[RayG (OP)]

Since mass increases with speed (apparently), while being accelerated to 99.999 percent of the speed of light, what does one of those little protons weigh when they collide?

[evan_au]

Since energy and mass are equivalent (according to Einstein), physicists often measure mass in electron-Volts (eV), which is a unit of energy.

The LHC is currently being upgraded to accelerate protons up to 7 teraelectronvolts (7 TeV or 7x10¹²eV or 1.12 microjoules).
A proton at rest has an energy of 938 MeV, or roughly 10⁹ eV.

So when the LHC reopens, these colliding protons will have a mass/energy which is about 7000 times higher than when they first come out of the hydrogen gas tank.

Because it collides two protons of 7 TeV traveling in opposite directions, the LHC will be able to explore nuclear reactions of up to 14 TeV - or even higher if you use lead "bullets".

PS: The idea of a moving particle gaining mass was taught when I was at school. However, physicists today prefer to say that the mass of the proton is unchanged from when it was stationary, but that it has gained energy & momentum.

[yor_on]

I used to think so too. But I think Pete actually moved me over with 'relativistic mass' those days, both descriptions works. As it's no energy measurable locally, unless we collide it with another particle. The other way to see it would be that 'energy' then is unmeasurable locally, only expressing itself in collisions. I don't like that one.

If 'energy' exist, on its own, it should be measurable as you gain 'speed'. It's also so that those protons may be accelerated, but at some point the LHC will fail to accelerate them any more as we get up in 'energy'. When that happens we will see the same type of energy released in a collision, but created from a uniform motion, instead of a acceleration.

Another problem is where that 'energy' is stored, if it's not stored measurably locally, neither measurably in the vacuum surrounding that particle. And that I think goes for both descriptions
=

Or maybe that is a ultimate outfall from taking frames of reference seriously? That you need two frames of reference interacting, for any transformation with 'energy' to exist?

[JP]

Yor_on, I'm not quite sure what you're getting at with local and stored energy, but in general energy is not a "thing" that we can fundamentally describe, but rather a currency that gets exchanged.  The conservation of energy is a fundamental law that tells us how things interact.  For an individual object not interacting with anything else, energy would be a meaningless concept.  For that reason, kinetic energy is not a fixed number for an object, but can be calculated from a given reference frame and describes interactions with respect to that reference frame.  Relativity ensures that all observers describe the same physics, even if they measure different values of energy because conservation of energy still holds in interactions even if the numbers are different.

[JP]

Another, subtle point is that the OP's question is about weight, not mass, which is not trivial to answer...

[lightarrow]

Since mass increases with speed (apparently), while being accelerated to 99.999 percent of the speed of light, what does one of those little protons weigh when they collide?

Before answering to your question I would like to know if you are aware that a proton is composed of the three quarks u, u, d.
(After your answer I will explain why I'm asking you).

--
lightarrow

[yor_on]

Yes JP. It's a currency, and as such not measurable other than in transformations. But then again, 'energy' is also what we think made a inflation make matter, isn't it? The photon universe, no matter its magnitude has to come from somewhere, or? I don't have that big a problem with using it your way, but when thinking of it as something 'contained in a universe' I get a headache, because then I want it to show itself on its own, and that is experiments proving it to exist.

And that photon (gamma gamma?) universe is a totally weird idea in its own right too But it wasn't really Ray that got me going there, it was Evan. By weight I guess Ray's asking about what their gravitational field would be?

[RayG (OP)]

Okay- I brought up the question since many documentaries on physics refer to the fact that as speed increases, the mass(weight, whatever) increases as you approach the speed of light. That it is "impossible" to travel at the speed of light because the the mass becomes so great, etc... a sort of a "catch-22" situation develops. Maybe a simpler comparison would be- "IF a proton weighed 1oz at it's static point, what would it weigh at the speeds developed in the LHC? Is it an exponential increase as it speeds up?

Apparently, a photon has no mass, so it CAN travel at the speed of light, thus bypassing the rule. As for the 3 quark construction, I am aware that they are part of the fundamental building blocks of particles like protons, etc... Does your question mean that some Q's have no mass, thus negating some of the effects? I'm no Rocket Surgeon, but these little niggling questions always pop into my head, even though they have absolutely no impact on my everyday life... other than being ultimately responsible for it. 

[lightarrow]

Okay- I brought up the question since many documentaries on physics refer to the fact that as speed increases, the mass(weight, whatever) increases

They make a mistake. Mass doesn't vary with speed. What varies is energy and it goes to infinite as speed approaches light speed.

as you approach the speed of light. That it is "impossible" to travel at the speed of light because the the mass becomes so great, etc... a sort of a "catch-22" situation develops. Maybe a simpler comparison would be- "IF a proton weighed 1oz at it's static point, what would it weigh at the speeds developed in the LHC?

How do you define weight in relativity?

Apparently, a photon has no mass,

Yes.

As for the 3 quark construction, I am aware that they are part of the fundamental building blocks of particles like protons, etc... Does your question mean that some Q's have no mass, thus negating some of the effects?

No, all quarks have mass. The point is that their mass doesn't vary with speed:
http://pdg8.lbl.gov/rpp2013v2/pdgLive/Particle.action?node=Q123

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lightarrow

[yor_on]

weight is a relation to mass, mass is a relation (equivalence) to 'energy' per Einstein. At a relativistic speed the mass grows, sometimes called relativistic mass, or just mass energy. Lightarrow speaks about the 'energy' of a particle, to differ it from its 'proper mass' which is the mass defined from matter as Earth being in a uniform motion, in a ideally flat vacuum without any other gravitational influences. The proper mass of Earth won't change if we double Earths, and its solar systems, speed. As long as it is in a uniform motion that is, but its relativistic mass or 'mass energy' must, as far as I get it.

