# Is the reason we haven't fully combined GR and QM purely mathematical (rather than conceptual or empirical)? [duplicate]

I am not a physicist.

For as long as I can remember, I've been told that the main problem in physics is to unify quantum mechanics and general relativity into a single theory.

I once heard someone say, that the reason we haven't combined general relativity with QM, is simply because in GR, quantum operators wouldn't be linear (due to the curvature of spacetime), so that the superposition principle fails.

In other words, that would mean we have no problem understanding how they would be unified, conceptually, we just don't know how to deal with the nonlinear mathematics that would result from this.

Is that understanding correct?

## marked as duplicate by AccidentalFourierTransform, stafusa, Chris♦, Kyle Kanos, Qmechanic♦ quantum-mechanics StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Mar 6 '18 at 17:21

• That's one approach to the solution. But non-linearity, while being mathematically difficult, is not the actual problem. The problem is a conceptual one. – Yuzuriha Inori Mar 5 '18 at 16:36
• Possible duplicate of A list of inconveniences between quantum mechanics and (general) relativity? – AccidentalFourierTransform Mar 5 '18 at 16:55
• Physics is made of mathematics. Not being able to write something down mathematically (at a physicist's level of rigor) is the same as not conceptually understanding it. – knzhou Mar 5 '18 at 17:24
• I'm not an expert in this area, but it's my understanding that there are both linear QM theories on curved spacetime and nonlinear theories in flat spacetime. The nonlinearity is due to the form of the differential equation, not necessarily the spacetime. – D. Halsey Mar 6 '18 at 0:31