# What does it mean when people say "Physics break down"?

So I keep hearing people talking about how physics break down at for example the center of a black hole. And maybe I am just to stupid but, why? How can we say that? For all we know a black hole could just be a very dense sphere. Kind of like a neutron star where are all the atoms sort of combine to become a single object. Just one step further.

Now I am pretty sure I don't out think everyone ever right now. Thus I most likely don't understand something that everyone else gets.

Can someone explain why we know that physics stops working?

• I would not say "physics break down", but rather . "our current physical theories break down" at the center of a black hole. Oct 31, 2020 at 13:00
• It's short for "The laws of physics break down" meaning "The laws of physics contradict each other and result in illogical math like division by zero" in black holes. Physics laws are not made to deal with infinitely strong time-space traps and matter and gravity in an infinitely small space of a gravity trap. For all we know, a black hole could be a generator of some sort, because where does entropy go in a black hole, if not much comes out? into another universe inside singularity? so black holes are fertile wombs that funnel time and space like an compressed-wave-multiplier-kaleidoscope. Nov 1, 2020 at 6:33
• @Thomas Fritsch : does a center of a black hole exists in up to date physics?
– dan
Nov 1, 2020 at 11:15
• @dan The centre of a black hole is a bit like next Tuesday: it doesn't exist until you get there. In more technical language, in GR, the singularity at the centre of a Schwarzschild black hole is never in the past light cone of any observer, including observers inside the event horizon. Nov 2, 2020 at 19:16
• Newtonian mechanics breaks down as one approaches light speed, for example
– Tom
Nov 3, 2020 at 14:40

"Physics breaks down" is a bad way of saying what people are trying to say. It's the sort of thing that sounds cool at first, but then it starts misleading people.

What scientists mean is "our best theory produces non-sensical or contradictory results in this situation, so we know the theory doesn't make good predictions there."

They do not mean that there can never be a theory that works, or that somehow there are no laws of physics whatsoever in the situation. It just means we don't know what the law is.

Every physicist fully expects that there are laws of physics that predict what happens at the center of a black hole. Probably something perfectly sensible happens, though it's probably something weird and unlike anything else we know.

• Is the term "center of a black hole" a sensical one?
– dan
Nov 1, 2020 at 11:19
• It takes a true scientist to be comfortable that things can be "weird" and "sensible" at the same time Nov 1, 2020 at 11:28
• General relativity does predict what happens inside a black hole, based on the assumption that infalling matter can't detect when it crosses the event horizon. The problem is, it's based on eternal black holes and predicts that if the black hole is spinning and you aim well enough, you could end up falling out of a white hole in a different universe (after you get blasted by infinitely strong electromagnetic radiation, but still) - so it's most likely wrong. Nov 1, 2020 at 18:41
• It is very well possible that the center doesn't actually exist, right? Nov 1, 2020 at 19:08
• @JohnDvorak GR's prediction is also entirely incompatible with what we know of quantum mechanics (unlike the majority of cases where the two actually play a lot more nicely together than you'd think by their reputation). This strongly seems to suggest that, beyond GR's predictions not necessarily applicable, that some quantum gravity effect would kick in and you'd get very different behaviour Nov 2, 2020 at 12:19

Let me give an example of a very, very mild case of 'theory breaks down'.

Boyle's law is stated as follows:

$$P_1V_1 = P_2V_2$$

Expressing that for a given quantity of gas the pressure and volume are inversely proportional to each other.

At low pressures Boyle's law holds good.

The reason that it holds good is that at low pressure the gas molecules take up only a small percentage of the total space.

If you keep increasing the pressure then eventually you reach the point where the molecules are touching all the time, and after that point even a huge increase in pressure leads to only a tiny reduction of the volume.

A dramatic way of saying the same thing is to state that at high pressure 'Boyle's law breaks down'. Of course, in the case of Boyle's law we have a deeper theory that we can move to.

There is another consideration, which is independent of observables.
As stated Boyle's law suggests that as pressure is increased volume can be decreased to an arbitrarily small value. In and of itself Boyle's law doesn't include any restriction. That is susipicious. A theory with a formula that allows infinities, that is an indication that the theory is only an approximation of a deeper theory.

Another comparison:
Coulomb's law of the electrostatic force gives that the magnitude of the force is inversely proportional to the distance.
Let's say that you have a theory that describes particles as entities that are true point particles. Then two charged particles can approach each other infinitly close, which would imply an infinitely large electrostatic force. That is suspicious

My understanding is that the black hole case is in some sense like Boyle's law; it doesn't disallow infinities in such a way that there is a suggestion that there is describable physics to be found, but it is out of scope of the theory.

A dramatic way of saying that is that at the singularity (as implied by the mathematics of GR) the theory breaks down.

