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12.2 General relativity and quantum gravity  (Page 6/16)

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Wormholes and time travel

The subject of time travel captures the imagination. Theoretical physicists, such as the American Kip Thorne, have treated the subject seriously, looking into the possibility that falling into a black hole could result in popping up in another time and place—a trip through a so-called wormhole. Time travel and wormholes appear in innumerable science fiction dramatizations, but the consensus is that time travel is not possible in theory. While still debated, it appears that quantum gravity effects inside a black hole prevent time travel due to the creation of particle pairs. Direct evidence is elusive.

The shortest time

Theoretical studies indicate that, at extremely high energies and correspondingly early in the universe, quantum fluctuations may make time intervals meaningful only down to some finite time limit. Early work indicated that this might be the case for times as long as 10 − 43 s size 12{"10" rSup { size 8{ - "43"} } `s} {} , the time at which all forces were unified. If so, then it would be meaningless to consider the universe at times earlier than this. Subsequent studies indicate that the crucial time may be as short as 10 − 95 s size 12{"10" rSup { size 8{ - "95"} } `s} {} . But the point remains—quantum gravity seems to imply that there is no such thing as a vanishingly short time. Time may, in fact, be grainy with no meaning to time intervals shorter than some tiny but finite size.

The future of quantum gravity

Not only is quantum gravity in its infancy, no one knows how to get started on a theory of gravitons and unification of forces. The energies at which TOE should be valid may be so high (at least 10 19 GeV size 12{"10" rSup { size 8{"19"} } `"GeV"} {} ) and the necessary particle separation so small (less than 10 − 35 m size 12{"10" rSup { size 8{ - "35"} } `m} {} ) that only indirect evidence can provide clues. For some time, the common lament of theoretical physicists was one so familiar to struggling students—how do you even get started? But Hawking and others have made a start, and the approach many theorists have taken is called Superstring theory, the topic of the Superstrings .

Section summary

  • Einstein’s theory of general relativity includes accelerated frames and, thus, encompasses special relativity and gravity. Created by use of careful thought experiments, it has been repeatedly verified by real experiments.
  • One direct result of this behavior of nature is the gravitational lensing of light by massive objects, such as galaxies, also seen in the microlensing of light by smaller bodies in our galaxy.
  • Another prediction is the existence of black holes, objects for which the escape velocity is greater than the speed of light and from which nothing can escape.
  • The event horizon is the distance from the object at which the escape velocity equals the speed of light c size 12{c} {} . It is called the Schwarzschild radius R S size 12{R rSub { size 8{S} } } {} and is given by
    R S = 2 GM c 2 , size 12{R rSub { size 8{S} } = { {2 ital "GM"} over {c rSup { size 8{2} } } } ","} {}

    where G size 12{G} {} is the universal gravitational constant, and M size 12{M} {} is the mass of the body.

  • Physics is unknown inside the event horizon, and the possibility of wormholes and time travel are being studied.
  • Candidates for black holes may power the extremely energetic emissions of quasars, distant objects that seem to be early stages of galactic evolution.
  • Neutron stars are stellar remnants, having the density of a nucleus, that hint that black holes could form from supernovas, too.
  • Gravitational waves are wrinkles in space, predicted by general relativity but not yet observed, caused by changes in very massive objects.
  • Quantum gravity is an incompletely developed theory that strives to include general relativity, quantum mechanics, and unification of forces (thus, a TOE).
  • One unconfirmed connection between general relativity and quantum mechanics is the prediction of characteristic radiation from just outside black holes.

Conceptual questions

Quantum gravity, if developed, would be an improvement on both general relativity and quantum mechanics, but more mathematically difficult. Under what circumstances would it be necessary to use quantum gravity? Similarly, under what circumstances could general relativity be used? When could special relativity, quantum mechanics, or classical physics be used?

Does observed gravitational lensing correspond to a converging or diverging lens? Explain briefly.

Suppose you measure the red shifts of all the images produced by gravitational lensing, such as in [link] .You find that the central image has a red shift less than the outer images, and those all have the same red shift. Discuss how this not only shows that the images are of the same object, but also implies that the red shift is not affected by taking different paths through space. Does it imply that cosmological red shifts are not caused by traveling through space (light getting tired, perhaps)?

What are gravitational waves, and have they yet been observed either directly or indirectly?

Is the event horizon of a black hole the actual physical surface of the object?

Suppose black holes radiate their mass away and the lifetime of a black hole created by a supernova is about 10 67 size 12{"10" rSup { size 8{"67"} } } {} years. How does this lifetime compare with the accepted age of the universe? Is it surprising that we do not observe the predicted characteristic radiation?

Problems&Exercises

What is the Schwarzschild radius of a black hole that has a mass eight times that of our Sun? Note that stars must be more massive than the Sun to form black holes as a result of a supernova.

23.6 km

Black holes with masses smaller than those formed in supernovas may have been created in the Big Bang. Calculate the radius of one that has a mass equal to the Earth’s.

Supermassive black holes are thought to exist at the center of many galaxies.

(a) What is the radius of such an object if it has a mass of 10 9 size 12{"10" rSup { size 8{9} } } {} Suns?

(b) What is this radius in light years?

(a) 2 . 95 × 10 12 m size 12{2 "." "95" times "10" rSup { size 8{"12"} } `m} {}

(b) 3 . 12 × 10 − 4 ly size 12{3 "." "12" times "10" rSup { size 8{ - 4} } `"ly"} {}

Construct Your Own Problem

Consider a supermassive black hole near the center of a galaxy. Calculate the radius of such an object based on its mass. You must consider how much mass is reasonable for these large objects, and which is now nearly directly observed. (Information on black holes posted on the Web by NASA and other agencies is reliable, for example.)
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Source:  OpenStax, General physics i phy2201ca. OpenStax CNX. Jul 03, 2013 Download for free at http://legacy.cnx.org/content/col11523/1.4
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