Physics question

[Mozart]

I hate thinking about astronomy/physics when in bed, it stops me from sleeping!

If an object is moving close to the speed of light, will it have a stronger gravitational field than if it were stationary?

[Mozart]

Anyone?

[M forever]

The speed of gravitational waves hasn't been measured yet, but they appear to be travelling at the speed of light. But the gravitational effect this object would have does not change, I would say, because it is not fast enough to "outrun" the gravitational waves caused by it.

[Mozart]

Would the object not gain mass if its traveling so fast because of the energy it took to get it to that speed?

[Soundproof]

No. It would actually lose mass, as a function of the energy consumed in order to achieve that speed. With an increase in velocity, the mass remains constant - minus the propellant consumed . What also increases with velocity is the object's resistance to acceleration. (Inertia).
With its mass invariant the object's impact upon the curvature of space-time will remain the same.

The concept of relativistic mass can throw one here. Which is why it's useful to ask: it travels at the speed of light relative to what?

http://www.ltn.lv/~elefzaze/?l=en&c=0503
http://www.phys.ualberta.ca/~gingrich/phys512/latex2html/node23.html

[bwv 1080]

Put simply yes

If gravity is proportional to mass, mass will increase with the speed at the rate of 1 / (1 -%C^2)^0.5  where %C is the speed as a percentage of the speed of light.  At .99C it is about a 7-1 increase in mass

[Soundproof]

Interesting. We have a MASSive disagreement. How do you consider this conforms with the scalar non-transformational properties of mass according to Lorentz Invariance?
And will we be seeing you in Stockholm soon? 

Wikipedia has a quite straightforward explanation of the principle involved. Go down to the sentence that begins with Given an object of invariant mass m, etc ... >There you'll see it states that mass is another form of energy, but go on and read the comments about Relativistic Mass.

http://en.wikipedia.org/wiki/Special_relativity

[bwv 1080]

How do you consider this conforms with the scalar non-transformational properties of mass according to Lorentz Invariance?

I don't, just going with Einstein there.

[Soundproof]

Relativistic mass (from Wiki's outline of Relativistic mass)

Introductory physics courses and some older textbooks on special relativity sometimes define a relativistic mass which increases as the velocity of a body increases. According to the geometric interpretation of special relativity, this is often deprecated and the term 'mass' is reserved to mean invariant mass and is thus independent of the inertial frame, i.e., invariant.
Using the relativistic mass definition, the mass of an object may vary depending on the observer's inertial frame in the same way that other properties such as its length may do so. Defining such a quantity may sometimes be useful in that doing so simplifies a calculation by restricting it to a specific frame. For example, consider a body with an invariant mass m moving at some velocity relative to an observer's reference system. That observer defines the relativistic mass of that body as:
M=gammam
"Relativistic mass" should not be confused with the "longitudinal" and "transverse mass" definitions that were used around 1900 and that were based on an inconsistent application of the laws of Newton: those used f=ma for a variable mass, while relativistic mass corresponds to Newton's dynamic mass in which p=Mv and f=dp/dt.
Note also that the body does not actually become more massive in its proper frame, since the relativistic mass is only different for an observer in a different frame. The only mass that is frame independent is the invariant mass. When using the relativistic mass, the applicable reference frame should be specified if it isn't already obvious or implied. It also goes almost without saying that the increase in relativistic mass does not come from an increased number of atoms in the object. Instead, the relativistic mass of each atom and subatomic particle has increased.
Physics textbooks sometimes use the relativistic mass as it allows the students to utilize their knowledge of Newtonian physics to gain some intuitive grasp of relativity in their frame of choice (usually their own!). "Relativistic mass" is also consistent with the concepts "time dilation" and "length contraction".

[mahlertitan]

I hate thinking about astronomy/physics when in bed, it stops me from sleeping!

If an object is moving close to the speed of light, will it have a stronger gravitational field than if it were stationary?

yes

[bwv 1080]

Relativistic mass

Introductory physics courses and some older textbooks on special relativity sometimes define a relativistic mass which increases as the velocity of a body increases. According to the geometric interpretation of special relativity, this is often deprecated and the term 'mass' is reserved to mean invariant mass and is thus independent of the inertial frame, i.e., invariant.
Using the relativistic mass definition, the mass of an object may vary depending on the observer's inertial frame in the same way that other properties such as its length may do so. Defining such a quantity may sometimes be useful in that doing so simplifies a calculation by restricting it to a specific frame. For example, consider a body with an invariant mass m moving at some velocity relative to an observer's reference system. That observer defines the relativistic mass of that body as:
M=gammam
"Relativistic mass" should not be confused with the "longitudinal" and "transverse mass" definitions that were used around 1900 and that were based on an inconsistent application of the laws of Newton: those used f=ma for a variable mass, while relativistic mass corresponds to Newton's dynamic mass in which p=Mv and f=dp/dt.
Note also that the body does not actually become more massive in its proper frame, since the relativistic mass is only different for an observer in a different frame. The only mass that is frame independent is the invariant mass. When using the relativistic mass, the applicable reference frame should be specified if it isn't already obvious or implied. It also goes almost without saying that the increase in relativistic mass does not come from an increased number of atoms in the object. Instead, the relativistic mass of each atom and subatomic particle has increased.
Physics textbooks sometimes use the relativistic mass as it allows the students to utilize their knowledge of Newtonian physics to gain some intuitive grasp of relativity in their frame of choice (usually their own!). "Relativistic mass" is also consistent with the concepts "time dilation" and "length contraction".