• "A theory with a formula that allows infinities, that is an indication that the theory is only an approximation of a deeper theory." 👏🏻. Isn’t this a secret fundamental meta-law of physics?
– dan
Nov 1, 2020 at 11:21
• I suppose quite the same happens with electric flow in superconductors. Ohm's law would "break" in that circumstance, provided that the superconductor retains its conductive properties under the voltage. Nov 2, 2020 at 0:26
• Some infinities are benign, and don't indicate a problem with the theory. Eg, the slope of a vertical line is infinite. Similarly, infinities can arise in coordinates, but they disappear (or moves elsewhere) with a change of coordinates. Eg, on a standard Mercator map, the north & south poles are infinitely distant from the equator. Nov 3, 2020 at 9:14
• @dan Not really, tell me a theory without infinities Jan 1 at 3:04

"Physics breaks down" sounds good, but it is confusing. A better phrasing would be "known physics breaks down." Physics attempts to model reality using mathematics. In this sense, physics has no "laws." In the famous words of Captain Barbossa, "They're more like guidelines." However, we have many of these guidelines which are so astonishingly reliable on the scale that humans live and breathe at that we find the word "guidelines" is too soft. If you are building a skyscraper, you are more likely to make one that stands up if you think of gravity as a "law" rather than a "guideline." Architects who call gravity a "guideline" tend not to be given the opportunity to design multi-million dollar skyscrapers using other people's money!

As such, we should not be surprised when guidelines break down in extraordinary circumstances.

Personally, I would define two versions of this "physics breaks down" concept. One of them is when these guidelines break down in known ways, changing into new regimes. Supersonic flight is one great example. You can learn lots of guidelines about how fluids (like air) flow, but those guidelines break down at the speed of sound in that fluid. We then have supersonic flow guidelines to help us from there. In this case, this breakdown was something observed, typically on the edge of a phase transition. We figured out that supersonic flow followed different guidelines than sonic flow because we flew something faster than the speed of sound, and it behaved differently.

The other, more complete meaning of "physics breaks down" occurs in things like black holes. These are cases where we have never observed the breakdown, but our guidelines lead us in counterintuitive directions. To the best of all of our study, we have never found an experiment or an astronomical observation which suggests that Einstein's theory of general relativity is anything less than a law. Like everything in physics, its just a guideline, but we have not been able to find any situation where it fails.

However, there's a catch. Mathematically, Einstein's theories make strange predictions about extremely massive dense objects. The equations behind it spiral out of control, and you end up with oddities like a "singularity," with 0 volume and finite mass. This means infinite density, and we generally don't think that kind of infinity happens in the universe. So we say "physics breaks down" here because we honestly believe that if we ever get to actually observe this part of a black hole, we will see one of those phase transitions where physics just stops doing the General Relativity thing and starts doing Something Else. We believe this because we are not comfortable with the possibility that such math involving infinities is "right."

Another place "physics breaks down" is on the Planck scale. Planck time and Planck length are very small units of time and space. They're on the order of $$10^{-43} \text s$$ and $$10^{-35} \text m$$. They are important for another guideline that has shown to be so effective that we call it a law: Quantum Mechanics. We have yet to see anything on the small scale which suggests that Quantum Mechanics is anything less than a law, just like we haven't seen anything on the large scale to suggest that General Relativity is anything less than a law. However, when we get down to these absurdly small scales, the math of quantum mechanics (in particular, quantum field theory) start to break down, failing to yield predictive answers about what happens at that scale because some of the tools simply stop working. In a very handwavy sense, its like cutting things with a knife, smaller and smaller things, until one day you realize that you're trying to cut something thinner than the edge of your knife. Our metaphorical mathematical knife (renormalization) simply stops cutting at this point.

Of course, we have no reason to believe that the universe "ends" at this scale. It's just the point where all of the guidelines which are so successful that they have earned the monicker "law" fall apart. And in the extreme cases, such as the issues at Planck scale or in black holes, its the mathematics of the theory itself which suggests that the theory falls apart.

And so, we spend countless hours devising new experiments with the goal of plumbing these uncertain regions, with the hope of one day writing new physics which doesn't "break down" at these levels.

• +1 Love "Architects who call gravity a "guideline"...". In the last paragraph, should "hole" be "hope"? Nov 1, 2020 at 7:32
• @TripeHound Good catch on the typo, fixed! Nov 1, 2020 at 7:58
• @Nij I think I fixed them all! Thanks! Nov 1, 2020 at 17:04

More generally, it’s often said that laws of physics ’break down’ under conditions where their underlying assumptions no longer hold. For example, Newtonian physics works very well most of the time, but at relativistic speed it becomes increasingly inaccurate. For comparison, it’s ok to assume that the Earth is flat if you’re building a house, but not if you’re building a long suspension bridge (far less launching a satellite). In the context of a black hole, we have no experience, for example, of how chemistry changes if atoms are compressed even by a few percent.

