Well, this is odd...

[Donut.Hole]

Not sure if this is the right place to post this, but why can't something accelerate past the speed of light? Can't you just give it more energy?

 

Very odd indeed.

[Cap'n Refsmmat]

The energy required to do so is infinite. The mass of the object grows as you accelerate it, so it takes more and more energy to accelerate the object.

[swansont]

The relationship between energy and speed is asymptotic and diverges at v=c. IOW, you need at add infinite energy just to get to c.

[Janus]

Put quite simply, because it would take an infinite amount of energy just to accelerate up to the speed of light. IOW, no matter how close to the speed of light you are or how much energy you add, it will only get you closer to the speed of light and never equal to or faster than.

[thedarkshade]

You indeed need infinite energy.

 

[math]E=\frac{m_0 c^2}{\sqrt{1-\beta^2}}[/math]

 

as [math]\beta[/math] is [math]\frac{v}{c}[/math] and you get at c, you get zero under the fraction (in the first equation) and you know what that means!

[Donut.Hole]

Thanks to all that answered, it really helped. I won't be checking back on this thread, but you're free to discuss it.

[Obelix]

Not sure if this is the right place to post this, but why can't something accelerate past the speed of light? Can't you just give it more energy?

 

Very odd indeed.

 

One can give an infinite amount of energy, but this will add to the MASS of the moving object, not to its SPEED.

[timo]

One can give an infinite amount of energy, ...

I doubt it.

...but this will add to the mass of the moving object, ...

Depends on what you mean by mass. If you mean energy, then, apart from the infinity problem, that's trivially true. If you mean mass as in "mass of a particle" (i.e. rest mass), then at least in the given scenario it's wrong.

 

... not to its speed.

Surely, increasing the kinetic energy of a massive particle increases its speed. |v|(E) is a strictly monotonous rising (although limited) function except for massless particles.

[Obelix]

I doubt it.

 

I mean one can increase its energy without any limits.

 

Depends on what you mean by mass. If you mean energy, then, apart from the infinity problem, that's trivially true. If you mean mass as in "mass of a particle" (i.e. rest mass), then at least in the given scenario it's wrong.

 

I mean mass as in mass of a particle. This is NOT NECESSARILLY its rest mass! Why do you say "it is wrong in the given scenario"? Do I need to remind you the relativistic mass increase?

 

[math]m=\frac{m_{0}}{\sqrt{1-\frac{\upsilon^{2}}{c^{2}}}}[/math]

 

Surely, increasing the kinetic energy of a massive particle increases its speed. |v|(E) is a strictly monotonous rising (although limited) function except for massless particles.

 

You seem to take into account the non - relativistic laws about kinetic energy, speed, and mass. Special Relativity definetely reveals that a continuous increase in energy does not add to the speed - in other words, the added energy does not come in the form of kinetic energy, necessarily. It does so in the low speed limit of Newtonian Mechanics and everyday experience, but not in realtivistic speeds (i.e. close to that of light).

[Klaynos]

Anyone who has done much relativity know that the idea of relativistic mass is a false idea, and that mass is invariant and other quantities (such as energy and momentum) should be the non-invariant parameters.

 

And I'm pretty sure that Atheist is correct on all his points, +KE = +v for massive particles.

[swansont]

You seem to take into account the non - relativistic laws about kinetic energy, speed, and mass. Special Relativity definetely reveals that a continuous increase in energy does not add to the speed - in other words, the added energy does not come in the form of kinetic energy, necessarily. It does so in the low speed limit of Newtonian Mechanics and everyday experience, but not in realtivistic speeds (i.e. close to that of light).

 

No, what SR tells us is that KE and speed do not have a simple quadratic relationship, though the deviation from this is small at small speeds.

[Obelix]

Anyone who has done much relativity know that the idea of relativistic mass is a false idea, and that mass is invariant and other quantities (such as energy and momentum) should be the non-invariant parameters.

 

Could you please be more specific? Are there any papers about that?

[Klaynos]

The concept of mass, L.B.Okun, Physics Today 42 (6): 31–36 (1989).

http://www.physicstoday.org/vol-42/iss-6/vol42no6p31_36.pdf

 

I've not read it but is referred to by some stuff I just read.

[swansont]

Also

On the Abuse and Use of Relativistic Mass by Gary Oas

http://arxiv.org/abs/physics/0504110

 

and another article by Lev Okun (specifically section 5: The Virus of Relativistic Mass)

http://arxiv.org/abs/hep-ph/0602037

[Obelix]

Thanks!

[JHAQ]

Referring to Obelix---- One can give an infinite amount of energy, but this will add to the MASS of the moving object, not to its SPEED.------- Wont this give rise to the Higgs particle & a mini black hole as per proposed experiment in Switzerland using the supercollider under construction ?

______________

[swansont]

Referring to Obelix---- One can give an infinite amount of energy, but this will add to the MASS of the moving object, not to its SPEED.------- Wont this give rise to the Higgs particle & a mini black hole as per proposed experiment in Switzerland using the supercollider under construction ?

______________

 

This is the misconception we're discussing. If you add energy to an object, you can increase its mass; a hot cup of coffee has slightly more mass than an otherwise identical cold cup. But not if that energy is kinetic energy — KE is frame-dependent.

 

IOW, if I had a sensitive enough scale, I could detect the mass difference in the case of the cup of coffee. But the scale does not change its reading because of relative motion between me and the scale.

[Slinkey]

Would I be right in thinking that a better way of seeing relativistic mass is that when we accelerate a massive body we are increasing its inertia? ie. the faster we "push" it the more inertia it has?

[swansont]

Would I be right in thinking that a better way of seeing relativistic mass is that when we accelerate a massive body we are increasing its inertia? ie. the faster we "push" it the more inertia it has?

