Particles approching the speed of light

[Honorable_Death]

Before i start this thread, if i say anything wrong please correct me,

According to special relativity a particle with rest mass as it approaches the speed of light increases in mass and when it hits the speed of light its mass is infinite. So as a particle is going towards a black hole and accelaraes towards the speed of light, wouldn't its mass increase greatley, and if so wouldn't it become a black hole itself?

 

[pervect]

For starters, a technical point.

Does mass change with velocity?

There is sometimes confusion surrounding the subject of mass in relativity. This is because there are two separate uses of the term. Sometimes people say "mass" when they mean "relativistic mass", mr but at other times they say "mass" when they mean "invariant mass", m0. These two meanings are not the same. The invariant mass of a particle is independent of its velocity v, whereas relativistic mass increases with velocity and tends to infinity as the velocity approaches the speed of light c.

It's correct (but as the FAQ mentions it's regarded by many as somewhat dated) to say that relativistic mass increases with velocity - but it's not correct to simply say that "mass" increases with velocity. Making the obvious pendantic correction, and assuming you meant relativistic mass increases with velocity leads to the next point.

Next up is the FAQ
If you go too fast, do you become a black hole?

The answer to this question is no, you do not.

In part the misunderstanding arises because of the use of the concept of relativistic mass in the equation E = mc2. Relativistic mass, which increases with the velocity and kinetic energy of an object, cannot be blindly substituted into formulae such as the one that gives the radius for a black hole in terms of its mass. One way to avoid this is to not speak about relativistic mass and think only in terms of invariant rest mass (see Relativity FAQ Does mass change with velocity?).

This is WHY relativistic mass is (in my opinion and many others) a bad idea - too many people make the mistake you just made, and ascribe characteristics to relativistic mass that it does not have.

The concept of the mass of a system in GR is actually quite subtle. In this particular case, though, a rough translation of the useful formulation of mass is to say that the total energy of the particle (which you can losely think of as the potential energy plus the kinetic energy) stays constant as the particle falls into the black hole. Be warned though that strictly speaking the idea of "potential energy" isn't quite correct except in the weak-field limit.

The more precise and correct way of saying what I said above is that there is a conserved energy associated with the geodesic motion (the motion of a freely falling particle) in the Schwarzschild geometry (the static geometry of space-time associated with a single large mass). This consered energy is generally given the label E₀, as it turns out to be the covariant compoent of the energy-momentum 4-vector of the infalling particle.

The end result is the same - there is a constant quantity, which you can think of as energy, that a particle orbiting or falling into a black hole has.

 

[StarshipX]

Is light really deflected by the Sun? I don't think light is really deflected in a gravitational field.

 

[jdavel]

Is light really deflected by the Sun? I don't think light is really deflected in a gravitational field.

I doubt you've tried to measure it.

Aristotle didn't think that a heavy and a light object would fall at the same rate when dropped. Why? Because he'd never bothered to try it. As a result of his arrogance, science went nowhere for 2000 years.

As a rule, actually doing an experiment before you decide how it will come out works better than the other way around.

 

[pervect]

Is light really deflected by the Sun? I don't think light is really deflected in a gravitational field.

Yes, light is deflected by massive bodies, this is sometimes called gravitational lensing. In GR, light is deflected twice as much as it would be under Newtonian theory. This was one of the first experimental successes of relativity.

See for instance the wikipedia article

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

 

[jdavel]

In GR, light is deflected twice as much as it would be under Newtonian theory.

Newton said light would be deflected by mass?

 

[StarshipX]

I know that is what general relativity http://archive.ncsa.uiuc.edu/Cyberia/NumRel/EinsteinTest.html. What bothers me is that light on Earth does not seem to be effected by gravitation (e.g lasers).

 

[inha]

I haven't crunched any numbers on this but I think the Earth's mass is way too small to cause an effect we could detect.

 

[jdavel]

I know that is what general relativity http://archive.ncsa.uiuc.edu/Cyberia/NumRel/EinsteinTest.html. What bothers me is that light on Earth does not seem to be effected by gravitation (e.g lasers).

Maybe the deflection of a laser beam in the Earth's gravitational field is too small for you to see by just looking at it. How much does general relativity say it should bend?

 

[nwall]

As a rule, actually doing an experiment before you decide how it will come out works better than the other way around.

Unless of course you're Einstein. A lot of his work on GR wasn't based on observations but predicted later observations.

 

[nwall]

Newton said light would be deflected by mass?

Yeah, I was confused about that too, but here it is, straight from the horse's mouth:

For a ray of light which passes the sun at a distance of D sun-radii from its centre, the angle of deflection (a) should amount to

a = (1.7 seconds of arc) / D​

It may be added that, according to the theory, half of this deflection is produced by the Newtonian field of attraction of the sun, and the other half by the geometrical modification ("curvature") of space caused by the sun.

- Einstein, Relativity: The Special and General Theory, Appendix Three: The Experimental Confirmation of the General Theory of Relativity

 

[JesseM]

In Newton's time there was a controversy over light was a wave or whether it was composed of "corpuscles" (basically an old word for particles)--see here for more info. Of course quantum theory showed that both are correct in a sense, but Newton himself favored the corpuscle theory (although he thought the motion of the corpuscles might be affected by waves moving through the 'Aether'), so presumably these corpuscles would have been expected to experience gravitational attraction like anything else. I'm not sure whether the believers in the wave theory of light would have expected gravity to have any influence on light, though.