For all we know a black hole could just be a very dense sphere ...

One you reach or pass the event horizon, the force required to prevent you falling towards the singularity at the centre of the black hole becomes infinite. The future path of any object within the event horizon reaches the singularity within a finite amount of time. So we can be certain that whatever is inside the event horizon of a black hole, it is not a very dense sphere, since no force could ever be strong enough to support such a sphere.

• Your statement is only true if General Relativity applies within the event horizon of a black hole, and it doesn't address the question of what is meant by "physics breaking down".
– Mark
Nov 3, 2020 at 2:49
• Is it possible for the black hole to be an "ever-compressing sphere"? Something that is falling in on itself, whose radius is ever-shrinking? Nov 3, 2020 at 9:28

You are asking about a black hole's singularity, and what we mean when you see phrases like "physics breaks down" or "there is an issue with renormalizability".

General relativity also works perfectly well as a low-energy effective quantum field theory. the real problem is not so much nonrenormalizability as high-energy behavior inconsistent with local quantum field theory. By doing ever-higher-energy scattering experiments, you learn about physics at ever-shorter-length scales. If you could collide two particles with center-of-mass energy much larger than the Planck scale, then when they collide their wave packets would contain more than the Planck energy localized in a Planck-length-sized region. This creates a black hole. If you scatter them at even higher energy, you would make an even bigger black hole, because the Schwarzschild radius grows with mass. So the harder you try to study shorter distances, the worse off you are: you make black holes that are bigger and bigger and swallow up ever-larger distances.

A list of inconveniences between quantum mechanics and (general) relativity?

The answer to your question is that there is a subtle issue with gravity at high energies. Contrary to popular belief, we do not mean that there is an issue between QFT and GR. In fact, at low energy levels, GR and QFT work perfectly well together.

You see, in QFT, if you want to do experiments to uncover objects at very short distances, you do use (scatter particles at) higher energy levels (in some ways, you can say this is thanks to the HUP).

Now here comes what really brakes down for gravity. What brakes down is this correspondence between short distances and high energy levels for gravity. You simply can't use this method (nor in the math) to find out how gravity works at high energy levels and low length scales.

The answer to your question is that maybe gravity is not a quantum phenomenon at all like for example electromagnetism (QED) is, or we just can't figure out how to interpret it.

A very simple example of physics breaking down can be explained via Newton's law of universal gravity:

## $$F = G\frac{ m_1 m_2 }{r^2}$$

Here $$r$$ is the distance between centers of the masses $$m_1$$ and $$m_2$$, and $$G$$ the gravitational constant.

The problems:

-If you have two massive object that can be brought infinitely close together, the force value would shoot up to infinity due to $$r \rightarrow 0$$ making them inseparable. In quantum field theory electrons have masses but basically no radius. Hence the equation would not make sense in this case - the physics would 'break down'.

-This equation assumes instantaneous affect. Meaning if a particle is formed on the other side of the universe, it would instantly apply a tiny force to all the other particles in the whole universe. But we know this cannot be true, and can at most be applied at the speed of light. Hence the equation would not make sense in this case - the physics would 'break down'.

-Does clearly not explain how the path of massless particles such as the photon is changed when passing massive objects such as black holes. Since the m=0 term would make F = 0. For massive objects the acceleration provided by F would be calculable. If we introduced an experimental limit to the photon mass, meaning photons must be weighing at most x due to experimental measurerements, general relativity would still be twice as accurate. Hence the equation would not make sense in this case - the physics would 'break down'.

• I don't think that these can be seen as "physics breakdown" in the same sense OP means. Newton's law is perfectly consistent within itself: it shows that photon paths aren't curved by gravity and that gravitational effects are instantaneous. While these things are wrong, they are consistent with Newton's theory. On the other hand, GR itself tells us that we can't use it to explain what happens in the central singularity of a black hole. We don't need to make observations to know that it's not the end of the story: we already do. Nov 3, 2020 at 13:41
• You claim my point of view is incorrect, yet you give an example of another theory that has similarly problems at limits, as if it were more correct. I dont think you understand what you are writing about. Nov 3, 2020 at 13:56
• I don't think your point of view is incorrect: the term "physics breakdown" can be ambiguous, and I think the meaning OP is talking about is that of inconsistency, not of wrongness when compared to experiments. As the accepted answer says, "our best theory produces non-sensical or contradictory results in this situation, so we know the theory doesn't make good predictions there". Nov 3, 2020 at 14:06
• I am giving a very simple example to his question "Can someone explain why we know that physics stops working?" if it is not very evident. Nov 3, 2020 at 14:23

"Physics break down" is a catchy phrase. It has a historical perspective. Some identify the phrase with the phenomenon of singularity in physics. And that is where it stems from. It is a phenomenon in statistical physics not to much designated to a single particle but to the kleinkanonics and großkanonics from the German statictical physicist that introduced it. It was than adopted and applied to the blackwhole theories. And it it well placed in the information theoretical appraoches to the singularity during the approach of the horizont surface of the black hole.