 

It depends on how you define inertia. If it's momentum, then yes. If it's mass, then no. (one must draw the distinction between inertia, the principle, and inertia, the property)

[Obelix]

This is the misconception we're discussing. If you add energy to an object, you can increase its mass; a hot cup of coffee has slightly more mass than an otherwise identical cold cup. But not if that energy is kinetic energy — KE is frame-dependent.

 

IOW, if I had a sensitive enough scale, I could detect the mass difference in the case of the cup of coffee. But the scale does not change its reading because of relative motion between me and the scale.

 

I'm afraid that yours is a tautology, after all:

 

"If one adds kinetic energy to a body, one will only increase its speed." This is what you seem to say.

 

The question is:

 

1) Is speed increase the only way to increase a body's kinetic energy? Mass increase would do the same job.

 

2) Is addition of kinetic energy, in the way of increasing speed, possible to a body moving close to the speed of light? One can add energy, yes, but can one add that energy in the form of kinetic energy, in the above way? You seem to take for granted that the answer is "Yes!" But this is the very thing to be proved!

 

If you take for granted that: "One can add kinetic energy to any body in any condition of motion but NOT in the way of increasing its mass" this means only one thing: "One can increase the body's speed".

 

Altogether, your reasoning seems to go as follows:

 

"If you increase the body's speed, this will only result in increasing its speed"!

 

Would I be right in thinking that a better way of seeing relativistic mass is that when we accelerate a massive body we are increasing its inertia? ie. the faster we "push" it the more inertia it has?

 

What does "Mass" mean? If it is Inertial Mass, it means a factor of proportion in the measure of Momentum and Force. There is no other way for it to manifest itself, either in relativity or Newtonian Mechanics.

 

So what you ask above seems to be: "Is this the only way to understand mass?" I think the answer is yes.

 

An increase in inertial properties (e.g. momentum) is the only way for mass itself to increase, as there is no other way for it to have a physical meaning.

 

It would be an interesting experimental test to check if relativistic inertial - mass increase results in an increase of gravitational mass by an equal amount. A confirmation, that is, of the Principle of Equivalence ([math]m_{Inertial} = m_{Gravitational}[/math]): "If adding energy to a body results in an increase of its inertial mass, is the additional mass equal to another additional quantity of gravitational mass?"

 

Anybody knows whether such an experiment has been carried out? I.e., have bodies or particles moving close to the speed of light ever been "weighed" in some way?

 

Is it known whether beams of particles accelerated to relativistic speeds in accelarators (such as CERN) have ever been observed to curve as a result of an equal increase in their gravitational properties?

[timo]

Free object (no potential energy):

Definition of rest/invariant/proper mass: [math]m^2 := p^\mu p_\mu = E^2 - |\vec p |^2[/math] modulo some factors of c that I don't want to look up. It's what physicists call an invariant or a Lorentz scalar.

Definition of kinetic energy: [math] E_{\text{kin}} := E - mc^2 = \gamma mc^2 - mc^2[/math]; obviously not a Lorentz scalar.

=> [math]| \vec v |(E_{\text{kin}}) = c\sqrt{1-\left( \frac{1}{E_{\text{kin}}/mc^2 + 1} \right)^2} [/math], [math]\lim_{E_{\text{kin}}\to \infty} | \vec v | = c[/math], [math]\frac{\partial | \vec v |}{\partial E_{\text{kin}}} > 0[/math].

 

Note that you can substitute the kinetic energy for total energy if you prefer that. Above is the standard definitions for kinetic energy and especially mass. Relativistic mass is merely the energy or an object expressed in different SI units (due to being divided by a constant factor c²).

[swansont]

I'm afraid that yours is a tautology, after all:

 

"If one adds kinetic energy to a body, one will only increase its speed." This is what you seem to say.

 

The question is:

 

1) Is speed increase the only way to increase a body's kinetic energy? Mass increase would do the same job.

 

Not if it wasn't moving, and it wouldn't be "otherwise identical" if you added mass.

 

2) Is addition of kinetic energy, in the way of increasing speed, possible to a body moving close to the speed of light? One can add energy, yes, but can one add that energy in the form of kinetic energy, in the above way? You seem to take for granted that the answer is "Yes!" But this is the very thing to be proved!

 

That's not the point under discussion. The issue is whether center-of-mass KE results in an increase in mass. But since I can get a change in KE from a change in frame of reference (it's not an invariant under a Lorentz transformation), the answer has to be "no."

[Obelix]

Please let me get something straight:

 

Is this font considered too large for this forum? It's only size 3. It doesn't look larger to me, compaired to the other fonts here.

 

I understand that this font (Size 4) is big - and I've given it up!

 

But THIS size too?

 

As for this size, I think it is this one that's annoying: Too small to read easily.

 

As for me, when something is written I pay attention to the meaning - not the font!

 

There is a saying in my country, about a finger that was pointing at the moon..and someone was taking a good look at the finger!

[Klaynos]

Why do you need to change font size at all?

 

The forum will do formatting of that kind of thing for you...

[Phi for All]

Why do you need to change font size at all?

I use fonts (and their attendant options) only for the occasional emphasis. Not pointing any fingers, mind you, but some folks feel the need to gussy up everything they write. I'm not sure if they're not confident in their choice of words and want to embellish or if they think it will make their posts more eye-catching, but I think a lot of readers are more likely to skim over posts that are green or ALLCAPS or use a decorative font that takes a bit to get used to.

 

So in the end, messing with the fonts too much is like reading bedtime stories at the top of your lungs; it defeats your original purpose.

 

[/off-topic urge to comment when I should be working]