Relativistic Mass Increase and Its Dependence on Relative Speed

[keepitmoving]

as i heard it, as an object increases velocity toward c, the mass of the object will increase as a result of the increasing energy which resulted from the increased speed. What is this speed relative to? - the object the speeding object departed from, or relative to an object in the direction of motion? What if those objects moved or ceased to exist - wouldn`t that change the relative speed and therefore the relative energy and therefore the mass?

 

[DaveC426913]

as i heard it, as an object increases velocity toward c, the mass of the object will increase as a result of the increasing energy which resulted from the increased speed. What is this speed relative to? - the object the speeding object departed from, or relative to an object in the direction of motion? What if those objects moved or ceased to exist - wouldn`t that change the relative speed and therefore the relative energy and therefore the mass?

Yep. You have to define what reference point you are observing from.

Note that if you define your observational reference point from a point that is pacing the object, you will not observe any untoward changes in mass, length or passage of time.

This is the meaning of relative in relavity. Your relationship with the object is relative and therefore, so are your measurements. There is no such things as an objective change in mass, length or passage of time.

 

[keepitmoving]

once the moving object approaches c, the other object which was used as a reference point is far away and maybe it has moved away with great speed. How can that object have an effect on the original moving object?

 

[Libohove90]

once the moving object approaches c, the other object which was used as a reference point is far away and maybe it has moved away with great speed. How can that object have an effect on the original moving object?

You still don't get it. There is no ORIGINAL moving object. Once the moving object approaches c, from the reference frame of the other object...it is increasing energy and mass only from the object's reference point.

Bring a third object that's moving at a different speed, it will measure different results than the previous object.

 

[keepitmoving]

i guess what i`m saying is how do the measurements of objects far away determine the ability of the original moving object to continue to accelerate? The ability to accelerate is controlled by it`s mass (it`s increasing mass) which according to what you say, is determined by measurements made by objects far away, objects that don`t even get the same measurements. I can see how their measurements might differ but how can their measurements determine the fate of the original moving object?

 

[bucher]

The relativistic mass is only in the reference frame of the observer, not the moving object itself. If you were to move near the speed of light, you wouldn't actually gain mass. However, if someone else were observing your movements, then they would observe you having more mass.

It's all relative to an observer.

 

[keepitmoving]

if, as i move close to the speed of light, i am only gaining mass according to the measurements of the observer, why can`t i continue to accelerate?

 

[darkhorror]

You can still continue to accelerate, on a spaceship you could accelerate forever at a constant acceleration. It's with respect to the outside observer that your acceleration will be slowing down, and since this is happening your mass seems to be increasing to that observer.

 

[keepitmoving]

but wouldn`t continued acceleration result in a velocity faster than c?

 

[fatra2]

but wouldn`t continued acceleration result in a velocity faster than c?

No. It would be the case if you follow Newton's 2nd law:
$$F=m\frac{dv}{dt}$$
which says that a force acting on an object will make it's velocity change.

But what Newton did not know is that the mass is not constant. With increasing kinetic energy, the mass of the object increases. You could still follow Newton's law, with this simple change:
$$F = \frac{d(mv)}{dt}$$
which says that a force acting on an object will make the combination of it's mass and velocity change.

Cheers

 

[HallsofIvy]

but wouldn`t continued acceleration result in a velocity faster than c?

The point you may be missing is that your speed is always relative to some other coordinate frame. In your frame, you mass doesn't change because your speed is always zero relative to your own frame. You are accelerating, and your speed approaching c, only relative to some other frame of reference. And relative to that other frame, your mass is increasing.

 

[keepitmoving]

are you saying that the expenditure of fuel causes the mass of the object to increase?

 

[fatra2]

You are talking about different things.

are you saying that the expenditure of fuel causes the mass of the object to increase?

You are referring to a technical point, which relates to the way we know of increasing the energy of a space ship. Of course that the more gasoline you use, the less your spaceship will have mass.