Bilanzing perspective Break down is therefore not so a process perspective but a bilanzing perspective. We can ask certain question about what approaches the singularity but can not state anything about the latest phase and the transitional transformation further to the event horizont surface. The discussion have transformed towards standpoints of is information preserved or not. Is information preserved for the emitting jets? What happens at the origin of the emitted jets? And so on.

Break down of methodology The break down is originally adressed to phase transition that were not copable with methodologies of thermodynamics neiter classical, semiclassical or quantumechanical. And which are nowadays not solvable with string theoretical methodologies. More than this the physics dreak down sticks to the old aged methdods. Phase transitional problems are already present in water, methan and carbondioxid and many of the modern environment polluting chemicals.

It is still a break down state of methodology that the standard model is not complete. That we do not know all about the elementary particles for example the neutrino. The neutrino is next to the photon which seems to be free of break down until we look at the focussing problem, high intensity question and ultra-short time phenomena. But the light is the very closed carrier of al information we can get from our environent. The electron is even rather complicated.

Physics break down as a classical phenomenon Some expert stated that we have to start at absolute zero temperature to get ideas about handling physics break down. So the most modern standard example is supra conductivity and super conductivity. Physics already breaks down in the Hill problem of three partciles even if they are classic. Only in certain situation the problem can be in a perspective of predictive physics be calculated.

Be patient, I will add more wiseness later.

Nearly all theories in physics are known to be approximations, and none are known to be precise. It's possible that even theories which are thought to be precise are in fact approximations, but are more accurate than any equipment which could be used to test them.

When a theory is said to "break down" under certain conditions, what that means is that its approximations of expected behavior diverge sufficiently from actual behavior under those conditions as to render it useless for making predictions. For example, if one knows that a certain mass of H2O fills up a certain volume at a pressure of one atmosphere when the temperature is 1400K, Charles's law would estimate that reducing the temperature to 700K would cut the volume in half, and that estimate would be fairly accurate. It would also estimate that reducing the temperature to 350K would cut the volume in half again, but that estimate would be off by orders of magnitude (the volume would shrink much more when the temperature fell below 373.15K and the H2O condensed).

Astronomical observations allow scientists to formulate approximations for how some things behave in conditions that cannot be created in a lab, but it's very difficult to make accurate observations about things very near the event horizon of a black hole, and under current theories it is impossible to make observations about anything inside one. Thus, not only are there no theories which can be shown to accurately approximate behavior of things inside black holes, but there isn't even any known method of gathering the data that would be necessary to formulate such approximations nor test their accuracy.

"Physics breaks down" is another way of saying that physicist have no clue how to deal with infinities arising in solutions of Einstein field equations. A mathematician would never say 'mathematics breaks down' because of divergence of function $$f(x)=1/x$$, for the argument $$x=0$$. Albert Einstein distinguished between two kinds of physical theories: a constructive and a principle theory. The first one models some limited range of a physical phenomenon, like Newton's gravitation theory, and the second, like General Relativity, is generally valid, due to the underlying principle [1]. Therefore, the generally acceptance of singularities as a breakdown of Einstein's theory means actually its downgrading to some kind of "improved Newton's gravitation theory", i.e. to a constructive theory. I presume, Einstein would not agree with this view. Sir Roger Penrose himself said about his singularity theorem: "What it really showed is that the space-time could not be continued, it must come to an end somewhere, but it doesn't say what the nature of that end is, it just says that the space-time cannot be continued indefinitely "[2]. Thus, a proper interpretation of the divergences arising in General Relativity is an interesting and promising research field, especially for young relativists - the "old" ones are difficult to "convert".

It means that their laws and rules for the particular case are not able to tell what they are observing.

An example of physics breaking down could be the conditions inside the event horizon of a black hole. If you enter it, there is no escape, because which ever way you turn, it leads directly to the center. So in a sense 3 dimensions are being reduced to 1; the straight line leading into the singularity. Also the center of a black hole is in constant collapse; in essence this means that ground zero in a black hole is tending towards being infinitely small and infinitely dense at the same time, but perhaps not actually being infinitely small or dense. You could also say that the center of a black hole is in constant flux.