Q: How/Why are Quantum Mechanics and Relativity incompatible?

Physicist: Quantum Mechanics (QM) and relativity are both 100% accurate, so far as we have been able to measure (and our measurements are really, really good).  The incompatibility shows up when both QM effects and relativistic effects are large enough to be detected and then disagree.  This condition is strictly theoretical today, but in the next few years our observations of Sagittarius A*, and at CERN should bring the problems between QM and relativity into sharp focus.

Relativity comes in two flavors: special and general.  Special relativity describes how time and distance are affected by movement (especially fast movement), and it replaces Newtonian mechanics, which is only accurate at low speeds.  Einstein came up with it by looking at the mathematical repercussions of the fact that all of physics works the same way, independent of movement (constant speed is the same as no speed).  Special relativity has been exhaustively tested (relativistic effects have been verified all the way down to walking speed), and works so perfectly that it is now held up as the yardstick against which all new theories are tested.  In fact, QM would make grossly inaccurate predictions if Dirac hadn’t shown up and tied QM together with special relativity to create “relativistic QM”.

General relativity, on the other hand, describes the stretching and bending of space and time by gravity.  Einstein came up with it when he thought about what the universe would be like if inertial and gravitational acceleration were the same (turns out they are).  By the way: gravitational acceleration is what pushes you toward the ground, and inertial acceleration is what pushes you back into the car seat when you step on the gas.  It’s general relativity that causes the problems.  Here’s two (of a possible untold many):

1) Smooth vs. Chunky: General relativity needs space to be “smooth”, or at the very least continuous.  So if you have two points side by side, then no matter how close you bring them together you can still tell which one is on the right or left.  Quantum mechanically you have to deal with position uncertainty.  At very small scales you can’t tell which is right or left.  In addition (as the name implies) QM requires everything to be “quantized”, or show up in discrete pieces.  You see this clearly with atoms, photons, and even phonons (which is quantized sound!  How awesome is that!?).  Less clear is the quantization of space, which would require space to be “chopped up”.  This choppiness will never be directly measured.  The predicted “chunky scale” should be no large than 10-35 m.  For comparison, a hydrogen atom is about a million, million, million, million times larger (10-24).

2) The Information Paradox: According to general relativity when stuff falls into a blackhole everything about it’s existence (with the exception of mass, charge, and momentum) is completely erased.  That doesn’t sound so bad.  We tend to think of blackholes as being like galactic garbage disposals.  However, if all the information about something is destroyed, then you lose time-reversibility.  Time-reversal is the idea that if you run time backwards, all the basic physical laws of the universe continue to work the same.  More obscurely, you can predict the future based on what you know now, and time reversal means that you can derive what happened in the past as well.  QM requires that time-reversibility (or “unitarity”, to a professional) holds.  So QM requires that blackholes cannot destroy information.  One way around this is amazingly complicated entanglement between all of the in-falling matter, and all of the Hawking Radiation that comes out later.  Again, we’ll never be able to measure this.  To get results we would have to exactly measure at least half of all of the photons generated by Hawking radiation over the essentially infinite life time of the blackhole (every blackhole that exists today will be around long, long after the heat death of the universe).

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24 Responses to Q: How/Why are Quantum Mechanics and Relativity incompatible?

  1. Scott says:

    I was under the impression that your second contradiction had been resolved, and information is not lost through Hawking radiation. Hawking himself conceded, apparently. The details were way over my head, but the problem and solution are pretty well detailed in this book http://tinyurl.com/yzmt9qy.

  2. The Physicist Physicist says:

    A resolution exists, but we have no way of proving that it resolves existence… So to speak.

  3. Scott says:

    Yeah, if I remember rightly (and I probably don’t) the logic of the resolution went something like “there is a way to resolve the problem, therefore the problem is resolved.” It’s a little like finding the Lagrangian for a system and then declaring that you know how the system will behave in time. Plus, the resolution requires the universe to be a hologram, whatever that means.


  5. Carole Heath says:

    My understanding although i am not a person of science. I do have an interest in Astronomy is that Quantum mechanics is the small objects in the universe atoms etc and relativity is to with the large planets etc. Why they are not compatible i am not to sure. Could the theory regarding dark matter or dark energy which many scientists think exsists be the missing link as to why Quantum mechanics and relativity do not marry together. As to me the universe must have some type of order to able to work as it does.

  6. Clinton says:

    Measures made at different scale,macro to micro.will have different results,because each dimension of size is measured.3 dimensional results for relativaty..and 11 or so for quantum…totally true laws for each are correct for each size measured..if I was to shrink and measure my surroundings,they would be different..if I shrank more near the plank length I would have qm results measured..space could give results of different levels ..imagine then growing ..bigger and bigger…your out side your universe space may look smoothly all around you but as you grow more space starts to look lumpy…its the size that matters…we are in between the micro and macro and the results we have from Einstein are for this size limit we live in. Which are 100 correct…and so are all the other level results..