The headache for me is that you can give this solar system any speed you like. But locally you won't see any difference in energy, as your light bulb suddenly emitting gamma radiation, through that increased speed. So the relativistic mass, or 'mass energy' created through a different relative (uniform) motion is in fact undetectable from any local measurement, as proven by your scale as you weight yourself. The way to prove its existence is through collisions, or locally defined accelerating. That's what the LHC does, although I'm not sure if they allow uniform motion at the collision, or if they just keeps accelerating the particles, all the way up to a collision.

The idea is that even though locally undetectable in a uniform motion it will exist as a cost for you, accelerating, forcing you in the end to expend a infinite 'energy' to reach the speed of light in a vacuum.

[yor_on]

In fact, the whole idea of being able to accelerate, measuring different energy expenditure through what different uniform motion you had before that acceleration, must give us a global definition of motion. Without such a notion there can be no relativistic mass or mass energy referable to a acceleration from a uniform motion. With less than we then assume that whatever speed you think, or measure, yourself to have relative something else won't matter.

And if it was that way there could be no added cost to your energy expenditure, depending on your former uniform motion, which means that as long as you take it in small steps, you could 'cheat' the energy accounting. So we have a definition of sorts I think, although? As we don't know what a 'lowest state of relative motion' is?
==

This is defining it 'globally' though, from a SpaceTime continuum. Definable through four dimensions interacting without a background for its existence, more than what itself create.
=

Defined locally, uniform motion won't matter. It's all equivalent to 'no motion at all' as I see it. What you have is accelerations, that becomes your measurement of energy lost. Using a local definition, assuming a background of constants, gravity being one, you only 'locally move' as you accelerate. But we find the same problem there, something must keep an account of that acceleration, otherwise we meet the same confusion as before.

[yor_on]

there is one more thing to it. Although Earth is accelerating at one gravity, it's not 'moving'. So when this accountant keeps tab, he'll have to differ between the energy spent by a Earth as compared to the energy spent by a rocket, uniformly accelerating at one constant gravity. This is defining 'energy' as measurable transformations of that rockets fuel, but maybe there is some other way to define it in which Earth too 'spend' something? Energy as a cost is measurable, but as something in its own right?

[lightarrow]

weight is a relation to mass, mass is a relation (equivalence) to 'energy' per Einstein.

But said this way it's too generic, I could also say that "displacement is a relation to work" since force multiplied displacement equals work.
Furthermore, the relation between mass and weight is simple only in newtonian mechanics, not in SR or GR.

At a relativistic speed the mass grows,

On which statement I disagree...

sometimes called relativistic mass, or just mass energy. Lightarrow speaks about the 'energy' of a particle, to differ it from its 'proper mass'

Energy is "energy" and mass is "mass", they are two distinct concepts.

which is the mass defined from matter as Earth being in a uniform motion, in a ideally flat vacuum without any other gravitational influences. The proper mass of Earth won't change if we double Earths, and its solar systems, speed. As long as it is in a uniform motion that is, but its relativistic mass or 'mass energy' must, as far as I get it.
The headache for me is that you can give this solar system any speed you like. But locally you won't see any difference in energy, as your light bulb suddenly emitting gamma radiation, through that increased speed. So the relativistic mass, or 'mass energy' created through a different relative (uniform) motion is in fact undetectable from any local measurement, as proven by your scale as you weight yourself. The way to prove its existence is through collisions, or locally defined accelerating.

Sorry, "the way to prove its existence" doesn't exist  []. You can prove that energy and momentum increases with speed, not mass, unless you *define* relativistic mass as energy/c^2, but this is not a prove, just a definition.

That's what the LHC does, although I'm not sure if they allow uniform motion at the collision, or if they just keeps accelerating the particles, all the way up to a collision.

The idea is that even though locally undetectable in a uniform motion it will exist as a cost for you, accelerating, forcing you in the end to expend a infinite 'energy' to reach the speed of light in a vacuum.

So what you only need to talk about to describe this fact is "energy" (and "momentum").

--
lightarrow

[yor_on]

Sure Lightarrow. I'm not disputing a proper mass, or the definition of how this 'mass energy' comes to be. What makes you want to define it this way is the same thing that bothers me I think. The impossibility of measuring this energy locally in a uniform motion. It won't exist in any local measurements I know of, and placing it in the vacuum becomes just too weird for me. If it is existing as a relation to the vacuum it has to be different from a Higgs field. Then again, a momentum is also a locally untouchable experimentally, until a collision or annihilation. When Einstein thought up the stress energy tensor it seems to me that he described it from a continuum, a whole SpaceTime of a defined magnitude in which you had certain parameters, as motion and mass (energy), that would tweak this continuum, locally defined. Then again, if you can't measure it, what is it and where does it reside? I can construct three observers in different uniform motion at different velocities, and they all will define two different time dilations per observer. They also will define a different energy which now either is defined to exist inside this continuum 'simultaneously', which I think it has to be defined as, if I want it to be a SpaceTime continuum, or it all becomes a illusion to me

A Higgs field is either a local definition or I should meet a same problem defining what this acceleration is. And that is locality to me. The one place where you can define things, and agree on measurements.
=

In a continuum simultaneity must exist, as I think. The moment I start to define a continuum locally, disputing that we can agree on a SpaceTime position experimentally I either has to define 'time' as a illusion, to keep my continuum, or let the continuum disappear. And it seems very strange disputing the fact that we all die. At the moment we're 7? (and assorted others) billion experiments proving that fact. A rather heavy indication of there existing a 'time' I would say. So then you get rid of the continuum, but that leaves you a universe, or SpaceTime, that only exist locally described, constants, principles, rules and properties joining it.