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Is there a simple layman way that I can use to explain the incompatibilities between quantum mechanics and (general) relativity to high school students (people with not much knowledge of the intricate math of quantum mechanics and (general) relativity)?

Qmechanic
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user10024395
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    Standard correction: it's not special relativity that's a problem, it's general relativity. – Javier May 04 '14 at 02:35
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    I'd settle for a simple way to explain it to advanced undergrads. – dmckee --- ex-moderator kitten May 04 '14 at 03:28
  • Related: http://physics.stackexchange.com/q/387/2451 and lins therein. – Qmechanic May 04 '14 at 06:34
  • Read the first paragraph here: https://en.wikipedia.org/wiki/D-brane#Theoretical_background – Siva Jan 24 '15 at 19:49
  • That the two theories are "incompatible" is a myth that relies on a false understanding of the word "theory". Every scientific theory has a range of applications. Continental drift, for instance, makes for a great explanation of geology on Earth but using it on a gas giant is complete nonsense. That doesn't invalidate continental drift. It simply shows that one has to be careful about the use of a theory. GR, so far, explains every known fact about gravity. QM explains radiation and matter. They simply do not overlap anywhere. THAT is the real problem. There is a hole there, not a clash. – FlatterMann Apr 21 '23 at 15:52

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For what it's worth, there's a simple argument which explains the need for quantum gravity, using just dimensional analysis:

  1. Quantum mechanics attaches a length scale $l$ to every mass $m$, called the Compton wavelength $l \sim \frac{h}{m c}$. If you consider a massive object (particle), at distances comparable to this (and smaller), quantum effects become strong.

  2. General relativity attaches a length scale $l$ to every mass $m$, called the Schwarschild radius $l \sim \frac{G M}{c^2}$. If you consider a massive object, at distances comparable to this (and smaller), general relativistic effects become strong.

Equating the two, we can derive a special scale called the Planck scale. An imaginary particle with Planck mass has a Compton wavelength and Schwarschild radius of about the same size, so for such particles (i.e. when we deal with such energy scales) both general relativistic effects and quantum effects become strong -- this is why we really need a theory incorporating both.

As for why combining the two is hard:

  1. GR tries to use physics to describe the geometry of spacetime. Due to quantum effects, there will be (severe) "quantum fluctuations" in the geometry of spacetime! So, in a sense, the problem is that we have no simple solution which we can use as a crutch. In physics, we almost always solve a simple case and perturb around that solution to push as far as possible. If perturbation theory fails (as it does for GR+QM) we're at a loss for what to do.

  2. From the perspective of particle physics, if you want to "zoom in" and probe what happens at short distances, then you use very energetic particles whose Compton wavelength is comparable to your length scale. However, as you keep increasing the energy of your particles, at the Planck mass, their Schwarschild radius overtakes the Compton wavelength. So even though your particles are very energetic, they form blackholes and stop you from probing small distances!

Siva
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  • "So even though your particles are very energetic, they form blackholes and stop you from probing small distances!" Holy cow! Is this considered a valid concept (proven) or just a far shot? – bright magus May 04 '14 at 10:53
  • Siva, I just checked your profile. If you find this "holy thing" offensive - please accept my deepest apologies. – bright magus May 04 '14 at 11:18
  • @brightmagus: Oh, don't worry :-) Though what I said is not incorrect, it is very (very) hand-wavy and imprecise (and some physicists might cringe). That's not the kind of statements physicists will tell each other. However, I can't think of another way to give high school students a feel for quantum gravity. – Siva May 04 '14 at 13:46
  • In topic 1., the Compton wavelength make effective the special relativity + quantum mechanics. – Nogueira Oct 17 '14 at 13:23
  • Are you basically saying the math is too complicated? Is that really necessarily an "incompatibility"? – B T Jan 23 '15 at 19:28
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Probably no simple explanation. It is however important to emphasize that the incompatibility applies only to general relativity. The special relativity and quantum mechanics are very compatible and were luckily married many decades ago, giving birth to the quantum field theory which is an incredibly successful framework in which physicists built the quantum electrodynamics, quantum flavordynamics, quantum chromodynamics and the whole standard model. The whole modern quantum physics would not be thinkable without combining quantum mechanics with special relativity.

General relativity is a different case however. The root cause of the issue is rather technical, so laymen terms do not reasonably work here. Basically, when you try to quantize gravity, you get nonsensical (infinite) results that cannot be remedied. A solution to this problem is not yet known.

mpv
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    Worth noting that special relativity and quantum mechanics both began development around 1905, but relativistic quantum mechanics didn't get going until the late 1920s. – rob May 04 '14 at 06:12
  • A solution to this problem is not yet known. I thought that string theory solved this problem. Although the theory might not be true. – jinawee May 04 '14 at 08:10
  • @jinawee The appearance of spin-2 particle in the string theory is very exciting, unfortunately string theory is still not finished and fully understood. It has so many problems that it cannot yet be seen as the solution to quantum gravity. – mpv May 04 '14 at 19:32
  • And what if gravity isn't quantized? How is it ruled out that gravity isn't continuous? The wave-function of particles is certainly continuous, so why can't gravity be continuous too? – B T Jan 23 '15 at 19:29
  • @BT You seem to be confusing "quantized" and "discretized". These 2 terms are not the same. Many things that are quantized can easily be continuous: for example quantum fields. So gravity can be continuous and quantized at the same time. – mpv Jan 23 '15 at 21:46
  • Hmm, perhaps I am. How would you describe the meaning of "to quantize"? The wikipedia article on quantization doesn't make it clear. – B T Jan 23 '15 at 22:35
  • @BT Quantization is a complicated subject which requires a lot of study to be mathematically understood. In very simplified terms quantization means that a quantity no longer has a definite value, but it is a superposition of (infinitely) many values. This is done by converting the quantity into an operator (by imposing the so called "canonical commutation relations"). The spectrum of the operator are the possible values of the quantity. The spectrum can be continuous or discrete. Thus the quantity can be continuous or discrete, depending on other conditions. – mpv Jan 25 '15 at 20:58