  7. Mitch says:

    There is a potential/apparent conflict between quantum mechanics (“QM”) and special reativity (“SR”), having nothing to do with gravity, about “simultaneity.”. Every day experience says that if we synchronize our watches, my watch will naturally keep telling me what time it is for you, and vice versa. SR denies this, while QM relies on it.

    In QM, making measurement A on a system before making measurement B will usually produce a different result than making measurement B first. This can apply even if parts of the system are arbitrarily far apart: which measurement happens first makes a big difference. (Look up “entanglement” for more on this.)

    But if measurements A and B are taken enough apart, they will be “space-like separated” according to SR, meaning that neither event precedes the other. Some observers will correctly believe that A happened first, others will know that B came first, and SR says that nobody is wrong. Time doesn’t work the way we usually think it does, so watches won’t agree for observers moving relative to each other.

    People often say that from the point of view of SR, QM requires that information travels between A and B too fast–faster than light. If that doesn’t sound scary enough to you, note that according to SR we could also describe “going faster than light” as going backwards in time. If measurement A “really” effects what happens when B is made, observers for whom B happens first will see effect preceding cause.

    But that presumes that we can tell if A effects B or the other way around, which is surprisingly hard to catch in action. See “EPR” for the history of Einstein following up on this clash between these two dialects of physics, with the apparent result that no experiment will let us tell whether information is going one way or the other. So this may be an *apparent* contradiction that a clever way of describing the two theories can avoid.

  8. The Physicist The Physicist says:

    Early on in the history of QM Dirac reformulated it to be relativistic (work with relativity). It actually resolved a lot of issues, and made some wild predictions that were later experimentally verified.
    While you will often hear claims about entanglement causing “action at a distance”, very few quantum information theorists (the physicists who work with this stuff) would say the same. There’s even a post that goes into how you might try to use entanglement to communicate faster than light, and why it doesn’t work!

  9. Mitch says:

    Is this the right place to ask about the “information paradox” described above?

    If so, do I have this right: from the point of view of observers safely outside of a black hole, nothing ever manages to finish falling into one? That is, objects hurtling into a black hole appear to slow down, asymptotically approaching stasis as they reach the event horizon. Meanwhile light keeps coming back from them, but the wavelength stretches out (redshifts) and the bitrate drops.
    So maybe the resolution to the paradox is that, in principle, the outside universe never loses contact with the information associated with objects that fall into a black hole: it’s just that accessing this information takes longer and longer?

  10. Stephen Tuck says:

    My name is Stephen Tuck and I have solved this problem along with my flaws in modern Science and mathematics. Einstein never finished Special Relativity because he never linked the Lorentz transformations of Mass-Increase and Time-Dilation to Mass-Energy Equivalence. The c^2 in E=mc^2 stands for the variables of Space and Time (initialized by the c-constant). Once this is done, you have the Tuck-Einstein Equation: Energy = (Space * Mass * Time) / (1 – (v^2/c^2))^0.5, which correctly replaces the Dirac Equation of Quantum Mechanics. It took me about 3-years to figure out how to integrate Gravitation and the Electromagnetic Force, but I was able to do it by integrating a variant of Ampère’s Force Law to the right-hand side of Einstein’s Field Equation. Einstein was wrong about gravity being a curvature of spacetime since it is really dipolar, rotational kinetic energy that transverses through Aether. This led to great things such as the derivation of the Quantum Thermodynamic Equation and unification of the linear equations of Physics relating to Stress-Energy (in the Entropic Equation as the inverse of Gravitation) to Chemistry (and thus Biology) as I had derived the Boltzmann. The extent is such that the very mathematical framework of Science is flawed. Additionally, Differential Equations are used when the mathematics of the TOE is Deterministic, Multivariate Calculus. I could finish my great work in Physics, but I don’t see the point because of all the greed and corruption within institutionalized Science. Nobody cares about the truth and least about me so it seems that I’ve pushed myself so hard for nothing (hoping for the great technological advancement of mankind). At least, it did provide a distraction to the emotional pain and suffering of my broken heart until numbness could set-in. Einstein’s intellectual ability like mine was a genetic gift (or curse) from our Neanderthal Neurobiology. Knowing too much about the world is disheartening because mankind is plagued by such a great evilness!

  11. Sleuth says:

    Very interesting!

    Why does relativity require space to be continuous?
    Why is it necessary to distinguish between the right and left point?
    Where is the boarder between distinguishing 2 atoms and fusing them together? (Or are the 2 points only meant for theoretical points that are infinatly small?)

    Are there other problems between QM and relativity?