 

[jdavel]

nwall,

Well, I learned something today (though I'm not sure what it is). Thanks!

Do you know what he's talking about? Maybe it's just the classical calculation of the bending of a beam of particles traveling at c (if that were possible) in a graviational field. I don't think Newton had any idea of the value of c, but he might have predicted the bending as a function of c, whatever it turned out to be.

But, like I said, I didn't know Newton had ever thought about such a thing!

 

[nwall]

Well, I'm not sure if Newton himself had a theory of what light would do when exposed to a gravitational field, but apparently Newton's equations predicted that light would bend in a gravitational field based on the knowledge of light in the 1900s.

Remember that Galileo observed that the acceleration due to gravity of a body is independent of the body's mass, so if you drop a golf ball and a bowling ball at the same time from the same height, they'll hit the ground at the same time. Based on this I suppose you could argue that if you dropped a hypothetical body of mass 0, it would still accelerate down at the same rate due to gravity. This is of course just speculation.

 

[JesseM]

Remember that Galileo observed that the acceleration due to gravity of a body is independent of the body's mass, so if you drop a golf ball and a bowling ball at the same time from the same height, they'll hit the ground at the same time. Based on this I suppose you could argue that if you dropped a hypothetical body of mass 0, it would still accelerate down at the same rate due to gravity. This is of course just speculation.

Newton would have no reason to think that light must have mass 0 anyway, that idea was only necessitated by relativity, although obviously he'd have to have believed the mass was pretty small since at the time measurements weren't good enough to detect any increase in an object's momentum when light was shone on it. But yeah, the fact that all objects should behave the same way in a gravitational field is probably the basis for a Newtonian prediction about how light would be deflected, its path would just be deflected the same amount as a comet traveling past the sun at c (which is allowable in Newtonian physics).

 

[pervect]

I know that is what general relativity http://archive.ncsa.uiuc.edu/Cyberia/NumRel/EinsteinTest.html. What bothers me is that light on Earth does not seem to be effected by gravitation (e.g lasers).

If you read the Wikipedia article I referred to, you'll see that the gravitational bending of light has been confirmed by experiment. Early experiments were perhaps not very accurate or conclusive, but later experiments are quite good.

The detection of gravitational lensing (another name for the gravitational bending of light) is downright routine nowadays.

As far as detection of gravitational bending of light on the Earth, I'm not sure iif it's been done or not - most of the experiments I've read about are astronmoical.

Note that you won't get the same factor of 2 that GR predicts for a local experiment on the Earth, because you won't have the same spatial curvature effects.

In a uniform field without the spatial curvature, as one would have on the surface of the Earth with a tabletop experiment, , you can use the classic .5*g*t^2 for the amount that a perfectly horizontal light beam would drop - i.e. 16t^2 if distance is measured in feet and time in seconds.

This follows from the principle of equivalence - imagine a rocket ship accelerating, the light beam will follow a straight path, but in 1 second a rocket accelerating at 1g will travel 16 ft. Thus a horizontal light beam would drop 16 ft over a 186,000 mile path.

 

[pmb_phy]

Before i start this thread, if i say anything wrong please correct me,

According to special relativity a particle with rest mass as it approaches the speed of light increases in mass and when it hits the speed of light its mass is infinite. So as a particle is going towards a black hole and accelaraes towards the speed of light, wouldn't its mass increase greatley, and if so wouldn't it become a black hole itself?

Even though its mass does increase as the body approaches the speed of light an object doesn't become a black hole simply because its mass increases to a certain value. E.g. its possible for an object the size of Mt. Everest to become a black hole.

This is WHY relativistic mass is (in my opinion and many others) a bad idea - too many people make the mistake you just made, and ascribe characteristics to relativistic mass that it does not have.

All that really happens is that they make a whole new set of errors. One must address the foundation of the error being made. In this case its the invalid assumption that it the mass of a body is greater than a certain value, even in its own rest frame, then it must become a black hole.

If a person knows how to use something they won't go wrong. People simply need to know/learn how to use concepts and not to be told "Don't go through that door - there be evil that way!"

If one thinks of GR more like EM and less like Newtonian gravity they'd be much better off. And in that case the gravitational charge would increase in speed.

pervect - I've covered all your objections (and all the ones I've seen in the past and the ones that I could imagine coming up in the future) in detail in this paper

http://www.geocities.com/physics_world/mass_paper.pdf

Pete

 

[pmb_phy]

Newton said light would be deflected by mass?

Nobody suggested that Newton made this prediction. It was others who followed who used his theory.

From Henry Cavendish, Johann von Soldner, and the deflection of light, Clifford M. Will, Am. J. Phys. 56, 413 (1988)

The gravitational deflection of light based on Newtonian theory and the corpuscular model of light was calculated, but never published, around 1784 by Henry Cavendish, almost 20 years earlier than the first published calculation by Johann Georg von Soldner. The two results are slightly different because, while Cavendish treated a light ray emitted from infinity, von Soldner treated a light ray emitted from the surface of the gravitating body. At the first order of approximation, they agree with each other; both are one-half the value predicted by general relativity and confirmed by experiment.