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