  12. clinton semley says:

    the left and right interaction of two atoms has something to do with mirror sym….i think some test have taken place on hubble ? That show some photons that have come from a pulsar …these photons have been measured to show that there may be a quantised state of space…because some of the photons are a tiny fraction slower due to interaction of small peices of clumpy space…

  13. Stephen Tuck says:

    Everything is quantized. Since all matter and space is composed of photons, the discrete quanta makeup the smallest packets of energy. The Planck Units are the minimums and maximums of energy. From the Tuck-Einstein Equation, I learned the boundaries of the Electromagnetic Spectrum (which are Planck Mass and Planck Length). Planck Mass is when all frequency-energy (the Time-component) has converted into wavelength (the Space-component; photonic-string length). Photons are not massless, which is why they impart momentum when they strike the surface of an object. Space does not have discontinualities because it behaves as Discrete, Multivariate Linear Equations. Differential Equations are incomplete approximations because if they had all the variables, they would be Multivariate Calculus Equations. The c-constant is an energy-constant (like a base unit) since the speed-of-light depends upon the Parameters-of-Space. That is why Gravitational Lensing could most accurately be described as Gravitational Refraction. The Physics behind light slowing-down as it travels through a glass of water is the same behind the bending of light around a massive object (such as the sun). You are probably looking for terms like Abelian and non-Abelian, but such formalisms are of no practical importance in the TOE since Space is commutative and Euclidian in nature. Also, throw out imaginary numbers because they are the product of light-cone mapping, which is due to the incorrect treatment of Time as a spatial coordinate rather than as kinetic energy. If you study my work on ToeQuest, you will find that the predominate mathematical framework of physics is incorrect (Lorentz-Invariance, Guage-Invariance). The preferred frame of reference is the Aether Rest-Frame because if you measure the universe from a frame-of-motion, the speed-of-light would appear superluminal due to Time-Dilation (meaning that it is Lorentz-variant). That is why the Gravitational-Constant has seasonal variation (due to mass-increase and time-dilation of the Lorentz transformation) since the earth is moving at a different speed along its elliptical-orbit. Of course, if the photonic-string manifold of a particle changes size (due to photonic-string lengthening; mass-increase), it means that matter is not Guage-Invarient because physically-meaningful quantities like mass and fiber-bundle size do change. The Higgs Mechanism is an incorrect theoretical construct because Spontaneous Symmetry Breaking explains nothing. The Higgs Mechanism is actually the Lorentz Mechanism, which is the action of the Lorentz transformations. Similarly the Lagrangian seems of little use in comparison to Hilbertian, through which I have integrated Schrodinger’s Equation with the Tuck-Einstein (that correctly replaces the Dirac Equation of Quantum Mechanics). We draw lines in the sand, but Quantum Mechanics is just Vector Calculus where Tensors are useful tools for group operations. The subatomic particles simultaneously interact at the Quantum Level forming stable orbits as kinetic-energy bonds. Things like the Lorentz Force take part in this orbital-stabilization between atoms in the Electron Perihelion Spheres of molecular formation. 

  14. Stephen Tuck says:

    When I wrote Hilbertian, what I meant was Hamiltonian. I have given some further thought to Space being Eiclidean. With Euclidean Geometry, you have to admit certain exceptions because physical objects are not completely rigid since they expand or contract. Thermodynamics itself is adding or removing energy in the form of heat (infrared photons), that changes the physical properties of matter or physically-meaningful properties in terms of Guage-Invariance. It causes phase-change and the increase or decrease in the mass of an object as well as affecting its kinetic energy. From my Quantum Thermodynamic Equation (Entropic Force), which is the inverse form of the integration of Ampère’s Force Law and the non-Riemannian Geometry component of Einstein’s Field Equation (the right-hand side), I know that Thermodynamics is due to the effects of Special Relativity since the absorption of infrared photons increases the kinetic energy of the molecules equivalent to an object being accelerated to a higher velocity. Interestingly, this naturally leads to the Lorentz transformations. However, it is a stationary form of increased kinetic energy in which heating generally leads to an expansion (decrease in density) and cooling leads to a contraction (increase in density). Instead of the normal effect of Time-Dilation of an object-in-motion, there is a increase in the rate of Time from heating because the frequency kinetic-energy (Time-component) increases rather than decreases. This highlights the difference between Stationary (bound) Kinetic-Energy and the Kinetic-Energy of Motion. That is why heat increases the rate of chemical reactions. Anyways, I was thinking that an increase in kinetic energy causes an expansion when applied to Matter, but a contraction when applied to Space since dipolar, subspace matter/anti-matter particle-pairs are in a high state of spin-induced Rotational Motion whereas Matter is in a state of higher Linear Motion (tangental velocity of electrons). A transformation of Space (Rotational Motion) into Matter (bound Linear Motion) should be possible just as matter falling into a black hole converts into Space, causing the accelerated expansion of the universe. Thus Euclidean Geometry isn’t adequate because the coordinate system (Space) isn’t Guage-Invarient just as Mass isn’t Guage-Invarient. I would rather refer to the geometry of the universe as Lorentzian (after the Lorentz transformations) rather than Euclidean. It seems that the universe has Lorentzian Space rather than Euclidean Space. At the center of every galaxy lies a black hole, which is a point of universal expansion. It looks like I will have to look into Differential Equations as a means of the functional variation of the rate of expansion of Space (using deterministic Multivariate Calculus for a rate-varying, differential coordinate system) rather than for approximating the missing variables of Multivariate Calculus Equations as it is most often incorrectly applied!

