in physics.

ah, okay. thanks.


longitudinal mass? that sounds... interesting. 🙂

Originally posted by adam warlock
I still don't follow your argument. Let's assume that you start in a non-moving state,then you accelerate till you reach 50 J of kinetic energy. You go on for that kinetic energy for a while. At any given time you can decelerate and only lose 20 or any other fraction of the 50 J. So I why if do you have to lose an infinite amount of energy to decelerate ...[text shortened]... is severely flawed though. We are using some very dubious (read wrong) mathematical reasoning.

My reasoning is:
1. Particle A is traveling at light speed.
2. Particle A collides with particle B resulting in a deceleration of particle A to sub-light speed.
3. To accelerate Particle A from sub-light speed to light speed requires infinite energy therefore the reverse will release infinite energy.
4. Alternatively finite energy is released with no reduction in speed to particle A.

Yes, it plays on the fact that you can subtract any finite number from infinity and still have infinity and therefore is severely flawed mathematically as you point out.