Thanks.  Does the energy increase with the relativistic mass or the invariant mass, i.e. if someone fires a 1 gram bullet at .99C do you use the relativistic mass or invariant mass to calculate the energy of impact?

[The new erato]

Put simply yes

If gravity is proportional to mass, mass will increase with the speed at the rate of 1 / (1 -%C^2)^0.5  where %C is the speed as a percentage of the speed of light.  At .99C it is about a 7-1 increase in mass

The mass increases with speed, and at the speed of light the mass becomes infinite, which is the reason that nothing can move faster than that.

[mahlertitan]

The mass increases with speed, and at the speed of light the mass becomes infinite, which is the reason that nothing can move faster than that.

that's what I believe will happen too.

[Soundproof]

Cool question.
Depends what you're firing at. If you're fed up with being stuck together with your co-traveller, and take a shot at him (her), then it's mass as we commonly understand it and a job for CSI; if you were able to take a shot at the guy who sent you on this mission, it's what we think of as relativistic mass.
Though that little bullet would probably also blow up that guy's planet upon impact. But that's a function of stored energy due to achieved momentum as a function of having expended a lot of energy in order to reach .99C

BTW - the "space traveler would be much younger when returning to earth after a journey at near light-speed" is a fool's paradox. Yes - time would dilate during near C travel, but in order to meet your twin on earth you would have to decelerate from near C, and during that process you would reacquire the proper age reference to match your twin's.

Lots of hogwash in popularized physics. Just to make clear - the mass remains the same, you're not adding atoms to the object while accelerating. But the object's momentum increases with velocity - however, that will not (according to theory) impinge upon the object's ability to influence the curvature of space-time.

[Soundproof]

The mass increases with speed, and at the speed of light the mass becomes infinite, which is the reason that nothing can move faster than that.

And there goes years of Relativity Theory ...

The speed of light is a constant, C.

All travel in space is a function of movement through the spatial and time dimensions. For simplicity's sake we postulate movement on the x, y and z axes, and add directional time.

Any object moving in space-time is already moving at the speed of light (as a function of spatial and time movement)-- that's what Relativity Theory means. However, everything is also moving relative to everything else, which means that we have different functions of spatial and time movements. Slow, fast, sluggish and blindingly fast all over.

Movement through Space + Movement through Time = C

Can't do anything about that. That's what Einstein's theory means. And that is also why, if you could move through space faster than C, Time would reverse. (Something's got to give) Paradox: Any movement where v=C, would mean that Time=0. If time ceases, you can have no movement ... Time is a direction, and though we, with our relativistic perception of it, consider it to be "moving" along in a discrete and easily parsed manner, that's down to our perception, and doesn't say anything about how fast time is actually moving. Could be that the "long" time measured by Earth's geological time scale from formation until today is 1/100 of a blink of the universes' eye.

As an object approaches the speed of light, its momentum increases exponentially (its resistance to continued acceleration) - but this is different from the kind of relativistic mass that tends to enter into such discussions.
For that object to have an increase in its gravitational field - that is, to influence the curvature of space-time - it would have to have mass added to it, i.e. more atoms. That's not what happens - it's momentum increases, but the elements constituting its mass remain the same. (Though we must subtract the loss in mass through the propellant used to accelerate to that speed, which means that the gravitational force actually becomes smaller, not bigger.)

[Maciek]

Soundproof, thanks for all your contributions here. My knowledge of more "advanced" physics is based primarily on popular science books, so it's nice to have someone clear up all those misunderstandings.

[Scriptavolant]

The mass increases with speed, and at the speed of light the mass becomes infinite, which is the reason that nothing can move faster than that.

For what I know, the mass doesn't increase with speed at all. It is the Energy which increases, and you' need infinite energy to pull an object beyond the speed of light, and that should be the reason why "nothing can move faster than that".

Interesting discussion, later I'll read it all through.

[71 dB]

Interesting discussion about relativistic physics.

I believe the gravitational field of a fast moving object is increased for observers due to the relativistic mass. Gravitational force is the gradient of curvatude of space. This curvatude will narrow when an object moves very fast (Lorentz contraction). That means greater gradient (gravitational force) in the direction of movement.

[mahlertitan]

my thanks to Soundproof and others, this thread has been very educational.

[Steve]

I hate thinking about astronomy/physics when in bed, it stops me from sleeping!

If an object is moving close to the speed of light, will it have a stronger gravitational field than if it were stationary?

Absolutely.