  15. Stephen Tuck says:

    I think that I can model a form of the Equation of Everything that extends to Photon Electrodynamics. Previously, I had thought that it would take different varients of the equation rather than an integrated approach, but all varient forms should work together as seemless extensions of Quantum Mechanics. The trick is that the mechanics of a photon does not merely vanish when it wraps-up into a particle manifold. I’ve already derived the String Function within the Tuck-Einstein Equation (that makes-up the Equation of Everything), which includes frequency or wavelength defining the velocity vector variable of the Lorentz transformation. The thing is that the string Tension or Rigidity will correlate to the vibrational frequency and wavelength. Imagine a guitar string where the diameter of the string and the tension on the string produce a specific audio frequency (pitch) based upon the amount of vibration applied by the guitarist (affecting the amplitude or loudness of the waves). It is the dimensional charactoristics of Length and Diameter that affect String Tension along with it’s Frequency and Wavelength. The Lorentz transformations (which are a function of Photonic-String Mechanics) is a transformation between Motion and Length or the Ratio of Length to Diameter where the 2 forms of Motion are Linear or Rotational. However, experienced musicians know that the Pitch and Loudness of a Musical Tone isn’t the only distinction among sounds created by different musical instruments, there’s an elusive element called Timbre in which the Wave Packet and interference patterns may need further study to accurately produce the right Cosmic Note along the Electromagnetic Spectrum. I guess we’ll have to figure out how to “Shiver me timbers.” Interestingly, the Pi-Constant as the ratio of a circle’s Circumference to Diameter (which is the bisection of a sphere) is always the same, but it is the photon’s length (affecting frequency, wavelength, mass and orbital-radius) that defines the Volume of all Matter and Space.

  16. Leonardo Rubino says:

    There’s a lot of hidden “relativity” in (quantum) Bohr’s atom…

  17. Massimo Auci says:

    About the compatibility between quantum mechanics and electromagnetism, my contribute puts in evidence how quantum mechanics and relativity are two consequences of electromagnetical interactions


  18. Geoff Zoref says:

    @Carole Heath:


    Carole: I believe that one way of looking at the problem is that if you were to make a model of an atom using classic physics (i.e. the Earth revolves around the Sun) then an Electron orbiting a Nucleus would crash into the Nucleus instead of orbiting it.

    Instead, a new type of physics needed to be discovered, and that was Quantum Theory. Electrons do not crash into their Nucleus because instead of the Gravity of Classical Physics, Atoms are kept together through the Strong Nuclear Force.

    But The Strong Nuclear Force, along with the Weak Nuclear Force and Electromagnetism, which are three of the four forces we know of in physics, are so many orders of magnitude more powerful than Gravity. Why that would be is still unknown.

    Hope that helps. As for Dark Energy/Matter, I cannot say.

  19. K Friesen says:


    The strong nuclear force is a nuclear force, it keeps neutrons and protons together, and is unrelated to electrons and their orbital configurations. The reason the electron encircles the nucleus but does not crash into it is indeed due to quantum mechanics, but it is related to the electromagnetic force.

  20. Massimo Auci says:

    Yes, I believe to have proved that electromagnetic theory has to do with quantum theory and relativity and, in a new at the moment unpublished article, a new atomic model based on the principles of the Bridge Electromagnetic Theory proves these foundations.

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  23. Don S says:

    A bunch of scientists are probably looking at our universe right now along with trillions of others through a giant collider that they just used to smash stuff with a big bang, and scratching their heads thinking, why won’t all these small bits jive up with our big bits? :)

  24. Paulj says:

    If some could direct me to the (civilian) explanation, it’d be great. It is my impression that GR depends on geometry and QM depends on statistics, is that right?

    I think I’ve also heard that the problem with GR is that spacetime(?) gets infinitely dense before it gets infinitely small, is that right? So, I think that’s why they invented strings?

    I’m not clear if there is a problem with QM, beyond that gravitons are too small to see. But if there is no problem with QM, why is there so much discussion on further work to unify it with GR.

    Anyway, thanks for the help.

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