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)?


2 Answers 2


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!

  • $\begingroup$ "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? $\endgroup$ May 4, 2014 at 10:53
  • $\begingroup$ Siva, I just checked your profile. If you find this "holy thing" offensive - please accept my deepest apologies. $\endgroup$ May 4, 2014 at 11:18
  • $\begingroup$ @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. $\endgroup$
    – Siva
    May 4, 2014 at 13:46
  • $\begingroup$ In topic 1., the Compton wavelength make effective the special relativity + quantum mechanics. $\endgroup$
    – Nogueira
    Oct 17, 2014 at 13:23
  • $\begingroup$ Are you basically saying the math is too complicated? Is that really necessarily an "incompatibility"? $\endgroup$
    – B T
    Jan 23, 2015 at 19:28

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.

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    $\begingroup$ 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. $\endgroup$
    – rob
    May 4, 2014 at 6:12
  • $\begingroup$ A solution to this problem is not yet known. I thought that string theory solved this problem. Although the theory might not be true. $\endgroup$
    – jinawee
    May 4, 2014 at 8:10
  • $\begingroup$ @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. $\endgroup$
    – mpv
    May 4, 2014 at 19:32
  • $\begingroup$ 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? $\endgroup$
    – B T
    Jan 23, 2015 at 19:29
  • $\begingroup$ @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. $\endgroup$
    – mpv
    Jan 23, 2015 at 21:46

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