Quark ---> singularity

[JacobEvans]

If an object gains mass as it approaches c, couldn't we hypothetically move something extremely tiny like a quarck, and move it so fast (like way more than 99.99999999999% of c) that it gains enough mass to cause it to collapse upon itself and become a singularity? Basically make a black hole by moving super fast?

Not likely that this happens very often (if ever) but could it?

And could you also give enough mass to a photon via e=mc^2 that it does the same thing? probably waaaaaaay more implausible, but if light has gravity, why not ? (Ignoring lights tendency to turn into matter at this point :lol: )

 

[Nelson]

The short answer is that it couldn't happen in either case. But there are a number of things wrong with the proposed situation.

To truly explain this situation you would need a decent understanding of general relativity, which I do not claim to have. However, from special relativity we know that even if the quark is moving at 99.99999999% c nothing will change from the reference frame of the quark. If the quark is moving at this speed relative to some observer, then the observer would measure some increase in mass, but an observer traveling with the quark would measure no such increase. So no, it is not possible to collapse something onto itself by moving it very fast.

With respect to the photon question; they have no mass at all. This is why they are the only particle that can move at the speed of light. Light can be affected by gravity, but photons do not produce a gravitational force themselves because they have no mass.

I can talk about these issues in more depth if you are interested but I thought I would just answer the questions for now. I hope this was helpful.

 

[JacobEvans]

But would a relative increase in mass affect objects gravitationally?

Eg. would the quark pull objects toward it as it moved faster?

 

[Nelson]

Yes, this is possible, because any observer moving at that speed relative to the quark would measure the increase in mass. But then you have to think that anything that it could possibly pull in would only be affected by the gravitational field for a very short period of time, since the object would be moving past it at very close to the speed of light. Also keep in mind that on the scale of quarks, gravity is essentially irrelevant. The interactions are dominated by the strong nuclear force which is:

about 10^38 times that of gravitation

Edit: I wanted to clarify that my main point is that you would measure an increase in the mass of the object, and therefore more gravity. However, when considering additional factors, I do not believe the quark would actually pull any objects toward it through gravitation.

 

[JacobEvans]

how about a baseball then?

 

[Nelson]

Yes, this is a better example. And now we are getting into more interesting stuff. So here are some calculations worked out.

The mass of a regulation baseball is 145g and the mass of our sun is 1.989x10^33 g. So, to increase the mass of a baseball to the mass of the sun we have a factor of 1.37x10^31.

This means that we will need a Lorentz factor of this in order to increase the mass of a baseball to the mass of the sun (from the perspective of an observer outside of the reference frame that is).

This Lorentz factor corresponds to a speed of 99.999999999999999999999999999999999999999999999999999999999999% of the speed of light (60 9's after the decimal). However there are some other interesting considerations.

A baseball has a diameter of about 7.4 cm. Due to length contraction, if we observed a ball moving by at this speed it would appear to be ~5x10^-33 meters across in the direction of its motion. This is only about 300 times the Planck length.

The Schwarzschild radius of a black hole is the radius inside of which nothing can escape. Inside of this radius, the escape velocity necessary to free an object from the gravitational field is greater than c. For an object as massive as our sun this is about 2.95 km. So, theoretically if we had a baseball moving at this ludicrous speed, any object within 3 km of it would be within the Schwarzschild radius. What this would actually mean in terms of the dynamics between the two objects, I'm not sure. Like I said earlier, I think general relativity is really needed to understand a situation like this.

 

[JacobEvans]

The Schwarzschild radius of a black hole is the radius inside of which nothing can escape. Inside of this radius, the escape velocity necessary to free an object from the gravitational field is greater than c. For an object as massive as our sun this is about 2.95 km. So, theoretically if we had a baseball moving at this ludicrous speed, any object within 3 km of it would be within the Schwarzschild radius. What this would actually mean in terms of the dynamics between the two objects, I'm not sure. Like I said earlier, I think general relativity is really needed to understand a situation like this.

Would it not just pull those objects with it? I think this would require calculus, which I have yet to learn.

Of course if my prediction is correct and it would pull everything with it as it travels, the energy of the ball would probably get lost in overcoming the inertia of what ever it's pulling on.

Basically to solve this problem we could just drop the baseball part of it and ask what happens if we move a black hole at a ludicrous speed? I think the relative velocity of the BH and what ever was in its path would work out much the same as any other relativity problem.

 

[Ozymandyus]

I'm not a physicist or anything, but I'm pretty sure that relativistic mass is not directly relatable to gravitational force the way inertial mass is... A baseball having enormous mass at relativistic speeds does not directly correlate to enormous gravitational force.

