Extreme Cases in Relativity

What does this suppose to mean, you ask. Isn’t Relativity already extreme enough?

A proton in CERN can reach the weight of a mosquito, due to its near light speed. During the acceleration a lot of energy has been transformed into the proton’s relativistic mass, just as Einstein would have wanted.

Speed it up some more, and it will weigh as much as a mouse or even an elephant. Then if it were to be accelerated to a speed even closer to c it would became so heavy as to equal the weight of a mountain or even that of a continent! Approximately at this point the proton would become a black hole. Not a microscopic black hole which would allegedly soon cease to be, but a substantial one, radiating the Hawking radiation in megawatts. If you were to push it even more after that, the resulting black hole would cool down, and thus reach a state where its mass would surpass the mass of a planet, with a radius of just one meter.

Only a fraction of the energy of a supernova explosion is needed to transform a proton into a black hole, more massive than the Earth, and with a radius of just 1 meter. So I have no concerns about the feasibility of such an experiment.

What worries me is this: It’s a black hole for the stationary observer, but for the observer on the space ship chasing it, it’s just a humble proton which will likely soon acquire an electron, and become a very innocent hydrogen atom – the most common thing in the Universe.

So you see, black holes can indeed be relative! For one observer an object can appear as nothing more than a small rock, for another it can be a super massive black hole!

This could be called an extreme case derived from the Theory of Relativity. The relativistic contraction only makes a relative black hole more achievable.

If the Einsteinian train shortens in addition to gaining mass, it collapses into a black hole even faster. Only for the observer on the platform of course! To the observer on the train (inside the black hole) everything looks normal.


7 thoughts on “Extreme Cases in Relativity

  1. msjr says:

    I have a problem understanding this… So, if a particle (may be also a train, huh) falls into this black hole, what happens for an observer on that fast spaceship? What does he see?

    • I am not sure if anybody understands it.

      At the beginning of the last century, it was beautiful if mind boggling picture. Two inertial observers meet at the near light speed. Or one observer stands on a platform and calls himself stationary. The other is ridding a near light speed train. The standing observer sees the train shortened and heavier and traveling clocks go slower. The ridding one sees the station shortened.

      To preserve the light speed principle, the geometry of space-time changes relative for those observers. Everything works just fine. All later observations agree.

      It’s in accordance with this:

      But when the train’s speed reaches 0.999999999999999999999999999999999999 c, instead of moderate 0.99 c – we are in troubles. Since the stationary observer measures the train very, very, very short and very, very, very massive – no light can leave the train due its large gravity. It’s a black hole for him.

      The same goes for the riding observer. The station is so dense (heavy), that no light can escape it.

      Both observers see each other as a speeding black hole, while see themselves – normal.

      If the train slows a little, it’s no more a black hole, but an every day Einsteinian train passing by!

      At least, this is what the theory says.


      I love the classical physics problems. For example that one, considering fast rotating planets that should be hotter. It’s not what all the Wikipedias say, but nobody sane will dare to argue in favor of them. He would be roasted quickly.

      In Relativity (as in QM) it’s another story:

      Her: “Have you actually solved the GR equations for this case?”

      Me: “No. Did you? Did anybody? Can you give me good a link?”

      Her: “No, but I saw my professor solved it once and I am sure all is fine. Unfortunately, the blackboard has been erased soon after!”

      Me: “What a shame …”

    • Or take it this way. A trans-galactic traveler fast enough, sees us as a black hole. Instead of a galaxy full of stars, it’s a supermassive black hole here. At least from his point of view. For the relativity of mass, he sees us so heavy, that we can’t emit any light – just another black hole.

      How does he explain the light we have shared with the space long ago, now colliding with his front window … well that’s just one problem.

  2. msjr says:

    So, according to this, ther should be possibility that we see (or already have seen) a black hole that changes into object. Or not?

    • It’s possible, but not certain. When a supernova explodes, there might be something like a “relative black hole” for a moment.

      The Crab Nebula is a candidate. There are jets visible, and maybe no black hole, anymore.

      Maybe it’s more likely that the Relativity breaks in such conditions.

  3. msjr says:

    Sorry for the late reply, but I’m a bit slow thinker and physics and maths are not my field. But, could this be a missing link between quantum theory and relativity? Here objects appear from “nothing” in quantum physics particles appear from “nothing”. As space is much bigger everything is much slower, but is the process basically the same? Is relativity just the form of quantum physics on a much larger scale? And the problem that we didn’t encounter any quantum effect on an universe level is just that there was not enough time yet?

    • The most we can hope for here is a free debate. Every thinker should feel free to express his or hers opinions about the Relativity or Quantum theory also. Regardless how “stupid” or “naive” they are.

      It’s an unhealthy atmosphere of censoring present around those two fields. We shall stand against it.

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