We are talking about the mass of an object that is accelerated, independant of the process to do so. For example, the astronaut's mass in the spaceship will increase with increasing velocity.

Cheers

 

[stone1]

or you could move so far away from the original object that space expansion kicks in and you can move relative to the original object at speeds higher than c.

 

[Matterwave]

You don't have to think of an increase in mass. The mass is invariant; however, the "inertia" it feels will change. The modification term, gamma, is usually lumped with the mass and people call that the "effective mass"; however, there is no reason that the gamma term actually suggests the actual mass of the thing ever changes. If you look at the equations, there's no reason to really lump gamma together with the mass, you very well may lump it with the entire quantity (mv).

 

[bucher]

but wouldn`t continued acceleration result in a velocity faster than c?

The energy required for you to accelerate would increase substantially as you approach c.

Kinetic Energy = mc²($$\gamma$$-1)

As you approach the speed of light, it will cause a near infinite amount of energy to accelerate you any further.

 

[Bob S]

Protons and antiprotons in the Fermilab Tevatron are accelerated to about 980 GeV (roughly gamma = 1043). As Fatra2 points out in Post 10, the acceleration in each turn is (during acceleration)

F=d(mv)/dt

If the beam goes through a voltage gap (RF cavity) of length dx each turn, then

Fdx = [d(mv)/dt] dx = d(mv) dx/dt = v d(mv) = d[(1/2) mv²] = dE (E = total energy)

So the protons and countercirculating antiprotons simultaneously gain some energy F dx each second during the acceleration phase in the 2 pi kilometer circumference superconducting ring.

The relativistic mass momentum energy equation is

E² = (pc)² + (m₀c²)² = γ² (m₀c²)²

α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ ς σ τ υ φ χ ψ ω .

 

[DaveC426913]

but wouldn`t continued acceleration result in a velocity faster than c?

While you are sitting in your spaceship, accelerating at a constant rate, you notice nothing untoward. Your mass does not change. Your velocity remains zero (in your own frame of reference). Looking out the window, you will notice some strange effects, notably that the star you are heading towards seems to be much closer than you knew it was when you started.

Others watching you fly past will note that your mass has greatly increased from its initial value and the lerngth of your ship has shrunk. They wil also note that, inosde your ship you are moving very slow.

They will also note that your velocity is very near c but never reaches c.

Meanwhile, back in your spaceship, you continue to accelerate. Note that there is no direct way of measuring your speed without looking at external objects.

This fact: relative to the external observer, time is slowing down for you. It is this fact that allows you to continually accelerate forever, yet your spaceship never reaches c.

 

[m.starkov]

Hi to everyone!

A very good question to discuss!
Because many people are frighten that there is not enough fuel to go to the stars.
Actually this is not true.
Mass is growing only for observers.
If you afraid to fly then you better don't talk to these observers :)
Nobody can stop your acceleration!
You will be "in time" at your destination point.
But the other question is what you will find at destination point... but it is another question to Relativity.
I have heard that increasing mass approaching "с" effect can be found in atomic accelerators (e.g. Tevatron).
These guys tells that they have to increase power of magnets to keep particles on the circle way with regards to relativity effect of increasing inertial mass.
What happens with gravitational mass in this case - I don't know.
But AFAIK they have accelerated particles almoust to "c".
So where is infinite gravitational mass there? :)
No infinite mass I had feel last years on the Earth.
Probably high mass particles went out of the circle and thus they were not measured :)
Actually I can hardly imagine the benefits from this effect.
It just complicate thinking about Starship construction.

 

[DaveC426913]

Probably high mass particles went out of the circle and thus they were not measured :)

Well, they might not be measured by the detectors, but a good tape measure across the crater in the tunnel wall of the accelerator installation where those particles impacted at .99c would have done the trick!

 

[m.starkov]

Well, they might not be measured by the detectors, but a good tape measure across the crater in the tunnel wall of the accelerator installation where those particles impacted at .99c would have done the trick!

At 1.01с where will be no any tricks ;-)