Whatever accelerating an object to relativistic speeds DOES to the gravitational force that object exerts I think would be more analogous to making a very shallow but enormously long 'groove' in space time, rather than a singularity like a black hole. But that's just speculation - the Einstein Field Equations could tell you probably, but sadly I can't read them.

This sort of speculation isn't too worthwhile in my opinion, because clearly none of us here understand these things very well, and its leading to all kinds of wrong thinking on it. It's fun of course, but don't come away thinking you know anything .

 

[Nelson]

Would it not just pull those objects with it? I think this would require calculus, which I have yet to learn.

Of course if my prediction is correct and it would pull everything with it as it travels, the energy of the ball would probably get lost in overcoming the inertia of what ever it's pulling on.

Basically to solve this problem we could just drop the baseball part of it and ask what happens if we move a black hole at a ludicrous speed? I think the relative velocity of the BH and what ever was in its path would work out much the same as any other relativity problem.

The problem is that a black hole moving at close to the speed of light is by no means a simple relativity problem. I have a very good understanding of calculus, and I believe a reasonably good understanding of special relativity. However, what we are dealing with here is really in the realm of general relativity, and I don't really know how to even begin to approach a problem like this.

This sort of speculation isn't too worthwhile in my opinion, because clearly none of us here understand these things very well, and its leading to all kinds of wrong thinking on it. It's fun of course, but don't come away thinking you know anything .

This is pretty much what I'm getting at as well. I can tell you what special relativity says about it, but I am also very much aware that special relativity is not capable of fully explaining the situation. Because this deals with gravity, it is clear that general relativity is necessary to paint a full picture. Unfortunately, I don't have a significant understanding of GR to confidently proceed any further.

(I have been drinking with my roommates for the last couple of hours, please forgive any incoherency)

 

[Pulsar]

This is indeed very advanced stuff (beyond my knowledge), and I don't think there's a clear-cut answer. I can quote http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_fast.html:

When an object approaches the speed of light, its mass increases without limit, and its length contracts towards zero. Thus its density increases without limit. Sometimes people think that this implies it should form a black hole; and yet, they reason, since its mass and volume haven't changed in its rest frame, it should not form a black hole in that frame--and therefore not in any other frame either. So does a black hole form or not?

The answer is that a black hole does not form. The idea that "if enough mass is squeezed into a sufficiently small space it will form a black hole" is rather vague. Crudely speaking, we might say that if an amount of mass, M, is contained within a sphere of radius 2GM/c2 (the Schwarzschild radius), then it must be a black hole. But this is based on a particular static solution to the Einstein field equations of general relativity, and ignores momentum and angular momentum as well as the dynamics of spacetime itself. In general relativity, gravity does not only couple to mass as it does in the newtonian theory of gravity. Gravity also couples to momentum and momentum flow; the gravitational field is even coupled to itself. It is actually quite difficult to determine the correct conditions for a black hole to form. Hawking and Penrose proved a number of useful singularity theorems about the formation of black holes. But even these theorems do assume certain conditions which we cannot be sure are true "out there".

Nonetheless, there's the work of Aichelburg and Sexl, who described a Schwarzschild metric in a moving frame, i.e. applying a Lorenz transform. Now, if I understand it correctly, the gravitational field of a moving object is no longer spherical, but axisymmetric (I guess due to Lorenz contraction in the direction of motion). In the limit of an object moving near the speed of light, its gravational field is compressed into a plane, perpedicular to the direction of motion. So it becomes a so-called pp-wave spacetime. So an observer would feel the gravitational force of such a moving object for a very short time, infinitely short in the limiting case.

But this makes me wonder: what happens with two identical objects, moving side by side? In one frame, both of them are moving, increasing their mass and their mutual attraction. But in their own rest frame, everything is normal. I suspect that time dilation compensates the difference in gravitational force, resolving this paradox. But what happens to two photons, moving side by side? Do they attract each other? :?:

 

[doloafing]

Someone with more knowledge of this please correct me if I'm wrong, but isn't mass dilation due to relativity a dilation of inertial mass?

In other words, things travelling very close to the speed of light become very difficult to accelerate, but they do not have a higher gravitational attraction.

I've never seen the proof for mass dilation, so I could be way off. This is just the impression I always had.

 

[Sparky]

Hmmm.... Perhaps I could find (Emeritus) Prof. Roy Kerr and ask him about some of this stuff. He is a professor of physics at my University and specialised in black holes/super massive objects. He made some ground-breaking work on rotating black holes (this can be seen in the below link).

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

If I remember to go see him I'll post what he says