My 9-year-old son has a physics questions that I couldn't answer

[zachooz]

My 9-year-old son has a physics questions that I couldn't answer...

Energy or mass can create a gravitational field, so what happens if someone goes the speed of light. Will this person create a gravitational field of their own and be able to pull someone else along with them?

What is the effect on those people near to the person traveling the speed of light?

Also, what do bystanders see when this person travels the speed of light?

Lastly, what if someone of infinite mass traveled the speed of light? What would happen then?


Steve + Zach (my son)

 

[Chris Hillman]

Attempt to offer some rough nontechnical answers

Hi, Steve,

I'll let you decide whether to pass any of this along to your son since what I'll say will probably go over the head of someone of that age.

Energy or mass can create a gravitational field, so what happens if someone goes the speed of light.

According to str, no rocket can accelerate to travel at the speed of light, no matter how hard and how long it fires its engine. Similarly, no particle with positive mass can be accelerated (say in a particle accelerator) to travel at the speed of light, although with sufficient energy input we can come as close as desired.

However, your son's question is closely related to this FAQ (from the Usenet Physics FAQ).

I'll try to fix his remaining questions so that we aren't trying to make any massive object move at the speed of light. It is also useful to know that in str as in Newtonian physics, mass is an invariant property of an object, but when it moves faster wrt ourselves, its kinetic energy increases faster in str than in Newtonian physics. Specifically,
$$\rm{KE}_{\rm{Einstein}} = -m+ \frac{m \, v}{\sqrt{1-v^2}} = \frac{m \; v^2}{2} + \frac{3 \, m \, v^4}{8} + O(v^6), \;|v| < 1$$
vice
$$\rm{KE}_{\rm{Newton}} = \frac{m \, v^2}{2}$$
The difference is only important for speeds near the speed of light (c=1 in these convenient units), but it is very important indeed for such speeds! As |v| approaches 1, the relativistic expression blows up (gets very large), which is another way of saying that in a particle accelerator, we can never accelerate a particle with nonzero mass, such as a proton, to travel at the speed of light. Here is another FAQ article which discusses this point.

Will this person create a gravitational field of their own and be able to pull someone else along with them?

This is somewhat related to the following puzzle: suppose we heat a tea kettle. As the water is heated, the molecules in the water move faster and this additional kinetic energy should make the gravitational field of the kettle a bit stronger. And it does; in general relativity the source of the gravitational field is all mass-energy, not just the mass in matter, so the energy we added by heating the kettle really does make it a bit more massive!

What is the effect on those people near to the person traveling the speed of light?

Suppose we are in a rocket ship in deep space far from any massive objects. Suddenly a massive object whizzes by at nearly the speed of light, with its distance from our ship at the moment of closest approach being $r$. What effects do its gravitational field cause? It turns out that according to general relativity, the effects are rather like the passage of a very strong but very brief duration gravitational wave! At the moment at the object whizzes by, the ship is briefly tugged toward the object like $m/r$, much stronger than the usual expression $m/r^2$ but this tug is only felt very briefly.

Also, what do bystanders see when this person travels the speed of light?

Suppose we look out the window of our rocket ship and see this massive object as it whizzes by. What does it look like? Do we see the so-called Lorentz contraction? Roger Penrose figured this out and the answer is quite interesting; see this FAQ article.

 

[A.T.]

Also, what do bystanders see when this person travels the speed of light?

Here is a nice http://www.spacetimetravel.org/fussball/fussball1.html"

 

[Chris Hillman]

Simulation from a physicist at Tuebingen, no less

Since there are so many dubious relativity-related websites out there, A.T. probably should have added that the author of the website spacetimetravel.org does have an academic affiliation at a respectable university, namely http://www.tat.physik.uni-tuebingen.de/~zahn/ (Physics, Tuebingen).

 

[zachooz]

Thank you for all the help.

My 9-year-old son listened carefully as I read everything to him. I'm not sure he grasped it all, but at least, he nodded his head in the right places.

Thanks again for the explanation and the links to other resources.


Steve